Abstract
Skyrmions are extended field configurations, initially proposed to describe baryons as topological solitons in an effective field theory of mesons. We investigate and confirm the existence of skyrmions within the electroweak sector of the Standard Model and study their properties. We find that the interplay of the electroweak sector with a dynamical Higgs field and the Skyrme term leads to a non-trivial vacuum structure with the skyrmion and perturbative vacuum sectors separated by a finite energy barrier. We identify dimension-8 operators that stabilise the electroweak skyrmion as a spatially localised soliton field configuration with finite size. Such operators are induced generically by a wide class of UV models. To calculate the skyrmion energy and radius we use a neural network method. Electroweak skyrmions are non-topological solitons but are exponentially long lived, and we find that the electroweak skyrmion is a viable dark matter candidate. While the skyrmion production cross section at collider experiments is suppressed, measuring the size of the Skyrme term in multi-Higgs-production processes at high-energy colliders is a promising avenue to probe the existence of electroweak skyrmions.
Highlights
Are within 30% of experimental values [10, 11], but there have been no direct experimental evidence for skyrmions in particle physics
We find that the interplay of the electroweak sector with a dynamical Higgs field and the Skyrme term leads to a non-trivial vacuum structure with the skyrmion and perturbative vacuum sectors separated by a finite energy barrier
Skyrmions were originally introduced as topologically stable static field configurations in relativistic quantum field theory
Summary
We start with the Lagrangian for the SM Higgs scalar coupled to the SU(2)L gauge fields, L. The finiteness of the energy integral in (2.8) requires that the Φ is continuous, otherwise the derivative term on the r.h.s. of (2.8) would result in delta functions giving an infinite contribution to the integral. There are three independent reasons for why topological solitons do not exist in the weak sector of the SM described by the Lagrangian (2.1). Fluctuations of dynamical s(x) field (i.e. interactions with the SM Higgs); 3Topological solitons here refer to extended particles with non-zero finite mass (energy) that are protected by the topological conservation law — their charge given by the winding number n is strictly conserved. For the neutral Higgs field with a finite mass, in (2.5), the zeros of s are possible and the winding number is no longer a conserved quantity. At best there are only finite energy barriers separating U -fields with different values of nH
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