Accurate decay-constant ratios $f_{B^*}/f_B$ and $f_{B_s^*}/f_{B_s}$ from Borel QCD sum rules

TL;DR

This paper accurately predicts ratios of vector to pseudoscalar decay constants for beauty mesons using dispersive sum rules, reducing uncertainties and confirming these ratios are less than one with high confidence.

Contribution

The study introduces a precise method for calculating decay constant ratios of beauty mesons, significantly reducing theoretical uncertainties compared to previous approaches.

Findings

Ratios $f_{B^*}/f_B$ and $f_{B_s^*}/f_{B_s}$ are less than one.

High-precision predictions with controlled systematic uncertainties.

Ratios are confirmed below unity at 2-2.5 sigma significance.

Abstract

We present our analysis of the decay constants of the beauty vector mesons $B^*$ and $B^*_s$ within the framework of dispersive sum rules for the two-point correlator of vector currents in QCD. While the decay constants of the vector mesons $f_{B^*}$ and $f_{B_s^*}$ $-$ similar to the decay constants of the pseudoscalar mesons $f_B$ and $f_{B_s}$ $-$ individually have large uncertainties induced by theory parameters not known with a satisfactory precision, these uncertainties almost entirely cancel out in the ratios of vector over pseudoscalar decay constants. These ratios may be thus predicted with very high accuracy due to the good control over the systematic uncertainties of the decay constants gained upon application of our hadron-parameter extraction algorithm. Our final results read $f_{B^*}/f_B=0.944\pm0.011_{\rm OPE}\pm0.018_{\rm syst}$ and $f_{B_s^*}/f_{B_s}=0.947\pm0.023_{\rm OPE}\pm0.020_{\rm syst}$. Thus, both $f_{B^*}/f_B$ and $f_{B_s^*}/f_{B_s}$ are less than unity at 2.5$\sigma$ and 2$\sigma$ level, respectively.