Abstract
We use the point-particle effective field theory (PPEFT) framework to describe particle-conversion mediated by a flavour-changing coupling to a point-particle. We do this for a toy model of two non-relativistic scalars coupled to the same point-particle, on which there is a flavour-violating coupling. It is found that the point-particle couplings all must be renormalized with respect to a radial cut-off near the origin, and it is an invariant of the flow of the flavour-changing coupling that is directly related to particle-changing cross-sections. At the same time, we find an interesting dependence of those cross-sections on the ratio k_out/k_in of the outgoing and incoming momenta, which can lead to a 1/k_in enhancement in certain regimes. We further connect this model to the case of a single-particle non-self-adjoint (absorptive) PPEFT, as well as to a PPEFT of a single particle coupled to a two-state nucleus. These results could be relevant for future calculations of any more complicated reactions, such as nucleus-induced electron-muon conversions, monopole catalysis of baryon number violation, as well as nuclear transfer reactions.
Highlights
It is often the case that physically interesting situations involve a hierarchy of characteristic scales
Solar system dynamics involve a variety of length scales, such as the sizes of the stars and planets involved, as well as the sizes of the orbits
In the realm of quantum field theory, this insight has led to the development of the highly successful effective field theories, which can reduce the complexity of quantum field theories by restricting to parameter subspaces in which an appropriate Taylor expansion can be used to put the theory into a simpler form
Summary
It is often the case that physically interesting situations involve a hierarchy of characteristic scales. For example, the nucleus carried two accessible energy states, say E↑ = M + /2 and E↓ = M − /2 (where ≪ M is some small excitation energy), two channels of interaction could be a single bulk particle interacting with each of the nuclear energy eigenstates In this case the “flavor-violating” cross section is again (1.3), where k1 and k2 are the incoming and outgoing singleparticle momenta, and k2/k1 = kout/kin = (k2in ± 2m )/k2in with the ± corresponding to the bulk particle impinging on a nucleus in the ground state (−) or the excited state (+), and where m is the mass of the single bulk species (recall we work in the non-recoil limit).
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