Double Copies of Fermions as Matter that Interacts Only Gravitationally

157

182

The duality between color and kinematics was originally observed for purely adjoint massless gauge theories, and later found to hold even after introducing massive fermionic and scalar matter in arbitrary gauge-group representations. Such a generalization was critical for obtaining both loop amplitudes in pure Einstein gravity and realistic gravitational matter from the double copy. In this paper we elaborate on the double copy that yields amplitudes in gravitational theories coupled to flavored massive matter with spin, which is relevant to the problems of black-hole scattering and gravitational waves. Our construction benefits from making the little group explicit for the massive particles, as shown on lower-point examples. For concreteness, we focus on the double copy of QCD with massive quarks, for which we work out the gravitational Lagrangian up to quartic scalar and vector-scalar couplings. We find new gauge-invariant double-copy formulae for tree-level amplitudes with two distinct-flavor pairs of matter and any number of gravitons. These are similar to, but inherently different from, the well-known Kawai-Lewellen-Tye formulae, since the latter only hold for the double copy of purely adjoint gauge theories.

Section: Bcj Relations and Klt-like Double Copymentioning

confidence: 99%

“…Inserting it into the double-copy relation M n,k = KβÃβ + K βÃ β , we see that the double copy takes a KLT-like form 13 [66] M n,k = AᾱSᾱβÃβ.…”

Section: Bcj Relations and Klt-like Double Copymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Double copy for massive quantum particles with spin

Johansson

Ochirov

2019

157

182

“…It also enables the construction from generalized double copy [18,20,21]. It would be interesting to connect the BCJ and KLT relations to those in the S-matrix with fundamental matter [16,[80][81][82][83][84][85] which we leave for future work.…”

Section: Amplitude Relationsmentioning

confidence: 99%

Gravitational radiation from color-kinematics duality

Shen¹

2018

140

118

We perturbatively calculate classical radiation in Yang-Mills theory and dilaton gravity, to next-to-leading order in couplings. The radiation is sourced by the scattering of two relativistic massive scalar sources with the dynamical effect taken into account, corresponding to the post-Minkowskian regime in gravity. We show how to arrange the Yang-Mills radiation such that the duality between color and kinematics is manifest, including the three-term Jacobi identity. The search for duality-satisfying expressions exploits an auxiliary bi-adjoint scalar theory as a guide for locality. The double copy is obtained by replacing the color factors in Yang-Mills with kinematic counterparts, following Bern-Carrasco-Johansson construction in S-matrix. On the gravity side, the radiation is directly computed at the third post-Minkowskian order with massive sources. We find perfect agreement between observables in dilaton gravity and the Yang-Mills double copy. This non-trivially generalizes the leading-order rules by Goldberger and Ridgway. For the first time, the kinematic Jacobi identity appears beyond field-theory S-matrix, suggesting that the color-kinematics duality holds more generally. Our results offer a path for simplifying analytical calculations in post-Minkowskian regime.

“…We derive KLT-type relations for tree-level amplitudes of biadjoint and bicolor theories using the color-factor symmetry possessed by these theories.arXiv:1802.01620v2 [hep-th] 19 Feb 2018 12 Earlier work on extensions of KLT relations to more general gravitational amplitudes includes refs. [33,[45][46][47]. 13 Recall that for k = 2 we must let sij → s ij in eq.…”

mentioning

confidence: 99%

KLT-type relations for QCD and bicolor amplitudes from color-factor symmetry

Brown

Naculich

2018

Color-factor symmetry is used to derive a KLT-type relation for tree-level QCD amplitudes containing gluons and an arbitrary number of massive or massless quarkantiquark pairs, generalizing the expression for Yang-Mills amplitudes originally postulated by Bern, De Freitas, and Wong. An explicit expression is given for all amplitudes with two or fewer quark-antiquark pairs in terms of the (modified) momentum kernel.We also introduce the bicolor scalar theory, the "zeroth copy" of QCD, containing massless biadjoint scalars and massive bifundamental scalars, generalizing the biadjoint scalar theory of Cachazo, He, and Yuan. We derive KLT-type relations for tree-level amplitudes of biadjoint and bicolor theories using the color-factor symmetry possessed by these theories.