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Two-loop QCD corrections to top quark width

Andrzej Czarnecki, Kirill Melnikov

TL;DR

The paper computes the two-loop QCD corrections (O(α_s^2)) to the top quark decay width in the limit m_t ≫ m_W, including a new treatment of non-planar t → W b b̄ interference diagrams. The result modifies the width by about −1.69 α_s^2 (with α_s(m_t) ≈ 0.11), giving an overall ~2% suppression of Γ_t, and shows the full correction is smaller than the prior BLM estimate by roughly 24%. The work relies on a heavy-quark expansion and phase-space factorization, and provides a refined SM prediction for Γ_t that, together with electroweak and W-width effects, approaches ~1% theoretical precision. A novel method to handle non-planar contributions and considerations on mass scheme choices (pole vs MSbar) are highlighted, with remaining uncertainties mainly from m_t and potential future experimental measurements.

Abstract

We present O(alpha_s^2) corrections to the decay t-->bW in the limit of a very large top quark mass, m_t >> m_W. We find that the O(alpha_s^2) effects decrease the top quark decay width Gamma_t by about 2%: Gamma_t = Gamma_0(1-0.8alpha_s(m_t)-1.7alpha_s^2). The complete corrections are smaller by about 24% than their estimate based on the BLM effects O(beta_0 alpha_s^2). We explain how to compute a new type of diagrams which contribute to Gamma(t --> bW) at the O(alpha_s^2) level.

Two-loop QCD corrections to top quark width

TL;DR

The paper computes the two-loop QCD corrections (O(α_s^2)) to the top quark decay width in the limit m_t ≫ m_W, including a new treatment of non-planar t → W b b̄ interference diagrams. The result modifies the width by about −1.69 α_s^2 (with α_s(m_t) ≈ 0.11), giving an overall ~2% suppression of Γ_t, and shows the full correction is smaller than the prior BLM estimate by roughly 24%. The work relies on a heavy-quark expansion and phase-space factorization, and provides a refined SM prediction for Γ_t that, together with electroweak and W-width effects, approaches ~1% theoretical precision. A novel method to handle non-planar contributions and considerations on mass scheme choices (pole vs MSbar) are highlighted, with remaining uncertainties mainly from m_t and potential future experimental measurements.

Abstract

We present O(alpha_s^2) corrections to the decay t-->bW in the limit of a very large top quark mass, m_t >> m_W. We find that the O(alpha_s^2) effects decrease the top quark decay width Gamma_t by about 2%: Gamma_t = Gamma_0(1-0.8alpha_s(m_t)-1.7alpha_s^2). The complete corrections are smaller by about 24% than their estimate based on the BLM effects O(beta_0 alpha_s^2). We explain how to compute a new type of diagrams which contribute to Gamma(t --> bW) at the O(alpha_s^2) level.

Paper Structure

This paper contains 4 sections, 22 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Non-planar diagrams $t\to bb\bar{b}W$
  3. Two-loop corrections to top decay rate
  4. Conclusion

Figures (2)

  • Figure 1: Non-planar diagrams contributing to the decay channel $t\to Wbb\bar{b}$.
  • Figure 2: Plots of the coefficient functions defined in eq. (\ref{['eq:a2']}): (a) $a_F$, (b) $a_A$, (c) $a_L$, (d) $a_H$. The variable on the horizontal axis is $m_b/m_t$.