Properties of light scalar mesons from lattice QCD

Lattice QCD with $N_f=2$ flavors of sea quark is used to explore the spectrum and decay of scalar mesons. We are able to determine the $b_1-a_0$ mass difference and this leads to the conclusion that the lightest nonsinglet scalar meson ($a_0$) has a mass of 1.01(4) GeV. We determine from the lattice the coupling strength to KK and $\pi \eta$. We compute the leptonic decay constant of the lightest nonsinglet scalar meson. We discuss the impact of these lattice results on the interpretation of the $a_0(980)$ state. We also discuss $K_0^{*}$ states.

Figure 1

Mass of the $b_1$ mesons (in units of $r_0\approx 0.5\mathrm{fm}$) versus quark mass. The strange quark mass corresponds to $(m(\pi )r_0{)}^2\approx 3.4$.

Figure 2

Mass difference of $b_1$ and $a_0$ mesons (in units of $r_0\approx 0.5\mathrm{fm}$) versus quark mass.

Figure 3

Quark diagrams involved in the decays listed in Table 4, where $D$ is the disconnected diagram and $T$ is the triangle diagram.

Figure 4

The normalized ratio $R(t)$ for the connected contribution ($T$) to the transition $S\to P_1{P}_2$. The contribution of $T$ to particular decays can be read off from Table 4. The number of lattice gauge configurations analyzed was 90 (U355), 165 (C410) and 30 for each U395 case. The dotted line illustrates the expected behavior with slope $xa$ for C410.

Figure 5

The effective coupling $g$ extracted from $R(t)$ as described in the text for the triangle graph $T$ for $S\to P_1{P}_2$ with zero momentum (also some results for nonzero momentum as discussed in the text). The dotted line at $g=1$ is to guide the eye.

Figure 6

The normalized ratio $R(t)$. Here $\mathrm{MOM}=0$, 1 refers to the transition $S(k)\to P_1(0)+P_2(k)$ with momenta $k=2n\pi /L$ with $n=0$ and 1.