Showing 1 - 10 of 10 Items

Date: 2013-04-19

Creator: Stephen G. Naculich, Horatiu Nastase, Howard J. Schnitzer

Access: Open access

The infrared singularities of gravitational amplitudes are one-loop exact, in that higher-loop divergences are characterized by the exponential of the one-loop divergence. We show that the contributions to SU(N) gauge-theory amplitudes that are mostsubleading in the 1/N expansion are also one-loop exact, provided that the dipole conjecture holds. Possible corrections to the dipole conjecture, beginning at three loops, could violate one-loop-exactness, though would still maintain the absence of collinear divergences. We also demonstrate a relation between L-loop four-point N = 8 supergravity and mostsubleading-color N = 4 SYM amplitudes that holds for the two leading IR divergences, (Formula presented.) and (Formula presented.), but breaks down at (Formula presented.).

Date: 2016-11-01

Creator: Robert W. Brown, Stephen G. Naculich

Access: Open access

Tree-level n-point gauge-theory amplitudes with n − 2k gluons and k pairs of (massless or massive) particles in the fundamental (or other) representation of the gauge group are invariant under a set of symmetries that act as momentum-dependent shifts on the color factors in the cubic decomposition of the amplitude. These symmetries lead to gauge-invariant constraints on the kinematic numerators. They also directly imply the BCJ relations among the Melia-basis primitive amplitudes previously obtained by Johansson and Ochirov.

Date: 2016-10-01

Creator: Robert W. Brown, Stephen G. Naculich

Access: Open access

We introduce a new set of symmetries obeyed by tree-level gauge-theory amplitudes involving at least one gluon. The symmetry acts as a momentum-dependent shift on the color factors of the amplitude. Using the radiation vertex expansion, we prove the invariance under this color-factor shift of the n-gluon amplitude, as well as amplitudes involving massless or massive particles in an arbitrary representation of the gauge group with spin zero, one-half, or one. The Bern-Carrasco-Johansson relations are a direct consequence of this symmetry. We also introduce the cubic vertex expansion of an amplitude, and use it to derive a generalized-gauge-invariant constraint on the kinematic numerators of the amplitude. We show that the amplitudes of the bi-adjoint scalar theory are invariant under the color-factor symmetry, and use this to derive the null eigenvectors of the propagator matrix. We generalize the color-factor shift to loop level, and prove the invariance under this shift of one-loop n-gluon amplitudes in any theory that admits a color-kinematic-dual representation of numerators. We show that the one-loop color-factor symmetry implies known relations among the integrands of one-loop color-ordered amplitudes.

Date: 2017-01-01

Creator: A. Luna, S. Melville, S. G. Naculich, C. D. White

Access: Open access

We examine the Regge (high energy) limit of 4-point scattering in both QCD and gravity, using recently developed techniques to systematically compute all corrections up to next-to-leading power in the exchanged momentum i.e. beyond the eikonal approximation. We consider the situation of two scalar particles of arbitrary mass, thus generalising previous calculations in the literature. In QCD, our calculation describes power-suppressed corrections to the Reggeisation of the gluon. In gravity, we confirm a previous conjecture that next-to-soft corrections correspond to two independent deflection angles for the incoming particles. Our calculations in QCD and gravity are consistent with the well-known double copy relating amplitudes in the two theories.

Date: 2020-03-01

Creator: Paolo Di Vecchia, Stephen G. Naculich, Rodolfo Russo, Gabriele Veneziano, Chris D., White

Access: Open access

High-energy massless gravitational scattering in N = 8 supergravity was recently analyzed at leading level in the deflection angle, uncovering an interesting connection between exponentiation of infrared divergences in momentum space and the eikonal exponentiation in impact parameter space. Here we extend that analysis to the first non trivial sub-leading level in the deflection angle which, for massless external particles, implies going to two loops, i.e. to third post-Minkowskian (3PM) order. As in the case of the leading eikonal, we see that the factorisation of the momentum space amplitude into the exponential of the one-loop result times a finite remainder hides some basic simplicity of the impact parameter formulation. For the conservative part of the process, the explicit outcome is infrared (IR) finite, shows no logarithmic enhancement, and agrees with an old claim in pure Einstein gravity, while the dissipative part is IR divergent and should be regularized, as usual, by including soft gravitational bremsstrahlung. Finally, using recent three-loop results, we test the expectation that eikonal formulation accounts for the exponentiation of the lower-loop results in the momentum space amplitude. This passes a number of highly non-trivial tests, but appears to fail for the dissipative part of the process at all loop orders and sufficiently subleading order in ϵ, hinting at some lack of commutativity of the relevant infrared limits for each exponentiation.

Date: 2014-09-01

Creator: Stephen G. Naculich

Access: Open access

Abstract: We generalize the scattering equations to include both massless and massive particles. We construct an expression for the tree-level n-point amplitude with n − 2 gluons or gravitons and a pair of massive scalars in arbitrary spacetime dimension as a sum over the (n − 3)! solutions of the scattering equations, à la Cachazo, He, and Yuan. We derive the BCJ relations obeyed by these massive amplitudes.

Date: 2014-01-01

Creator: Stephen G. Naculich

Access: Open access

Inspired by recent developments on scattering equations, we present a constructive procedure for computing symmetric, amplitude-encoded, BCJ numerators for n-point gauge-theory amplitudes, thus satisfying the three virtues identified by Broedel and Carrasco. We also develop a constructive procedure for computing symmetric, amplitude-encoded dual-trace functions τ for n-point amplitudes. These can be used to obtain symmetric kinematic numerators that automatically satisfy color-kinematic duality. The S n symmetry of n-point gravity amplitudes formed from these symmetric dual-trace functions is completely manifest. Explicit expressions for four- and five-point amplitudes are presented. © 2014 The Author(s).

Date: 2021-02-01

Creator: Stephen G. Naculich

Access: Open access

We examine in detail the structure of the Regge limit of the (nonplanar) N = 4 SYM four-point amplitude. We begin by developing a basis of color factors Cik suitable for the Regge limit of the amplitude at any loop order, and then calculate explicitly the coefficients of the amplitude in that basis through three-loop order using the Regge limit of the full amplitude previously calculated by Henn and Mistlberger. We compute these coefficients exactly at one loop, through O(ϵ 2) at two loops, and through O(ϵ) at three loops, verifying that the IR-divergent pieces are consistent with (the Regge limit of) the expected infrared divergence structure, including a contribution from the three-loop correction to the dipole formula. We also verify consistency with the IR-finite NLL and NNLL predictions of Caron-Huot et al. Finally we use these results to motivate the conjecture of an all-orders relation between one of the coefficients and the Regge limit of the N = 8 supergravity four-point amplitude.

Date: 2018-03-01

Creator: Robert W. Brown, Stephen G. Naculich

Access: Open access

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 quark-antiquark 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.

Date: 2015-09-26

Creator: Stephen G. Naculich

Access: Open access

Abstract: In the formulation of Cachazo, He, and Yuan, tree-level amplitudes for massless particles in gauge theory and gravity can be expressed as rational functions of the Lorentz invariants ka · kb, ϵa · kb, and ϵa · ϵb, valid in any number of spacetime dimensions. We use dimensional reduction of higher-dimensional amplitudes of particles with internal momentum κ to obtain amplitudes for massive particles in lower dimensions. In the case of gauge theory, we argue that these massive amplitudes belong to a theory in which the gauge symmetry is spontaneously broken by an adjoint Higgs field. Consequently, we show that tree-level n-point amplitudes containing massive vector and scalar bosons in this theory can be obtained by simply replacing ka · kb with ka · kb − κaκb in the corresponding massless amplitudes, where the masses of the particles are given by |κa|.