Weak production of strange and charmed ground-state baryons in nuclei

We present results for the quasielastic weak production of $\mathrm{\Lambda }$ and $\mathrm{\Sigma }$ hyperons induced by $\overline{\nu }$ scattering off nuclei in the kinematical region of interest for accelerator neutrino experiments. We employ realistic hole spectral functions and we describe the propagation of the hyperons in the nuclear medium by means of a Monte Carlo cascade. The latter strongly modifies the kinematics and the relative production rates of the hyperons, leading to a nonvanishing ${\mathrm{\Sigma }}^{+}$ cross section, to a sizable enhancement of the $\mathrm{\Lambda }$ production and to a drastic reduction of the ${\mathrm{\Sigma }}^0$ and ${\mathrm{\Sigma }}^{-}$ distributions. We also compute the quasielastic weak ${\mathrm{\Lambda }}_c$ production cross section, paying special attention to estimate the uncertainties induced by the model dependence of the vacuum $n\to {\mathrm{\Lambda }}_c$ weak matrix element. In this regard, the recent BESIII measurements of the branching ratios of ${\mathrm{\Lambda }}_c\to \mathrm{\Lambda }{l}^{+}{\nu }_l$ ($l=e,\mu$) are used to benchmark the available theoretical predictions.

Figure 1

Differential cross section $d^2\sigma ({\overline{\nu }}_{\mu }+{}^{16}\mathrm{O}\to \mathrm{\Lambda }+{\mu }^{+}+X)/(dcos{\theta }^{\prime }d{q}^0)$ for $E_{\overline{\nu }}=1$ GeV and two fixed antimuon scattering angles, ${\theta }^{\prime }={20}^{\circ }$ and ${\theta }^{\prime }={70}^{\circ }$, shown in the top and bottom panels, respectively. The blue dashed, green dot-dashed, and orange short dashed lines correspond to the LFG, CBF-SF, and LDA-SF calculations, respectively. The red solid and black dotted curves stand for the LDA-SF and CBF-SF cross sections, when a mean-field potential is included in the energy spectrum of the hyperon. All the results have been obtained without employing the MCC.

Figure 2

The $d\sigma /d{Q}^2$ cross sections, per number of target protons or neutrons, for $\mathrm{\Lambda }$, ${\mathrm{\Sigma }}^{-}$, ${\mathrm{\Sigma }}^0$, and ${\mathrm{\Sigma }}^{+}$ production in oxygen and $E_{\overline{\nu }}=1$ GeV. For each type of hyperon, we show results from the LFG, CBF-SF, and LDA-SF approaches, which are depicted as blue dashed, black dotted, and red solid lines, respectively. The MCC and NO MCC labels denote whether the nuclear cascade algorithm has been applied or not.

Figure 3

Hyperon kinetic energy distributions, $d\sigma /d{E}_{\mathrm{kin}}^Y$, for $\mathrm{\Lambda }$, ${\mathrm{\Sigma }}^{-}$, ${\mathrm{\Sigma }}^0$, and ${\mathrm{\Sigma }}^{+}$ production in oxygen and $E_{\overline{\nu }}=1$ GeV. The different curves correspond to the LFG and CBF-SF predictions, with and without the inclusion of MCC effects. The mean-field potential corrections to the energy spectrum of the hyperon have not been included. The shaded areas correspond to $E_{\mathrm{kin}}^Y\le 50$ MeV.

Figure 4

Total cross sections for $\mathrm{\Lambda }$, ${\mathrm{\Sigma }}^{-}$, ${\mathrm{\Sigma }}^0$, and ${\mathrm{\Sigma }}^{+}$ production on ${}^{16}\mathrm{O}$ per active nucleon as a function of the energy of the incoming ${\overline{\nu }}_{\mu }$. As for the $\mathrm{\Lambda }$, ${\mathrm{\Sigma }}^{-}$, and ${\mathrm{\Sigma }}^0$ hyperons, we show results obtained with and without the MCC, while the ${\mathrm{\Sigma }}^{+}$ hyperon can only be produced through secondary collisions.

Figure 5

Total ${\mathrm{\Sigma }}^{-}$ and $\mathrm{\Lambda }$ production cross sections in ${}^{12}\mathrm{C}$, ${}^{16}\mathrm{O}$, and ${}^{40}\mathrm{Ca}$, as a function of the antineutrino energy. The results are obtained using the LDA-SF to model the initial nuclear state and the hyperon secondary collisions are accounted for through the MCC. The three lower (upper) curves correspond to the ${\mathrm{\Sigma }}^{-}$ ($\mathrm{\Lambda }$) production.

Figure 6

Differential cross section $d\sigma ({\nu }_{\mu }+{}^{16}\mathrm{O}\to {\mu }^{-}+{\mathrm{\Lambda }}_c^{+}+X)/d{q}^2$ (${10}^{-40}{\text{cm}}^2{\text{GeV}}^{-2}$) per nucleon as a function of $E_{\nu }$. The results are obtained within the LFG model for the initial nuclear state and assuming a free ${\mathrm{\Lambda }}_c$ propagation in the final state. The weak-transition form factors are taken from the RCQM of Ref. [12] and are extrapolated to the $Q^2>0$ region.

Figure 7

Form factors for the $n\to {\mathrm{\Lambda }}_c$ transition deduced from extrapolating to $Q^2=-q^2>0$ the results reported in Refs. [14] (LQCD), [12] (RCQM), and [10] (MBM and NRQM).

Figure 8

Total cross section, per number of neutrons, for the ${\nu }_{\mu }{+}^{16}\text{O}\to {\mu }^{-}+{\mathrm{\Lambda }}_c^{+}+X$ reaction, as a function of the incoming neutrino energy. The LFG model for the initial nuclear state is adopted and no FSI for the ${\mathrm{\Lambda }}_c$ are accounted for. In the left panel the curves represent the set of weak transition form factors analyzed in the text: LQCD [13, 14], NRHOQM [8], NRQM [10], and RCQM [9, 12]. The curves labeled as SU(3) represent the results attained multiplying the ${\mathrm{\Lambda }}_c\to \mathrm{\Lambda }$ form factors by the appropriate Clebsh-Gordan coefficient. The 68% CL bands for the LQCD predictions are obtained from the Gaussian covariance matrices of Refs. [13, 14]. In the right panel, we display results corresponding to the direct calculations of the ${\mathrm{\Lambda }}_c\to N$ form factors, the only exception being the SU(3) NRHOQM predictions for which they are not available. The “RCQM $\times 1.4$” curve represents the results of Ref. [12] rescaled by a factor 1.4, as inferred from the discussion on the ${\mathrm{\Lambda }}_c\to \mathrm{\Lambda }{e}^{+}{\nu }_e$ reported in the Appendix pp3.

Figure 9

${\mathrm{\Lambda }}_c\to \mathrm{\Lambda }{e}^{+}{\nu }_e$ differential decay width from NRHOQM [8], RCQM [9], MBM and NRQM [10], CQM approaches, and the LQCD simulation of Ref. [13].

Figure 10

Vector and axial form factors for the ${\mathrm{\Lambda }}_c\to \mathrm{\Lambda }$ transition calculated for the different models as detailed in Sec. 2b2. The form factors are multiplied by the Clebsh-Gordan coefficient $\sqrt{3/2}$ in order to estimate them for the $n\to {\mathrm{\Lambda }}_c$ transition, assuming unbroken SU(3) flavor symmetry. Negative values of $Q^2$ correspond to the kinematics of the ${\mathrm{\Lambda }}_c$ semileptonic decay, while $Q^2$ is positive for the ${\mathrm{\Lambda }}_c$ neutrino production.