Gauge invariance from on-shell massive amplitudes and tree-level unitarity - INSPIRE

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Gauge invariance from on-shell massive amplitudes and tree-level unitarity

Da Liu
(
- UC, Davis, QMAP
)
,
Zhewei Yin
(
- Uppsala U.
)

Apr 27, 2022

50 pages

Published in:

Phys.Rev.D 106 (2022) 7, 076003

Published: Oct 1, 2022

e-Print:

2204.13119 [hep-th]

DOI:

10.1103/PhysRevD.106.076003 (publication)

Report number:

UUITP-23/22

View in:

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Abstract: (APS)

We study the three-particle and four-particle scattering amplitudes for an arbitrary, finite number of massive scalars, spinors and vectors by employing the on-shell massive spinor formalism. We consider the most general three-particle amplitudes with energy-growing behavior at most of

O (E)

. This is the special case of the requirement of tree unitarity, which states that the

N

-particle scattering amplitudes at tree level should grow at most as

O (E^{4 - N})

in the high-energy hard-scattering limit, i.e., at fixed nonzero angles. Then the factorizable parts of the four-particle amplitudes are calculated by gluing the on-shell three-particle amplitudes together and utilizing the fact that tree-level amplitudes have only simple poles. The contact parts of the four-particle amplitudes are further determined by tree unitarity, which also puts strong constraints on the possible allowed three-particle coupling constants and the masses. The derived relations among them converge to the predictions of gauge invariance in the UV theory. This provides a purely on-shell understanding of spontaneously broken gauge theories.

Note:

39 pages + appendices; matched to the published version in v2

invariance: gauge
energy: high
spinor: massive
unitarity
tree approximation
scattering amplitude
gauge field theory
spontaneous symmetry breaking
hard scattering
pole

References(105)

Figures(0)

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