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تسجيل مستخدم جديدEmergence of the $rho$ resonance from the HAL QCD potential in lattice QCD
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We investigate the $I=1$ $pi pi$ interaction using the HAL QCD method in lattice QCD. We employ the (2+1)-flavor gauge configurations on $32^3 times 64$ lattice at the lattice spacing $a approx 0.0907$ fm and $m_{pi} approx 411$ MeV, in which the $rho$ meson appears as a resonance state. We find that all-to-all propagators necessary in this calculation can be obtained with reasonable precision by a combination of three techniques, the one-end trick, the sequential propagator, and the covariant approximation averaging (CAA). The non-local $I=1$ $pi pi$ potential is determined at the next-to-next-to-leading order (N$^2$LO) of the derivative expansion for the first time, and the resonance parameters of the $rho$ meson are extracted. The obtained $rho$ meson mass is found to be consistent with the value in the literature, while the value of the coupling $g_{rho pi pi}$ turns out to be somewhat larger. The latter observation is most likely attributed to the lack of low-energy information in our lattice setup with the center-of-mass frame. Such a limitation may appear in other P-wave resonant systems and we discuss possible improvement in future. With this caution in mind, we positively conclude that we can reasonably extract the N$^2$LO potential and resonance parameters even in the system requiring the all-to-all propagators in the HAL QCD method, which opens up new possibilities for the study of resonances in lattice QCD.
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The $XiXi$ interaction in the $^1$S$_0$ channel is studied to examine the convergence of the derivative expansion of the non-local HAL QCD potential at the next-to-next-to-leading order (N$^2$LO). We find that (i) the leading order potential from the
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We calculate the parameters describing elastic $I=1$, $P$-wave $pipi$ scattering using lattice QCD with $2+1$ flavors of clover fermions. Our calculation is performed with a pion mass of $m_pi approx 320::{rm MeV}$ and a lattice size of $Lapprox 3.6$
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