Analytic Structure Of Amplitudes Research Articles

Leading Singularities in Higher-Derivative Yang–Mills Theory and Quadratic Gravity

In this work, we explore general leading singularities of one-loop amplitudes in higher-derivative Yang–Mills and quadratic gravity. These theories are known to possess propagators which contain quadratic and quartic momentum dependence, which leads to the presence of an unstable ghostlike resonance. However, unitarity cuts are not to be taken through unstable particles and therefore unitarity is still satisfied. On the other hand, this could engender issues when calculating leading singularities which are generalizations of unitarity cuts. Nevertheless, we will show with explicit examples how leading singularities are still well defined and accordingly they are able to capture relevant information on the analytic structure of amplitudes in such higher-derivative theories. We discuss some simple one-loop amplitudes which clarify these features.

The analytic structure of amplitudes on backgrounds from gauge invariance and the infra-red

Gauge invariance and soft limits can be enough to determine the analytic structure of scattering amplitudes in certain theories. This prompts the question of how gauge invariance is connected to analytic structure in more general theories. Here we focus on QED in background plane waves. We show that imposing gauge invariance introduces new virtuality poles into internal momenta on which amplitudes factorise into a series of terms. Each term is gauge invariant, has a different analytic structure in external momenta, and exhibits a hard/soft factorisation. The introduced poles are dictated by infra-red behaviour, which allows us to extend our results to scalar Yukawa theory. The background is treated non-perturbatively throughout.

ANALYTIC STRUCTURE OF AMPLITUDES IN GAUGE THEORIES WITH CONFINEMENT

For gauge theories with confinement, the analytic structure of amplitudes is explored. It is shown that the analytic properties of physical amplitudes are the same as those obtained on the basis of an effective theory involving only the composite, physical fields. The corresponding proofs of dispersion relations remain valid. Anomalous thresholds are considered. They are related to the composite structure of particles. It is shown that there are no such thresholds in physical amplitudes which are associated with confined constituents, like quarks and gluons in QCD. Unphysical amplitudes are considered briefly, using propagator functions as an example. For general, covariant, linear gauges, it is shown that these functions must have singularities at finite, real points, which may be associated with confined states.