Person:

Sajjad, Aqil

We describe work on the construction of an effective field theory on a spherical light shell. The motivation arises from classical electromagnetism: If a collision produces charged particles with zero net charge emerging simultaneously from a point and instantaneously accelerating to the speed of light, then the electromagnetic fields due to these charges lie entirely on a spherical shell expanding at the speed of light. We show that this also applies to classical color radiation from high-energy collisions that produce colored particles. Specifically, the color fields produced in such a process are associated with a non-linear σ-model on the 2D light shell with specific symmetry-breaking terms. The quantum version of such a picture exhibits asymptotic freedom and should therefore be a useful starting point for a light-shell effective theory for QCD. We start in the simplified context of zero-flavor scalar quantum electrodynamics. Our effective theory has 3 major ingredients: breaking down the fields into soft and hard sectors with the large energy of the hard fields in the radial direction scaled out, a special gauge called light-shell gauge in which the picture simplifies, and a gauge-invariant source defined on a spherical light shell having infinitesimal radius. We match the fields between the effective theory and the full theory, meaning zero-flavor scalar QED. This allows us to compute the amplitude for the production of any number of scalars from the gauge-invariant source. We then find the tree-level amplitude for the emission of a photon using our effective theory and show that our result agrees with the full theory. To calculate loop effects in our effective theory, we need the photon propagator in light-shell gauge. We derive this propagator and use it to calculate the 1-loop correction to the amplitude for the production of a scalar and anti-scalar pair arising from virtual photon effects. This reduces to a pair of purely angular integrals in the effective theory and reproduces the familiar double logs of the full theory subject to an appropriate interpretation of an angular cutoff.

We discuss our work toward the construction of a light-shell effective theory (LSET), an effective field theory for describing the matter emerging from high-energy collisions and the accompanying radiation. We work in the highly simplified venue of 0-flavor scalar quantum electrodynamics, with a gauge invariant product of scalar fields at the origin of space-time as the source of high-energy charged particles. Working in this simple gauge theory allows us to focus on the essential features of LSET. We describe how the effective theory is constructed and argue that it can reproduce the full theory tree-level amplitude. We study the 1-loop radiative corrections in the LSET and suggest how the leading double-logs in the full theory at 1-loop order can be reproduced by a purely angular integral in the LSET.

We derive the photon propagator in light-shell gauge (LSG), introduced in [1] in the context of light-shell effective theory.

We study the classical color radiation from very high energy collisions that produce colored particles. In the extreme high energy limit, the classical color fields are confined to a light-shell expanding at c and are associated with a non-linear σ-model on the 2D light-shell with specific symmetry breaking terms. We argue that the quantum version of this picture exhibits asymptotic freedom and may be a useful starting point for an effective light-shell theory of the structure between the jets at a very high energy collider.

Many models of dark matter scattering with baryons may be treated either as a simple contact interaction or as the exchange of a light mediator particle. We study an alternative, in which a continuum of light mediator states may be exchanged. This could arise, for instance, from coupling to a sector which is approximately conformal at the relevant momentum transfer scale. In the non-relativistic effective theory of dark matter–baryon scattering, which is useful for parametrizing direct detection signals, the effect of such continuum mediators is to multiply the amplitude by a function of the momentum transfer q, which in the simplest case is just a power law. We develop the basic framework and study two examples: the case where the mediator is a scalar operator coupling to the Higgs portal (which turns out to be highly constrained) and the case of an antisymmetric tensor operator Oµν that mixes with the hypercharge field strength and couples to dark matter tensor currents, which has an interesting viable parameter space. We describe the effect of such mediators on the cross sections and recoil energy spectra that could be observed in direct detection.

We explore naturalness constraints on the masses of the heavy Higgs bosons (H^0) , (H^ ±), and (A^0) in supersymmetric theories. We show that, in any extension of MSSM which accommodates the 125 GeV Higgs at the tree level, one can derive an upper bound on the SUSY Higgs masses from naturalness considerations. As is well-known for the MSSM, these bounds become weak at large tan β. However, we show that measurements of b → sγ together with naturalness arguments lead to an upper bound on tan β, strengthening the naturalness case for heavy Higgs states near the TeV scale. The precise bound depends somewhat on the SUSY mediation scale: allowing a factor of 10 tuning in the stop sector, the measured rate of b → sγ implies tan β ≲ 30 for running down from 10 TeV but tan β ≲ 4 for mediation at or above 100 TeV, placing m A near the TeV scale for natural EWSB. Because the signatures of heavy Higgs bosons at colliders are less susceptible to being “hidden” than standard superpartner signatures, there is a strong motivation to make heavy Higgs searches a key part of the LHC’s search for naturalness. In an appendix we comment on how the Goldstone boson equivalence theorem links the rates for H → hh and H → ZZ signatures.