Masses of scalar and axial-vector B mesons revisited

Hai-Yang Cheng; Fu-Sheng Yu

doi:10.1140/epjc/s10052-017-5252-4

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2017) 77: 668
https://doi.org/10.1140/epjc/s10052-017-5252-4

Regular Article - Theoretical Physics

Masses of scalar and axial-vector B mesons revisited

Hai-Yang Cheng¹ and Fu-Sheng Yu²^*

¹ Institute of Physics, Academia Sinica, Taipei, 115, Taiwan, Republic of China
² School of Nuclear Science and Technology, Lanzhou University, Lanzhou, 730000, People’s Republic of China

^* e-mail: yufsh@lzu.edu.cn

Received: 2 August 2017
Accepted: 22 September 2017
Published online: 7 October 2017

Abstract

The SU(3) quark model encounters a great challenge in describing even-parity mesons. Specifically, the $q\bar{q}$ quark model has difficulties in understanding the light scalar mesons below 1 GeV, scalar and axial-vector charmed mesons and $$1^+$$ charmonium-like state X(3872). A common wisdom for the resolution of these difficulties lies on the coupled channel effects which will distort the quark model calculations. In this work, we focus on the near mass degeneracy of scalar charmed mesons, $D_{s0}^*$ and $D_0^{*0}$ , and its implications. Within the framework of heavy meson chiral perturbation theory, we show that near degeneracy can be qualitatively understood as a consequence of self-energy effects due to strong coupled channels. Quantitatively, the closeness of $D_{s0}^*$ and $D_0^{*0}$ masses can be implemented by adjusting two relevant strong couplings and the renormalization scale appearing in the loop diagram. Then this in turn implies the mass similarity of $B_{s0}^*$ and $B_0^{*0}$ mesons. The $$P_0^* P'_1$$ interaction with the Goldstone boson is crucial for understanding the phenomenon of near degeneracy. Based on heavy quark symmetry in conjunction with corrections from QCD and $$1/m_Q$$ effects, we obtain the masses of $B^*_{(s)0}$ and $B'_{(s)1}$ mesons, for example, $M_{B_{s0}^*}= (5715\pm 1)\,\mathrm{MeV}+\delta \Delta _S$ , $M_{B'_{s1}}=(5763\pm 1)\,\mathrm{MeV}+\delta \Delta _S$ with $\delta \Delta _S$ being corrections. We find that the predicted mass difference of 48 MeV between $B'_{s1}$ and $B_{s0}^*$ is larger than that of 20–30 MeV inferred from the relativistic quark models, whereas the difference of 15 MeV between the central values of $M_{B'_{s1}}$ and $M_{B'_1}$ is much smaller than the quark model expectation of 60–100 MeV. Experimentally, it is important to have a precise mass measurement of $$D_0^*$$ mesons, especially the neutral one, to see if the non-strange scalar charmed meson is heavier than the strange partner as suggested by the recent LHCb measurement of the $D_0^{*\pm }$ .