SciPost: SciPost Physics Proceedings: issue detail

SciPost Physics Proceedings issue 7

15th International Symposium on Radiative Corrections: Applications of Quantum Field Theory to Phenomenology (RADCOR2021)

Event dates: from 2021-05-17 to 2021-05-21.

This is the 15th International Symposium on Radiative Corrections (RADCOR) which is dedicated to the application of quantum field theory techniques to particle physics phenomenology. The conference covers subjects on:

Higher-loop and higher-multiplicity calculations in the Standard Model
Cross sections for new physics
New techniques for calculations
Advances in computer-algebra methods
New theoretical developments

Nota bene: for submissions, a limit of 7 pages has been set.

(Guest) Fellows responsible for this Issue

Prof. Fernando Febres Cordero
Prof. Manfred Kraus
Prof. Laura Reina

Master integrals contributing to two-loop leading colour QCD helicity amplitudes for top-quark pair production in the gluon fusion channel

Ekta Chaubey

SciPost Phys. Proc. 7, 001 (2022) · published 20 June 2022 | · pdf

We discuss the analytic structure of the master integrals relevant for computing the com- plete set of leading-colour analytic helicity amplitudes for top-quark pair production via gluon fusion at two loops in QCD. This includes corrections due to massive fermion loops which give rise to integrals involving elliptic curves. We also elaborate on the structure of singularities that play an important role in the numerical evaluation of the iterated integrals and their analytic continuation.
Double Virtual Contributions for Massless 2 -> 3 Scattering in NNLO QCD

Vasily Sotnikov

SciPost Phys. Proc. 7, 002 (2022) · published 20 June 2022 | · pdf

We review the recent advances in the calculation of two-loop QCD corrections for massless five-point scattering that paved the way for their broad phenomenological applications in calculation of NNLO QCD predictions. We first discuss the construction of a transcendental function basis which facilitates derivation of compact analytic representations for two-loop amplitudes and enables their fast and stable numerical evaluation over physical phase space. We then present the recent calculations of the leading-color two-loop corrections for hadroproduction of three photons and three jets.
Mixed QCD-electroweak corrections to $Z$ and $W$ boson production and their impact on the $W$ mass measurements at the LHC

Arnd Behring

SciPost Phys. Proc. 7, 003 (2022) · published 20 June 2022 | · pdf

We report on recently computed mixed QCD-electroweak corrections to on-shell $W$ and $Z$ boson production. We use these differential predictions to estimate their impact on the $W$ boson mass determination at the LHC.
NNLO EW⊗QCD corrections to on-shell Z production

Narayan Rana

SciPost Phys. Proc. 7, 004 (2022) · published 20 June 2022 | · pdf

In this proceeding, we outline the computational details and present the results for NNLO mixed EW⊗QCD corrections to on-shell production of Z boson at the LHC. We use the method of differential equation to obtain all the master integrals analytically, appearing in virtual and real-emission contributions. These results increase the accuracy of the predictions and contribute to reduce the theoretical uncertainties.
On the discrepancy between the FOPT and CIPT approaches for hadronic tau spectral function moments

Andre H. Hoang, Christoph Regner

SciPost Phys. Proc. 7, 005 (2022) · published 20 June 2022 | · pdf

The discrepancy between the FOPT and CIPT approaches for hadronic tau spectral function moments constitutes the major theoretical uncertainty for strong coupling determinations from tau decay data. We show that the discrepancy can be analytically understood since the Borel representations -- which have been assumed to be identical for both approaches previously -- differ in the presence of IR renormalons. This implies that the OPE condensate corrections are different for both approaches and that the discrepancy may eventually be reconciled. In the talk we explain the difference and some mathematical aspects of the FOPT and CIPT Borel representations and show numerical results.
NLO QCD corrections for off-shell $t\bar{t}b\bar{b}$

Michele Lupattelli

SciPost Phys. Proc. 7, 006 (2022) · published 20 June 2022 | · pdf

We present a full off-shell NLO QCD calculation of $pp \rightarrow e^+ \nu_e b \mu^- \bar{\nu}_\mu \bar{b} b \bar{b} + X$. Results are obtained using the \textsc{Helac-Nlo} Monte Carlo framework. We discuss a comparison to previous results and to experimental measurements. We also investigate the contribution of the initial states involving $b$-quarks and we introduce two $b$-jet tagging schemes.
Two-parton scattering in the high-energy limit: climbing two- and three-Reggeon ladders

G. Falcioni, E. Gardi, N. Maher, C. Milloy, L. Vernazza

SciPost Phys. Proc. 7, 007 (2022) · published 20 June 2022 | · pdf

We review recent progress on the calculation of scattering amplitudes in the high-energy limit. We start by illustrating the shockwave formalism, which allows one to calculate amplitudes as iterated solutions of rapidity evolution equations. We then focus on our recent results regarding 2 -> 2 parton scattering. We present the calculation of the imaginary part of the amplitude, at next-to-leading logarithmic accuracy in the high-energy logarithms, formally to all orders, and in practice to 13 loops. We then discuss the computation of the real part of the amplitude at next-to-next-to-leading logarithmic accuracy and through four loops. Both computations are carried in full colour, and provide new insight into the analytic structure of scattering amplitudes and their infrared singularity structure.
A pitfall in applying non-anticommuting $γ_5$ in $q\overline{q} \rightarrow ZH$ amplitudes

Taushif Ahmed

SciPost Phys. Proc. 7, 008 (2022) · published 20 June 2022 | · pdf

In computing the two-loop QCD corrections to a class of Feynman diagrams for the process $q\overline{q} \rightarrow ZH$ in Higgs effective field theory, we discover a striking phenomenon. We find the need for an additional local composite operator in the renormalised Lagrangian while employing a non-anticommuting $\gamma_5$ in dimensional regularisation. The computation using anticommuting $\gamma_5$, however, does not require any such amendment.
Proving the dimension-shift conjecture

Ruth Britto, Guy R. Jehu, Andrea Orta

SciPost Phys. Proc. 7, 009 (2022) · published 20 June 2022 | · pdf

We prove the conjecture made by Bern, Dixon, Dunbar, and Kosower that describes a simple dimension shifting relationship between the one-loop structure of N = 4 MHV amplitudes and all-plus helicity amplitudes in pure Yang-Mills theory. The proof captures all orders in dimensional regularisation using unitarity cuts, by combining massive spinor-helicity with Coulomb-branch supersymmetry. The form of these amplitudes can be given in terms of pentagon and box integrals using a generalised D-dimensional
On the modeling of $t\bar{t}W^\pm$ signatures at the LHC

Manfred Kraus

SciPost Phys. Proc. 7, 010 (2022) · published 20 June 2022 | · pdf

We discuss our recent progress on improving the theoretical description of the $pp\to t\bar{t}W^\pm$ process with particular focus on fiducial signatures that include top-quark decays. We employ a wide range of techniques from parton shower matching, narrow width approximation to full off-shell computations to assess the importance of the different modeling approaches.
A new Wilson line-based classical action for gluodynamics

Hiren Kakkad, Piotr Kotko, Anna Stasto

SciPost Phys. Proc. 7, 011 (2022) · published 20 June 2022 | · pdf

We develop a new classical action that in addition to $\mathrm{MHV}$ vertices contains also $\mathrm{N^kMHV}$ vertices, where $1\leq k \leq n-4$ with $n$ the number of external legs. The lowest order vertex is the four-point MHV vertex -- there is no three point vertex and thus the amplitude calculation involves fewer vertices than in the CSW method. The action is obtained by a canonical transformation of the Yang-Mills action in the light-cone gauge, where the field transformations are based on Wilson line functionals.
The diagrammatic coaction and cuts of the double box

Einan Gardi, Aris Ioannou

SciPost Phys. Proc. 7, 012 (2022) · published 20 June 2022 | · pdf

The diagrammatic coaction encodes the analytic structure of Feynman integrals by mapping any given Feynman diagram into a tensor product of diagrams defined by contractions and cuts of the original diagram. Feynman integrals evaluate to generalized hypergeometric functions in dimensional regularization. Establishing the coaction on this type of functions has helped formulating and checking the diagrammatic coaction of certain two-loop integrals. In this talk we study its application on the fully massless double box diagram. We make use of differential equation techniques, which, together with the properties of homology and cohomology theory of the resulting hypergeometric functions, allow us to formulate the coaction on a range of cuts of the double box in closed form.
The Soft Anomalous Dimension at four loops in the Regge Limit

Niamh Maher, Giulio Falcioni, Einan Gardi, Calum Milloy, Leonardo Vernazza

SciPost Phys. Proc. 7, 013 (2022) · published 20 June 2022 | · pdf

The soft anomalous dimension governs the infrared divergences of scattering amplitudes in general kinematics to all orders in perturbation theory. By comparing the recent Regge-limit results for $2\to2$ scattering (through Next-to-Next-to-Leading Logarithms) in full colour to a general form for the soft anomalous dimension at four loops we derive powerful constraints on its kinematic dependence, opening the way for a bootstrap-based determination.
pySecDec as a tool for expansion by regions and loop amplitude evaluation

Emilio Villa

SciPost Phys. Proc. 7, 014 (2022) · published 20 June 2022 | · pdf

We present the new release of pySecDec, a toolbox for the evaluation of dimensionally regulated parameter integrals. The main new features consist of an automated way to perform expansions, based on the geometric approach to the method of expansion by regions, and a new algorithm to efficiently evaluate linear combinations of integrals as needed for the calculation of scattering amplitudes. The other new features are also summarised briefly.
IR-Improved Amplitude-Based Resummation in Quantum Field Theory: New Results and New Issues

B.F.L. Ward, S. Jadach, W. Placzek, M. Skrzypek, Z. Was, S. A. Yost

SciPost Phys. Proc. 7, 015 (2022) · published 20 June 2022 | · pdf

With the advancement of strategies for the precision physics programs for the HL-LHC, FCC-ee, FCC-hh, ILC, CLIC, CEPC, and CPPC, the need for proper control of the attendant theoretical precision tags is manifest. We discuss the role that amplitude-based resummation may play in this regard with examples from the LHC, the proposed new colliders and quantum gravity.
New developments in KKMChh: Quark-level exponentiated radiative corrections and semi-analytical results

S.A. Yost, M. Dittrich, S. Jadach, B.F.L. Ward, Z. Wąs

SciPost Phys. Proc. 7, 016 (2022) · published 20 June 2022 | · pdf

We describe a new semi-analytical program, KKhhFoam, which provides a simplified framework for testing the amplitude-level exponentiation scheme (CEEX) of the full KKMChh program in the semi-soft limit. The structure of the KKhhFoam integrand is also helpful for elucidating the structure of CEEX. We also discuss the representation of ISR in KKMChh and compare the ISR added by KKMChh to the effect of switching to a QED-corrected PDF, at the individual quark level, and suggest a new approach to running KKMChh with QED-corrected PDFs.
Developments since Kira 2.0

Fabian Lange, Philipp Maierhöfer, Johann Usovitsch

SciPost Phys. Proc. 7, 017 (2022) · published 21 June 2022 | · pdf

Last year we released version 2.0 of the Feynman integral reduction program Kira. In this contribution we first report on changes and new features since then and, secondly, on new features for upcoming releases.
Two-loop amplitude generation in OpenLoops

Stefano Pozzorini, Natalie Schär, Max F. Zoller

SciPost Phys. Proc. 7, 018 (2022) · published 21 June 2022 | · pdf

Numerical tools, such as OpenLoops, provide NLO scattering amplitudes for a very wide range of hard scattering amplitudes in a fully automated way. In order to match the numerical precision of current and future experiments, however, the higher precision of NNLO calculations is essential, and their automation in a similar tool highly desirable. In our approach, D-dimensional amplitudes are decomposed into loop-momentum tensor integrals with coefficients constructed in four dimensions and rational terms. We present a fully generic algorithm for the efficient numerical construction of the tensor coefficients, which constitutes an important building block for an automated NNLO tool.
Leading fermionic three-loop corrections to W-boson mass and Z-pole observables

Lisong Chen, Ayres Freitas

SciPost Phys. Proc. 7, 019 (2022) · published 21 June 2022 | · pdf

In this proceeding, we highlight the computation of leading fermionic three-loop corrections to electroweak precision observables (EWPOs) accomplished recently. We summarize the numerical analysis and provide an outlook.
Eikonal Dressed Gluon Exponentiation to study power corrections to Thrust, C-parameter, and Angularity

Neelima Agarwal, Ayan Mukhopadhyay, Sourav Pal, Anurag Tripathi

SciPost Phys. Proc. 7, 020 (2022) · published 21 June 2022 | · pdf

Dressed Gluon Exponentiation is a well known method to study power corrections. We present here its eikonalized version -- Eikonal Dressed Gluon Exponentiation (EDGE) \cite{Agarwal:2020uxi} to determine the dominant power corrections to shape variables such as Thrust, $ C $- parameter, and Angularity. Our method remarkably simplifies the calculations.
Automation of Beam and Jet functions at NNLO

Guido Bell, Kevin Brune, Goutam Das, Marcel Wald

SciPost Phys. Proc. 7, 021 (2022) · published 21 June 2022 | · pdf

We present a novel framework to streamline the calculation of jet and beam functions to next-to-next-to-leading order (NNLO) in perturbation theory. By exploiting the infrared behaviour of the collinear splitting functions, we factorise the singularities with suitable phase-space parametrisations and perform the observable-dependent integrations numerically. We have implemented our approach in the publicly available code {\tt pySecDec} and present first results for sample jet and beam functions.
The pion-photon transition form factor at two loops in QCD

Jing Gao, Tobias Huber, Yao Ji, Yu-Ming Wang

SciPost Phys. Proc. 7, 022 (2022) · published 21 June 2022 | · pdf

We report on the fully analytic calculation of the leading-power contribution to the photon-pion transition form factor $\gamma \, \gamma^{\ast} \to \pi^0$ at two loops in QCD. The applied techniques are based on hard-collinear factorization, together with modern multi-loop methods. We focus both, on the technical details such as the treatment of evanescent operators, and the phenomenological implications. Our results indicate that the two-loop correction is numerically comparable to the one-loop effect in the same kinematic domain. We also demonstrate that our results will play a key role in disentangling various models for the twist-two pion distribution amplitude thanks to the envisaged precision at Belle II.
Feynman integrals for binary systems of black holes

Philipp Alexander Kreer, Robert Runkel, Stefan Weinzierl

SciPost Phys. Proc. 7, 023 (2022) · published 21 June 2022 | · pdf

The initial phase of the inspiral process of a binary black-hole system can be described by perturbation theory. At the third post-Minkowskian order a two-loop double box graph, known as H-graph, contributes. In this talk we report how all master integrals of the H-graph with equal masses can be expressed up to weight four in terms of multiple polylogarithms. We also discuss techniques for the unequal mass case. The essential complication (and the focus of the talk) is the occurrence of several square roots.
Local Unitarity

Zeno Capatti

SciPost Phys. Proc. 7, 024 (2022) · published 21 June 2022 | · pdf

Within the Local Unitarity formalism, any physical cross-section is re-written in such a way that cancellations of infrared singularities between real and virtual contributions are realised locally. Consequently, phase-space and loop integrals are regulated locally without the need of any counter-terms or dimensional regularisation aside from those strictly needed to achieve ultraviolet regularisation. This Local Unitarity representation is especially suitable to direct Monte Carlo integration. As such, it offers a clear and direct path to automate the computation of fixed-order differential observables in Quantum Field Theories.
Towards two- and three-loop QCD corrections to the width difference in $B_s-\bar{B}_s$ mixing

Vladyslav Shtabovenko

SciPost Phys. Proc. 7, 025 (2022) · published 21 June 2022 | · pdf

In this work we address the issue of large perturbative uncertainties in the theory prediction for $\Delta \Gamma_s$, the width difference in the $B^0_s - \bar{B}^0_s$ mixing process. To this aim we complete important steps towards the full analytic result for the previously unknown Wilson coefficients from the matching between $|\Delta B|=1$ and $|\Delta B|=2$ effective Hamiltonians at next-to-next-leading order (NNLO) in the strong coupling constant. We provide a thorough discussion of technical and conceptual difficulties behind this computation and give an outlook regarding the availability of the new NNLO theory prediction for $\Delta \Gamma_s$.
Higher-order corrections to the kinetic mass definition for the bottom and the charm quarks

Matteo Fael

SciPost Phys. Proc. 7, 026 (2022) · published 21 June 2022 | · pdf

In these proceedings we discuss the relation between the kinetic and the on-shell schemes for the bottom and the charm quarks and present the methods for the calculation of the mass relation to higher orders in perturbative QCD. The bottom mass in the kinetic scheme is a pivotal input parameter in the inclusive determination of $|V_{cb}|$ from $B\to X_c \ell \nu_\ell$ decays. By combining the relation between the kinetic and the on-shell mass with well-know results for the $\overline{\mathrm{MS}}$-on-shell conversion, we obtain a prediction for $m_b^\mathrm{kin}$ based on precise determinations of $\overline{m}_b(\overline{m}_b)$.
$\mathcal{O}(α_s^3)$ corrections to semileptonic $b \to c$ decays in the heavy daughter approximation

Kay Schoenwald

SciPost Phys. Proc. 7, 027 (2022) · published 21 June 2022 | · pdf

We present our recent calculation of the third order corrections to the semileptonic $b \to c$ and the muon decays. The calculation has been performed in an expansion around the limit $m_c \sim m_b$, but shows decent convergence even for $m_c=0$ from which the contribution to the muon decay can be extracted. For the semileptonic $b \to c$ decay we find large perturbative corrections in the on-shell scheme which can be significantly reduced by changing to the kinetic scheme for the bottom quark mass. These results are important input for the inclusive determination of $|V_{cb}|$ and the Fermi coupling constant $G_F$.
$N^3LO$ calculations for $2 \to 2$ processes using simplified differential equations

Dhimiter D. Canko, Federico Gasparotto, Luca Mattiazzi, Costas G. Papadopoulos, Nikolaos Syrrakos

SciPost Phys. Proc. 7, 028 (2022) · published 21 June 2022 | · pdf

We present the computation of the massless three-loop ladder-box family with one external off-shell leg using the Simplified Differential Equations (SDE) approach. We also discuss the methods we used for finding a canonical differential equation for the two tennis-court families with one off-shell leg, and the application of the SDE approach on these two families.
Higher-order $β$-functions in the Standard Model and beyond

Florian Herren

SciPost Phys. Proc. 7, 029 (2022) · published 21 June 2022 | · pdf

In this contribution we consider the recent computation of the gauge coupling $\beta$-function at four loops and the Yukawa matrix $\beta$-function at three loops in the most general, renormalizable and four-dimensional quantum field theory. Furthermore, we discuss ambiguities and divergences arising in Yukawa matrix $\beta$-functions.
Multiscale pentagon integrals to all orders

Dhimiter D. Canko, Costas G. Papadopoulos, Nikolaos Syrrakos

SciPost Phys. Proc. 7, 030 (2022) · published 21 June 2022 | · pdf

We present analytical results for one-loop five-point master integrals with up to three off-shell legs. The method of canonical differential equations along with the Simplified Differential Equations approach is employed. All necessary boundary terms are given in closed form, resulting to solutions in terms of Goncharov Polylogarithms of arbitrary weight. Explicit results up to weight six will be presented.
Top quark mass corrections to single and double Higgs boson production in gluon fusion

Joshua Davies

SciPost Phys. Proc. 7, 031 (2022) · published 21 June 2022 | · pdf

In this talk we discuss recent computations of the top quark mass dependence of QCD amplitudes describing Higgs boson production in gluon fusion. We compute terms in the expansion for a large top quark mass, which reduces the Feynman diagrams to products of massless integrals and massive tadpole integrals which contain the top mass dependence. In particular we discuss the real and virtual corrections to double Higgs production at NNLO, and the virtual corrections to single Higgs production at N3LO.
A differential-geometry approach to operator mixing in massless QCD-like theories and Poincaré-Dulac theorem

Matteo Becchetti

SciPost Phys. Proc. 7, 032 (2022) · published 21 June 2022 | · pdf

We review recent progress on operator mixing in the light of the theory of canonical forms for linear systems of differential equations and, in particular, of the Poincar\'e-Dulac theorem. We show that the matrix $A(g) = -\frac{\gamma(g)}{\beta(g)} =\frac{\gamma_0}{\beta_0}\frac{1}{g} + \cdots $ determines which different cases of operator mixing can occur, and we review their classification. We derive a sufficient condition for $A(g)$ to be set in the one-loop exact form $A(g) = \frac{\gamma_0}{\beta_0}\frac{1}{g}$. Finally, we discuss the consequences of the unitarity requirement in massless QCD-like theories, and we demonstrate that $\gamma_0$ is always diagonalizable if the theory is conformal invariant and unitary in its free limit at $g =0$.
Applications of the Perturbative Gradient Flow

Fabian Lange

SciPost Phys. Proc. 7, 033 (2022) · published 21 June 2022 | · pdf

Over the last decade the gradient flow formalism became an important tool for lattice simulations of Quantum Chromodynamics. It offers remarkable renormalization properties which pave the way for cross-fertilization between perturbative and lattice calculations. In this contribution we discuss the perturbative approach. As first application we compute vacuum expectation values of flowed operators which could help to extract parameters like the strong coupling constant from lattice simulations. Afterwards, we apply the flowed operator product expansion to the time-ordered product of two currents which could be employed for an alternative first-principle evaluation of vacuum polarization functions on the lattice.
NLO electroweak and QCD corrections to off-shell ttW production at the LHC

Ansgar Denner, Giovanni Pelliccioli

SciPost Phys. Proc. 7, 034 (2022) · published 21 June 2022 | · pdf

The foreseen luminosities for the next LHC runs will enable precise differential measurements of the associated production of top-antitop pairs with a W boson. Therefore, providing accurate theory predictions for this process is needed for realistic final states. We present the first combination of NLO electroweak and QCD corrections to off-shell ttW$^+$ production in the three-charged-lepton channel, including non-resonant effects, full spin-correlations and interferences. Such radiative corrections comprise the electroweak and QCD corrections to the leading QCD order, and the QCD corrections to the leading electroweak order.
W+c-jet production at the LHC with NNLO QCD accuracy

Michal Czakon, Alexander Mitov, Mathieu Pellen, Rene Poncelet

SciPost Phys. Proc. 7, 035 (2022) · published 21 June 2022 | · pdf

In these proceedings, we highlight some aspects of the recent computation of NNLO QCD corrections for W production in association with a charm jet at the LHC. The results are presented in the form of cross sections and differential distributions and are compared to ATLAS data.
Two-Loop renormalization of High-Dimensional QCD operators and Higgs EFT amplitudes

Qingjun Jin, Ke Ren, Gang Yang, Rui Yu

SciPost Phys. Proc. 7, 036 (2022) · published 21 June 2022 | · pdf

We consider two-loop renormalization of high-dimensional operators in QCD and the relevant Higgs EFT amplitudes. Efficient unitarity-IBP strategy is used to compute the two-loop minimal form factors of length-3 operators up to dimension sixteen. From the ultraviolet divergences of form factor results, we extract the renormalization matrices and compute anomalous dimensions. We also obtain the analytic finite remainder functions which exhibit several universal transcendentality structures. The form factors we compute are equivalent to Higgs plus three-gluon amplitudes that capture high-order top mass corrections in Higgs effective field theory.
Recent progress on two-loop massless pentabox integrals with one off-shell leg

D. Canko, A. Kardos, C. G. Papadopoulos, A. V Smirnov, N. Syrrakos, C. Wever

SciPost Phys. Proc. 7, 037 (2022) · published 21 June 2022 | · pdf

Analytic expressions in terms of polylogarithmic functions for all three families of planar two-loop five-point Master Integrals with one off-shell leg are presented. The Simplified Differential Equations approach is the only known way to fulfil this task due to its unique factorisation property of the symbols of the canonical differential equation. The results are relevant to the study of many $2\to 3$ scattering processes of interest at the LHC.
PMC$_\infty$: Infinite-Order Scale-Setting method using the Principle of Maximum Conformality and preserving the Intrinsic Conformality

Leonardo Di Giustino, Stanley J. Brodsky, Xing-Gang Wu, Sheng-Quan Wang

SciPost Phys. Proc. 7, 038 (2022) · published 21 June 2022 | · pdf

We show results for Thrust and C-parameter in $e^+ e^-$ annihilation to 3 jets obtained using the recently developed new method for eliminating the scale ambiguity and the scheme dependence in pQCD namely the Infinite-Order Scale-Setting method using the Principle of Maximum Conformality (PMC$_\infty$). This method preserves an important underlying property of gauge theories: intrinsic Conformality (iCF). It leads to a remarkably efficient method to eliminate the conventional renormalization scale ambiguity at any order in pQCD. A comparison with Conventional Scale Setting method (CSS) is also shown.
The two-loop radiative gluon jet function for $gg\to h$ via a light quark loop

Marvin Schnubel

SciPost Phys. Proc. 7, 039 (2022) · published 22 June 2022 | · pdf

The Higgs-boson production channel $gg\to h$ mediated by light-quark loops receives large logarithmic corrections in QCD, which can be resummed using factorization formulae derived in soft-collinear effective theory. In these factorization formulae the radiative gluon jet function appears, which is a central object in the study of factorization beyond the leading order in scale ratios. We calculate this function at two-loop order for the first time and present the subtleties that come along with this.
Next-to-leading power SCET in Higgs amplitudes induced by light quarks

Xing Wang

SciPost Phys. Proc. 7, 040 (2022) · published 22 June 2022 | · pdf

In this article, we report how to use the "plus-type" subtraction scheme to deal with endpoint divergences in $h\rightarrow\gamma\gamma$ or $gg\rightarrow h$ amplitudes induced by light quark loop, which can be formulated by next-to-leading power (NLP) SCET. This subtraction is ensured by two re-factorization conditions, which have been proven to all orders in $\alpha_s$. Based on these conditions, cutoffs emerge naturally after some re-arrangements to handle endpoint divergences and renormalization is compatible with that. Our formalism can analytically reproduce three-loop amplitudes up to $\ln^3(-M_h^2/m_b^2-i0)$ and resum to next-to-leading logarithm and beyond.
A semi-numerical method for one-scale problems applied to the $\overline{\rm MS}$-on-shell relation

Matteo Fael, Fabian Lange, Kay Schönwald, Matthias Steinhauser

SciPost Phys. Proc. 7, 041 (2022) · published 22 June 2022 | · pdf

We discuss a practical approach to compute master integrals entering physical quantities which depend on one parameter. As an example we consider four-loop QCD corrections to the relation between a heavy quark mass defined in the $\overline{\rm MS}$ and on-shell scheme in the presence of a second heavy quark.
NNLO photon fragmentation within antenna subtraction

Thomas Gehrmann, Robin Schürmann

SciPost Phys. Proc. 7, 042 (2022) · published 22 June 2022 | · pdf

We report on our recent progress towards including the photon fragmentation contribution in next-to-next-to-leading order (NNLO) QCD predictions for photon production cross sections. This extension to previous NNLO calculations requires the identification of the photon in singular parton-photon collinear limits. We discuss how these limits can be subtracted within antenna subtraction using fragmentation antenna functions and we outline their integration.
Two-loop gauge coupling $β$-function in a four-dimensional framework: the Standard Model case

Adriano Cherchiglia

SciPost Phys. Proc. 7, 043 (2022) · published 22 June 2022 | · pdf

At present, the gauge coupling $\beta$-function in the Standard Model (SM) is known up to four-loop order. As most SM calculations, dimensional regularization was employed. Despite its striking success, other regularization schemes have emerged, which aim to stay in the physical dimension as far as possible. In this contribution, we apply Implicit Regularization, a scheme defined in momentum space that complies with BPHZ, to obtain the two-loop gauge coupling $\beta$-function in the Standard Model. We reproduce the same result obtained when applying dimensional regularization.
Timelike transition form factor for CP-odd Higgs boson production

Ken Sasaki, Tsuneo Uematsu

SciPost Phys. Proc. 7, 044 (2022) · published 22 June 2022 | · pdf

We investigate the production of CP-odd Higgs boson $A^0$ associated with a real $\gamma$ in $e^+e^-$ collisions. Because of the properties of $A^0$ coupling to the other fields, the main contribution comes from the top-quark triangle loop diagrams. We obtain the timelike transition form factor which describes the production amplitude of $A^0$ in the $e^+e^-$ collisions. This timelike transition form factor is related to the spacelike transition form factor relevant for the $A^0$ production in $e^-\gamma$ collisions. It turns out that the possible extra contributions from chargino-sneutrino and neutralino-selectron box diagrams do not give sizable effects.
Background field method and generalized field redefinitions in effective field theories

Andrea Quadri

SciPost Phys. Proc. 7, 045 (2022) · published 22 June 2022 | · pdf

We study the non-linear background field redefinitions arising at the quantum level in a spontaneously broken effective gauge field theory. The non-linear field redefinitions are crucial for the symmetric (i.e. fulfilling all the relevant functional identities of the theory) renormalization of gauge-invariant operators. In a general $R_\xi$-gauge the classical background-quantum splitting is also non-linearly deformed by radiative corrections. In the Landau gauge these deformations vanish to all orders in the loop expansion.
Three-loop soft anomalous dimensions in QCD

Nikolaos Kidonakis

SciPost Phys. Proc. 7, 046 (2022) · published 22 June 2022 | · pdf

I present results for soft anomalous dimensions through three loops for many QCD processes. In particular, I give detailed expressions for soft anomalous dimensions in various processes with electroweak and Higgs bosons as well as single top quarks and top-antitop pairs.
Geometry and causality for efficient multiloop representations

German F. R. Sborlini

SciPost Phys. Proc. 7, 047 (2022) · published 22 June 2022 | · pdf

Multi-loop scattering amplitudes constitute a serious bottleneck in current high-energy physics computations. Obtaining new integrand level representations with smooth behaviour is crucial for solving this issue, and surpassing the precision frontier. In this talk, we describe a new technology to rewrite multi-loop Feynman integrands in such a way that non-physical singularities are avoided. The method is inspired by the Loop-Tree Duality (LTD) theorem, and uses geometrical concepts to derive the causal structure of any multi-loop multi-leg scattering amplitude. This representation makes the integrand much more stable, allowing faster numerical simulations, and opens the path for novel re-interpretations of higher-order corrections in QFT.
All-order renormalization of electric charge in the Standard Model and beyond

Stefan Dittmaier

SciPost Phys. Proc. 7, 048 (2022) · published 22 June 2022 | · pdf

Electric charge, as defined in the Thomson limit of the electron--photon interaction vertex, is renormalized to all orders both in the Standard Model and in any spontaneously broken gauge theory with gauge group GxU(1) with a group factor U(1) that mixes with electromagnetic gauge symmetry. In the framework of the background-field method the charge renormalization constant $Z_e$ is directly obtained from the photon wave-function renormalization constant, similar to the situation in QED, which proves charge universality as a byproduct. Exploiting charge universality in arbitrary $R_\xi$ gauge by formulating the charge renormalization condition for a ``fake fermion'' that couples only via an infinitesimal electric charge, $Z_e$ can be expressed in terms of renormalization constants that are obtained solely from gauge-boson self-energies.