Narrow Results

In this exploratory study, I present, for the first time, the implications of the charge symmetry breaking (CSB) that arise from the $u$ and $d$ quark-mass differences on gluon and sea quark distribution functions of the pion and kaon in the framework of the Nambu–Jona-Lasino (NJL) model, which is a quark-level chiral effective theory of QCD, with the help of the proper-time regularization scheme to simulate color confinement of QCD. From the analysis, one finds that the charge symmetry (CS) gluon distribution for the pion has a good agreement with the prediction results obtained from the recent lattice QCD simulation and JAM global fit QCD analysis at a higher scale of $Q^2=5$GeV². The size of the CSB effects on gluon and sea quark distributions for the pion with the realistic ratios of $m_u/m_d=0.5$ at $Q^2=5$GeV² are, respectively, estimated by 1.3% and 2.0% at $x\simeq 1$ in comparison with those for $m_u/m_d=1.0$, while those for the kaon are approximately about 0.3% and 0.5% at $x\simeq 1$, respectively. A remarkable result is found that the CSB effects on gluon distribution for the kaon are smaller than that for the pion, which has a similar prediction result as that for the CS case.

Charge symmetry breaking effects can be used as an experimental tool to study quark mass effects. Using recent high precision data from TRIUMF and IUCF an international theory collaboration is working on a consistent description within the framework of chiral pertubation theory. The WASA-at-COSY collaboration has started an experimental program extending the studies on the reaction dd → ⁴Heπ⁰ towards higher excess energies in order to provide necessary information on the contribution of p-waves. First preliminary results on the total cross section at Q = 60 MeV are presented.