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 exploit their loop-tree 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.
Integrated subtraction terms and finite remainders for arbitrary processes with massless partons at colliders in the nested soft-collinear subtraction scheme
SLAC National Accelerator Laboratory, Stanford University（斯坦福大学 SLAC 国家加速器实验室）；Institute for Theoretical Particle Physics, KIT（卡尔斯鲁厄理工学院理论粒子物理研究所）；Tif Lab, Dipartimento di Fisica, Universitá di Milano and INFN, Sezione di Milano（米兰大学物理系 Tif 实验室及意大利国家核物理研究院米兰分部）；Max-Planck-Institut für Physik（马克斯·普朗克物理学研究所）
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.
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 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 …
A new method for local subtraction at next-to-next-to-leading order in QCD is sketched, attempting to conjugate the minimal counterterm structure arising from a sector partition of the radiation phase space with the simplifications following from analytic integration of the counterterms.
Within the framework of local analytic sector subtraction, we present the subtraction of next-to-leading-order QCD singularities for processes featuring massless coloured particles in the initial as well as in the final state. The features of the method are explained in detail, including the introduction of an optimisation procedure aiming at improving numerical stability at the cost of no extra analytic complexity. A numerical validation is provided for a variety of processes relevant to lepton as well as hadron colliders. This work constitutes a relevant step in view of the application of ou…
We consider higher-order QCD corrections to the production of high-mass systems in hadron collisions within the transverse-momentum (q$_{\rm T}$) subtraction formalism. We present a method to consistently remove the linear power corrections in q$_{\rm T}$ which appears when fiducial kinematical cuts are applied on the final state system. We consider explicitly the case of fiducial cross sections for Drell-Yan lepton pair production at the Large Hadron Collider up to next-to-next-to-next-to-leading order (N$^3$LO) in QCD. We have implemented our method within the DYTurbo numerical program and w…
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-lead…
We consider the extension of the transverse-momentum ($q_T$) subtraction method at next-to-next-to-next-to-leading order (N$^3$LO) in perturbative QCD. While all the $q_T$-subtraction ingredients at $q_T \neq 0$ are known in analytical form, the third-order collinear functions and helicity-flip functions, which contribute only at $q_T=0$, are approximated using a prescription which uses the known result for the total Higgs boson cross section at this order. As a first application of the third-order $q_T$-subtraction method, we present the N$^3$LO rapidity distribution of the Higgs boson at the…
We introduce a novel construction of a contour deformation within the framework of Loop-Tree Duality for the numerical computation of loop integrals featuring threshold singularities in momentum space. The functional form of our contour deformation automatically satisfies all constraints without the need for fine-tuning. We demonstrate that our construction is systematic and efficient by applying it to more than 100 examples of finite scalar integrals featuring up to six loops. We also showcase a first step towards handling non-integrable singularities by applying our work to one-loop infrared…
We present a detailed derivation of the power corrections to the factorization theorem for the 0-jettiness event shape variable $\mathcal{T}$. Our calculation is performed directly in QCD without using the formalism of effective field theory. We analytically calculate the next-to-leading logarithmic power corrections for small $\mathcal{T}$ at next-to-leading order in the strong coupling constant, extending previous computations which obtained only the leading-logarithmic power corrections. We address a discrepancy in the literature between results for the leading-logarithmic power corrections…
We present the colourful antenna subtraction method, a reformulation of the antenna subtraction scheme for next-to-next-to-leading order (NNLO) calculations in QCD. The aim of this new approach is to achieve a general and process-independent construction of the subtraction infrastructure at NNLO. We rely on the predictability of the infrared singularity structure of one- and two-loop amplitudes in colour space to generate virtual subtraction terms and, subsequently, we define an automatable procedure to systematically infer the expression of the real subtraction terms, guided by the correspond…
We report on our recent progress towards including the photon fragmentation contribution in next-to-next-to-leading order (NNLO) QCD predictions for photon production cross sections. This extension to previous NNLO calculations requires the identification of the photon in singular parton-photon collinear limits. We discuss how these limits can be subtracted within antenna subtraction using fragmentation antenna functions and we outline their integration.
We present a fully differential description of a decay of a scalar Higgs boson into massive b-quarks valid at next-to-next-to-leading order (NNLO) in perturbative quantum chromodynamics (QCD). We work within the nested soft-collinear subtraction scheme extended to accommodate massive partons. We include the loop-induced contribution involving a Higgs coupling to a top quark. We test our calculation against results existing in the literature, comparing the predictions for the total decay width and jet rates.
We present a new method for the local subtraction of infrared divergences at next-to-next-to-leading order (NNLO) in QCD, for generic infrared-safe observables. Our method attempts to conjugate the minimal local counterterm structure arising from a sector partition of the radiation phase space with the simplifications following from analytic integration of the counterterms. In this first implementation, the method applies to final-state massless particles. We show how our method compactly organises infrared subtraction at NLO, we deduce in detail the general structure of the subtraction terms …
In this paper a complete generalisation of the Catani-Seymour dipole subtraction method to next-to-leading order electroweak calculations is presented. All singularities due to photon and gluon radiation off both massless and massive partons in the presence of both massless and massive spectators are accounted for. Particular attention is paid to the simultaneous subtraction of singularities of both QCD and electroweak origin which are present in the next-to-leading order corrections to processes with more than one perturbative order contributing at Born level. Similarly, embedding non-dipole-…
We report on a new calculation of the next-to-next-to-leading order (NNLO) QCD radiative corrections to the inclusive production of top-quark pairs at hadron colliders. The calculation is performed by using the $q_T$ subtraction formalism to handle and cancel infrared singular contributions at intermediate stages of the computation. We present numerical results for the total cross section in $pp$ collisions at $\sqrt{s}=8$ TeV and $13$ TeV, and we compare them with those obtained by using the publicly available numerical program Top++. Our computation represents the first complete application …
We discuss the subleading power corrections to one-jet production processes in $N$-jettiness subtraction using vector-boson plus jet production as an example. We analytically derive the next-to-leading power leading logarithmic corrections (NLP-LL) through ${\cal O}(α_S)$ in perturbative QCD, and outline the calculation of the next-to-leading logarithmic corrections (NLP-NLL). Our result is differential in the jet transverse momentum and rapidity, and in the vector boson momentum squared and rapidity. We present simple formulae that separate the NLP corrections into universal factors valid for…
We present compact analytic formulas that describe the decay of colorless particles to both $q \bar q$ and $gg$ final states through next-to-next-to-leading order in perturbative QCD in the context of the nested soft-collinear subtraction scheme. In addition to their relevance for the description of decays like $V \to q \bar q'$, $V= Z,W$, $H \to b \bar b$ and $H \to gg$, these results provide an important building block for calculating NNLO QCD corrections to arbitrary processes at colliders within the nested soft-collinear subtraction scheme.
A novel subtraction scheme for double-real radiation at NNLO
本文导出了一个通用的减影方案STRIPPER（SecToR Improved Phase sPacE for real Radiation），用于计算双实辐射对末态至少有两个粒子处于首阶过程的次首阶（NNLO）QCD贡献。其结果是在维正则化的参数中的洛朗展开，其系数应通过数值蒙特卡罗积分来评估。两个主要的想法是一个两级分解的相空间，第二个因式分解的振幅的奇异极限，和一个合适的参数化的运动学允许推导的减法和集成减法项程函因子和分裂函数，而无需非平凡的解析积分。
We extend the antenna subtraction method to include hadron fragmentation processes up to next-to-next-to-leading order (NNLO) in QCD in $e^+e^-$ collisions. To handle collinear singularities associated with the fragmentation process, we introduce fragmentation antenna functions in final-final kinematics with associated phase space mappings. These antenna functions are integrated over the relevant phase spaces, retaining their dependence on the momentum fraction of the fragmenting parton. The integrated antenna functions are cross-checked against the known NNLO coefficient functions for identif…
We introduce a system of parameters for the Monte Carlo generation of Lorentz invariant phase space that is particularly well-suited to the treatment of the infrared divergences that occur in the most singular, Born-like configurations of $1\to n$ QCD processes. A key feature is that particle momenta are generated independently of one another, leading to a simple parameterisation of all such IR limits. We exemplify the use of these variables in conjunction with the projection to Born subtraction technique at next-to-next-to-leading order. The geometric origins of this parameterisation lie in a…
We consider higher-order QCD corrections to Higgs boson production through gluon-gluon fusion in the large top quark mass limit in hadron collisions. We extend the transverse-momentum ($q_T$) subtraction method to next-to-next-to-next-to-leading order (N$^3$LO) and combine it with the NNLO Higgs-plus-jet calculation to numerically compute differential infrared-safe observables at N$^3$LO for Higgs boson production in gluon fusion. To cancel the infrared divergences, we exploit the universal behaviour of the associated $q_T$ distributions in the small-$q_T$ region. We document all the necessary…
The stochastic gravitational-wave backgrounds (SGWBs) for current detectors are dominated by binary black-hole (BBH) and binary neutron-star (BNS) coalescences. The sensitivity of current networks of gravitational-wave (GW) detectors allows only a small fraction of BBHs and BNSs to be resolved and subtracted, but previous work indicated that the situation should significantly improve with next-generation (XG) observatories. We revisit these conclusions by taking into account waveform-modeling uncertainties, updated astrophysical models, and (crucially) the full set of parameters that must be e…
