Noncommutative fermions and quarkonia decays

Abstract

The recent introduction of a deformed non-minimal version of the noncommutative Standard Model in the enveloping-algebra approach, having a one-loop renormalisable gauge sector involving a higher order gauge term, motivates us to consider the possibility of extending the fermion sector with additional deformations, i.e. higher order fermionic terms. Since the renormalisability properties of the fermion sector of the model are not yet fully known, we work with an effective fermion lagrangian which includes noncommutative higher order terms involving a contraction with the noncommutative $θ$ tensor aside from the star products, so that these terms annihilate in the commutative limit. Some of these terms violate CPT in the weak sector, and some violate CP in the strong and hypercharge sectors. We apply this framework to the reevaluation of the decay rates of quarkonia (\bar{q}q_{1} = J/ψ, Υ) into two photons. These decays, which are forbidden in the ordinary Standard Model, had been previously studied as possible signals for noncommutativity, but not in the framework of the better behaved deformed non-minimal version of the noncommutative Standard Model. Weak CPT or strong-hypercharge CP violating interactions do not contribute to the result. If the parameters of the model take natural values, for the vast majority of configurations the resulting branching ratios are enhanced with respect to their values in the minimal version of the noncommutative Standard Model. Also for more than half of the parameter space, the rates are larger than the maximal rates that were calculated in the undeformed version of the non-minimal noncommutative Standard Model. Tuning the dimensionless parameters the predicted branching ratios can fall within the current experimental bounds.