RG of GR from on-shell amplitudes

Abstract

We study the renormalization group of generic effective field theories that include gravity. We follow the on-shell amplitude approach, which provides a simple and efficient method to extract anomalous dimensions avoiding complications from gauge redundancies. As an invaluable tool we introduce a modified helicity $$ \tilde{h} $$ h ˜ under which gravitons carry one unit instead of two. With this modified helicity we easily explain old and uncover new non-renormalization theorems for theories including gravitons. We provide complete results for the one-loop gravitational renormalization of a generic minimally coupled gauge theory with scalars and fermions and all orders in MPl, as well as for the renormalization of dimension-six operators including at least one graviton, all up to four external particles.

Towards the renormalisation of the Standard Model effective field theory to dimension eight: Bosonic interactions II

“…(4.2) at some heavy scale Λ at which they are generated at tree-level, the positivity bounds are violated at scales μ < Λ upon evolving with the RGEs triggered by λ, g 1 and g 2 . (Not so by gravity [18]. )…”

Amplitude bases in generic EFTs

“…which resemble the fully massless identities (13). Classifying the structures up to equations of motion means that we can put forward the identification…”

“…The structure s n 13 [13] 2 [24] 2 does not belong to our basis and we have to re-write it as a linear combination of elements of our basis. We can do this using the algorithm presented in Section 2 and we always verify such relations on rational kinematics, as presented in Appendix B.…”

“…For instance, such methods have been applied to compute the anomalous dimension in generic EFTs [6][7][8][9][10][11][12][13][14], and to understand the patterns of zeros in the one-loop anomalous dimension matrix for dimension-six operators in the SMEFT [15][16][17] and in Wilson coefficients when integrating out heavy modes [18]. In the study of gravitational binary systems, scattering amplitude techniques allowed to compute the conservative two-body scattering dynamics up to O(G 4 ) in all orders in velocity [19][20][21][22][23][24][25][26][27][28][29], and to lower orders in G including spin effects [22,[30][31][32][33][34][35][36][37], tidal effects [38][39][40][41][42] and higher-derivative interactions [43,44].…”

A Green's basis for the bosonic SMEFT to dimension 8

“…3. While helicity-amplitude methods have been proved powerful to address the computation of some anomalous dimensions strictly on-shell [6][7][8][9][10][11][12][13][14][15], to the best of our knowledge they are not yet mature enough to be used in a number of cases. These include renormalisation triggered by operators with smaller number of legs than the resulting amplitude or mixing of amplitudes of different mass dimensions.…”