Determination of the spin triplet $p\mathrm{\Lambda }$ scattering length from the final state interaction in the $\vec{p}p\to p{K}^{+}\mathrm{\Lambda }$ reaction

The $\vec{p}p\to p{K}^{+}\mathrm{\Lambda }$ reaction has been measured with the COSY-TOF detector at a beam momentum of $2.7\mathrm{GeV}/c$. The polarized proton beam enables the measurement of the beam analyzing power by the asymmetry of the produced kaon $\left(A_N^K\right)$. This observable allows the $p\mathrm{\Lambda }$ spin triplet scattering length to be extracted for the first time model independently from the final state interaction in the reaction. The obtained value is $a_t=(-2.{55}_{-1.39}^{+0.72}{}_{\mathrm{stat}.}\pm 0.6_{\mathrm{syst}.}\pm 0.3_{\mathrm{theo}.})\mathrm{fm}$. This value is compatible with theoretical predictions and results from model-dependent analyses.

Figure 1

Dalitz plot of the selected event sample at $2.7\mathrm{GeV}/c$ beam momentum corrected for acceptance and reconstruction efficiency. The red arrows indicate the region of the $N\mathrm{\Sigma }$ thresholds.

Figure 2

$p\mathrm{\Lambda }$ invariant mass spectrum for the selected event sample at $2.7\mathrm{GeV}/c$ beam momentum corrected for acceptance and reconstruction efficiency (AC). The upper limit of the fit range is marked by the vertical dashed (red) line. The fit applied later (see Fig. 5) and its continuation over the whole spectrum is shown by the solid (red) line. The vertical dash-dotted (blue) line indicates the lower $N\mathrm{\Sigma }$ threshold ($n{\mathrm{\Sigma }}^{+}$).

Figure 3

The beam analyzing power determined by the kaon asymmetry, $A_N^K$, as a function of $cos\left({\theta }_K^{*}\right)$ for the full $m_{p\mathrm{\Lambda }}$ range. The solid (red) line shows the fit with $\alpha P_1^1+\beta P_2^1$. The individual contributions of the associated Legendre polynomials are shown by the dash-dotted (green) and dotted (blue) lines, respectively.

Figure 4

The coefficients $\alpha \left(m_{p\mathrm{\Lambda }}\right)$ (filled circles, green) and $\beta \left(m_{p\mathrm{\Lambda }}\right)$ (open squares, blue) from the fit of $A_N^K$ with associated Legendre polynomials as a function of $p\mathrm{\Lambda }$ invariant mass. The dashed (red) vertical line indicates the upper limit of the fitting range applied to the invariant mass spectrum.

Figure 5

The amplitude squared $|\tilde{A}\left(m_{p\mathrm{\Lambda }}\right){|}^2$ corresponding to the $p\mathrm{\Lambda }$ invariant mass distribution divided by the volume of available phase space. The solid (red) line shows a fit to the data by Eq. (2). The fit values are $C_0=-0.{139}_{-0.033}^{+0.031}$, $C_1=(0.{121}_{-0.007}^{+0.008})\mathrm{GeV}/c^2$, and $C_2=(4.{158}_{-0.004}^{+0.003})\mathrm{GeV}/c{}^2$. The vertical (red) dashed line marks the upper limit of the fitting range.

Figure 6

The $|b_1\left(m_{p\mathrm{\Lambda }}\right)|$ distribution determined from $|\tilde{A}\left(m_{p\mathrm{\Lambda }}\right){|}^2$ and $\left|\alpha \right(m_{p\mathrm{\Lambda }}\left)\right|$. The solid (red) line shows the fit with the parametrization (2) from which the spin triplet $p\mathrm{\Lambda }$ scattering length is determined. The fit values are $C_0=0.{599}_{-0.233}^{+0.171}$, $C_1=(0.{046}_{-0.020}^{+0.035})\mathrm{GeV}/c^2$, and $C_2=(4.{200}_{-0.017}^{+0.010})\mathrm{GeV}/c^2$. The vertical (red) dashed line marks the upper limit of the fitting range.