The high-energy asymptotic form of the scattering amplitude of colorless particles in quantum chromodynamics is obtained in the leading logarithmic approximation. It is argued that such a calculation is justified for the amplitudes of scattering in which charmed quarks participate. The cross section for formation of two pairs of charmed quarks in ..gamma gamma.. collisions is found in explicit form.

On the Pomeranchuk singularity in the quantum chromodynamics

The prescription for the γ5 matrix within dimensional regularization in multiloop calculations is elaborated. The three-loop anomalous dimension of the singlet axial current is calculated.

The renormalization of the axial anomaly in dimensional regularization

We consider the resummation of the logarithmic contributions to the region of small transverse momenta in the distributions of high-mass systems (lepton pairs, vector bosons, Higgs particles, ....) produced in hadron collisions. We point out that the resummation formulae that are usually used to compute the distributions in perturbative QCD involve process-dependent form factors and coefficient functions. We present a new universal form of the resummed distribution, in which the dependence on the process is embodied in a single perturbative factor. The new form simplifies the calculation of non-leading logarithms at higher perturbative orders. It can also be useful to systematically implement process-independent non-perturbative effects in transverse-momentum distributions. We also comment on the dependence of these distributions on the factorization and renormalization scales.

Universality of non-leading logarithmic contributions in transverse-momentum distributions

Collider physics at the precision frontier

This Report summarizes the proceedings of the 2019 Les Houches workshop on Physics at TeV Colliders. Session 1 dealt with (I) new developments for high precision Standard Model calculations, (II) the sensitivity of parton distribution functions to the experimental inputs, (III) new developments in jet substructure techniques and a detailed examination of gluon fragmentation at the LHC, (IV) issues in the theoretical description of the production of Standard Model Higgs bosons and how to relate experimental measurements, and (V) Monte Carlo event generator studies relating to PDF evolution and comparisons of important processes at the LHC.

Les Houches 2019: Physics at TeV Colliders: Standard Model Working Group Report

We present here the first result on the three-loop gluon jet function in perturbative QCD. Using the three-loop coefficient functions [1,2] 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 [3]. These jet functions being universal ingredients for many collider and decay processes, will play an important role in the phenomenological studies at the Large Hadron Collider.

Gluon jet function at three loops in QCD

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.

/pdf/two-loop-massless-qcd-corrections-to-the-g-g-h-h-four-point-3tv16jif97.pdf

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

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 QCD$\times$QED using K+G 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 QCD$\times$QED 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 QCD$\times$QED at the LHC energies taking into account the dominant NNLO QCD corrections.

/pdf/nnlo-qcd-qed-corrections-to-higgs-production-in-bottom-quark-1jcmgo1c8r.pdf

NNLO QCD ⊕ QED corrections to Higgs production in bottom quark annihilation

We present three point form factors (FF) in $$ \mathcal{N}=4 $$
 Super Yang Mills theory for both the half-BPS and the Konishi operators at two loop level in the ‘t Hooft coupling using Feynman diagrammatic approach. We have chosen on shell final states consisting of gϕϕ and ϕλλ, where ϕ, λ, g are scalar, Majorana fermion and gauge fields respectively. The computation is done both in the modified dimensional reduction as well as in the four dimensional helicity scheme. We have studied the universal structure of infrared (IR) singularities in these FFs using Catani’s IR subtraction operators. Exploiting the factorisation property of the IR singularities and following BDS like ansatz for the IR sensitive terms in FFs, we determine the finite remainders of them. We find that the finite remainders of FFs of the half-BPS for both the choices of final states give not only identical results but also contain terms of uniform transcendentality of weight two and four at one and two loop levels, respectively. In the case of the Konishi operator, the finite remainders depend on the external states and do not exhibit uniform transcendentality. However, surprisingly, the leading transcendental terms for gϕϕ agree with that of the half-BPS. We have demonstrated the role of on shell external states for the FFs in the context of maximum transcendentality principle.

/pdf/finite-remainders-of-the-konishi-at-two-loops-in-mathcal-n-4-1sn0fk0ku2.pdf

Finite remainders of the Konishi at two loops in \mathcal{N}=4 SYM

We present three point form factors (FF) in ${\cal N}=4$ Super Yang Mills theory for both the half-BPS and the Konishi operators at two loop level in the `t Hooft coupling using Feynman diagrammatic approach. We have chosen on shell final states consisting of $g \phi \phi$ and $\phi \lambda \lambda$, where $\phi,\lambda, g$ are scalar, Majorana fermion and gauge fields respectively. The computation is done both in the modified dimensional reduction as well as in the four dimensional helicity scheme. We have studied the universal structure of infrared (IR) singularities in these FFs using Catani's IR subtraction operators. Exploiting the factorisation property of the IR singularities and following BDS like ansatz for the IR sensitive terms in FFs, we determine the finite remainders of them. We find that the finite remainders of FFs of the half-BPS for both the choices of final states give not only identical results but also contain terms of uniform transcendentality of weight two and four at one and two loop levels, respectively. In the case of the Konishi operator, the finite remainders depend on the external states and do not exhibit uniform transcendentality. However, surprisingly, the leading transcendental terms for $g \phi \phi$ agree with that of the half-BPS. We have demonstrated the role of on shell external states for the FFs in the context of maximum transcendentality principle.

/pdf/finite-remainders-of-the-konishi-at-two-loops-in-cal-n-4-sym-uurtptcgcc.pdf

Prasanna K. Dhani

Papers

Gluon jet function at three loops in QCD

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

NNLO QCD ⊕ QED corrections to Higgs production in bottom quark annihilation

Finite remainders of the Konishi at two loops in \mathcal{N}=4 SYM

Finite remainders of the Konishi at two loops in ${\cal N}=4$ SYM