NLO fragmentation functions for a quark into a spin-singlet quarkonium: same flavor case

In the paper, we calculate the fragmentation functions for c → ηc and b → ηb up to next-to-leading-order (NLO) QCD accuracy. The ultraviolet divergences in the real corrections are removed through operator renormalization under the modified min- imal subtraction scheme. We then obtain the fragmentation functions $$ {D}_{c\to {\eta}_c} $$ D c → η c (z, μF) and $$ {D}_{b\to {\eta}_b} $$ D b → η b (z, μF) up to NLO QCD accuracy, which are presented as figures and fitting functions. The numerical results show that the NLO corrections are significant. The sensitives of the fragmentation functions to the renormalization scale and the factorization scale are analyzed explicitly.

Dual subtractions

We propose a novel local subtraction scheme for the computation of Next-to-Leading Order contributions to theoretical predictions for scattering processes in perturbative Quantum Field Theory. With respect to well known schemes proposed since many years that build upon the analysis of the real radiation matrix elements, our construction starts from the loop diagrams and exploits their dual representation. Our scheme implements exact phase space factorization, handles final state as well as initial state singularities and is suitable for both massless and massive particles.

Fully exclusive heavy quark-antiquark pair production from a colourless initial state at NNLO in QCD

We present a local subtraction scheme for computing next-to-next-to-leading order QCD corrections to the production of a massive quark-antiquark pair from a colourless initial state. The subtraction terms are built following the CoLoRFulNNLO method and refined in such a way that their integration gives rise to compact, fully analytic expressions. All ingredients necessary for a numerical implementation of our subtraction scheme are provided in detail. As an example, we calculate the fully differential decay rate of the Standard Model Higgs boson to massive bottom quarks at next-to-next-to-leading order accuracy in perturbative QCD.

One-loop jet functions by geometric subtraction

In factorization formulae for cross sections of scattering processes, final-state jets are described by jet functions, which are a crucial ingredient in the resummation of large logarithms. We present an approach to calculate generic one-loop jet functions, by using the geometric subtraction scheme. This method leads to local counterterms generated from a slicing procedure; and whose analytic integration is particularly simple. The poles are obtained analytically, up to an integration over the azimuthal angle for the observable- dependent soft counterterm. The poles depend only on the soft limit of the observable, characterized by a power law, and the finite term is written as a numerical integral. We illustrate our method by reproducing the known expressions for the jet function for angularities, the jet shape, and jets defined through a cone or kT algorithm. As a new result, we obtain the one-loop jet function for an angularity measurement in e+e− collisions, that accounts for the formally power-suppressed but potentially large effect of recoil. An implementation of our approach is made available as the GOJet Mathematica package accompanying this paper.

Combining single and double parton scatterings in a parton shower

Double parton scattering (DPS) processes in which there is a perturbative “1 → 2” splitting in both protons overlap with loop corrections to single parton scattering (SPS). Any fundamental theoretical treatment of DPS needs to address this double-counting issue. In this paper, we augment our Monte-Carlo simulation of DPS, dShower, to be able to generate kinematic distributions corresponding to the combination SPS+DPS without double counting. To achieve this, we formulate a fully-differential version of the subtraction scheme introduced in Diehl et al. (JHEP 06 (2017) 083). A shower is attached to the subtraction term, and this is combined with the dShower DPS shower along with the usual SPS shower. We perform a proof-of-concept study of this new algorithm in the context of Z0Z0 production. Once the subtraction term is included, we verify that the results do not depend strongly on the artificial “DPS-SPS demarcation” scale ν. As part of the development of the new algorithm, we improve the kinematics of the 1 → 2 splitting in the DPS shower (and subtraction term), allowing the daughter partons to have a relative transverse momentum. Several reasonable choices for the transverse profile in the 1 → 2 splitting are studied. We find that many kinematic distributions are not strongly affected by the choice, although we do observe some differences in the region where the transverse momenta of both bosons are small.

Radiative correction to the Casimir energy for Lorentz-violating scalar field in d + 1 dimensions

The renormalization program in every renormalized theory should run consistently with the type of boundary condition imposed on quantum fields. To maintain this consistency, the counterterms usually appear in the position-dependent form. In this study, using such counterterms, we calculated the radiative correction to the Casimir energy for massive and massless Lorentz-violating scalar field constrained with Dirichlet boundary condition between two parallel plates in [Formula: see text] spatial dimensions. In the calculation procedure, to remove infinities appearing in the vacuum energies, the box subtraction scheme (BSS) supplemented by the cutoff regularization technique and analytic continuation technique was employed. Normally, in the BSS, two similar configurations are defined and their vacuum energies are subtracted from each other in the appropriate limits. Our final results regarding all spatial dimensions were convergent and consistent with the expected physical basis. We further plotted the Casimir energy density for the time-like and space-like Lorentz-violating systems in a number of odd and even dimensions; multiple aspects of the obtained results were ultimately discussed.

Analytic results for deep-inelastic scattering at NNLO QCD with the nested soft-collinear subtraction scheme

We present analytic results that describe fully-differential NNLO QCD corrections to deep-inelastic scattering processes within the nested soft-collinear subtraction scheme. This is the last building block required for the application of this scheme to computations of NNLO QCD corrections to arbitrary processes at hadron colliders.