Abstract
We present next-to-next-to leading order (NNLO) quantum electrodynamics (QED) corrections to the production of the Higgs boson in bottom quark annihilation at the Large Hadron Collider (LHC) in the five flavor scheme. We have systematically included the NNLO corrections resulting from the interference of quantum chromodynamics (QCD) and QED interactions. We have investigated the infrared (IR) structure of the bottom quark form factor up to two loop level in QED and in QCD$\times$QED using K+G equation. We find that the IR poles in the form factor are controlled by the universal cusp, collinear and soft anomalous dimensions. In addition, we derive the QED as well as QCD$\times$QED contributions to soft distribution function as well as to the ultraviolet renormalization constant of the bottom Yukawa coupling up to second order in strong coupling and fine structure constant. Finally, we report our findings on the numerical impact of the NNLO results from QED and QCD$\times$QED at the LHC energies taking into account the dominant NNLO QCD corrections.
Highlights
The discovery of the Standard Model (SM) Higgs boson by ATLAS [1] and CMS [2] collaborations at the Large Hadron Collider (LHC) has put the SM in a strong footing and opened up a plethora of physics programs that can probe physics beyond the SM (BSM)
While this is a subdominant process at the LHC, in certain BSM contexts, the rates are significantly appreciable leading to interesting phenomenological studies
We have systematically investigated both quantum chromodynamics (QCD) and quantum electrodynamics (QED) IR singularities up to second order in their couplings taking into account the interference effects
Summary
The discovery of the Standard Model (SM) Higgs boson by ATLAS [1] and CMS [2] collaborations at the Large Hadron Collider (LHC) has put the SM in a strong footing and opened up a plethora of physics programs that can probe physics beyond the SM (BSM). The precise predictions [24] taking into account radiative corrections from QCD and EW are known for many of these processes Among these subdominant processes, production of the Higgs boson in bottom quark annihilation has been a topic of interest both in the SM as well as BSM contexts. The algorithm contains a set of transformations on the color factors/Casimirs of SU(N) that transforms QCD results for the partonic subprocesses to the corresponding QED results This way both pure QED as well as QCD × QED contributions to inclusive production cross section for the Z boson in the DY process have been obtained in [47] at NNLO level. In order to scrutinize the very approach of Abelianization, we explicitly compute pure QED and QCD × QED corrections to inclusive production of the Higgs boson in bottom quark annihilation up to NNLO level in U(1) and SUðNÞ × Uð1Þ. The universal constants that appear in the soft distribution function, FFs of vector current and bottom quarks and the mass factorized partonic and photonic cross sections are presented in the Appendices A, B and C, respectively
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