Abstract
We discuss new bounds on vectors coupled to currents whose nonconservation is due to mass terms, such as $U(1{)}_{{L}_{\ensuremath{\mu}}\ensuremath{-}{L}_{\ensuremath{\tau}}}$. Due to the emission of many final state longitudinally polarized gauge bosons, inclusive rates grow exponentially fast in energy, leading to constraints that are only logarithmically dependent on the symmetry breaking mass term. This exponential growth is unique to Stueckelberg theories and reverts back to polynomial growth at energies above the mass of the radial mode. We present bounds coming from the high transverse mass tail of $\mathrm{monolepton}+\mathrm{MET}$ events at the LHC, which beat out cosmological bounds to place the strongest limit on Stueckelberg $U(1{)}_{{L}_{\ensuremath{\mu}}\ensuremath{-}{L}_{\ensuremath{\tau}}}$ models for most masses below a keV. We also discuss a stronger, but much more uncertain, bound coming from the validity of perturbation theory at the LHC.
Highlights
New light weakly coupled particles have increasingly become a focus as either a mediator to a dark sector [1,2,3], as dark matter itself [4,5,6,7,8], or to explain potential anomalies [9,10,11,12,13,14]
In order to demonstrate the exponential growth of amplitudes, we will consider the toy scenario of a gauge boson coupled to only the left handed piece of a Dirac fermion ν, whose current is not conserved due to explicit breaking by a small Dirac mass term mν
Amplitudes have an exponential growth in energy and the strongest growth comes from emitting multiple gauge bosons
Summary
New light weakly coupled particles have increasingly become a focus as either a mediator to a dark sector [1,2,3], as dark matter itself [4,5,6,7,8], or to explain potential anomalies [9,10,11,12,13,14]. A Stueckelberg theory coupled to a nonconserved current can have inclusive rates that grow exponentially fast in energy due to multiparticle emission [31] This exponential growth is unique to the Stueckelberg limit and becomes polynomial at energies above the mass of the radial mode. Comparing this with Eq (1) taking mX=gX ≃ 1 GeV, motivated by our later results, and m ≃ 0.05 eV, as the mass of the neutrino, we find that Λ ∼ Λa=10 This shows that despite the extremely small neutrino mass, its nonzero value still gives a unitarity bound almost an order of magnitude more stringent than the anomaly does. In this paper we will focus on gauge bosons coupled to the lepton number currents, which are only nonconserved because of the extremely small neutrino masses. For mX ≲ 1 keV, this is the strongest constraint on these models beating out even cosmological bounds.
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