The Hyperfine Splittings in Bottomonium and the $B_q (q=n,s,c)$ Mesons

TL;DR

This paper presents a universal approach to hyperfine splittings in bottomonium and $B_q$ mesons using a consistent strong coupling constant, successfully matching experimental data and predicting new meson mass differences.

Contribution

It introduces a universal strong coupling constant in a spin-spin potential to describe hyperfine splittings across different mesons, with calculations within the Field Correlator Method.

Findings

HFS values for $B$ and $B_s$ mesons match experimental data.

HFS in bottomonium agrees with BaBar measurements for $n_f=5$.

Predicted HFS for excited states and new meson masses.

Abstract

A universal description of the hyperfine splittings (HFS) in bottomonium and the $B_q (q=n,s,c)$ mesons is obtained with a universal strong coupling constant $\alpha_s(\mu)=0.305(2)$ in a spin-spin potential. Other characteristics are calculated within the Field Correlator Method, taking the freezing value of the strong coupling independent of $n_f$. The HFS $M(B^*)- M(B)=45.3(3)$ MeV, $M(B_s^*) - M(B_s)=46.5(3)$ MeV are obtained in full agreement with experiment both for $n_f=3$ and $n_f=4$. In bottomonium, $M(\Upsilon(9460))- M(\eta_b)=70.0(4)$ MeV for $n_f=5$ agrees with the BaBar data, while a smaller HFS, equal to 64(1) MeV, is obtained for $n_f=4$. We predict HFS $M(\Upsilon(2S))-M(\eta_b(2S))=36(1)$ MeV, $M(\Upsilon(3S))- M(\eta(3S))=27(1)$ MeV, and $M(B_c^*) - M(B_c)= 57.5(10)$ MeV, which gives $M(B_c^*)=6334(1)$ MeV, $M(B_c(2 {}^1S_0))=6865(5)$ MeV, and $M(B_c^*(2S {}^3S_1))=6901(5)$ MeV.