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

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.

💡 Research Summary

The authors present the first systematic lattice QCD investigation of proton–Λ (p‑Λ) scattering in the isospin‑½ channel, employing seven (2+1)-flavor ensembles that span pion masses from the physical point (135 MeV) up to 317 MeV and three lattice spacings (a = 0.105, 0.077, 0.052 fm). By constructing interpolating operators in both the rest frame and a moving frame with total momentum P = (0,0,1), they extract the finite‑volume two‑particle energy shifts ΔE using the generalized eigenvalue problem (GEVP) and ratio techniques that remove the non‑interacting contributions. The energy shifts are then related to the infinite‑volume scattering phase shift via Lüscher’s formula, which involves the generalized zeta function Z_{00}^{d}(1;q²) and, for moving frames, the Lorentz factor γ.

The phase‑shift data are fitted to the effective‑range expansion (ERE) for S‑wave scattering, k cot δ = 1/a + ½ r k² + …, yielding scattering lengths a and effective ranges r for each ensemble. Statistical uncertainties are assessed with 3000 bootstrap replicas; the resulting distributions are often non‑Gaussian, so the median is quoted as the central value with 1σ quantiles as errors. The raw lattice results show a clear trend of attractive interaction (positive 1/a) across all pion masses and lattice spacings.

To obtain physical predictions, the authors perform simultaneous chiral and continuum extrapolations of the inverse scattering length (1/a) and the effective range (r) using a linear ansatz in (m_π² − m_π,phys²) and a². The extrapolated values at the physical pion mass and in the continuum limit are:

• ¹S₀ channel: 1/a = 0.177 ± 0.083 GeV, r = 2.9 ± 1.4 fm;
• ³S₁ channel: 1/a = 0.016 ± 0.076 GeV, r = 1.8 ± 1.1 fm.

Both channels thus exhibit modestly attractive interactions with relatively large effective ranges. Spin‑averaging the two channels gives ā = 3.5 ± 3.8 fm and r̄ = 2.08 ± 0.90 fm, which are consistent within errors with the STAR measurement from p‑Λ correlations (a ≈ 2.3 fm, r ≈ 3.5 fm). Using the extracted S‑wave phase shifts, the authors compute the spin‑averaged elastic cross section σ(p‑Λ) = 4πk² sin²δ for laboratory momenta up to ~0.3 GeV. Their results lie within the experimental uncertainties of older bubble‑chamber data (Refs.