Infrared finiteness and forward scattering

Abstract

Infrared divergences have long been heralded to cancel in sufficiently inclusive crosssections, according to the famous Kinoshita-Lee-Nauenberg theorem which mandates an initial and final state sum. While well-motivated, this theorem is much weaker than necessary: for finiteness, one need only sum over initial or final states. Moreover, the cancellation generically requires the inclusion of the forward scattering process. We provide a number of examples showing the importance of this revised understanding: in e + e − → Z at next-to-leading order, one can sum over certain initial and final states with an arbitrary number of extra photons, or only over final states with a finite number of photons, if forward scattering is included. For Compton scattering, infrared finiteness requires the indistinguishability of hard forward-scattered electrons and photons. This implies that in addition to experimental limits on the energy and angular resolution, there must also be an experimental limit on the momentum at which electric charge can be observed. Similar considerations are required to explain why the rate for γγ to scatter into photons alone is infrared divergent but the rate for γγ to scatter into photons or charged particles is finite. This new understanding sheds light on the importance of including degenerate initial states in physical predictions, the relevance of disconnected Feynman diagrams, the importance of dressing initial or final-state charged particles, and the quest to properly define the S matrix.

Unitarity and CP violation in leptogenesis at NLO: general considerations and top Yukawa contributions

“…Especially worth noticing are possible interferences between connected and disconnected diagrams, like L b with T b . Disconnected diagrams have also been found to be necessary to cancel infrared divergences, as demanded by unitarity [24] (see also [35][36][37]). This point will be discussed in somewhat more detail in the next section.…”

“…3). We have used the MS renormalization scheme with the scaleμ = M i to deal with the ultraviolet divergences, while the infrared ones have been 2 An insightful analysis about infrared divergences and the KLN theorem has been presented recently in [37]. In particular, the cancellation of infrared divergences in the joint sum of two-and three-body decays of a heavy neutral particle, was related to the unitarity requirement of probabilities adding up to a finite value (one!…”

Cutting multiparticle correlators down to size

“…While we use particle energies E i here to simplify the notation, in a hadron collider context these would be replaced with particle transverse momenta p T i . The EFPs are IRC-safe observables, which are guaranteed to be finite and computable in perturbative quantum field theory [19][20][21][22][23]. An observable is IRC safe if it is unchanged by the addition of a soft particle with E → 0 or by the collinear splitting of one particle into two with p µ → {λp µ , (1 − λ)p µ } for any λ ∈ [0, 1].…”

Conformally-regulated direct integration of the two-loop heptagon remainder

“…In [70], the six-point logarithm was shown to take the form 6 5 We have added a factor of 1/2 relative to [24] to match conventions for the coupling a. 6 nota bene: for six particles, (w 1 · · ·w 6 ) = (w 1 w 2 w 3 ) 2 , with w i more familiarly denoted {u,v,w}.…”

“…= Ω(2,4),(3,5) , I 2 := Ω (2,4),(3,6) , I 3 := Ω (2,5),(3,6) ,I 4 := Ω(7) (2,4),(3,7) , I 5 := Ω(7) (2,5),(3,7) . (2.12)…”