<p>We present for the first time the second-order corrections of pseudoscalar(<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>A</mi></mrow></math>) Higgs decay to three parton to higher orders in the dimensional regulator. We compute the one- and two-loop amplitudes for processes, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>A</mi><mo stretchy="false">→</mo><mi>g</mi><mi>g</mi><mi>g</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>A</mi><mo stretchy="false">→</mo><mi>q</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mi>g</mi></math>, in the effective theory framework. With suitable crossing of the external momenta, these calculations are well-suited for predicting the differential distribution of pseudoscalar Higgs in association with a jet at hadron colliders, up to next-to-next-to-leading order in the strong coupling constant. These results expanded to higher orders in the dimensional regulator will contribute to the full three-loop cross section. We implement the finite pieces of the amplitudes in a numerical code which can be used with any Monte Carlo phase space generator.</p>

Italy

Pulak Banerjee

India

Chinmoy Dey

M.C. Kumar

V. Ravindran

Pseudoscalar Higgs boson decay to three parton amplitudes at NNLO to higher orders in the dimensional regulator

We present a calculation of the full set of next-to-next-to-leading-order QED corrections to unpolarized Møller scattering. This encompasses photonic, leptonic, and nonperturbative hadronic corrections and includes electron mass effects as well as hard photon radiation. The corresponding matrix elements are implemented in the Monte Carlo framework mcmule allowing for the computation of fully differential observables. As a first application we show results tailored to the kinematics and detector design of the PRad II experiment where a high-precision theory prediction for Møller scattering is required to achieve the targeted precision. We observe that the corrections become essential to reliably calculate the corresponding differential distributions especially in regions where the leading-order contribution is absent.

Switzerland

Tim Engel

Nicolas Schalch

Adrian Signer

United Kingdom

Yannick Ulrich

Møller scattering at NNLO

A critical subject in fully differential QED calculations originates from numerical instabilities due to small fermion masses that act as regulators of collinear singularities. At next-to-next-to-leading order (NNLO) a major challenge is therefore to find a stable implementation of numerically delicate real-virtual matrix elements. In the case of Bhabha scattering this has so far prevented the development of a fixed-order Monte Carlo at NNLO accuracy. In this paper we present a new method for stabilising the real-virtual matrix element. It is based on the expansion for soft photon energies including the non-universal subleading term calculated with the method of regions. We have applied this method to Bhabha scattering to obtain a stable and efficient implementation within the McMule framework. We therefore present for the first time fully differential results for the photonic NNLO corrections to Bhabha scattering.

Bhabha scattering at NNLO with next-to-soft stabilisation

We present the first calculations of two-point two-loop form factors (FFs) with a two identical operators insertion in maximally supersymmetric Yang-Mills theory. In this article, we consider the supersymmetry protected half-BPS primary and unprotected Konishi operators. Unlike the FFs of a single operator insertion of the half-BPS primary, the FFs involving two half-BPS operators are found to contain lower transcendentality weight terms in addition to the highest ones. Moreover, in contrast to Sudakov FFs, the highest weight terms of the FFs of a double half-BPS no longer match with that of a double Konishi. We also find that the principle of maximal transcendentality, which dictates the presence of identical highest weight terms in the scalar FFs of half-BPS and quark/gluon FFs in QCD, does not hold true anymore for insertions of two identical operators. We discover the absence of any additional ultraviolet counterterm that could arise from the contact interaction between two composite operators.

Germany

Taushif Ahmed

Amlan Chakraborty

Prasanna K. Dhani

Form factors with two operator insertions and the principle of maximal transcendentality

We present next-to-next-to leading order (NNLO) quantum electrodynamics (QED) corrections to the production of the Higgs boson in bottom quark annihilation at the Large Hadron Collider (LHC) in the five flavor scheme. We have systematically included the NNLO corrections resulting from the interference of quantum chromodynamics (QCD) and QED interactions. We have investigated the infrared (IR) structure of the bottom quark form factor up to two-loop level in QED and in <math><mrow><mi>QCD</mi><mo>×</mo><mi>QED</mi></mrow></math> using <math><mrow><mi>K</mi><mo>+</mo><mi>G</mi></mrow></math> equation. We find that the IR poles in the form factor are controlled by the universal cusp, collinear and soft anomalous dimensions. In addition, we derive the QED as well as <math><mrow><mi>QCD</mi><mo>×</mo><mi>QED</mi></mrow></math> contributions to soft distribution function as well as to the ultraviolet renormalization constant of the bottom Yukawa coupling up to second order in strong coupling and fine structure constant. Finally, we report our findings on the numerical impact of the NNLO results from QED and <math><mrow><mi>QCD</mi><mo>×</mo><mi>QED</mi></mrow></math> at the LHC energies taking into account the dominant NNLO QCD corrections.

Ajjath A H

Pooja Mukherjee

Narayan Rana

NNLO <math><mrow><mi>QCD</mi><mo>⊕</mo><mi>QED</mi></mrow></math> corrections to Higgs production in bottom quark annihilation

In this article we have studied the transverse momentum distribution of the pseudo-scalar Higgs boson at the Large Hadron Collider (LHC). The small p  T  region which provides the bulk of the cross section is not accessible to fixed order perturbation theory due to the presence of large logarithms in the series. Using the universal infrared behaviour of the QCD we resum these large logarithms up to next-to-next-to-leading logarithmic (NNLL) accuracy. We observe a significant reduction in theoretical uncertainties due to the unphysical scales at NNLL level compared to the previous order. We present the p  T  distribution matched to NNLO A +NNLL, valid for the whole p  T  region and provide a detailed phenomenological study in the context of both 14 TeV and 13 TeV LHC using different choices of masses, scales and parton distribution functions which will be useful for the search of such particle at the LHC in near future.

Neelima Agarwal

Goutam Das

Prasanna Dhani

Ayan Mukhopadhyay

Anurag Tripathi

Resummed transverse momentum distribution of pseudo-scalar Higgs boson at NNLO A +NNLL

We compute the two-loop massless QCD corrections to the four-point amplitude g + g → H + H resulting from effective operator insertions that describe the interaction of a Higgs boson with gluons in the infinite top quark mass limit. This amplitude is an essential ingredient to the third-order QCD corrections to Higgs boson pair production. We have implemented our results in a numerical code that can be used for further phenomenological studies.

CERN

Sophia Borowka

Thomas Gehrmann

Two-loop massless QCD corrections to the g + g → H + H four-point amplitude

We present the first results on the two-loop massless QCD corrections to the four-point amplitude   <math> <mi>b</mi> <mo>+</mo> <mover> <mi>b</mi> <mo>¯</mo> </mover> <mo>→</mo> <mi>H</mi> <mo>+</mo> <mi>H</mi> </math>  $$ b+\overline{b}\to H+H $$  in the five flavor scheme, treating bottom quarks as massless. This amplitude is sensitive to the trilinear Higgs boson coupling. Our two-loop result for this amplitude constitutes of purely virtual contributions to the next-to-next-to-leading order QCD predictions for the production of a pair of Higgs bosons at the Large Hadron Collider. Using these two loop amplitudes and exploiting the universality of the soft contributions in perturbative QCD, we obtain the NNLO QCD effects in the soft plus virtual approximation. We find that the inclusion of higher order terms reduce the uncertainties resulting from the unphysical renormalisation and factorisation scales.

A. Ajjath

Higgs pair production from bottom quark annihilation to NNLO in QCD

We report our findings on the perturbative structure of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 supersymmetric Yang-Mills (SYM) theory in the infrared sector by computing inclusive scattering cross sections of on-shell particles. We use half-BPS, energy-momentum tensor and Konishi operators to produce singlet states in the scattering processes to probe the soft and the collinear properties of the cross sections. By appropriately defining the infrared safe observables, we obtain collinear splitting functions up to second order in the perturbation theory. The splitting functions and the infrared finite cross sections demonstrate several interesting connections with those in the perturbative QCD. We also determine the process independent soft distribution function up to third order in the perturbation theory and show that it is universal i.e. independent of the operators as well as the external states. Interestingly, the soft distribution function in   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 SYM theory matches exactly with the leading transcendental part of the corresponding one in the QCD. This enables us to predict the third order soft plus virtual cross section for the production of the on-shell singlet states.

Satyajit Seth

Second order splitting functions and infrared safe cross sections in   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 SYM theory

We present here the first result on the three-loop gluon jet function in perturbative QCD. Using the three-loop coefficient functions [J. A. M. Vermaseren, A. Vogt, and S. Moch, Nucl. Phys. B724, 3 (2005)., G. Soar, S. Moch, J. A. M. Vermaseren, and A. Vogt, Nucl. Phys. B832, 152 (2010).] for deep-inelastic scattering via the exchange of a virtual photon that couples to quarks or a scalar that couples to gluons and employing the KG equation, renormalization group invariance and factorization theorem, we obtain both the quark and the gluon jet functions up to the three-loop level. The former agrees with the recent result [R. Brüser, Z. L. Liu, and M. Stahlhofen, Phys. Rev. Lett. 121, 072003 (2018).]. These jet functions being universal ingredients in the SCET framework, will play an important role in the phenomenological studies at the Large Hadron Collider, such as resummation of jet observables and also in N-jettiness subtraction method.