Abstract
Near a critical value of the wino mass where there is a zero-energy S-wave resonance at the neutral-wino-pair threshold, low-energy winos can be described by a zero-range effective field theory (ZREFT) in which the winos interact nonperturbatively through a contact interaction and charged winos also have electromagnetic interactions. At energies near the wino-pair thresholds, the Coulomb interaction from photon exchange between charged winos must also be treated nonperturbatively. The parameters of ZREFT can be determined by matching wino-wino scattering amplitudes calculated by solving the Schrödinger equation for winos interacting through a potential due to the exchange of electroweak gauge bosons. With Coulomb resummation, ZREFT at leading order gives a good description of the low-energy two-body observables for winos.
Highlights
Weak interactions between low-energy wimps are nonperturbative in the same sense as Coulomb interactions between low-energy charged particles: the exchange of gauge bosons must be summed to all orders in the gauge coupling constant
zero-range effective field theory (ZREFT) is applicable if M is close enough to a critical value that |a| is large compared to the range 1/mW of the weak interactions
Low-energy winos can be described by a nonrelativistic effective field theory in which they interact through potentials that arise from the exchange of weak gauge bosons and in which charged winos have electromagnetic interactions
Summary
We assume the dark-matter particle is the neutral member of an SU(2) triplet of Majorana fermions with zero hypercharge. We are interested in a mass M at the TeV scale so that effects from the exchange of electroweak gauge bosons between nonrelativistic winos must be summed to all orders. The splitting from one-loop radiative corrections is determined by M and Standard Model parameters only [14,15,16]. The splitting δ between the masses of w± and w0 arises from electroweak radiative corrections. Matsumoto, and Nojiri pointed out that if the mass of the wino is large enough that α2M is of order mW or larger, loop diagrams in which electroweak gauge bosons are exchanged between nonrelativistic winos are not suppressed [3]. By summing ladder diagrams from the exchange of electroweak bosons between the winos to all orders. The resummation of the ladder diagrams to all orders can be carried out more by solving a Schrodinger equation in a nonrelativistic effective field theory for the winos
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