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.
Highlights
JHEP05(2021)258 means is required to probe baryon-number violating new physics with the help of experimental data from proton decay searches
We have calculated the hadronic matrix elements of the full set of baryonnumber violating dimension-six SM effective field theory (SMEFT) operators (2.1) using light-cone sum rules (LCSRs) techniques
These hadronic matrix elements are needed to predict the rates of the main proton decay modes in GUTs, where a proton decays into a pseudoscalar meson and an anti-lepton
Summary
The main goal of the following analysis is to calculate the hadronic matrix element HΓΓ (pp, q) of the p → π0 transition, HΓΓ (pp, q)up(pp) ≡ π0(pπ)| abc dTa CP Γub P Γ uc |p(pp) ,. For an on-shell proton the above matrix element can be decomposed into two form factors as follows, HΓΓ (pp, q)up(pp) = iP Γ. To obtain a parametrisation of the hadronic matrix elements HΓΓ (pp, q) we insert a complete set of intermediate states that have the same quantum numbers as the proton into (2.6) and isolate the pole contribution of the proton to obtain the hadronic representation of the correlation function: ΠhΓaΓd(pp, q). Separating the ground-state contribution from the contribution of heavy states denoted by ρcΓoΓnt,α(s, Q2), the four spectral densities appearing in (2.9) can be cast into the form ρhΓaΓd,α(s, Q2) = iλpm2p δ s − m2p WΓαΓ (s, Q2) + ρcΓoΓnt,α(s, Q2) ,. A more detailed discussion on how to fix s0 is provided in section 4, but ideally it is chosen low enough to cover even the lightest excitation, which is the Roper resonance with a mass of 1.44 GeV
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
