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Three-Loop Chromomagnetic Interaction in HQET

A. G. Grozin, P. Marquard, J. H. Piclum, M. Steinhauser

Abstract

We compute the three-loop QCD corrections to the quark chromomagnetic moment and thus obtain the matching coefficient and the anomalous dimension of the chromomagnetic interaction in HQET. As a byproduct we obtain the three-loop corrections to the quark anomalous magnetic moment.

Three-Loop Chromomagnetic Interaction in HQET

Abstract

We compute the three-loop QCD corrections to the quark chromomagnetic moment and thus obtain the matching coefficient and the anomalous dimension of the chromomagnetic interaction in HQET. As a byproduct we obtain the three-loop corrections to the quark anomalous magnetic moment.

Paper Structure

This paper contains 7 sections, 38 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The Calculation
  3. Chromomagnetic moment
  4. Application: heavy-meson mass splittings
  5. Matching coefficient and renormalization group invariant quark mass
  6. Magnetic moment
  7. Conclusion

Figures (2)

  • Figure 1: Sample diagrams contributing to the quark chromomagnetic moment. Solid, curly and dotted lines denote quarks, gluons and ghosts, respectively. $\otimes$ represents the coupling of the background field. In the closed quark loops all flavours have to be considered.
  • Figure 2: $C_{\rm mag}$ and $C_{\rm spin}$ as a function of $\Lambda_{\rm QCD}/m_Q$ for $n_l=0$ (left) and $n_l=4$ (right). The upper group of lines corresponds to $C_{\rm spin}$ while the lower shows $C_{\rm mag}$. Inside these groups the dotted, dashed and solid lines show the LO, NLO and NNLO, respectively. The estimation for the NNNLO result is shown by the dash-dotted line. The region relevant for the bottom quark is indicated by the vertical line.