Loops and Legs in Quantum Field Theory

14 Apr 2024, 16:00 → 19 Apr 2024, 14:30 Europe/Berlin

Wittenberg

Matthias Steinhauser (KIT), Peter Marquard (DESY)

copyright by martas|Hotel Lutherstadt Wittenberg

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Sunday, 14 April

19:00 → 20:30 Dinner

Monday, 15 April

09:00 → 10:30 Plenary 1

Convener: Peter Marquard (DESY)

welcome.pdf

09:00 NNLO corrections to Z+H production at lepton colliders

This contribution reports on a semi-numerical technique for the efficient calculation of electroweak NNLO corrections for 2->2 scattering processes. The method is based on dispersion relations and Feynman parameters, as well as suitable subtraction terms for the UV divergencies. As an important phenomenological application, the NNLO electroweak corrections with closed fermion loops to the Higgs-strahlung process (e+e- -> ZH) are presented.

Speaker: Ayres Freitas (University of Pittsburgh)

ll24_freitas.pdf

09:30 Renormalization of the Dark Abelian Sector Model and Predictions for the W-boson mass

The Dark Abelian Sector Model (DASM) is an extension of the Standard Model with an additional spontaneously broken $U_d(1)$ gauge symmetry connected to a dark sector, i.e. the SM particles do not carry the corresponding charge. In addition to the gauge boson resulting from the extra $U_d(1)$ gauge symmetry, the particle content is extended by a further Higgs boson, one Dirac fermion as well as right-handed neutrinos. Employing the $U_Y(1)$ field strength tensor as well as the SM Higgs mass operator (the only two singlet operators of the SM with dimension less than 4) and the right-handed neutrino fields, we open three portals to the dark sector.

In this talk, after an introduction of the model, we discuss a renormalization scheme for the complete model with a special focus on the renormalization of the mixing angles. Finally, as an example of application, we present the prediction for the W-boson mass derived from the muon decay for the DASM.

Speaker: Heidi Rzehak (University of Tübingen)

LL2024.pdf

10:00 Top-Bottom Interference Contribution to Fully-Inclusive Higgs Production

We evaluate the top-bottom interference contribution to the fully-inclusive Higgs production cross section at next-to-next-to-leading order in QCD. To this end, we compute the relevant two-loop master integrals that enter the real-virtual contribution numerically using the method of differential equations. In addition, the Higgs-gluon form factor at three loops in QCD with two different massive quark flavors must be included for consistency and is derived in terms of deep asymptotic expansions. With this result, we address one of the leading theory uncertainties of the cross section.

Speaker: Marco Niggetiedt (Max-Planck-Institut für Physik)

niggetiedt.pdf

10:30 → 11:00 Coffee break

11:00 → 12:30 Plenary 1

Convener: Peter Marquard (DESY)

welcome.pdf

11:00 Analytic third-order QCD corrections to top-quark and semileptonic b → u decays

We present the first analytic results of N3LO QCD corrections to the top-quark decay width. We focus on the dominant leading color contribution, which includes light-quark loops. At NNLO, this dominant contribution accounts for 95% of the total correction. By utilizing the optical theorem, the N3LO corrections are related to the imaginary parts of the four-loop self-energy Feynman diagrams, which are calculated with differential equations. The results are expressed in terms of harmonic polylogarithms, enabling fast and accurate evaluation. The third-order QCD corrections decrease the LO decay width by 0.667%, and the scale uncertainty is reduced by half compared to the NNLO result. The most precise prediction for the top-quark width is now 1.321 GeV for mt = 172.69 GeV. Additionally, we obtain the third-order QCD corrections to the dilepton invariant mass spectrum and decay width in the semileptonic b → u transition. The perturbative series in the on-shell mass scheme exhibits poor convergence behavior. In the MS mass scheme, the scale dependence is greatly improved. A more precise determination of the CKM matrix element Vub could be obtained with such higher-order corrections.

Speaker: Jian Wang (Shandong University in China)

JianWang_LL2024.pdf

11:30 Taming the N3LO correction to semileptonic $b \to u$ decay

We present the QCD corrections of order $\alpha_s^3$ to the decay rate of $b \to u l \bar \nu_l$, originating from diagrams with closed fermion loops and neglecting the mass of the up quark. Our calculation relies on integration-by-parts reduction of Feynman integrals with one propagator raised to a symbolic power in Kira.
The five-loop master integrals are then evaluated with AMFlow numerically, together with an ad hoc interface to Kira. This allows us to obtain results for the fermionic contributions to the total semileptonic rate with an accuracy of more than thirty digits

Speaker: Matteo Fael (CERN)

LL_Fael.pdf

12:00 Non-Planar Two-Loop Amplitudes for Five-Parton Scattering

I present the recent calculation of the two-loop amplitudes required to obtain next-to-next-to-leading order predictions for three-jet production at the Large Hadron Collider. This calculation is performed in full color, that is including contributions from non-planar Feynman diagrams. I review the method of numerical generalized unitarity and the integrand decomposition technique employed to generate finite-field samples of the amplitude. I will then focus on the analytic reconstruction of the coefficient functions from said numerical samples. A novel algorithm, based on the correlation of codimension-one residues, helps tame the complexity of the calculation. Rescalings of the gluon amplitude, inspired by supersymmetry Ward identities, facilitate the computation of the quark amplitudes. I touch upon various interdisciplinary aspects of the computation, including elements of number theory, computational algebraic geometry, constraint programming, memoization, and GPU acceleration.

Speaker: Giuseppe De Laurentis (University of Edinburgh)

L&L_GDL.pdf

L&L_GDL (web)

13:00 → 14:30 Lunch

14:30 → 16:00 Parallel A

Convener: David Broadhurst (Open University, UK)

14:30 Challenges in Incorporating Massive Feynman Integrals for Precision Physics

With the upgraded Large Hadron Collider (LHC) operating at higher luminosity and the promise of even higher energy reach for future colliders, it has become imperative to compute precise theoretical predictions to contribute to this era of precision physics. It is particularly important to not only compute higher-order corrections but also include the contributions due to massive particles to scattering processes. Therefore, it is necessary to tame the challenges appearing in analytic computations of multi-loop Feynman integrals due to the presence of massive internal particles. In this talk, while focusing on the computation of analytic scattering amplitudes, I will explain how to counter the challenges arising from massive Feynman integrals whose analytic expressions have a more complicated function space.

Speaker: Ekta Chaubey (University of Bonn)

Talk_ekta.pdf

15:00 Four-loop QCD corrections to the rho parameter

We calculate four-loop QCD corrections to the rho parameter with a non-vanishing b-quark mass. Previously, it was observed at three-loop order that elliptic integrals contribute to this observable. This prompts the question which classes of functions appear at the next order. We report on the results of our calculation with a focus on the mathematical structures that emerge at four loops.

Speaker: Arnd Behring (CERN)

ll2024-talk.pdf

15:30 Calabi-Yaus all over the place

In recent years, it has become clear that in higher-loop computations, Calabi-Yau geometries are becoming unavoidable. Especially, periods and their iterated integrals define the function space four higher-loop integrals appearing in Feynman integral computations and also in black whole scattering processes. Therefore, an understanding of Calabi-Yau geometries is essential.
In my talk, I want to discuss on the current status of Calabi-Yaus in loop computations. In particular, how the function space of iterated Calabi-Yau periods emerges during the process of construction an $\epsilon$-factorized differential equation.

Speaker: Christoph Nega (TUM)

Loops&Legs.pdf

14:30 → 16:00 Parallel B

Convener: Massimiliano Grazzini (University of Zurich)

14:30 Analytic electroweak corrections to gg -> HH

We consider next-to-leading order electroweak corrections to Higgs boson pair production. This requires the computation of two-loop four-point amplitudes with massive internal particles such as top quarks, Higgs and gauge bosons. We perform analytic calculations in various kinematical limits and show that their combination covers the whole phase space, thus circumventing time-consuming numerical approaches.

Speaker: Hantian Zhang (Karlsruhe Institute of Technology)

EW_diHiggs_LL2024.pdf

15:00 Higgs pair production at NNLO

The two-loop (NLO) corrections to Higgs pair production are large, and suffer from large uncertainties due to the renormalization scheme and scale of the top quark mass. This strongly motivates a three-loop (NNLO) computation of the cross section. In this talk I will discuss progress towards this goal, by investigating the NNLO virtual corrections in an expansion around the forward scattering limit. Despite the expansion, this proves a very computationally challenging endeavour.

Speaker: Joshua Davies (University of Liverpool)

slides.pdf

15:30 Higgs Self-Coupling and Yukawa Corrections to Higgs Boson Pair Production

We present a calculation of the electroweak corrections to Higgs boson pair production in gluon fusion, involving Yukawa interactions and Higgs self-couplings only. The integrals appearing in the two-loop amplitude are evaluated numerically using both sector decomposition and series expansion of the differential equations. The full dependence on the masses of the top quark and Higgs boson are kept throughout the calculation.

Speaker: Matthias Kerner (KIT)

LL24_Kerner.pdf

16:00 → 16:30 Coffee break

16:30 → 18:30 Parallel A

Convener: David Broadhurst (Open University, UK)

16:30 Two-loop power-spectrum of the Effective Field Theory of Large Scale Structure

The main analytical tool for analyzing Large Scale Structure surveys is the Effective Field Theory of Large Scale Structure (EFTofLSS). With increasing survey detail, higher precision in theoretical predictions becomes essential. However, extending integrations beyond the one-loop power spectrum faces limitations due to analytical challenges and computational costs. In this presentation, we discuss an approach that enhances both analytical and numerical efficiency by fitting the linear power spectrum with cosmology-independent functions. This enables us to map loop integrals in cosmology to QFT integrals featuring massive propagators. Additionally, we present novel numerical computations of the two-loop corrections to the power spectrum.

Speaker: Andrea Favorito (ETH Zurich)

EFTofLSS_at_LL.pdf

17:00 Worldline integration of photon amplitudes

It has been known for many years that methods inspired by string theory, such as the worldline formalism, allow one to write down integral representations that combine large numbers of Feynman diagrams of different topologies. However, to make this fact useful for state-of-the-art calculations one has to confront non-standard integration problems where neither the known integration techniques for Feynman diagrams nor algebraic manipulation programs are of much help. Here I will give a progress report on this long-term project focusing on photon amplitudes at one and two loops, in vacuum and in external fields.

Speaker: Christian Schubert (Facultad de Ciencias Físico-Matemáticas, Universidad Michoacana de San Nicolas de Hidalgo)

talk_LL2024.pdf

17:30 No-$pi$ schemes for multi-coupling theories

We show that even $\zeta$-functions may be removed from the $\beta$-functions of general multi-coupling theories up to high loop order by means of coupling redefinitions. For theories whose $\beta$-function is determined by the anomalous dimensions of the fields, such as supersymmetric theories, this corresponds to a renormalisation scheme change to a momentum subtraction scheme.

Speaker: Ian Jack (University of Liverpool)

LandL_Jack.pdf

18:00 Perspective on properties of renormalization schemes at high loops

We present recent results of renormalizing QCD to high loop order in a variety of different renormalization schemes. For instance several schemes naturally depend only on the odd zetas up to five loops. This property is explored in other models and other spacetime dimensions.

Speaker: John Gracey (University of Liverpool)

witt24.pdf

16:30 → 18:30 Parallel B

Convener: Massimiliano Grazzini (University of Zurich)

16:30 Status of two-loop QCD corrections to pp->ttj scattering

I will discuss recent developments in the computation of the two-loop QCD corrections to top pair production in association with a jet in the leading colour approximation. In particular, I will focus on the usage of differential equations and generalised series expansions in the evaluation of master integrals, and I will describe some aspects of the analytic structure of the solution.

Speaker: Matteo Becchetti (University of Bologna)

LL24_Becchetti.pdf

17:00 Complete NLO corrections to top-quark pair production with isolated photons

We report on the computation of NLO QCD corrections to top-quark pair production in association with two photons at the LHC. Higher-order effects and photon bremsstrahlung are taken into account in the production and decays of the top-quark pair. Top-quark and W-boson decays are treated in the Narrow Width Approximation conserving spin correlations up to NLO in QCD. This is the first time that the complete set of NLO QCD corrections to the pp → ttγγ process including top-quark decays is calculated. We present results at the integrated and differential cross-section level in the di-lepton and lepton + jet channel. In addition, we investigate the effect of photon bremsstrahlung in tt production and top-quark decays, as well as the mixed contribution. The latter contribution, in which two photons occur simultaneously in the production and decay of the tt pair, proved to be significant at both the integrated and differential cross-section level.

Speaker: Malgorzata WOREK (RWTH Aachen University)

MWorek-LL2024.pdf

17:30 Towards a full NNLO QCD calculation of $\Delta \Gamma$ in the $B$-$\overline{B}$ system

In this talk I will discuss recent advances made in the calculation of the NNLO QCD corrections to the width difference between B and B mesons. This work focuses on the perturbative high-energy part of the calculation, more specifically the matching coefficients between the Δ B = 1 effective operators of the Weak Interaction and the Δ B = 2 transition operator are calculated as a deep expansion in mc/mb.

This calculation yields novel results for the NNLO contributions with penguin operators which had not been considered previously at this order. Moreover, the NNLO contributions with two current-current operators, which were previously only known up to O(mc/mb), are calculated to a higher precision.

Speaker: Pascal Reeck (KIT TTP)

ll_presentation.pdf

18:00 2-loop Quarkonium Hamiltonian (Non-annihilation Channel)

We calculate the Hamiltonian of a heavy quarkonium system at two loops of
potential-NRQCD effective field theory (Non-annihilation channel).
We compute the quark-antiquark scattering amplitude in the non-annihilation
channel up to two loops in QCD, in the non-relativistic region in expansion in
beta. Then we match it to the scattering amplitude in potential-NRQCD.
We develop a method by combining threshold expansion and differential
equations for calculating the beta expansions of the master integrals.

Speaker: Yukinari Sumino (Tohoku University)

2LoopQuarkoniumHamiltonian.pdf

19:00 → 20:30 Dinner

Tuesday, 16 April

09:00 → 10:30 Parallel 1

Convener: York Schröder (Universidad del Bio-Bio)

09:00 Subleading operators and gamma5-scheme dependence in SMEFT for Higgs boson pair production

We present the calculation of the contributions from the chromomagnetic and four-top-quark operators within Standard Model Effective Field Theory (SMEFT) to Higgs boson pair production in gluon fusion, combined with NLO QCD corrections. The four-quark operators enter at two loops in this process and require the choice of a scheme to continue $\gamma_5$ to D dimensions. We report about new findings related to the interplay between different operators and illustrate the impact on Higgs phenomenology.

Speaker: Gudrun Heinrich (KIT Karlsruhe)

LL2024_GH.pdf

09:30 Renormalization of chiral Gauge Theories with non-anticommuting $\gamma_5$ in the BMHV Scheme at the 3-Loop Level and Beyond

The dimensional renormalization of chiral gauge theories such as the electroweak Standard Model inevitably leads to the problem of accommodating the manifestly 4-dimensional nature of $\gamma_{5}$ in $D$ dimensions. In order to avoid inconsistencies at the multi-loop level, $\gamma_{5}$ can be treated rigorously as a non-anticommuting object using the Breitenlohner-Maison/'t Hooft-Veltman (BMHV) scheme within dimensional regularization (DReg). Employing the BMHV scheme, however, violates gauge invariance, which subsequently needs to be restored using symmetry-restoring counterterms guaranteed to exist by the methods of algebraic renormalization. We have successfully performed this renormalization procedure up to the 3-loop level in an abelian chiral gauge theory, serving as a toy model for the investigation of new theoretical concepts, obtaining a consistently renormalized theory with ultimately restored BRST invariance. The obtained results will soon be published. With this application in mind, serving as a proof of concept of our method at the multi-loop level, we have started first attempts to both, increasing the loop order in the abelian model, as well as applying it to the Standard Model. While this talk mainly focuses on computations in the abelian sector at higher loop-levels, accompanying talks consider 2-loop calculations in non-abelian theories, including difficulties arising due to the more complicated gauge group, as well as conceptual issues regarding the Standard Model. Ultimately, this renormalization procedure will be needed for high-precision calculations of e.g. electroweak observables.

Speaker: Matthias Weißwange (TU Dresden)

LL24-MatthiasWeisswange.pdf

10:00 Non-Anticommuting $\gamma_5$ in a Non-Abelian model at two loop

We apply the mathematically consistent Breitenlohner-Maison-'t Hooft-Veltman scheme to the dimensional renormalization of chiral gauge theories. Anticommutativity of $\gamma_5$ is given up, which spuriously breaks gauge invariance at the regularized level, but can be repaired by finite counterterms.
With the Standard Model in mind, we study chiral toy models as prototypes, such as previously a Non-Abelian model with scalars at one loop and the Abelian case at two loops. This talk will focus on the advances for a generic Non-Abelian chiral model at two loop including the counterterm structure, an exposition of corresponding Slavnov-Taylor identities and Non-Abelian peculiarities.
Accompanying talks discuss the extension of the Abelian model to three loop as well as conceptual intricacies regarding the SM.

Speaker: Paul Kühler (TU Dresden)

G5Talkv3.pdf

09:00 → 10:30 Parallel 2

Convener: Marco Bonetti (RWTH TTK)

09:00 Corrections to BSM triple Higgs couplings and their phenomenological consequences

tbc

Speaker: Sven Heinemeyer (IFCA (CSIC, Santander))

sven.pdf

09:30 Non-factorizable corrections to Higgs production in Vector Boson Fusion

Higgs production in Vector Boson Fusion (VBF) has the second largest cross section at the LHC. Its signature on collider is characterized by two energetic jets in the forward region. The previous high-order corrections to VBF Higgs production usually neglect the non-factorizable contribution which is color-suppressed compared to its factorizable counterpart. It was however found in the leading eikonal approximation that the non-factorizable contribution had an enhancement by a factor Pi squared. In this talk, I will present two improvements in the understanding of the non-factorizable corrections. One is to go beyond eikonal approximation and obtain the first power correction. Another is to address the problem of strong dependence on the renormalization scale of the leading eikonal corrections. The new sub-leading contribution will change the current estimate of the non-factorizable corrections to VBF cross section by about 20 percent. Furthermore, including the effects of the running coupling constant reduces the scale dependence in cross section and kinematic distributions.

Speaker: Ming-Ming Long (KIT, TTP)

mmlong_LL2024.pdf

10:00 Precision Drell-Yan phenomenology at N3LO QCD

I would like to report recent progress of phenomenology studies with N3LO QCD corrections. This includes non-local slicing methods applied to relative simple process at the LHC such as Drell-Yan and its application on mW and alphaS determination.

Speaker: Xuan Chen (Shandong University)

LL2024XuanChen.pdf

10:30 → 11:00 Coffee break

11:00 → 12:30 Parallel 1

Convener: York Schröder (Universidad del Bio-Bio)

11:00 Causality and differential cross sections

We discuss how causality, specifically in the loop-tree duality, can provide an efficient guiding principle to achieve theoretical predictions at higher orders for differential cross sections at colliders.

Speaker: Germán Rodrigo (IFIC UV-CSIC)

2024_04_LL_rodrigo.pdf

11:30 Loop Tree Duality with generalized propagator powers: numerical UV subtraction for two-loop Feynman integrals

An explicit Loop Tree Duality (LTD) formula for two-loop Feynman integrals with integer power of propagators is presented and used for a numerical UV divergence subtraction algorithm. This algorithm proceeds recursively and it is based on the R operator and the Hopf algebraic structure of UV divergences. After a short review of LTD and the numerical evaluation of multi-loop integrals, LTD is extended to two-loop integrals with generalized powers of propagators. The R operator and the tadpole UV subtraction are employed for the numerical calculation of two-loop UV divergent integrals, including quadratic divergences.

Speaker: Daniele Artico (Humbold Universitaet zu Berlin)

LnL24_Artico.pdf

12:00 Yang-Mills Theory with Graphical Functions

Graphical functions are a well established tool to perform high loop order calculations for some QFT processes. Most notably, they were used to calculate the 7 loop $\phi^4$ and the 6 loop $\phi^3$ beta functions.
A new project aims to extend the use of graphical functions to particles with spin, with particular focus on Yang-Mills theory. We report on the status of this project.

Speaker: Oliver Schnetz (UNI/TH (Uni Hamburg, Institut fuer Theoretische Physik))

GraphicalFunctionsLL2024.pdf

11:00 → 12:30 Parallel 2

Convener: Marco Bonetti (RWTH TTK)

11:00 Linear power corrections to top quark production processes

We discuss the linear power corrections in $\Lambda_{\text{QCD}}$ to top quark production processes in hadron collisions using renormalon calculus. We show how such non-perturbative corrections can be obtained using the Low-Burnett-Kroll theorem, which provides the first subleading term to the expansion of the real-emission amplitudes around the soft limit. We demonstrate that there are no linear power corrections to the total cross sections provided that these cross sections are expressed in terms of a short-distance top quark mass. We also derive a universal formula for the linear power corrections to generic observables that involve the top-quark momentum.

Speaker: Melih Arslan Ozcelik (IJCLab)

LL2024_OZCELIK.pdf

11:30 Analytic results for massive three-loop form factors

We present our recent progress in the calculation of massive three-loop form factors in the non-singlet case, using the method of large moments and differential equations derived from them. The expansion coefficients of the solutions to these differential equations correspond to the series of rational numbers multiplying each of the constants appearing in the form factors at different kinematic points. These coefficients are thus computed with very large precision, which allows us to use the PSLQ algorithm to obtain all of them in terms of known constants in the low energy limit, and in terms of a few new additional constants at threshold. We discuss the computer algebra techniques used in our calculations and compare with numerical results in the literature.

Speaker: Abilio de Freitas (None)

LL-abilio-2024.pdf

12:00 Revealing Hidden Regions and Forward Scattering

We discuss a class of Feynman Integrals which contain hidden regions that are not straightforwardly identified using the standard Geometric/Newton polytope approach to the Method of Regions. Using existing analytic results, we analyse the appearance of such regions in forward scattering and on-shell wide-angle scattering and discuss how they can be exposed in both the momentum and parametric representations. We demonstrate that some such integrals contain leading Landau singularities that prevent their direct numerical evaluation in parameter space and describe how they can be re-parameterised to circumvent this problem.

Speaker: Stephen Jones (CERN)

sjones_ll24.pdf

13:00 → 14:30 Lunch

14:30 → 16:00 Parallel 3

Convener: Andreas von Manteuffel (University of Regensburg)

14:30 A new method for the reconstruction of rational functions

In this talk, I present a new method for the reconstruction of
rational functions through finite-field sampling that can significantly
reduce the number of samples required. The method works by exploiting all
the independent linear relations among target functions.
Subsequently, the explicit solutions of the functions can be efficiently
obtained by solving the linear system. As a first application, I utilize
the method to address various examples within the context of Feynman
integrals reduction. These examples demonstrate that the method
can substantially improve the computational efficiency, making it useful
for future computations in particle physics.

Speaker: Xiao Liu (Oxford)

LL24_liux.pdf

15:00 Learning Feynman integrals from differential equations with neural networks

I present a new approach for evaluating Feynman integrals numerically. We apply the framework of physics-informed deep learning to train neural networks to approximate the solution to the differential equations satisfied by Feynman integrals. I discuss a proof-of-concept implementation, and showcase a number of one- and two-loop examples.

Speaker: Simone Zoia (CERN)

zoia_L&Ls_2024.pdf

15:30 Selection rule of canonical differential equations from Intersection theory

Symbolology is the language that organizes the analytic structure of Feynman integrals and is encoded in the canonical differential equations. Using the d log-bases and simple formulas of intersection numbers, we give an algebraic procedure to compute the entries in the coefficient matrix of CDE, including the symbol letters and the rational coefficients. We also provide a selection rule to decide whether a given matrix element of CDE must be zero. This procedure shows that the symbol letters are deeply related to the poles of the d log integrands.

Speaker: Jiaqi Chen (Beijing Computational Science Research Center (CSRC))

CDE selection rule jiaqi chen.pptx

14:30 → 16:00 Parallel 4

Convener: Thomas Gehrmann (University of Zurich)

14:30 Top-quark loops in $gg \to ZZ$ at NLO in QCD

We present the calculation of the virtual corrections to $gg \to ZZ$ at next-to-leading order in QCD, focusing on the contribution from top quarks, which lacks a full analytic evaluation. The two-loop box diagrams are computed using a small-tansverse-momentum expansion, and the results are merged with those available in the high-energy expansion, in order to obtain an analytic description in the complete phase space. Our results allow for an improved modeling of the continuum background in off-shell Higgs production.

Speaker: Marco Vitti (Karlsruhe Institute of Technology - TTP & IAP)

Wittenberg_Vitti.pdf

15:00 Full top-quark mass dependence in diphoton production at NNLO in QCD

We consider the diphoton production in hadronic collisions at the next-to-next-to-leading order (NNLO) in perturbative QCD, taking into account for the first time the full top quark mass dependence. We present the computation of the two-loop form factors for diphoton production in the quark annihilation channel, that are relevant for the phenomenological studies of the full NNLO. The MIs are written in the so-called canonical logarithmic form, except for the elliptic ones. We perform a study on the Maximal Cut in order to show the elliptic behaviour of the non-planar topology. The Master Integrals are evaluated by means of differential equations in a semy-analitical approach through the generalised power series technique. Finally we use this result with all the other contributions showing selected numerical distributions.

Speaker: Federico Coro (IFIC)

Coro_loops_and_legs.pdf

15:30 Top quark mass effect in Z boson pair production through gluon fusion

Based on our calculation of the two-loop helicity amplitudes for on-shell W/Z boson pair production in gluon fusion with exact top quark mass dependence, we present preliminary results on the impact of the top quark mass effect to the Z boson pair production. Integral reduction is performed numerically for each phase space point and the master integrals are evaluated using the auxiliary mass flow method and the differential equation method in the phase space, enabling efficient phase space integration.

Speaker: Chen-Yu Wang (MPP)

ll2024.pdf

16:00 → 16:30 Coffee break

16:30 → 18:30 Parallel 3

Convener: Andreas von Manteuffel (University of Regensburg)

16:30 Evaluating Parametric Integrals in the Minkowski Regime without Contour Deformation

In this talk, we present selected examples demonstrating an alternative approach to contour deformation for numerically computing loop integrals in the Minkowski regime. This method focuses on identifying singular hypersurfaces (varieties of the F polynomial) and mapping them to known points which can then be resolved by employing blow-ups/sector decomposition techniques, thereby avoiding the need for contour deformation. Using this technique, we achieve improved convergence properties without the need for contour deformation, which is known to significantly increase the complexity of the integrand by introducing, for example, derivatives of the F polynomial and complicated Jacobians. We highlight that while we have only tested the approach on selected 1-, 2- and 3-loop massless and 1-loop massive examples, it shows promise for practical applications, offering potential benefits over the traditional approach. Evaluation times are compared with existing contour deformation implementations to illustrate the performance of this alternative method.

Speaker: Thomas Stone (IPPP, Durham University)

TomStoneLL24.pdf

17:00 p-adic reconstruction of rational functions in loop calculations

The calculation and manipulation of large multi-variable rational functions is a key bottleneck in multi-loop calculations. In this talk I will present work using p-adic numbers to reconstruct rational functions in a compact form. I will apply this to examples such as rational functions appearing in non-planar 2-loop 5-point amplitudes.

Speaker: Herschel Chawdhry (Florida State University)

Chawdhry_padic_reconstruction_LoopsAndLegs_WittenbergGermany_2024_04_16.pdf

17:30 Challenges of the large moment method

The large moment methods is a powerful tool to produce many coefficients of power series solutions of coupled systems of linear differential equations. This method with all its variants relies on the crucial observation that the coefficients can be described by (coupled systems) of linear recurrences. In this talk we will discuss various algorithmic challenges (uncoupling of the underlying system, parallel computing, memory issues) in order to calculate thousands of such coefficients. Given this number of coefficients (say 8K), one can produce, e.g., linear recurrences and differential equations of the underlying physical problem for further analysis. We will illustrate these considerations by concrete examples coming from massive 3-loop form factors.

Speaker: Carsten Schneider (RISC, Johnnes Kepler University Linz)

LL24.pdf

18:00 Analytic Evaluation of Multiple Mellin-Barnes Integrals

I will discuss a novel approach based on the triangulation of point configurations to evaluate higher-fold Mellin-Barnes (MB) integrals in terms of hypergeometric functions. I will show that this new approach is computationally more efficient than the existing conic hull approach to evaluate MB integrals. As an application of this triangulation approach, I will first present new, simpler hypergeometric solutions of the conformal two-loop double box and one-loop hexagon Feynman integrals. Furthermore, using MB integrals, I will present new convergent series solutions of multiple polylogarithms commonly appearing in Feynman integral calculus.

Speaker: Sumit Banik (University of Zurich & Paul Scherrer Institut)

Loops_Legs_2024.pdf

16:30 → 18:30 Parallel 4

Convener: Thomas Gehrmann (University of Zurich)

16:30 NNLO+PS predictions for Z boson production in association with b-jets at the LHC

We present the first NNLO-accurate event generation for $Z$ boson production in association with a bottom-quark pair. This is achieved by matching the NNLO calculation in the 4FS to a parton shower within the MiNNLO$_\mathrm{PS}$ method, which we extend to accommodate the class of processes with a color singlet and a heavy-quark pair in the final state. We find that NNLO corrections to $Zb\bar{b}$ production are large and remarkably reduce the tension between 4FS predictions and $Z$+$b$-jet ATLAS and CMS measurements. The long-standing discrepancy between 4FS and 5FS predictions is therefore largely alleviated.

Speaker: Vasily Sotnikov (University of Zurich (UZH))

sotnikov_Zbb_LL2024.pdf

17:00 Third order QCD predictions for W and Z-boson production

Measurements of W and Z-boson production have reached percent-level precision, imposing challenging demands on theoretical predictions. Such predictions directly limit the precision of measurements like the W-boson mass. We present calculations of W- and Z- boson production at the level of $\alpha_s^3$ at fixed order and including transverse-momentum resummation. We discuss technical and numerical challenges, future improvements, and compare with LHC measurements with a focus on PDF and truncation uncertainties.

Speaker: Tobias Neumann (William & Mary)

Neumann_Tobias_LoopsLegs2024.pdf

PDF

Web version

17:30 Top-Quark Decay at Next-to-Next-to-Next-to-Leading Order in QCD

We present the first complete QCD corrections to both the inclusive decay width $\Gamma_t$, $W$-helicity fractions and semi-inclusive distributions for the top-quark decay process to the third order in the strong coupling constant $\alpha_s$, accomplished through a very efficient approach readily to be employed in many more related applications. We find, in particular, that the pure $\mathcal{O}(\alpha_s^3)$ correction decreases $\Gamma_t$ by $0.8\%$ of the previous $\mathcal{O}(\alpha_s^2)$ result, exceeding the error estimate by the usual scale-variation precription. Our to-date most precise theoretical prediction reads $\Gamma_t = 1.3148^{+0.003}_{-0.005} + 0.027\,(m_t - 172.69)\,$GeV, the error of which now meets the request by future colliders.

Speaker: Long Chen (Shandong University)

LL2024_Chen.pdf

18:00 Towards three loop amplitudes for V/H+jet production

I will present recent developments in the computation of N3LO corrections to vector boson + Jet production and Higgs + Jet production in QCD.
N3LO corrections to these processes are needed to reach the desirable sub-percent theoretical accuracy. Among all the ingredients to be computed are the corresponding three loop scattering amplitudes and lower loop amplitudes up to the needed power in the dimensional regulator. While the latter has been recently obtained, the three loop amplitude is known only in leading color approximation for the vector boson production. The computation of three loop Feynman integrals is one of the outstanding tasks to be addressed: while all the relevant planar topologies have been recently computed, only a few of the non-planar topologies are already known. Recent developments in the computation of the remaining non-planar topologies will be covered in the talk.

Speaker: cesare carlo mella (TUM)

LL24_Mella.pdf

19:00 → 20:30 Dinner

Wednesday, 17 April

09:00 → 10:30 Plenary 3

Convener: E.W.N. Glover

FORM_Symbolica.pdf

09:00 Heavy flavor QCD corrections in deep-inealstic scattering at 3-loop order

We report on the heavy flavor QCD corrections in deep-inealstic scattering at 3-loop order.

Speaker: Johannes Bluemlein (Z_ZPPT (Zeuthen Particle PhysicsTheory))

LL2024.pdf

09:30 QCD splitting functions at four-loop order

Splitting functions, also known as DGLAP evolution kernel, govern the scale evolution of parton distribution functions. One of the most efficient methods for calculating these splitting functions is by utilizing off-shell operator matrix elements. However, in the singlet sector, complications arise as physical operators become intertwined with non-physical operators, leading to intricate renormalization challenges.

In this talk, we systematically address these renormalization issues and present our latest results with certain color structures for four-loop splitting functions in QCD.

Speaker: Tongzhi Yang (University of Zurich)

LL2024_TZY.pdf

10:00 Four loop splitting functions in QCD

We have extended our previous computations of the even-N moments of the flavour-singlet four-loop splitting functions to N = 12 for the pure-singlet quark case and N = 10 for all other cases. These results, obtained using physical quantities in inclusive deep-inelastic scattering, have been and will be used to validate conceptionally much more challenging determinations of these splitting functions from off-shell operator matrix elements (OMEs). For the quark-gluon and gluon-gluon splitting functions, which have yet to be computed to higher N using OMEs, we construct approximations based on our moments and endpoint constraints, where we present new large-x results for the gluon-gluon case. These approximations facilitate an approximate N^3LO evolution of parton distributions which are sufficiently accurate outside the region of small momentum fractions x.

Speaker: Sven-Olaf Moch (UNI/TH (Uni Hamburg, Institut fuer Theoretische Physik))

moch-ll2024.pdf

10:30 → 11:00 Coffee break

11:00 → 12:30 Plenary 3

Convener: E.W.N. Glover

FORM_Symbolica.pdf

11:00 The gradient-flow formalism in perturbation theory

The gradient-flow formalism constitutes a regularization scheme for ultra-violet divergences which can be implemented both in perturbation theory and on the lattice. This paves unique ways of combining these two approaches to quantum field theoretical calculations in a consistent way. I will present a number of examples where such synergy effects have been explored. The focus of this talk is on the associated higher-order perturbative calculations, and is meant as an encouragement to transfer some of the expertise from conventional higher-order calculations to those in required in the gradient-flow formalism.

Speaker: Robert Harlander (RWTH Aachen University)

Loops&Legs.pdf

11:30 Two-loop amplitude reduction with HELAC

I will present recent progress in constructing a generic two-loop amplitude reduction algorithm within the computational framework HELAC. Following HELAC tree- and one-loop paradigm, we have completed the generation and validation of the two-loop amplitude-integrand in QCD. Following the well-known OPP reduction approach, we express the amplitude in terms of Feynman integrals which are further reduced to master integrals by IBP identities. I will also discuss the computation of the so-called rational terms. Preliminary results on four- and five-gluon amplitudes will be presented.

Speaker: Costas Papadopoulos (NCSR-D)

LL20224.pdf

12:00 Two-Loop Master Integrals for Leading-Color $pp \rightarrow t\overline{t}H$ Amplitudes with a Light-Quark Loop

In this talk, we discuss the computation of the two-loop master integrals for
leading-color QCD scattering amplitudes including a closed light-quark loop in
$t\overline{t}H$ production at hadron colliders. Exploiting numerical
evaluations in modular arithmetic, we construct a basis of master integrals
satisfying a system of differential equations in $\epsilon$-factorized form.
We present the analytic form of the differential equations in terms of a
minimal set of differential one-forms. Interestingly, we uncover the presence
of a new analytic feature – a nested square root. We explore properties of the
function space of analytic solutions to the differential equations in terms of
iterative integrals and finally solve the differential equations using
generalized series expansions to numerically evaluate the master integrals in
physical phase space.

Speaker: Ben Page (Ghent University)

LoopsAndLegs2024Page.pdf

12:30 → 13:30 Lunch

13:45 → 17:00 City tour

19:00 → 22:00 Conference dinner

Thursday, 18 April

09:00 → 10:30 Parallel 5

Convener: Johannes Bluemlein (Z_ZPPT (Zeuthen Particle PhysicsTheory))

09:00 NNLO QCD corrections to semi-inclusive DIS

In this talk, we present the NNLO QCD corrections to the semi-inclusive deep-inelastic scattering process. We use the state-of-the-art techniques namely, the method of reverse unitarity, IBP reduction and the method of differential equations to compute both virtual and phase-space integrals analytically.
After performing the mass-subtraction appropriately, we find the
finite partonic cross-section. We also perform a numerical analysis to
demonstrate the impact of NNLO correction.

Speaker: Narayan Rana (NISER)

LL24_Rana.pdf

09:30 NNLO corrections to SIDIS coefficient functions

Hadron production in lepton-proton scattering (semi-inclusive deep inelastic scattering, SIDIS) probes the structure of hadrons at a higher level of detail than fully inclusive processes. A wealth of SIDIS data is available especially from fixed-target experiments. In this talk, we present the calculation of NNLO corrections to the full set of SIDIS coefficient functions and discuss their impact on precision phenomenology. Our results enable for the first time a fully consistent treatment of hadron fragmentation processes in DIS at NNLO and provide the basis for studies of hadron structure, hadron fragementation and identified particle cross sections at colliders.

Speaker: Leonardo Bonino (University of Zurich)

bonino_sidis.pdf

10:00 Higher Order Corrections in Polarized DIS

We present higher order corrections for jet observables in longitudinally polarized deep inelastic lepton-nucleon scattering. Specifically, we consider the cases of single-inclusive and di-jet production in DIS, mediated by both neutral and charged currents. We study the perturbative stability and phenomenological consequences of the QCD corrections for Electron-Ion Collider kinematics.

Speaker: Ignacio Borsa (Tübingen University)

BORSA_LL24.pdf

09:00 → 10:30 Parallel 6

Convener: Roberto Bonciani (Sapienza Universita' di Roma, Roma, Italy)

09:00 Resummed predictions for differential rates of inclusive B-meson decays.

The smallest element of the CKM matrix, $|V_{ub}|$, can be extracted from measurements of semileptonic B meson decay $B\to X_ul\bar{\nu}$. However, the experimental signal of this process is obscured by large background $B\to X_cl\bar{\nu}$.
This background is kinematically forbidden at the edge of the phasespace, but this region is sensitive to nonperturbative effects. Factorization theorems derived in Soft-Collinear Effective Theory are used to isolate these nonperturbative effects into a so-called shape function and to systematically resum the perturbative corrections in this region. The shape function cannot be calculated perturbatively, but it can be measured in $B\to X_s\gamma$ decay.

I will present resummed predictions of differential decay rates for $B\to X_s\gamma$ at ${\rm N^3LL'{+}N^3LO}(c_k)$ and for $B\to X_ul\bar{\nu}$ at ${\rm N^3LL{+}NLO}$. The few unknown 3-loop perturbative ingredients are parameterized using nuisance parameters, and the corresponding error is estimated.

I will discuss the impact of different definitions of the b-quark mass on the convergence of perturbative series (the renormalon problem) and I will argue that the MSR mass scheme yield more stable results than the 1S mass scheme. I will highlight the importance of the missing fixed-order NNLO corrections to the differential $B\to X_ul\bar{\nu}$ decay. I will make some comparisons with experimental measurements of this decay by the Belle collaboration and point out some limitations of the inclusive approach related to violation of local quark-hadron duality.

Speaker: Ivan Novikov (KIT)

LL2024_Novikov.pdf

09:30 Nonleptonic B decays at NNLO

The decay of B mesons can be predicted within the Heavy Quark Ex-
pansion as the decay of a free bottom quark plus corrections which are
suppressed by powers of 1/𝑚𝑏. This talk will describe the calculation
of the NNLO corrections to nonleptonic decays of a free bottom quark
including charm quark mass effects. In particular we will describe
challenges in connection to the computation of master integrals, the
renormalization of the effective Hamilton operator and the problems
which arise from calculating traces with $\gamma_5$ in $d \neq 4$ dimensions.

Speaker: Manuel Egner

ManuelEgnerLL24.pdf

10:00 Renormalization with non-anticommuting gamma5 applied to the SM and related theories

Chiral gauge theories such as the electroweak SM involve the gamma5 matrix which cannot be defined in dimensional regularization without breaking important properties. The rigorouse t Hooft/Veltman/Breitenlohner/Maison scheme gives up anticommutativity of gamma5. As a result, gauge invariance is broken. In our research programme we determine the required gauge-invariance restoring counterterms. Other talks will focus on progress on the multi-loop level for abelian and non-abelian generic models. This talk will focus particularly on additional difficulties arising in the Standard Model. If time permits the talk will also discuss related issues arising in non-renormalizable EFTs, Fierz identities, and renormalization group beta functions.

Speaker: Dominik Stöckinger (TU Dresden)

2024AprilLL.pdf

10:30 → 11:00 Coffee break

11:00 → 13:00 Parallel 5

Convener: Johannes Bluemlein (Z_ZPPT (Zeuthen Particle PhysicsTheory))

11:00 Evolution kernels of twist-two operators

The evolution kernels that govern the scale dependence of the generalized parton distributions are invariant under transformations of the $SL(2,R)$
collinear subgroup of the conformal group. Beyond one loop the symmetry generators, due to quantum effects, differ from the canonical ones. We construct the transformation that brings the full symmetry generators back to their canonical form and show that the eigenvalues (anomalous dimensions) of the new, canonically invariant, evolution kernel coincide with the so-called parity respecting anomalous dimensions. We develop an efficient method that allows one to restore an invariant kernel from the corresponding anomalous dimensions. As an example, the explicit expressions for next-to-next-to-leading order invariant kernels for the twist-two flavor-nonsinglet operators in QCD and for the planar part of the universal anomalous dimension in $N=4$
supersymmetric Yang-Mills are presented.

Speaker: Alexander Manashov (UNI/TH (Uni Hamburg, Institut fuer Theoretische Physik))

manashov.pdf

11:30 Threshold parton distribution functions beyond leading power

The soft function that appears in threshold Drell-Yan or Higgs production contains infrared divergencies. This issue can be ignored at leading power without any significant impact on computations, which allowed the achievement of high logarithmic accuracy for threshold resummation. However, if we go beyond leading power in threshold expansion, the factorization of collinear modes inside the parton distribution functions and soft modes appearing in the threshold expansion must be carefully reconsidered. By redefining the parton distribution functions, we can achieve consistent next-to-leading power factorization in the threshold, which is a prerequisite to the resummation of subleading power logarithms. I will demonstrate this procedure using the formalism of soft-collinear effective field theory and discuss how these threshold PDFs are related to standard collinear PDFs.

Speaker: Robert Szafron (Brookhaven National Laboratory)

LL_DIS.pdf

12:00 Anomalous dimensions of leading twist operators to four loops

The anomalous dimensions of the twist-2 operators control the scale evolution of the Parton Distribution Functions. The precision targets set by the forthcoming experiments at the LHC and at the EIC require the calculation of the four-loop anomalous dimensions. I will describe a theoretical framework, based on the renormalisation of off-shell correlators, which allows to determine these quantities efficiently. Finally, I will discuss recent progress obtained within this approach.

Speaker: Giulio Falcioni (University of Zuerich and University of Turin)

falcioni.pdf

12:30 Full and approximated NLO predictions for like-sign W-boson scattering at the LHC

The talk presents a new calculation of next-to-leading-order (NLO)
corrections of the strong and electroweak interactions to like-sign
W-boson scattering at the Large Hadron Collider, implemented in the
Monte Carlo integrator Bonsay. The calculation includes leptonic decays
of the W bosons and the whole tower of next-to-leading-order
contributions. Confirming an earlier NLO calculation, we find large pure
electroweak corrections of the order of ~ −12% for integrated cross
sections and even larger corrections in high-energy tails of
distributions. The electroweak corrections account for the major part of
the complete next-to-leading-order correction, which amounts to 15–20%
in size, depending on the details of the event selection chosen for
analysing vector-boson-scattering. Moreover, we compare the full
next-to-leading-order corrections to approximate results based on the
neglect of contributions that are not enhanced by the vector-boson
scattering kinematics (VBS approximation) and on resonance expansions
for the W-boson decays (double-pole approximation); the quality of this
approximation is good within ≲ 1.5% for integrated cross sections and
the dominating parts of the differential distributions. Finally, for the
leading-order predictions, we construct different versions of effective
vector-boson approximations, which are based on cross-section
contributions that are enhanced by collinear emission of W bosons off
the initial-state (anti)quarks; in line with previous findings in the
literature, it turns out that the approximative quality is rather
limited for applications at the LHC.

Speaker: Stefan Dittmaier (University of Freiburg)

ll24-VBS.pdf

11:00 → 13:00 Parallel 6

Convener: Roberto Bonciani (Sapienza Universita' di Roma, Roma, Italy)

11:00 N3LO corrections to zero-jettiness soft function

We discuss the analytical computation of N3LO corrections to zero-jettiness soft function in QCD. We present the results of triple emission contribution together with one-loop corrections to the double-emission cases. In particular, for the most complicated contributions, we provide details of master integrals calculation and IBP reduction in the presence of Heaviside functions.

Speaker: Andrey Pikelner (KIT TTP)

pikelner-SF-LL2024.pdf

11:30 N-jettiness soft function at NNLO in QCD

Motivated by the possibility of using advances in developing NNLO subtraction schemes to derive representations for building blocks of modern slicing methods, we derive a simple finite representation of the renormalized N-jettiness soft function at NNLO. The number of hard partons N appears as a parameter in the finite remainder. The cancellation of all infra-red and collinear singularities between the bare soft function and its renormalization constant is demonstrated analytically.

Speaker: Ivan Pedron (KIT)

Talk_N_jettiness_pedron.pdf

12:00 Subleading power corrections for event shape variables in e+e- collisions

The precise computation of cross section for scattering processes relevant at colliders involves the evaluation of phase-space integral that are IR divergent in d=4 dimensions. The subtraction of those divergences is a key ingredient to obtain fully-differential predictions for physical observables. One possibility is offered by non-local subtraction methods built upon suitably defined IR-safe resolution variables. Prominent examples for NNLO calculations are given by N-jettiness and qt-subtraction. A new variable, named ktness, has been recently proposed and used to perform NLO calculations for jet processes. The computation of the perturbative ingredients needed for the non-local subtraction formalism is performed in a leading power expansion around the soft and/or collinear limits. Hence, the performance of the method crucially relies on the size of the neglected power suppressed terms.
We discuss a class of resolution variables relevant for the calculation of higher-order QCD corrections in electron-positron collisions.
We present results at NLO and we compute the corresponding power corrections with analytical and numerical methods.
We also report on our ongoing work towards an extension of ktness subtraction to NNLO.

Speaker: Flavio Guadagni (University of Zurich)

Flavio_Guadagni.pdf

12:30 Refactorisation and subtraction

In the context of infrared subtraction algorithms beyond NLO, it is necessary
to consider nested infrared limits of scattering amplitudes, in which several particles
become soft or collinear in a strongly-ordered sequence, as well as mixed real-virtual
contributions. I will discuss these configurations from the point of view of infrared factorisation,
and provide general definitions of strongly-ordered soft and collinear kernels in terms
of gauge-invariant operator matrix elements, leading to the construction of local subtraction
counterterms for strongly-ordered configurations. Because of their factorised structure,
these counterterms, upon integration, cancel the infrared poles of real-virtual contributions
by construction, streamlining an important sector of subtraction algorithms to any order.

Speaker: Lorenzo Magnea (University of Torino)

LoopsAndLegs24.pdf

13:00 → 14:30 Lunch

14:30 → 16:00 Parallel 7

Convener: Ayres Freitas (University of Pittsburgh)

14:30 ALARIC: A NLL accurate Parton Shower algorithm

We present the parton shower algorithm ALARIC that extends the coherent branching formalism and allows for a direct analytic proof of NLL accuracy by means of a suitable kinematics mapping and choice of evolution variable. Final-state and initial-state evolution are treated in a unified manner, and the matching to NLO calculations is straightforward.
We discuss the general structure of the algorithm and present new developments, such as the inclusion of massive parton evolution.

Speaker: Florian Herren (Universität Zürich)

LoopsAndLegs2024_Herren.pdf

15:00 Towards High-energy logarithmic resummation at full next-to-leading logarithmic accuracy

We derive the first components necessary for evaluating QCD scatting amplitudes to next-to-leading logarithmic accuracy in the high energy limit. Specifically, we derive both real and virtual corrections to the so-called jet impact factor to NLL accuracy within a formalism, which allows for overall energy and momentum conservation to be observed. We extract the virtual corrections from the full one-loop result for the four-parton amplitude. We recount why the high-energy limit is universal between all four-parton amplitudes.
While the impact factor has previously been calculated to the same logarithmic accruacy, it has not previously been expressed in a form, which allows for energy and momentum conservation to be observed in the resummation. This is important for ensuring the full NLL accuracy in log(s) of the constructed cross section.

Speaker: Jeppe R. Andersen (IPPP)

Andersen.pdf

15:30 Energy-Energy Correlations on Tracks: Factorization and Resummation

To do experimentally clean measurements, one of the proposed strategies is to use track-based observables, which means working exclusively with final-state charged hadrons (tracks). A field-theoretic framework, the so-called track function formalism, for calculating track-based observables has been introduced. Although the case of most experimental interest is tracks, this framework is based on the factorization and universality of collinear divergences, and thus can be applied to measurements on any subset of final-state hadrons with a set of particular quantum numbers. While the track function formalism has existed for eleven years, it’s just in the past few years that we’ve extended it beyond leading order, making it practical in higher-order calculations comparable to experimental data. We illustrate its power by calculating the energy-energy correlation (EEC) on charged hadrons in $e^+e^-$ in QCD at two-loop order and achieving its first resummation both in the collinear limit at next-to-next-to-leading logarithmic (NNLL) accuracy and in the back-to-back limit at next-to-next-to-next-to-leading (N$^3$LL) logarithmic accuracy. This makes the track EEC a prime candidate for precision QCD studies. We also believe that our study in the Sudakov region is crucial for understanding the non-perturbative effects of EECs and those in transverse-momentum-dependent observables.

Speaker: Yibei Li (Zhejiang University)

slides_LL2024.pdf

14:30 → 16:00 Parallel 8

Convener: Lorenzo Tancredi (TUM)

14:30 Three-loop vertices with massive particles

Vertex corrections with massive particles are important
building blocks for higher order corrections, since they
describe the virtual corrections for many observables.
In this talk we present new analytical and semi-analytic
results for vertices with non-symmetric mass assignements
on the external legs. In particular, we will focus on corrections
to the inclusive decays of $b \to s \gamma$ and $b \to u l \bar{\nu}$.

Speaker: Kay Schönwald (UZH)

LL_2024.pdf

15:00 Antenna subtraction for final-state radiation at N$^3$LO

I this talk, I will present recent integrations of all the necessary antenna functions in final-final kinematics at N$^3$LO, and the study of their infrared structure. I will describe how these universal ingredients can be used to construct subtraction terms for simple processes with final-state QCD radiation, such as jet production in lepton collisions.

Speaker: Petr Jakubčík (University of Zurich)

LL2024_Petr_Jakubcik.pdf

15:30 A subtraction scheme at NLO exploiting the privilege of kT-factorization

We present a subtraction scheme for the calculation of real-radiation integrals at NLO in hybrid kT-factorization. The main difference with known methods for collinear factorization is that we subtract the momentum recoil, occurring due to the mapping from an (n+1)-particle phase space to an n-particle phase space, from the initial-state momenta, instead of distributing it over the final-state momenta.

Speaker: Andreas van Hameren (IFJ PAN)

vanHameren.pdf

16:00 → 16:30 Coffee break

16:30 → 18:30 Parallel 7

Convener: Ayres Freitas (University of Pittsburgh)

16:30 Towards the next Kira release

The reduction of Feynman integrals to a basis of master integrals plays a crucial role for many high-precision calculations and Kira is one of the leading tools for this task. In this talk I will discuss the new features and improvements we are currently developing for the next release of Kira.

Speaker: Fabian Lange (Universität Zürich and Paul Scherrer Institut)

ll2024_lange_kira.pdf

17:00 New multiloop capabilities of FeynCalc 10

We report on a new version of the FeynCalc package (arXiv:2312.14089) that features a large collection of useful routines for multiloop calculations. Those include topology identification and minimization, optimized tensor reduction, detection of equivalent or scaleless loop integrals and construction of Feynman parametric as well as graph representations for master integrals. In addition to that, we provide a collection of
convenient interfaces ("FeynHelpers") to popular tools such as QGRAF, Fiesta, pySecDec, LoopTools, KIRA, FIRE or Fermat. All this is intended to maximally streamline multiloop calculations when using FeynCalc and FeynHelpers together with a FORM-based calculational setup. Furthermore, we will briefly discuss how this machinery was employed in a study of "soft-overlap" contribution to $B_c \to \eta_c$ transition form factors at large hadronic recoil (arXiv:2309.08410).

Speaker: Vladyslav Shtabovenko (University of Siegen)

talk.pdf

17:30 Auxiliary mass flow method for master integrals around non-analytic points

The calculation of phase-space integrals via reverse unitarity and differential equations often faces bottlenecks in fixing boundary conditions. In this talk we present a general and analytical method to derive boundary conditions for phase-space master integrals. Our strategy is based on the auxiliary mass flow method (AMFlow), but it is purely analytic. It is suited for the calculation of boundary conditions near the non-analytic endpoint region of phase space integrals, where a numerical approach is not feasible. It is based on the introduction of an auxiliary mass to some properly chosen propagators, on the construction and subsequent solution of a DE system with respect to the auxiliary mass and an analytic flow to vanishing auxiliary mass for recovering the physical solution. We present some applications to DIS-like phase space integrals at two-loops and an outlook to three-loops.

Speaker: Gaia Fontana (University of Zürich)

L&L2024_fontana.pdf

18:00 Status of two-loop automation in OpenLoops

The development of a fully automated tool for the numerical calculation
of NNLO corrections to scattering amplitudes is a highly desirable goal for the LHC era.
In our approach, D-dimensional two-loop amplitudes are decomposed into Feynman integrals with four-dimensional numerators as well as (D-4)-dimensional remainders, which can contribute to the finite result through the interaction with the poles of Feynman integrals.
The integrals with four-dimensional numerators are then expressed as tensor integrals in the loop momenta contracted with tensor coefficients.
Hence, the calculation can be structured into the computation of the tensor coefficients, the treatment of (D-4)-dimensional numerator parts, the renormalisation procedure, and the reduction and evaluation of the tensor integrals.

In this talk, we present the status of OpenLoops with respect to these building blocks.
A highly efficient algorithm for the construction of the tensor coefficients has been developed and fully implemented for QED and QCD corrections to the SM. Recently, the renormalisation procedure as well as the reconstruction of the interplay of (D-4)-dimensional numerator parts with UV poles through two-loop rational counterterms has been implemented and validated. In order to test this framework we implemented an in-house library for the reduction of simple tensor integrals. This is currently being used to reproduce first two-loop amplitudes for simple processes with off-shell particles, which constitute the first application of the concept of two-loop rational terms of UV origin. Finally, we give an outlook on the current and nexts steps towards the automation of two-loop calculations in OpenLoops.

Speaker: Max Zoller (UZH / PSI)

Zoller_LL_2024.pdf

16:30 → 18:30 Parallel 8

Convener: Lorenzo Tancredi (TUM)

16:30 Locally finite two-loop amplitudes for Higgs production in gluon fusion process

A universal numerical approach for computing loop amplitudes would permit to achieve high precision in theoretical predictions for a wide range of phenomenologically relevant processes. A major obstacle in developing such methods is the treatment of infrared and ultraviolet singularities. These need to be removed at the integrand level before numerical integration becomes feasible. In this talk, I will present a framework under development to construct locally finite two-loop amplitudes for arbitrary processes. It is based on the universality of infrared singularities, realizing infrared factorization manifestly on the local level. As a specific example, I will explain the construction of locally finite two-loop amplitudes for gluon-fusion processes with an arbitrary number of Higgs final states. We find that the infrared singularities of the QCD ampltiudes reside in graphs of a simpler “scalar” QED theory and that the IR counterterms are simple amplitudes for well-known $2\to 1$ processes. Anticipating a generalization of our method to more complicated classes of QCD processes, I will also discuss our progress on the intricate problem of enabling Ward identity cancellations of collinear singularities locally with the introduction of novel “Feynman rules”.

Speaker: Julia Karlen (ETH Zurich)

LandLs_JuliaKarlen.pdf

17:00 Numerical threshold subtraction in physical amplitudes

We present numerical loop (and phase-space) integration for the virtual correction to the process $q \bar{q} \to \gamma \gamma \gamma$ and $q \bar{q} \to \gamma^* \gamma^* \gamma^*$ at one-loop and two-loop $N_f$ orders. The approach involves employing infrared and ultraviolet local subtraction counterterms to achieve a locally finite amplitude in 4 dimensions. Subsequently, this locally finite amplitude is numerically integrated in loop momentum space using the cross-free-family representation and the threshold subtraction technique. Finally, the infrared and ultraviolet counterterms are analytically integrated to obtain the complete result.

Speaker: Matilde Vicini (ETH zurich)

loops_and_legs_2024_matilde_vicini_.pdf

17:30 LASS, the numerics

In my talk I present the first numerical implementation of the LASS scheme to calculate event shape observables for three-jet production in electron-positron annihilation at Next-to-Next-to-Leading Order accuracy in QCD. Since these observables were already calculated in the past by other subtraction schemes I plan to make a detailed comparison of the various methods with emphasis on CPU time and numerical accuracy.

Speaker: Adam Kardos (University of Debrecen)

kardos.pdf

18:00 Analysis of $(n+1)$ and $n$-parton lines in LASS

In this talk I will present the status of a calculation of $RV$ and $VV$ contributions to 3-jet production in electron-positron annihilation at NNLO within the framework of Local Analytic Sector Subtraction. We will demonstrate the cancellation of infrared singularities and put on display the results of a numerical phase-space integration over the finite remainders. This is a step forward towards automation of NNLO calculations.

Speaker: Bakar Chargeishvili (Universität Hamburg, II Institut für Theoretische Physik)

Bakar_RV_VV_LL_18Apr2024.pdf

19:00 → 20:30 Dinner

Friday, 19 April

09:00 → 10:30 Plenary 4

Convener: Matthias Steinhauser (KIT)

Poster_QCDatLHC2024.pdf

radcor.pdf

09:00 Radiative corrections to nuclear processes

One loop radiative corrections to beta-decays of hadrons are significantly enhanced with respect to analogous corrections to the muon decay. The nature of this enhancement will be presented, stressing similarities and differences with the Sommerfeld enhancement near the threshold. Extension to two loops will be discussed, as well as applications to other processes including the solar proton-proton fusion.

Speaker: Andrzej Czarnecki (University of Alberta)

NuclearRC.pdf

09:30 Two-loop virtual amplitudes for qq->ttH production (the Nf-part)

I'd like to present the results for the numerical calculation of the 2-loop virtual amplitudes for qq->ttH production based on the recent work of arXiv:2402.03301, describing the methods (i.e. sector decomposition), the tools (pySecDec and Ratracer), and the outlook for the remaining work.

Speaker: Vitaly Magerya (ITP KIT)

magerya-qqtth-ll2024.pdf

10:00 NNLO QCD corrections for the production of a heavy-quark pair in association with a massive boson

The current frontier of NNLO computations is represented by $2\to3$ processes with external massive legs. In this talk we will present recent progresses in NNLO QCD computations for processes where a heavy-quark pair is produced in association with a massive boson, mainly focusing on $t \bar{t} H$, $Wb\bar b$ and $Wt\bar t$ production.
The achievement of a complete NNLO calculation for this class of processes is a challenging task since it requires the availability of the corresponding scattering amplitudes as well as an efficient method to handle and cancel infrared singularities. In our framework, the latter is achieved thanks to the well-established $q_T$-subtraction, properly extended to the case of heavy-quark production in association with a colourless system.
Despite recent remarkable progress in multi-loop calculations, the computation of two-loop amplitudes for $2\to 3$ and higher-multiplicity processes, with several masses involved, is still at the frontier of current techniques.
We will discuss the approximations we adopted to circumvent the bottleneck of the missing double-virtual contribution, mainly focusing on a soft-boson approximation and the massification technique. Finally, we will present results for the total cross section and phenomenologically relevant distributions.

Speaker: Chiara Savoini (University of Zurich)

Savoini_LL24.pdf

10:30 → 11:00 Coffee break

11:00 → 12:30 Plenary 4

Convener: Matthias Steinhauser (KIT)

Poster_QCDatLHC2024.pdf

radcor.pdf

11:00 Towards QCD at five loops

I report on recent progress in the calculation of heavy-quark correlation functions at five loops.

Speaker: Andreas Martin Maier (DESY)

ll2024_amaier.pdf

11:30 Regge pole and Regge cuts in full colour

Scattering amplitudes in the high-energy limit can be described in terms of their singularity structure in the complex angular momentum plane, consisting of Regge poles and cuts. In QCD, gluon Reggeization has long been understood as a manifestation of a Regge pole, but until recently Reggeization violation remained largely obscure. New methods based on rapidity evolution equations allow for direct computation of components of the amplitude which are mediated by multi-Reggeon exchange, a manifestation of Regge cuts. Upon disentangling the Regge cut from the pole we are now able to extract the pole parameters from state-of-the-art fixed-order computations (3 loops) and make predictions regarding certain components of the amplitude to higher loop orders. In this talk I review the key ideas which led to this progress, describe where we stand in exploring the structure of $2\to 2$ and $2\to 3$ amplitudes in the (multi-) Regge limit, and comment on the interplay between this research and the study of infrared factorization.

Speaker: Einan Gardi (The University of Edinburgh)

Loops_and_Legs_2024.pdf

12:00 Polylogs from diagrams with elliptic obstructions

Numerical evaluations of 2-loop kites and 3-loop tadpoles
with elliptic obstructions lead to remarkable empirical
evaluations in terms of polylogarithms, for which proofs
are very hard to find, notwithstanding intensive use of packages
such as HyperInt and MZIteratedIntegral. I shall describe the
efficient methods by which these puzzlingly simple evaluations
were obtained and current efforts to demystify them.

Speaker: David Broadhurst (Open University, UK)

Broadhurst_LL2024 (2).pdf

13:00 → 14:30 Lunch