Worldline master formulas for the dressed electron propagator. Part I. Off-shell amplitudes

Abstract

In the first-quantised worldline approach to quantum field theory, a longstanding problem has been to extend this formalism to amplitudes involving open fermion lines while maintaining the efficiency of the well-tested closed-loop case. In the present series of papers, we develop a suitable formalism for the case of quantum electrodynamics in vacuum (part one and two) and in a constant external electromagnetic field (part three), based on second-order fermions and the symbol map. We derive this formalism from standard field theory, but also give an alternative derivation intrinsic to the worldline theory. In this first part, we use it to obtain a Bern-Kosower type master formula for the fermion propagator, dressed with N photons, in terms of the "N -photon kernel," where offshell this kernel appears also in "subleading" terms involving only N − 1 of the N photons. Although the parameter integrals generated by the master formula are equivalent to the usual Feynman diagrams, they are quite different since the use of the inverse symbol map avoids the appearance of long products of Dirac matrices. As a test we use the N = 2 case for a recalculation of the one-loop fermion self energy, in D dimensions and arbitrary covariant gauge, reproducing the known result. We find that significant simplification can be achieved in this calculation by choosing an unusual momentum-dependent gauge parameter.

Combined analysis of neutrino decoherence at reactor experiments

“…These experiments are characterized, to a very good approximation, by a single, well-known baseline. In [3], we found, for RENO and Daya Bay data, nontrivial correlations between sin 2 θ 13 , |∆m 2 31 | and the decoherence parameter σ. Future JUNO data, in the absence of strong decoherence effects, are expected to significantly weaken these correlations.…”

“…We refer to [3] for a more careful discussion of these parameters and their effects. If no loss of coherence occurs during neutrino propagation, ξ jk (= ξ kj ) = 0.…”

“…If no loss of coherence occurs during neutrino propagation, ξ jk (= ξ kj ) = 0. We further define the coherence lengths as [3,7,11,18]…”

“…In the near future, the Jiangmen Underground Neutrino Observatory (JUNO) is expected to extract the most precise measurement of sin 2 2θ 12 and, perhaps, determine the neutrino mass ordering (sign of ∆m 2 31 ) [2]. In [3], we argued that reactor neutrino experiments can also be used to place interesting constraints on how coherent nuclear reactors are as sources of antineutrinos. There,…”

The dimension-shift conjecture for one-loop amplitudes

“…Systematic rules which generalise a string-based computation of field-theory amplitudes were developed by Bern and Kosower [31], and it was shown that they can also be directly derived from the Schwinger worldline formalism as derived by Bern and Dunbar [32]. As a computational alternative to Feynman diagrams worldline approaches maintain significant interest [33,34] providing a context to study asymptotic states in scattering problems [35], and for computing gravitational-radiation contributions to black-hole scattering [36].…”