$Λ$-deuteron momentum correlation functions incorporating deuteron breakup contributions in Faddeev formulation

TL;DR

The paper addresses how deuteron breakup influences the $\Lambda d$ momentum correlation function in a three-body framework. It advances a rigorous Faddeev-based approach with NN and YN interactions from chiral EFT to construct full $\Lambda np$ three-body wave functions, including breakup in both incident and rearrangement channels, and computes $C(q_0)$ using a Green-function spectral representation. The main findings are that incident-channel breakup is negligible while rearrangement-channel breakup modestly enhances $C(q_0)$, with the size of the effect depending on the YN interaction and total angular momentum; the results emphasize the need to account for breakup when interpreting experimental data and suggest that $\Lambda d$ correlations can constrain the relative strengths of the $^1S_0$ and $^3S_1$ $\Lambda N$ interactions. Overall, the work provides a quantitative, three-body-consistent assessment of breakup effects that informs hyperon-nucleon interaction studies and future analyses of correlation measurements.

Abstract

The effects of the deuteron breakup are estimated for the $Λ$-deuteron momentum correlation function. Faddeev amplitudes in calculating low-energy $Λ$-deuteron scattering can provide not only the elastic scattering part but also breakup wave functions in the incident and the rearrangement channels. Calculations are carried out using nucleon-nucleon (NN) and hyperon-nucleon (YN) interactions parametrized in chiral effective field theory. The effects of the breakup in the incident channel are found to be marginally insignificant. Those of the rearrangement channel are not negligible, but not large when the source radius is larger than 2.5 fm. Nevertheless, it is worthwhile to have the information on the magnitude of these effects in analyzing the experimental data.

Figures (4)

• Figure 1: Two sets of Jacobi momenta.
• Figure 2: Correlation functions evaluated by the $\Lambda d$ relative elastic wave functions for $J=3/2$ with the N$^4$LO$^+$ NN RKE18 and NLO19 YN NLO19 interactions. The thin dotted curves are the same as those given in Fig. 6 in Ref. KK24 in which the source function $D(r_{np};\sqrt{2}R_s)D(r_{\Lambda d};\sqrt{2}R_s)$ is used. The thick dashed curves are the results calculated with the source function given in Eq. (10): $D(r_{np};\sqrt{2}R_s)D(r_{\Lambda d};\sqrt{3/2}R_s)$.
• Figure 3: The solid curves show the correlation functions evaluated by the full $\Lambda np$ three-body wave function for the $J=1/2$ channel with the N$^4$LO$^+$ NN and NLO19 YN interactions. The NLO13 YN interaction provides almost same results. The dashed curves are calculated only with the elastic part. The source function of Eq. (\ref{['eq:sf']}) is used with the three cases of $R_s=1.2, 2.5$, and $5.0$ fm.
• Figure 4: Same as Fig. 3, but for the $J=3/2$ channel. The upper (lower) panel shows the results with the NLO13 (NLO19) YN interactions.