A Lattice QCD study of $p-Λ$ scattering in continuum and chiral limits

Abstract

We present a first systematic study of $I=1/2$ proton-$Λ$ ($p$-$Λ$) scattering from lattice QCD, using seven sets of $(2+1)$-flavor lattice ensembles with pion masses spanning 135-317 MeV and three lattice spacings with $a=(0.052,0.077, 0.105)$ fm. Using Lüscher's finite-volume method, effective range expansion and chiral/continuum extrapolations, we obtain the inverse of scattering length and effective range for the $^1S_0$ channel as 0.177(83) GeV and 2.9(1.4) fm, and for the $^3S_1$ channel as 0.016(76) GeV and 1.8(1.1) fm. From the derived S-wave phase shifts, we provide an estimate of the $p-Λ$ scattering cross section. Our results for scattering length, effective range and cross sections are in good agreement with available experimental measurements. We also find that the $p-Λ$ system sustains attractive interactions. These results provide critical input for the unification of nuclear force theories and the construction of neutron star equations of state.

Figures (13)

• Figure 1: The values of $k\cot\delta$ as a function of $k^2$. The data points are from the ensembles C24P29 and C32P29, having the same pion mass and lattice spacing. The gray bands are the fits to Eq. \ref{['eq:ERE']} and the width of the bands indicate 1$\sigma$ statistical uncertainty. The black curves are $ik$. The upper and lower panels are for the $^1S_0$ and $^3S_1$ channels, respectively.
• Figure 2: Results for the $1/a_0$ extraplation according to Eq. \ref{['eq:joint-extrapolate']} for the channel $^1S_0$ (upper panel) and $^3S_1$ (lower panel) with the corresponding $\chi^2/d.o.f=0.15$ and $\chi^2/d.o.f=0.18$. The black point corresponds to the physical point and continuum limit.
• Figure 3: Results for the $r_0$ extraplation according to Eq. \ref{['eq:joint-extrapolate']} for the channel $^1S_0$ and $^3S_1$ with the corresponding $\chi^2/d.o.f=1.2$, and the corresponding $\chi^2/d.o.f=1.1$. The black point corresponds to the physical point and continuum limit.
• Figure 4: Comparison of the spin-averaged cross section with experimental meesurements Alexander:1968acuSechi-Zorn:1968maoKadyk:1971tc
• Figure 5: The $m_{pole}-m_p-m_{\Lambda}$ of the virtual state for $^1S_0$. We performed a joint extrapolation($m_{pole} = m_{pole,\rm phys} + c_5(m_\pi^2 -m_{\pi, {\rm phys}}^2) + c_6 a^2$) of the pole trajectory to the physical point. The mass difference at the physical point are $-3(18)\rm MeV$.