Light-cone sum rules for proton decay

Abstract

We estimate the form factors that parametrise the hadronic matrix elements of proton-to-pion transitions with the help of light-cone sum rules. These form factors are relevant for semi-leptonic proton decay channels induced by baryon-number violating dimension-six operators, as typically studied in the context of grand unified theories. We calculate the form factors in a kinematical regime where the momentum transfer from the proton to the pion is space-like and extrapolate our final results to the regime that is relevant for proton decay. In this way, we obtain estimates for the form factors that show agreement with the state-of-the-art calculations in lattice QCD, if systematic uncertainties are taken into account. Our work is a first step towards calculating more involved proton decay channels where lattice QCD results are not available at present.

Semi-leptonic three-body proton decay modes from light-cone sum rules

“…Convergence criteria are now applied to the remaining LCSRs in order to determine the Borel window for each Π α . Notice that compared to the correlator studied for GUT-like proton decay in [19] the hadronic representation of the correlation function (3.6) comprises a larger number of independent Lorentz structures. This feature leads to simpler analytic LCSR expressions for the correlation functions Π α , but it also renders the numerical impact of the dimension-five condensate qg s G • σq with G • σ ≡ G µν σ µν larger than in the GUT case.…”

“…In what follows we discuss the necessary steps to calculate the hadronic tensor H µν (p p , q) with the help of LCSRs in QCD. We employ the notation and the conventions introduced in our earlier article [19]. The starting point for the sum rules is the correlation function…”

“…The derivation of the QCD results for the LCSRs proceeds in full analogy to section 3 of our earlier work [19] to which we refer the interested reader for all technical details. The analytic expressions for the QCD correlation functions relevant in the context of this article can be found in appendix B.…”

“…This feature leads to simpler analytic LCSR expressions for the correlation functions Π α , but it also renders the numerical impact of the dimension-five condensate qg s G • σq with G • σ ≡ G µν σ µν larger than in the GUT case. As a result the LCSRs analysed below will have larger uncertainties than those that have been studied in [19]. In the following, we will use the LCSRs for Π S , Π A 1 ,…”

“…Model estimates of three-body final-state proton decay rates are therefore available only for selected modes [18] or rely on naive dimensional analysis and phase-space arguments [3,4]. In our recent article [19] we have shown that by employing light-cone sum rules (LCSRs) [20][21][22][23][24][25] it is possible to reproduce the LQCD results for the hadronic matrix elements relevant for GUT-like proton decay. The goal of this work is to apply the LCSRs formalism developed in the latter publication to the case of semileptonic three-body proton decay processes.…”