The analytic structure of amplitudes on backgrounds from gauge invariance and the infra-red

Abstract

Gauge invariance and soft limits can be enough to determine the analytic structure of scattering amplitudes in certain theories. This prompts the question of how gauge invariance is connected to analytic structure in more general theories. Here we focus on QED in background plane waves. We show that imposing gauge invariance introduces new virtuality poles into internal momenta on which amplitudes factorise into a series of terms. Each term is gauge invariant, has a different analytic structure in external momenta, and exhibits a hard/soft factorisation. The introduced poles are dictated by infra-red behaviour, which allows us to extend our results to scalar Yukawa theory. The background is treated non-perturbatively throughout.in which D is the tensor structure of the photon propagator in some gauge, v is the

Classical and quantum double copy of back-reaction

“…This is because K µ E µν = 0 is not equivalent to the covariant gauge-fixing condition ∇ µ h µν in the background. In terms of spin-1 projectors (5.25), the dressed polarization tensor is 27) where P µνλσ is the same spin-2 projector that we encountered before in (4.21). The undressed polarization µν is assumed to be traceless with respect to the plane wave metric.…”

“…This allows for the exact treatment of arbitrarily strong backgrounds, ensures the existence of a well-defined Smatrix, and has recently enabled calculations approaching the generality achieved in trivial backgrounds. For instance, the singularity structure of amplitudes in QED on an electromagnetic plane wave background is tightly constrained by gauge invariance [27], and all-multiplicity formulae for tree-level MHV scattering of gluons and gravitons in chiral plane waves can be found [28].…”

“…the classical radiation field at infinity is: 27) where an irrelevant overall phase has been dropped.…”

Generation of quasi-monoenergetic positron beams in chirped laser fields

“…Employing a many-cycle laser pulse will lead to outgoing photon spectra similar to those in a monochromatic background [3,4]: well-defined harmonic fringes in lightfront momenta and emission angle. Collision with short laser pulses will lead to a broadening of outgoing particle harmonic peaks [5][6][7] and richer spectral structures: infrared structure [8,9], asymmetry in emission angle [10], and pronounced interference phenomena [11,12]. The spectral broadening can be attributed to the inhomogeneous effective mass of the charged particle moving in the intense laser pulse [13][14][15][16]: the variation of the effective mass modifies the velocity of the changed particle during the scattering [17][18][19][20].…”

Pulse envelope effect on nonlinear Compton scattering in electron-laser collisions

“…Interference effects in the nonlinear Compton process at the level of the pulse length have been studied in deltafunction pulses [30], in the shape of ultra-short pulses [31] and in double-pulses [32]. The IR part of the photon spectrum includes radiative loop corrections [33,34] and can receive significant contributions from much higher orders of expansion in dressed vertices [35][36][37][38][39][40], which has contributed to discussion of the Ritus-Narozhny conjecture [41][42][43][44]. The motivation for wanting to better understanding this part of the photon spectrum in nonlinear Compton scattering is in part due to upcoming highenergy particle-laser experiments such as E320 [45] at SLAC and LUXE [46] at DESY which, by virtue of using low-emittance traditionally-accelerated electron beams, will measure the nonlinear Compton process at a higher precision than has so far been possible.…”