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

A bstract 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 $$ \mathcal{O}\left({\alpha}_s^4\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> <mml:mn>4</mml:mn> </mml:msubsup> </mml:mfenced> </mml:math> for the process induced by the bottom quark Yukawa coupling, assuming massless final states, and the corresponding corrections beyond $$ \mathcal{O}\left({\alpha}_s^2\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:mfenced> </mml:math> are found to be less than 0 . 2%. We present an analytical result for the decay into massive bottom quarks at $$ \mathcal{O}\left({\alpha}_s^3\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> <mml:mn>3</mml:mn> </mml:msubsup> </mml:mfenced> </mml:math> 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 ϵ -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 $$ \mathcal{O}\left({\alpha}_s^3\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> <mml:mn>3</mml:mn> </mml:msubsup> </mml:mfenced> </mml:math> corrections increase the decay width, relative to the result up to $$ \mathcal{O}\left({\alpha}_s^2\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:mfenced> </mml:math> , by 1% due to the large logarithms $$ {\log}^i\left({m}_H^2/{m}_b^2\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mo>log</mml:mo> <mml:mi>i</mml:mi> </mml:msup> <mml:mfenced> <mml:mrow> <mml:msubsup> <mml:mi>m</mml:mi> <mml:mi>H</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>/</mml:mo> <mml:msubsup> <mml:mi>m</mml:mi> <mml:mi>b</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:mrow> </mml:mfenced> </mml:math> with 1 ≤ i ≤ 4 in the small bottom quark mass limit. The coefficient of the double logarithm is proportional to C A – C F , which is the typical color structure in the resummation of soft quark contributions at subleading power.