On the kinematic algebra for BCJ numerators beyond the MHV sector - INSPIRE

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On the kinematic algebra for BCJ numerators beyond the MHV sector

Gang Chen
(
- Zhejiang Normal U. and
- Uppsala U. and
- Queen Mary, U. of London
)
,
Henrik Johansson
(
- Uppsala U. and
- Nordita and
- Royal Inst. Tech., Stockholm
)
,
Fei Teng
(
- Uppsala U.
)
,
Tianheng Wang
(
- Uppsala U. and
- Nanjing U. and
- Humboldt U., Berlin
)

Jun 25, 2019

44 pages

Published in:

JHEP 11 (2019) 055

Published: Nov 11, 2019

e-Print:

1906.10683 [hep-th]

DOI:

10.1007/JHEP11(2019)055

Report number:

UUITP-22/19,
NORDITA 2019-064,
HU-EP-19/17,
QMUL-PH-19-14

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Abstract: (Springer)

The duality between color and kinematics present in scattering amplitudes of Yang-Mills theory strongly suggests the existence of a hidden kinematic Lie algebra that controls the gauge theory. While associated BCJ numerators are known on closed forms to any multiplicity at tree level, the kinematic algebra has only been partially explored for the simplest of four-dimensional amplitudes: up to the MHV sector. In this paper we introduce a framework that allows us to characterize the algebra beyond the MHV sector. This allows us to both constrain some of the ambiguities of the kinematic algebra, and better control the generalized gauge freedom that is associated with the BCJ numerators. Specifically, in this paper, we work in dimension-agnostic notation and determine the kinematic algebra valid up to certain 𝒪 ((εi · εj )

^{2}

) terms that in four dimensions compute the next-to-MHV sector involving two scalars. The kinematic algebra in this sector is simple, given that we introduce tensor currents that generalize standard Yang-Mills vector currents. These tensor currents control the generalized gauge freedom, allowing us to generate multiple different versions of BCJ numerators from the same kinematic algebra. The framework should generalize to other sectors in Yang-Mills theory.

Note:

43 pages, 4 figures

Scattering Amplitudes
Gauge Symmetry
gauge field theory: Yang-Mills
scattering amplitude
kinematics
tree approximation
multiplicity
duality
color
algebra

References(95)

Figures(0)

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