NNLO QCD ⊕ QED corrections to Higgs production in bottom quark annihilation

We consider the higher-order resummation of Sudakov double logarithms in the presence of multiple coupled gauge interactions. The associated evolution equations depend on the coupled β functions of two (or more) coupling constants α a and α b , as well as anomalous dimensions that have joint perturbative series in α a and α b. We discuss possible strategies for solving the system of evolution equations that arises. As an example, we obtain the complete three-loop (NNLL) QCD⊗QED Sudakov evolution factor. Our results also readily apply to the joint higher-order resummation of electroweak and QCD Sudakov logarithms. As part of our analysis we also revisit the case of a single gauge interaction (pure QCD), and study the numerical differences and reliability of various methods for evaluating the Sudakov evolution factor at higher orders. We find that the approximations involved in deriving commonly used analytic expressions for the evolution kernel can induce noticeable numerical differences of several percent or more at low scales, exceeding the perturbative precision at N 3 LL and in some cases even NNLL. Therefore, one should be cautious when using approximate analytic evolution kernels for high-precision analyses.

Section: Jhep03(2020)182mentioning

confidence: 99%

Higher-order Sudakov resummation in coupled gauge theories

Billis

Tackmann

Talbert

2020

“…soft distribution function Φ I up to second order in a s from QCD, in a e from QED and in a s a e from QCD×QED. We found in [29] that the soft distribution functions extracted from two different processes satisfy a remarkable relation, namely Φ q = Φ b up to second order in both the couplings a s and a e demonstrating the universality among QCD, QED and QCD×QED results. It was found in [55] that this relation is valid up to three loops in QCD.…”

Section: Soft Distribution Functionmentioning

confidence: 68%

“…For earlier work on this can be found in [28]. NNLO QED as well as QCD×QED corrections to Higgs production in bottom quark annihilation were obtained [29] to estimate the impact of QED radiative corrections. More recently, NNLO EW-QCD effects to single vector boson production were reported in [30,31].…”

Section: Jhep08(2020)156mentioning

confidence: 99%

“…One finds that the abelianization can be used to relate ultraviolate and infrared anomalous dimensions of QCD with those of QED. In [29], explicit computation of form factors of vector and scalar operators in QED and QCD×QED set up to second order in perturbation theory demonstrates the usefulness of abelianization. In addition, the results on inclusive cross sections for DY process, such as di-lepton or W/Z productions and also for Higgs production in bottom quark annihilation support this procedure of abelianization up to NNLO level in QED as well as in QCD×QED.…”

Section: Jhep08(2020)156mentioning

confidence: 99%

“…In [29], we computed UV finiteσ II up to NNLO in QCD, QED and QCD×QED , the two loop corrected bare FFs and the overall renormalisation constant Z b λ to obtain the JHEP08(2020)156…”

Section: Soft Distribution Functionmentioning

confidence: 99%

See 2 more Smart Citations

Infrared structure of SU(N) × U(1) gauge theory to three loops

Ajjath

Mukherjee

Ravindran

2020

Self Cite

We study the infrared (IR) structure of SU(N) × U(1) (QCD × 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)×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) × 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.

On next to soft threshold corrections to DIS and SIA processes

Ajjath

Mukherjee

Ravindran

et al. 2021

Self Cite

We study the perturbative structure of threshold enhanced logarithms in the coefficient functions of deep inelastic scattering (DIS) and semi-inclusive e+e− annihilation (SIA) processes and setup a framework to sum them up to all orders in perturbation theory. Threshold logarithms show up as the distributions ((1−z)−1 logi(1−z))+ from the soft plus virtual (SV) and as logarithms logi(1−z) from next to SV (NSV) contributions. We use the Sudakov differential and the renormalisation group equations along with the factorisation properties of parton level cross sections to obtain the resummed result which predicts SV as well as next to SV contributions to all orders in strong coupling constant. In Mellin N space, we resum the large logarithms of the form logi(N) keeping 1/N corrections. In particular, the towers of logarithms, each of the form $$ {a}_s^n/{N}^{\alpha }{\log}^{2n-\alpha }(N),{a}_s^n/{N}^{\alpha }{\log}^{2n-1-\alpha }(N)\cdots $$ a s n / N α log 2 n − α N , a s n / N α log 2 n − 1 − α N ⋯ etc for α = 0, 1, are summed to all orders in as.