We present a comprehensive study of energy correlation functions and jet angularities for heavy-flavour QCD jets. In particular, we discuss the possibility of using these observables to expose the dead cone effect, i.e. the suppression of collinear QCD radiation around massive quarks, and to investigate the sensitivity of different observable definitions to the presence of quark masses. Our calculations are presented as all-order resummed predictions at next-to-leading-logarithmic accuracy, matched to (partial) fixed-order results to obtain a better description of the transition around the dead cone threshold. We also compare our analytic results with Pythia, Herwig and Sherpa Monte Carlo predictions to estimate the impact of non-perturbative contributions such as hadronisation, underlying events and -hadron decays.

Spain

Prasanna Dhani

United States

Oleh Fedkevych

Italy

Andrea Ghira

Simone Marzani

France

Gregory Soyez

Heavy flavour jet substructure

We present the first proof-of-concept application to decay processes at higher perturbative orders of loop-tree duality (LTD) causal unitary, a novel methodology that exploits the causal properties of vacuum amplitudes in the LTD and is directly well-defined in the four physical dimensions of the space-time. The generation of loop- and tree-level contributions to the differential decay rates from a kernel multiloop vacuum amplitude is shown in detail, and explicit expressions are presented for selected processes that are suitable for a lightweight understanding of the method. Specifically, we provide a clear physical interpretation of the local cancellation of soft, collinear and threshold singularities, and of the local renormalisation of ultraviolet singularities. The presentation is illustrated with numerical results that showcase the advantages of the method.

Mexico

Selomit Ramírez-Uribe

Andrés Rentería-Olivo

David Rentería-Estrada

Jorge Martínez de Lejarza

Leandro Cieri

Roger Hernández-Pinto

German Sborlini

United Kingdom

William Torres Bobadilla

Germán Rodrigo

Vacuum amplitudes and time-like causal unitary in the loop-tree duality

We analyze in detail the most singular behaviour of processes involving triple-collinear splittings with massive particles in the quasi-collinear limit, and present compact expressions for the splitting amplitudes and the corresponding splitting kernels at the squared-amplitude level. Our expressions fully agree with well-known triple-collinear splittings in the massless limit, which are used as a guide to achieve the final expressions. These results are important to quantify dominant mass effects in many observables, and constitute an essential ingredient of current high-precision computational frameworks for collider phenomenology.

Triple-collinear splittings with massive particles

The singular behaviour of QCD squared amplitudes in the collinear limit is factorized and controlled by splitting kernels with a process-independent structure. We use these kernels to define collinear functions that can be used in QCD resummation formulae of hard-scattering observables. Different collinear functions are obtained by integrating the splitting kernels over different phase-space regions that depend on the hard-scattering observables of interest. The collinear functions depend on an auxiliary vector n  μ  that can be either light-like (n 2 = 0) or time-like (n 2 &gt; 0). In the case of transverse-momentum dependent (TMD) collinear functions, we show that the use of a time-like auxiliary vector avoids the rapidity divergences, which are instead present if n 2 = 0. The perturbative computation of the collinear functions lead to infrared (IR) divergences that can be properly factorized with respect to IR finite functions that embody the logarithmically-enhanced collinear contributions to hard-scattering cross sections. We evaluate various collinear functions and their n  μ  dependence at   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (α S). We compute the azimuthal-correlation component of the TMD collinear functions at   <math> <mi>O</mi> <mfenced> <msubsup> <mi>α</mi> <mi>S</mi> <mn>2</mn> </msubsup> </mfenced> </math>  $$ \mathcal{O}\left({\alpha}_{\textrm{S}}^2\right) $$ , and we present the results of the   <math> <mi>O</mi> <mfenced> <msubsup> <mi>α</mi> <mi>S</mi> <mn>2</mn> </msubsup> </mfenced> </math>  $$ \mathcal{O}\left({\alpha}_{\textrm{S}}^2\right) $$  contribution of linearly-polarized gluons to transverse-momentum resummation formulae. Beyond   <math> <mi>O</mi> <mfenced> <msubsup> <mi>α</mi> <mi>S</mi> <mn>2</mn> </msubsup> </mfenced> </math>  $$ \mathcal{O}\left({\alpha}_{\textrm{S}}^2\right) $$  the collinear functions of initial-state colliding partons are process dependent, as a consequence of the violation of strict collinear factorization of QCD squared amplitudes.

Stefano Catani

Collinear functions for QCD resummations

Production of the Higgs boson, H in association with a massive vector boson, V, i.e., the V H process, plays an important role in the explorations of Higgs physics at the Large Hadron Collider, both for a precise study of Higgs’ Standard Model couplings and for probing New Physics. In this publication we present the two-loop corrections in mass- less quantum chromodynamics (QCD) to the amplitude of the Higgs production associated with a Z boson via the bottom quark-antiquark annihilation channel with a non-vanishing bottom-quark Yukawa coupling, which is a necessary ingredient of the full next-to-next- to-leading-order QCD corrections to the V H process in the five-flavour scheme. The computation is performed by projecting the D-dimensional scattering amplitude directly onto an appropriate set of Lorentz structures related to the linear polarisation states of the Z boson. We provide analytic expressions of the complete set of renormalised polarised amplitudes in terms of polylogarithms of maximum weight four. To give an estimation of the size of contributions from amplitudes considered in this work, we compute numerically the resulting cross sections under the soft-virtual approximation. We also take the opportunity to make a dedicated discussion regarding an interesting subtlety appearing in the conventional form factor decomposition of amplitudes involving axial currents regularised in D dimensions.

Germany

Taushif Ahmed

India

A.H. Ajjath

Long Chen

Pooja Mukherjee

V. Ravindran

Polarised amplitudes and soft-virtual cross sections for b    <math> <mover> <mi>b</mi> <mo>¯</mo> </mover> </math> $$ \overline{b} $$ → Z H at NNLO in QCD

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

Pulak Banerjee

Goutam Das

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

Switzerland

Thomas Gehrmann

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

The two-loop four-point amplitude of two massless SU(N) colored scalars and two color singlet operators with different virtuality described by a half-BPS and Konishi operators is calculated analytically in maximally supersymmetric Yang-Mills theory. We verify the ultraviolet behaviour of the unprotected composite operator and exponentiation of the infrared divergences with correct universal values of the anomalous dimensions in the modified dimensional reduction scheme. The amplitude is found to contain lower transcendental weight terms in addition to the highest ones and the latter has no similarity with similar amplitudes in QCD.

Two-loop doubly massive four-point amplitude involving a half-BPS and Konishi operator

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

Amlan Chakraborty

Narayan Rana

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