Infrared structure of $SU(N)\times U(1)$ gauge theory to three loops

Abstract

We study the infrared (IR) structure of $SU(N)\times U(1)$ (QCD $\times$ QED) gauge theory with $n_f$ quarks and $n_l$ leptons within the framework of perturbation theory. In particular, we unravel the IR structure of the form factors and inclusive real emission cross sections that contribute to inclusive production of color neutral states, such as a pair of leptons or single W/Z in Drell-Yan processes and a Higgs boson in bottom quark annihilation, in Large Hadron Collider (LHC) in the threshold limit. Explicit computation of the relevant form factors to third order and the use of Sudakov's $K+G$ equation in $SU(N)\times U(1)$ gauge theory demonstrate the universality of the cusp anomalous dimensions ($A_I,I=q,b$). The abelianization rules that relate $A_I$ of $SU(N)$ with those from $U(1)$ and $SU(N)\times U(1)$ can be used to predict the soft distribution that results from the soft gluon emission subprocesses in the threshold limit. Using the latter and the third order form factors, we can obtain the collinear anomalous dimensions ($B_I$ ) and the renormalisation constant $Z_b$ to third order in perturbation theory. The form factors, the process independent soft distribution functions can be used to predict fixed and resummed inclusive cross sections to third order in couplings and in leading logarithmic approximation respectively.

arXiv commentThe updated version, which include corrected expression for beta function, mixed QCD-QED anomalous dimensions and soft-virtual parsonic cross section

References in corpus (42)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• Parton distributions for the LHC
• Parton distributions for the LHC Run II
• An effective field theory for collinear and soft gluons: heavy to light decays
• New parton distribution functions from a global analysis of quantum chromodynamics
• Soft-Collinear Factorization in Effective Field Theory
• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• Summing Sudakov logarithms in B -> X_s + gamma in effective field theory
• The Singular Behaviour of QCD Amplitudes at Two-loop Order
• Five-Loop Running of the QCD coupling constant
• On the Structure of Infrared Singularities of Gauge-Theory Amplitudes
• Infrared singularities of scattering amplitudes in perturbative QCD
• Calculation of the quark and gluon form factors to three loops in QCD
• Quark and gluon form factors to three loops
• Electroweak Radiative Corrections to Neutral-Current Drell-Yan Processes at Hadron Colliders
• Electroweak radiative corrections to W-boson production at hadron colliders
• Three-Loop Results for Quark and Gluon Form Factors
• Higher-Order threshold effects to inclusive processes in QCD
• Three-loop corrections to the soft anomalous dimension in multi-leg scattering
• Mixed QCD-electroweak O(α_sα) corrections to Drell-Yan processes in the resonance region: pole approximation and non-factorizable corrections
• Weak radiative corrections to dijet production at hadron colliders
• On Sudakov and Soft resummations in QCD
• Drell-Yan Production at Threshold to Third Order in QCD
• Electroweak Radiative Corrections to pp/ppbar -> W+/- -> l+/- nu Beyond the Pole Approximation
• QED Radiative Corrections to $Z$ Boson Production and the Forward Backward Asymmetry at Hadron Colliders
• Introduction to Soft-Collinear Effective Theory
• QCD$\oplus$QED NNLO corrections to Drell Yan production
• Two-Loop Master Integrals for the mixed EW-QCD virtual corrections to Drell-Yan scattering
• Two-loop QED corrections to the Altarelli-Parisi splitting functions
• Two-Loop Renormalization in the Standard Model Part III: Renormalization Equations and their Solutions
• Double-real corrections at O(alpha alpha_s) to single gauge boson production
• Pseudo-scalar Form Factors at Three Loops in QCD
• NNLO QCD$\times$EW corrections to Z production in the $q\bar{q}$ channel
• Two-Loop Virtual Corrections to Drell-Yan Production at order alpha_s alpha^3
• NNLO QCD$\oplus$QED corrections to Higgs production in bottom quark annihilation
• Two-loop electroweak corrections to Higgs production in proton-proton collisions
• Two-Loop Renormalization in the Standard Model Part II: Renormalization Procedures and Computational Techniques
• Konishi Form Factor at Three Loop in $\mathcal{N}=4$ SYM
• Three loop form factors of a massive spin-2 particle with nonuniversal coupling
• The Two-Loop Infrared Structure of Amplitudes with Mixed Gauge Groups
• Weak radiative corrections to dijet production at the LHC