Bridgingp-wave π production and weak processes in few-nucleon systems with chiral perturbation theory

Abstract

I study an aspect of chiral perturbation theory (\ensuremath{\chi}PT) that enables one to ``bridge'' different reactions. That is, an operator fixed in one of the reactions can then be used to predict the other. For this purpose, I calculate the partial-wave amplitude for the $p$-wave pion production ($\mathit{pp}\ensuremath{\rightarrow}\mathit{pn}{\ensuremath{\pi}}^{+}$) using the pion production operator from the lowest and the next nonvanishing orders. The operator includes a contact operator whose coupling has been fixed using a matrix element of a low-energy weak process ($\mathit{pp}\ensuremath{\rightarrow}{\mathit{de}}^{+}{\ensuremath{\nu}}_{e}$). I find that this operator does not reproduce the partial-wave amplitude extracted from experimental data, showing that the bridging over the reactions with significantly different kinematics is not necessarily successful. I study the dependence of the amplitude on the various inputs such as the $\mathit{NN}$ potential, the $\ensuremath{\pi}N\ensuremath{\Delta}$ coupling, and the cutoff. I argue the importance of a higher-order calculation. To gain an insight into a higher-order calculation, I add a higher-order counter term to the operator used above and fit the couplings to both the low-energy weak process and the pion production. The energy dependence of the partial-wave amplitude for the pion production is described by the operator consistently with the data. However, I find a result that tells us to be careful about the convergence of the chiral expansion for the $\mathit{pp}\ensuremath{\rightarrow}\mathit{pn}{\ensuremath{\pi}}^{+}$ reaction.