We present the calculation at next-to-leading order (NLO) in alpha_s of the fragmentation function of a gluon into heavy quarkonium in the color-octet spin-singlet S-wave channel. To calculate the real NLO corrections, we adapt a subtraction scheme introduced by Frixione, Kunszt, and Signer. Ultraviolet and infrared divergences in the real NLO corrections are calculated analytically by evaluating the phase-space integrals of the subtraction terms using dimensional regularization. The subtracted phase-space integrals are then evaluated in 4 space-time dimensions. The divergences in the virtual NLO corrections are also calculated analytically. After renormalization, all the divergences cancel. The NLO corrections significantly increase the fragmentation probability for a gluon into the spin-singlet quarkonium states eta_c and eta_b.
I formulate in a colour-friendly way the FKS method for the computation of QCD cross sections at the next-to-leading order accuracy. This is achieved through the definition of subtraction terms for squared matrix elements, constructed with single colour-dressed or pairs of colour-ordered amplitudes. The latter approach relies on the use of colour flows, is exact to all orders in $N$, and is thus particularly suited to being organized as a systematic expansion in 1/N.
We present the complete automation of the universal subtraction formalism proposed by Frixione, Kunszt, and Signer for the computation of any cross section at the next-to-leading order in QCD. Given a process, the only ingredient to be provided externally is the infrared- and ultraviolet-finite contribution of virtual origin. Our implementation, currently restricted to the case of e+e- collisions, is built upon and works in the same way as MadGraph. It is particularly suited to parallel computation, and it can deal with any physical process resulting from a theory implemented in MadGraph, thus…
We compare two approaches to evaluate cross sections of heavy-quarkonium production at next-to-leading order in nonrelativistic QCD involving $S$- and $P$-wave Fock states: the customary approach based on phase space slicing and the approach based on dipole subtraction recently elaborated by us. We find reasonable agreement between the numerical results of the two implementations, but the dipole subtraction implementation outperforms the phase space slicing one both with regard to accuracy and speed.
We present an extension of the FKS subtraction scheme beyond next-to-leading order to deal with soft singularities in fully differential calculations within QED with massive fermions. After a detailed discussion of the next-to-next-to-leading order case, we show how to extend the scheme to even higher orders in perturbation theory. As an application we discuss the computation of the next-to-next-to-leading order QED corrections to the muon decay and present differential results with full electron mass dependence.
We present the key features relevant to the automated computation of all the leading- and next-to-leading order contributions to short-distance cross sections in a mixed-coupling expansion, with special emphasis on the first subleading NLO term in the QCD+EW scenario, commonly referred to as NLO EW corrections. We discuss, in particular, the FKS subtraction in the context of a mixed-coupling expansion; the extension of the FKS subtraction to processes that include final-state tagged particles, defined by means of fragmentation functions; and some properties of the complex mass scheme. We combi…
Universität Heidelberg（海德堡大学）；University of Cambridge（剑桥大学）；Université catholique de Louvain（天主教鲁汶大学）；Interdisciplinary Center for Scientific Computing (IWR), Universität Heidelberg（海德堡大学跨学科科学计算中心）；Università degli Studi di Milano & INFN Sezione di Milano（米兰大学与意大利国家核物理研究所米兰分部）
We present the first calculation at next-to-leading order (NLO) in $α_s$ of a fragmentation function into quarkonium whose form at leading order is a nontrivial function of $z$, namely the fragmentation function for a gluon into a spin-singlet S-wave state at leading order in the relative velocity. To calculate the real NLO corrections, we introduce a new subtraction scheme that allows the phase-space integrals to be evaluated in 4 dimensions. We extract all ultraviolet and infrared divergences in the real NLO corrections analytically by calculating the phase-space integrals of the subtraction…
We present the status of the automation of NLO processes within the event generator WHIZARD. The program provides an automated FKS subtraction and phase space integration over the FKS regions, while the (QCD) NLO matrix element is accessed via the Binoth Les Houches Interface from an externally linked one-loop program. Massless and massive test cases and validation are shown for several e+e- processes. Furthermore, we discuss work in progress and future plans. The second part covers the matching of the NRQCD prediction with NLL threshold resummation to the NLO continuum top pair production at …
We describe an implementation of a subtraction scheme in the nonrelativistic-QCD treatment of heavy-quarkonium production at next-to-leading-order in the strong-coupling constant, covering $S$- and $P$-wave bound states. It is based on the dipole subtraction in the massless version by Catani and Seymour and its extension to massive quarks by Phaf and Weinzierl. Important additions include the treatment of heavy-quark bound states, in particular due to the more complicated infrared-divergence structure in the case of $P$-wave states.
In the paper, we calculate the fragmentation functions for a quark to fragment into a spin-singlet quarkonium, where the flavor of the initial quark is different from that of the constituent quark in the quarkonium. The ultraviolet divergences in the phase space integral are removed through the operator renormalization under the modified minimal subtraction scheme. The fragmentation function $D_{q \to η_Q}(z,μ_F)$ is expressed as a two-dimensional integral. Numerical results for the fragmentation functions of a light quark or a bottom quark to fragment into the $η_c$ are presented. As an appli…
In the paper, we calculate the fragmentation functions for $c \to η_c$ and $b \to η_b$ up to next-to-leading-order (NLO) QCD accuracy. The ultraviolet divergences in the real corrections are removed through operator renormalization under the modified minimal subtraction scheme. We then obtain the fragmentation functions $D_{c \to η_c}(z,μ_F)$ and $D_{b \to η_b}(z,μ_F)$ 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 th…
A semi-spectral Chebyshev method for solving numerically singular integral equations is presented and applied in the quarkonium bound-state problem in momentum space. The integrals containing both, logarithmic and Cauchy singular kernels, can be evaluated without subtractions by dedicated automatic quadratures. By introducing a Chebyshev mesh and using the Nystrom algorithm the singular integral equation is converted into an algebraic eigenvalue problem that can be solved by standard methods. The proposed scheme is very simple to use, is easy in programming and highly accurate.
We present results on NLO electroweak (EW) corrections to multiple massive boson production processes at a future muon collider. Inclusive cross sections with $\mathcal{O}(α)$ corrections for processes for up to four bosons in the final state as well as differential distributions for $HZ$ production are computed for $\sqrt{s}=3$, $10$ and $14$ TeV by using FKS subtraction in the NLO EW automated Monte-Carlo framework WHIZARD+RECOLA. Large logarithmic effects due to collinear ISR and EW virtual correction factors as well as the impacts of an energy cut on hard photons are discussed with an emph…
We address the unphysical energy dependence of quarkonium-hadroproduction cross sections at Next-to-Leading Order (NLO) in alpha_S which we attribute to an over-subtraction in the factorisation of the collinear singularities inside the PDFs in the MSbar scheme. Such over- or under-subtractions have a limited phenomenological relevance in most of the scattering processes in particle physics. On the contrary, it is particularly harmful for P_T-integrated charmonium hadroproduction which renders a wide class of NLO results essentially unusable. Indeed, in such processes, alphaS is not so small, t…
We give a status report on the automation of next-to-leading order processes within the Monte Carlo event generator WHIZARD, using GoSam and OpenLoops as provider for one-loop matrix elements. To deal with divergences, WHIZARD uses automated FKS subtraction, and the phase space for singular regions is generated automatically. NLO examples for both scattering and decay processes with a focus on e+e- processes are shown. Also, first NLO-studies of observables for collisions of polarized leptons beams, e.g. at the ILC, will be presented. Furthermore, the automatic matching of the fixed-order NLO …
R-symmetry leads to a distinct realisation of SUSY with a significantly modified coloured sector featuring a Dirac gluino and a scalar colour octet (sgluon). We present the impact of R-symmetry on squark production at the 13 TeV LHC. We study the total cross sections and their NLO corrections from all strongly interacting states, their dependence on the Dirac gluino mass and sgluon mass as well as their systematics for selected benchmark points. We find that tree-level cross sections in the R-symmetric model are reduced compared to the MSSM but the NLO K-factors are generally larger in the ord…
The aim of this thesis is the completion of the NLO automated framework of the MC program WHIZARD, accounting for NLO corrections in the full SM for cross sections and distributions of processes at hadron and lepton colliders. Specifically, it builds on the implemented FKS subtraction scheme for NLO QCD calculations, and extends it to automated NLO EW and QCD-EW mixed corrections. To that end, the implemented FKS scheme is generalised to systematically subtract QED and QCD infrared (IR) divergences in mixed coupling expansions. The automated computation of NLO contributions is validated for a …
We construct a nonrelativistic effective field theory description of heavy quarkonium hybrids from QCD. We identify the symmetries of the system made of a heavy quark, a heavy antiquark, and glue in the static limit. Corrections to this limit can be obtained order by order in an expansion in the inverse of the mass $m$ of the heavy quark. At order $1/m$ in the expansion, we obtain at the level of potential Non-Relativistic QCD a system of coupled Schrödinger equations that describes hybrid spin-symmetry multiplets, including the mixing of different static energies into the hybrid states, an ef…
In the paper, we derive the next-to-leading order (NLO) fragmentation function for a heavy quark, either charm or bottom, into a heavy quarkonium $J/Ψ$ or $Υ$. The ultra-violet divergences in the real corrections are removed through the operator renormalization, which is performed under the modified minimal subtraction scheme. We then obtain the NLO fragmentation function at an initial factorization scale, e.g. $μ_{F}=3 m_c$ for $c\to J/Ψ$ and $μ_{F}=3m_b$ for $b\to Υ$, which can be evolved to any scale via the use of Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation. As an initial applicati…
