Color ordering in QCD

Self Cite

A self-consistent exposition of the theory of tree-level superamplitudes of the 4d N = 4 and 6d N = (1, 1) maximally supersymmetric Yang-Mills theories is provided. In 4d we work in non-chiral superspace and construct the superconformal and dual superconformal symmetry generators of the N = 4 SYM theory using the non-chiral BCFW recursion to prove the latter. In 6d we provide a complete derivation of the standard and hidden symmetries of the tree-level superamplitudes of N = (1, 1) SYM theory, again using the BCFW recursion to prove the dual conformal symmetry. Furthermore, we demonstrate that compact analytical formulae for tree-superamplitudes in N = (1, 1) SYM can be obtained from a numerical implementation of the supersymmetric BCFW recursion relation. We derive compact manifestly dual conformal representations of the five-and six-point superamplitudes as well as arbitrary multiplicity formulae valid for certain classes of superamplitudes related to ultra-helicity-violating massive amplitudes in 4d. We study massive tree superamplitudes on the Coulomb branch of the N = 4 SYM theory from dimensional reduction of the massless superamplitudes of the six-dimensional N = (1, 1) SYM theory. We exploit this correspondence to construct the super-Poincaré and enhanced dual conformal symmetries of massive tree superamplitudes in N = 4 SYM theory which are shown to close into a finite dimensional algebra of Yangian type. Finally, we address the fascinating possibility of uplifting massless 4d superamplitudes to 6d massless superamplitudes proposed by Huang. We confirm the uplift for multiplicities up to eight but show that finding the uplift is highly non-trivial and in fact not of a practical use for multiplicities larger than five.

Section: Discussionmentioning

confidence: 99%

Section: Jhep01(2015)098mentioning

confidence: 99%

See 1 more Smart Citation

From six to four and more: massless and massive maximal super Yang-Mills amplitudes in 6d and 4d and their hidden symmetries

Plefka

Schuster

Verschinin

2015

Self Cite

“…Tree amplitudes in QCD with any number of external quarks can be decomposed systematically into gauge-invariant primitive amplitudes with a fixed cyclic ordering [2,16,17]. Let us consider a tree-level primitive QCD amplitude with n external particles, out of which n q particles are quarks, n q particles are anti-quarks and n g particles are gluons.…”

Section: Overviewmentioning

confidence: 99%

Proof of the fundamental BCJ relations for QCD amplitudes

Cruz

Kniss

Weinzierl

2015

Abstract:The fundamental BCJ-relation is a linear relation between primitive tree amplitudes with different cyclic orderings. The cyclic orderings differ by the insertion place of one gluon. The coefficients of the fundamental BCJ-relation are linear in the Lorentz invariants 2p i p j . The BCJ-relations are well established for pure gluonic amplitudes as well as for amplitudes in N = 4 super-Yang-Mills theory. Recently, it has been conjectured that the BCJ-relations hold also for QCD amplitudes. In this paper we give a proof of this conjecture. The proof is valid for massless and massive quarks.

“…These formulae were tested numerically using S@M [38] and GGT [39,40] for a wide range of MHV, NMHV and NNMHV amplitudes from lengths 6 through 14. Importantly these formulae do not have a "local" expression, i.e.…”

Section: Jhep07(2015)135mentioning

confidence: 99%

Double-soft limits of gluons and gravitons

Klose

McLoughlin

Nandan

et al. 2015

The double-soft limit of gluon and graviton amplitudes is studied in four dimensions at tree level. In general this limit is ambiguous and we introduce two natural ways of taking it: a consecutive double-soft limit where one particle is taken soft before the other and a simultaneous limit where both particles are taken soft uniformly. All limits yield universal factorisation formulae which we establish by BCFW recursion relations down to the subleading order in the soft momentum expansion. These formulae generalise the recently discussed subleading single-soft theorems. While both types of limits yield identical results at the leading order, differences appear at the subleading order. Finally, we discuss double-scalar emission in N = 4 super Yang-Mills theory. These results should be of use in establishing the algebraic structure of potential hidden symmetries in the quantum gravity and Yang-Mills S-matrix.