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B_c - meson sum rules at next-to-leading order

Andrei I. Onishchenko

TL;DR

This work develops and applies next-to-leading order NRQCD two-point sum rules to the $B_c$ meson, aiming to extract precise heavy-quark parameters and resonance properties. It combines perturbative spectral density with summed Coulomb corrections and nonperturbative gluon-condensate contributions, then uses dispersion relations and NRQCD–QCD matching to compute moments of the correlator. The study yields estimates for the charm-quark mass in multiple schemes (e.g., $M_c^{\text{pole}}$, $M_c^{1S}$, $\bar{m}_c(\bar{m}_c)$) and constrained $B_c$ resonance parameters, including a ground-state mass near the perturbative expectation $M_{B_c} \approx 6.32$ GeV. The results highlight scale dependencies and the importance of higher-order (NNLO) corrections for reduced theoretical uncertainties, with implications for SM parameter determinations and heavy-quark spectroscopy.

Abstract

We present B_c-meson two-point sum rules at next-to-leading order in NRQCD approximation. Analitycal results for perturbative spectral density and gluon condensate contribution with account for summed Coulomb corrections are given. Estimates of various c-quark masses together with couplings and masses of lowest lying B_c-meson resonances are performed.

B_c - meson sum rules at next-to-leading order

TL;DR

This work develops and applies next-to-leading order NRQCD two-point sum rules to the meson, aiming to extract precise heavy-quark parameters and resonance properties. It combines perturbative spectral density with summed Coulomb corrections and nonperturbative gluon-condensate contributions, then uses dispersion relations and NRQCD–QCD matching to compute moments of the correlator. The study yields estimates for the charm-quark mass in multiple schemes (e.g., , , ) and constrained resonance parameters, including a ground-state mass near the perturbative expectation GeV. The results highlight scale dependencies and the importance of higher-order (NNLO) corrections for reduced theoretical uncertainties, with implications for SM parameter determinations and heavy-quark spectroscopy.

Abstract

We present B_c-meson two-point sum rules at next-to-leading order in NRQCD approximation. Analitycal results for perturbative spectral density and gluon condensate contribution with account for summed Coulomb corrections are given. Estimates of various c-quark masses together with couplings and masses of lowest lying B_c-meson resonances are performed.

Paper Structure

This paper contains 10 sections, 67 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Two-point sum rules
  3. NRQCD approximation
  4. Calculation of NRQCD correlator
  5. Solution of the Schrödinger equation
  6. Determination of the short distance coefficients
  7. Dispersion integration
  8. Nonperturbative corrections
  9. Numerical results
  10. Conclusion

Figures (5)

  • Figure 1: Ratios of experimental and theoretically calculated moments $\frac{M_n^{exp}}{M_n^{th}}$ as functions of momentum number (The solid line is for $M_c^{pole} = 2.03$ GeV, the line with short dashes is for $M_c^{pole} = 1.9$ GeV and the one with long dashes is for $M_c^{pole} = 2.1$ GeV. All ratios are plotted for $\mu_{hard} = 2.0$ GeV and $\mu_{soft} = 1.1$ GeV ).
  • Figure 2: Ratios of experimental and theoretically calculated moments $\frac{M_n^{exp}}{M_n^{th}}$ as functions of momentum number in modified TITP (The solid line is for $M_c^{pole} = 1.96$ GeV, the line with short dashes is for $M_c^{pole} = 1.85$ GeV and the one with long dashes is for $M_c^{pole} = 2.05$ GeV. All ratios are plotted for $\mu_{hard} = 2.0$ GeV and $\mu_{soft} = 1.3$ GeV ).
  • Figure 3: Ratio of experimental and theoretically calculated moments $\frac{M_n^{exp}}{M_n^{th}}$ as functions of momentum number in modified TITP ($M_c^{1S} = 1.52$ GeV, $\mu_{hard} = 2.0$ GeV and $\mu_{soft} = 1.3$ GeV ).
  • Figure 4: The values of $B_c$ - meson mass extracted from the two-point NRQCD sum rules in moment scheme.
  • Figure 5: The values of $B_c$ - meson coupling constant extracted from the two-point NRQCD sum rules in moment scheme.