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Effective QCD Interactions of CP-odd Higgs Bosons at Three Loops

K. G. Chetyrkin, B. A. Kniehl, M. Steinhauser, W. A. Bardeen

TL;DR

This paper derives a heavy-top-quark–based effective Lagrangian for a CP-odd Higgs boson A interacting with gluons in the limit M_A << 2m_t and computes the corresponding coefficient functions through three-loop QCD. It confirms that the C1 operator, responsible for G G̃, receives no QCD corrections up to O(α_s^2) in the MS-bar scheme, in line with the non-renormalization aspect of the Adler-Bardeen theorem, and determines the leading C2 contribution that governs A→gg via light-quark operators. Using these results, the authors obtain the A→gg partial decay width to O(α_s^2), including a precise numerical factor that yields a total correction factor around 1.91 for M_A = 100 GeV, and they compare different scale-optimization predictions. The work provides a framework to incorporate higher-order QCD effects in CP-odd Higgs phenomenology by reducing calculations to massless five-flavor QCD with an effective ggA coupling, with implications for MSSM Higgs production and decay analyses at the LHC.

Abstract

In the virtual presence of a heavy quark t, the interactions of a CP-odd scalar boson A, with mass M_A << 2M_t, with gluons and light quarks can be described by an effective Lagrangian. We analytically derive the coefficient functions of the respective physical operators to three loops in quantum chromodynamics (QCD), adopting the modified minimal-subtraction (MS-bar) scheme of dimensional regularization. Special attention is paid to the proper treatment of the gamma_5 matrix and the Levi-Civita epsilon tensor in D dimensions. In the case of the effective ggA coupling, we find agreement with an all-order prediction based on a low-energy theorem in connection with the Adler-Bardeen non-renormalization theorem. This effective Lagrangian allows us to analytically evaluate the next-to-leading QCD correction to the A -> gg partial decay width by considering massless diagrams. For M_A = 100GeV, the resulting correction factor reads 1+(221/12)alpha_s^(5)(M_A)/pi +165.9(alpha_s^(5)(M_A)/pi)^2 approx 1+0.68+0.23. We compare this result with predictions based on various scale-optimization methods.

Effective QCD Interactions of CP-odd Higgs Bosons at Three Loops

TL;DR

This paper derives a heavy-top-quark–based effective Lagrangian for a CP-odd Higgs boson A interacting with gluons in the limit M_A << 2m_t and computes the corresponding coefficient functions through three-loop QCD. It confirms that the C1 operator, responsible for G G̃, receives no QCD corrections up to O(α_s^2) in the MS-bar scheme, in line with the non-renormalization aspect of the Adler-Bardeen theorem, and determines the leading C2 contribution that governs A→gg via light-quark operators. Using these results, the authors obtain the A→gg partial decay width to O(α_s^2), including a precise numerical factor that yields a total correction factor around 1.91 for M_A = 100 GeV, and they compare different scale-optimization predictions. The work provides a framework to incorporate higher-order QCD effects in CP-odd Higgs phenomenology by reducing calculations to massless five-flavor QCD with an effective ggA coupling, with implications for MSSM Higgs production and decay analyses at the LHC.

Abstract

In the virtual presence of a heavy quark t, the interactions of a CP-odd scalar boson A, with mass M_A << 2M_t, with gluons and light quarks can be described by an effective Lagrangian. We analytically derive the coefficient functions of the respective physical operators to three loops in quantum chromodynamics (QCD), adopting the modified minimal-subtraction (MS-bar) scheme of dimensional regularization. Special attention is paid to the proper treatment of the gamma_5 matrix and the Levi-Civita epsilon tensor in D dimensions. In the case of the effective ggA coupling, we find agreement with an all-order prediction based on a low-energy theorem in connection with the Adler-Bardeen non-renormalization theorem. This effective Lagrangian allows us to analytically evaluate the next-to-leading QCD correction to the A -> gg partial decay width by considering massless diagrams. For M_A = 100GeV, the resulting correction factor reads 1+(221/12)alpha_s^(5)(M_A)/pi +165.9(alpha_s^(5)(M_A)/pi)^2 approx 1+0.68+0.23. We compare this result with predictions based on various scale-optimization methods.

Paper Structure

This paper contains 4 sections, 28 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Effective Lagrangian
  3. $A\to gg$ decay
  4. Discussion and conclusions

Figures (2)

  • Figure 1: Typical Feynman diagrams contributing to the coefficients $\tilde{C}_i^0$ in Eq. (\ref{['eff']}). Looped, bold-faced, and dashed lines represent gluons, $t$ quarks, and $A$ bosons, respectively.
  • Figure 2: Typical Feynman diagrams contributing to the correlator $\langle\tilde{O}_1^\prime\tilde{O}_1^\prime\rangle$. Looped, solid, and dashed lines represent gluons, light quarks, and $A$ bosons, respectively. Solid circles represent insertions of $\tilde{O}_1^\prime$.