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Higgs Decay into Gluons up to O(α_s^3 G_F m_t^2)

Matthias Steinhauser

TL;DR

This work addresses the decay of the Higgs boson to gluons in the intermediate-mass range, focusing on electroweak corrections enhanced by the top-quark mass. By integrating out the top quark, the authors develop an effective Lagrangian and compute the gluon-Higgs coupling coefficient $C_1$ using both direct three-loop vertex diagrams and a low-energy theorem, including corrections of ${\cal O}(\alpha_s^2 x_t)$. They derive decoupling constants $\zeta_g$ and $\zeta_{m_q}$ up to the same order to connect the full and effective theories, and provide explicit expressions for these quantities along with $C_{2_q}$. Numerically, the ${\cal O}(\alpha_s^2 x_t)$ corrections are small compared to pure QCD effects but sizable relative to leading electroweak terms, illustrating the interplay between QCD and heavy-quark electroweak physics and supporting reliable predictions for Higgs production and decay at colliders.

Abstract

The decay of the Standard Model Higgs boson in the intermediate-mass range into gluons is considered where special emphasis is put on the influence of the leading electroweak corrections proportional to G_F m_t^2. An effective Lagrangian approach is used where the top quark is integrated out. The evaluation of the coefficient function is performed using two different methods. The first one is concerned with the direct evaluation of the vertex diagrams and the second method is based on a low-energy theorem. In a first step the tools needed for the computation are provided namely the renormalization constants of the QCD Lagrangian are computed up to O(α_s^2 G_F m_t^2). Also the decoupling constants for the strong coupling constant α_s and the light quark masses relating the quantities of the full theory to the corresponding quantities of the effective one are evaluated up to order α_s^2 G_F m_t^2.

Higgs Decay into Gluons up to O(α_s^3 G_F m_t^2)

TL;DR

This work addresses the decay of the Higgs boson to gluons in the intermediate-mass range, focusing on electroweak corrections enhanced by the top-quark mass. By integrating out the top quark, the authors develop an effective Lagrangian and compute the gluon-Higgs coupling coefficient using both direct three-loop vertex diagrams and a low-energy theorem, including corrections of . They derive decoupling constants and up to the same order to connect the full and effective theories, and provide explicit expressions for these quantities along with . Numerically, the corrections are small compared to pure QCD effects but sizable relative to leading electroweak terms, illustrating the interplay between QCD and heavy-quark electroweak physics and supporting reliable predictions for Higgs production and decay at colliders.

Abstract

The decay of the Standard Model Higgs boson in the intermediate-mass range into gluons is considered where special emphasis is put on the influence of the leading electroweak corrections proportional to G_F m_t^2. An effective Lagrangian approach is used where the top quark is integrated out. The evaluation of the coefficient function is performed using two different methods. The first one is concerned with the direct evaluation of the vertex diagrams and the second method is based on a low-energy theorem. In a first step the tools needed for the computation are provided namely the renormalization constants of the QCD Lagrangian are computed up to O(α_s^2 G_F m_t^2). Also the decoupling constants for the strong coupling constant α_s and the light quark masses relating the quantities of the full theory to the corresponding quantities of the effective one are evaluated up to order α_s^2 G_F m_t^2.

Paper Structure

This paper contains 6 sections, 47 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Theoretical framework
  3. Renormalization group functions up to ${\cal O}(\alpha_s^2 x_t)$
  4. Decoupling relations
  5. Hadronic Higgs decay
  6. Conclusions

Figures (3)

  • Figure 1: Feynman diagrams contribution to the coefficient function $C_1$. The internal dashed line either represents the Higgs boson ($h$) or the neutral ($\chi$) or charged ($\phi^\pm$) Goldstone boson. The external dashed line corresponds to the Higgs boson.
  • Figure 2: Feynman diagrams contribution to $Z_3$ and $\zeta_g^0$. The dashed line either represents the Higgs boson ($h$) or the neutral ($\chi$) or charged ($\phi^\pm$) Goldstone boson.
  • Figure 3: Feynman diagrams contribution to $Z_{2_q}$, $Z_{m_q}$ and $\zeta_{m_q}^0$. The dashed line either represents the Higgs boson ($h$) or the neutral ($\chi$) or charged ($\phi^\pm$) Goldstone boson.