Abstract
We calculate the exact width for a dark photon decaying to three photons at one loop order for dark photon masses m' below the e+e- production threshold of 2m_e. We find substantial deviations from previous results derived from the lowest order Euler-Heisenberg effective Lagrangian in the range m_e < m' < 2m_e, where higher order terms in the derivative expansion are nonnegligible. This mass range is precisely where the three photon decay takes place on cosmologically relevant timescales. Our improved analysis opens a window for dark photons in the range 850 keV < m' < 2m_e, 10^-5 < epsilon < 10^-4.
Highlights
Matter with no standard model gauge charges may be charged under an Abelian gauge group of its own
A new gauge boson of this type may kinetically mix with the standard model photon [3] via a gauge invariant dimensionfour operator Omix 1⁄4 −εF0μνFμν=2, where F0 is the field strength of the dark photon A0 and F is the field strength of the standard model photon A
Most searches for the dark photon rely on the observation of the products of its decay after it has been produced in lowenergy terrestrial experiments [4,5,6,7,8,9,10,11,12,13,14,15,16], some search strategies are sensitive even to invisibly decaying or effectively stable dark photons [17,18,19,20,21]
Summary
Matter with no standard model gauge charges may be charged under an Abelian gauge group of its own. The Euler-Heisenberg Lagrangian is the low-energy effective Lagrangian that is matched to quantum electrodynamics at energies below the electron mass This Lagrangian predicts gauge boson self-couplings that do not exist at higher energies, leading to photon self-interactions [23]. This is well known for QED: the cross section for light-by-light scattering was obtained by Karplus and Neuman [26] and these “nonlinearities” were fully explored by de Tollis and collaborators [27] There, they reproduced the m−e 8 scaling predicted by the EulerHeisenberg Lagrangian at small energy transfer, but found that this deviated from the full result close to the electron mass. For four-photon interactions, the first two subleading Lagrangian terms containing two and four derivatives have been obtained by a matching calculation using the full QED scattering cross section [28]. The corrections to the three photon decay are naïvely similar to the corrections for light-by-light scattering, and our exact calculations described below reveal that the corrections in this context can be even larger
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