Analytic decay width of the Higgs boson to massive bottom quarks at order ${\alpha }_s^3$

Abstract

The Higgs boson decay into bottom quarks is the dominant decay channel contributing to its total decay width, which can be used to measure the bottom quark Yukawa coupling and mass. This decay width has been computed up to $\mathcal{O}({\alpha }_s^4)$ for the process induced by the bottom quark Yukawa coupling, assuming massless final states, and the corresponding corrections beyond $\mathcal{O}({\alpha }_s^2)$ are found to be less than $0.2\%$. We present an analytical result for the decay into massive bottom quarks at $\mathcal{O}({\alpha }_s^3)$ that includes the contribution from the top quark Yukawa coupling induced process. We have made use of the optical theorem, canonical differential equations and the regular basis in the calculation and expressed the result in terms of multiple polylogarithms and elliptic functions. We propose a systematic and unified procedure to derive the $\epsilon$-factorized differential equation for the three-loop kite integral family, which includes the three-loop banana integrals as a sub-sector. We find that the $\mathcal{O}({\alpha }_s^3)$ corrections increase the decay width, relative to the result up to $\mathcal{O}({\alpha }_s^2)$, by $1\%$ due to the large logarithms ${\log }^i(m_H^2/m_b^2)$ with $1\le i\le 4$ in the small bottom quark mass limit. The coefficient of the double logarithms is proportional to $C_A-C_F$, which is the typical color structure in the resummation of soft quark contributions at subleading power.

arXiv comment39 pages, 7 figures; v2: version published in JHEP

References in corpus (59)

• FeynRules 2.0 - A complete toolbox for tree-level phenomenology
• Generating Feynman Diagrams and Amplitudes with FeynArts 3
• Multiloop integrals in dimensional regularization made simple
• Renormalons
• FeynCalc 9.3: New features and improvements
• RunDec: a Mathematica package for running and decoupling of the strong coupling and quark masses
• LiteRed 1.4: a powerful tool for the reduction of the multiloop integrals
• The three loop relation between the \bar {MS} and the pole quark masses
• Integral Reduction with Kira 2.0 and Finite Field Methods
• Version 3 of {\tt RunDec} and {\tt CRunDec}
• PolyLogTools - Polylogs for the masses
• AMFlow: a Mathematica package for Feynman integrals computation via Auxiliary Mass Flow
• Quark mass relations to four-loop order
• Scalar Correlator at O(alpha_s^4), Higgs Decay into b-quarks and Bounds on the Light Quark Masses
• A Systematic and Efficient Method to Compute Multi-loop Master Integrals
• Correlator of the quark scalar currents and Γ_{tot}(H --> hadrons) at O(α_s^3) in pQCD
• Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral
• The kite integral to all orders in terms of elliptic polylogarithms
• Heavy-quark production in gluon fusion at two loops in QCD
• $\overline{\mathrm{MS}}$-on-shell quark mass relation up to four loops in QCD and a general SU$(N)$ gauge group
• Second Order QCD Corrections to Scalar and Pseudoscalar Higgs Decays into Massive Bottom Quarks
• FeynCalc 10: Do multiloop integrals dream of computer codes?
• The large top quark mass expansion for Higgs boson decays into bottom quarks and into gluons
• The fully differential decay rate of a Higgs boson to bottom-quarks at NNLO in QCD
• Higgs boson decay into b-quarks at NNLO accuracy
• On Higgs decays to hadrons and the R-ratio at N^4LO
• Determining Feynman integrals with only input from linear algebra
• High-Energy Limit of QCD beyond Sudakov Approximation
• Three-Loop O(alpha_s^2 G_F M_t^2) Corrections to Hadronic Higgs Decays
• Next-to-leading power endpoint factorization and resummation for off-diagonal "gluon" thrust
• Differential decay rates of CP-even and CP-odd Higgs bosons to top and bottom quarks at NNLO QCD
• Taming Calabi-Yau Feynman integrals: The four-loop equal-mass banana integral
• On a procedure to derive $\epsilon$-factorised differential equations beyond polylogarithms
• Bananas of equal mass: any loop, any order in the dimensional regularisation parameter
• Completing the hadronic Higgs boson decay at order ${\alpha }_s^4$
• Virtual Top-Quark Effects on the H->bb-bar Decay at Next-to-Leading Order in QCD
• The Soft Quark Sudakov
• Complete QCD Corrections of Order O(α_s^3) to the Hadronic Higgs Decay
• Calculation of Feynman loop integration and phase-space integration via auxiliary mass flow
• The three-loop equal-mass banana integral in $\epsilon$-factorised form with meromorphic modular forms
• The ice cone family and iterated integrals for Calabi-Yau varieties
• Exact Top Yukawa corrections to Higgs boson decay into bottom quarks
• Large-x resummation of off-diagonal deep-inelastic parton scattering from d-dimensional refactorization
• Higgs Decay to Top Quarks at O(α_s^2)
• The order $O(\bar{\alpha }{\bar{\alpha }}_s)$ and $O({\bar{\alpha }}^2)$ corrections to the decay width of the neutral Higgs boson to the $\bar{b}b$ pair
• Higgs decay into massive b-quarks at NNLO QCD in the nested soft-collinear subtraction scheme
• Decoupling of heavy quarks at four loops and effective Higgs-fermion coupling
• NNLOPS description of the H$\to b\bar{b}$ decay with MINLO
• $H\to b\overline{b}j$ at Next-to-Next-to-Leading Order Accuracy
• Factorization at Next-to-Leading Power and Endpoint Divergences in $gg\to h$ Production
• On the resummation of double logarithms in the process Higgs --> two photons
• Leading logarithmic large-x resummation of off-diagonal splitting functions and coefficient functions
• Fully exclusive heavy quark-antiquark pair production from a colourless initial state at NNLO in QCD
• $\epsilon$-regular basis for non-polylogarithmic multiloop integrals and total cross section of the process $e^{+}{e}^{-}\to 2(Q\bar{Q})$
• The $Higgs\to b\bar{b},c\bar{c},gg$ measurement at CEPC
• Renormalization group summation and analytic continuation from spacelike to timeline regions
• Analytic decay width of the Higgs boson to massive bottom quarks at next-to-next-to-leading order in QCD
• Higgs boson decay into four bottom quarks in the SM and beyond
• Analytic NNLO QCD corrections to top quark pair production in electron-positron collisions

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