New insights into soft gluons and gravitons

Abstract

The study of gluon radiation in QCD, in the limit of small ("soft") momentum, remains an active research area, with a variety of phenomenological and theoretical applications. Soft gluon emission leads to large logarithms in perturbation theory which have to be summed up to all orders in the coupling, and also governs the structure of infrared singularities. Recently, new techniques and mathematical structures have been discovered, which enhance our understanding of these allorder properties. This contribution will review a number of key topics, including the relationship between QCD and gravity.

Soft photon theorem for high energy amplitudes in Yukawa and scalar theories

“…The radiative jet functions are derived from the matrix element definitions above by inserting an electromagnetic current operator [40]. For example, the elastic jet function in (34) becomes the radiative leading jet…”

“…Soft theorems in gravity and gauge theories have also been studied from several other viewpoints, including scattering equations [25][26][27], string theory techniques [28][29][30], path integral and diagrammatic methods [31][32][33][34][35][36][37][38], and effective field theory [39]. In particular, Ref.…”

Soft graviton emission at high and low energies in Yukawa and scalar theories

“…with H the hard function of the elastic amplitude as in (26). Next, we may proceed with the expansion about the elastic configuration following (22) and (23). Consequently, the hard part is no longer expanded only in q, but also in the ξ i 's,…”

“…where we have used the kinematics relations (21) to (23). The "•" notation stands for a contraction between matching Minkowski indices, with the understanding that q is always contracted with ∂ ∂k i and ξ j is always paired with ∂ ∂k j .…”

“…While the Ward identities familiar from gauge invariance are adequate to derive many of these results [4], and they may reflect other symmetries as well [2], the role of loop corrections, especially in the high-energy and massless limits has received a lot of further study [5][6][7][8][9][10]. Other approaches to the study of soft theorems include scattering equations [11][12][13], string theory methods [14][15][16][17], the one particle irreducible effective action [18,19], and path integral and diagrammatic analyses [20][21][22][23][24][25][26][27].…”