QCD sum rule study of a charged bottom-strange scalar meson

Using the QCD sum rule approach, we investigate the possible four-quark structure for the new observed $B_s^0{\pi }^{\pm }$ narrow structure (D0). We use a diquak-antidiquark scalar current and work to the order of $m_s$ in full QCD, without relying on $1/m_Q$ expansion. Our study indicates that although it is possible to obtain a stable mass in agreement with the state found by the D0 collaboration, more constraint analysis (simultaneous requirement of the OPE convergence and the dominance of the pole on the phenomenological side) leads to a higher mass. We also predict the masses of the bottom scalar tetraquark resonances with zero and two strange quarks.

Figure 1

The pole (solid line) and the continuum (dashed line) contribution for $\sqrt{s_0}=6.0\mathrm{GeV}$.

Figure 2

The $X$ mass as a function of the Borel mass for different values of the continuum threshold: $\sqrt{s_0}=5.9\mathrm{GeV}$ (solid line), $\sqrt{s_0}=6.0\mathrm{GeV}$ (dashed line), $\sqrt{s_0}=6.1\mathrm{GeV}$ (dotted line).

Figure 3

The OPE convergence in the region $2.0\le M^2\le 7{\mathrm{GeV}}^2$ for $s_0=36\mathrm{GeV}$. We start with the relative perturbative contribution (the perturbative contribution divided by the total contribution), and each subsequent line represents the addition of the relative contribution of a condensate of higher dimension in the expansion.

Figure 4

The OPE convergence in the region $3.5\le M^2\le 5.5{\mathrm{GeV}}^2$ for $s_0=46\mathrm{GeV}$. We start with the relative perturbative contribution (the perturbative contribution divided by the total contribution), and each subsequent line represents the addition of the relative contribution of a condensate of higher dimension in the expansion.

Figure 5

The pole (solid line) and the continuum (dashed line) contribution for $s_0=46.0{\mathrm{GeV}}^2$.

Figure 6

The $X$ mass as a function of the Borel mass for different values of the continuum threshold: $s_0=46{\mathrm{GeV}}^2$ (solid line), $s_0=48{\mathrm{GeV}}^2$ (dashed line), $s_0=50{\mathrm{GeV}}^2$ (dotted line). The crosses in the figure indicate the allowed Borel window.

Figure 7

The $B_0^{0s}$ mass as a function of the Borel mass for different values of the continuum threshold: $s_0=43{\mathrm{GeV}}^2$ (solid line), $s_0=45{\mathrm{GeV}}^2$ (dashed line), $s_0=47{\mathrm{GeV}}^2$ (dotted line). The crosses in the figure indicate the allowed Borel window.

Figure 8

The $B_0^{2s}$ mass as a function of the Borel mass for different values of the continuum threshold: $\sqrt{s_0}=46{\mathrm{GeV}}^2$ (solid line), $s_0=48{\mathrm{GeV}}^2$ (dashe line), $s_0=50{\mathrm{GeV}}^2$ (dotted line). The crosses in the figure indicate the allowed Borel window.