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Register a new userKibble mechanism for electroweak magnetic monopoles and magnetic fields
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We develop topological criteria for the existence of electroweak magnetic monopoles and Z-strings and extend the Kibble mechanism to study their formation during the electroweak phase transition. The distribution of magnetic monopoles produces magnetic fields that have a spectrum $B_lambda propto lambda^{-2}$ where $lambda$ is a smearing length scale. Even as the magnetic monopoles annihilate due to the confining Z-strings, the magnetic field evolves with the turbulent plasma and may be relevant for cosmological observations.
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We use the $SU(5)$ model to show the presence in grand unified theories of an electroweak monopole and a magnetic dumbbell (meson) made up of a monopole-antimonopole pair connected by a $Z$-magnetic flux tube. The monopole is associated with the spontaneous breaking of the weak $SU(2)_L$ gauge symmetry by the induced vacuum expectation value of a heavy scalar $SU(2)_L$ triplet with zero weak hypercharge contained in the adjoint Higgs 24-plet. This monopole carries a Coulomb magnetic charge of $(3/4) (2pi/e)$ as well as $Z$-magnetic charge, where $2pi/e$ denotes the unit Dirac magnetic charge. Its total magnetic charge is $sqrt{3/8}(4pi/e)$, which is in agreement with the Dirac quantization condition. The monopole weighs about 700 GeV, but because of the attached $Z$-magnetic tube it exists, together with the antimonopole, in a magnetic dumbbell configuration whose mass is expected to lie in the TeV range. The presence of these topological structures in $SU(5)$ and $SO(10)$ and in their supersymmetric extensions provides an exciting new avenue for testing these theories in high-energy colliders.
We show that the presence of a magnetic monopole in position space gives rise to a violation of the fermion number conservation in chiral matter. Using the chiral kinetic theory, we derive a model-independent expression of such a violation in nonequilibrium many-body systems of chiral fermions. In local thermal equilibrium at finite temperature and chemical potential, in particular, this violation is proportional to the chemical potential with a topologically quantized coefficient. These consequences are due to the interplay between the Dirac monopole in position space and the Berry monopole in momentum space. Our mechanism can be applied to study the roles of magnetic monopoles in the nonequilibrium evolution of the early Universe.
Dark sectors with Abelian gauge symmetries can interact with ordinary matter via kinetic mixing. In such scenarios, magnetic monopoles of a broken dark $U(1)$ will appear in our sector as confined milli-magnetically charged objects under ordinary electromagnetism. Halo ellipticity constraints are shown to significantly bound the strength of dark magnetic Coulomb monopole interactions. The bound monopole ground state, which in vacuum is stable and has no magnetic charge or moment, is shown to become quantum mechanically unstable in the presence of an external, ordinary magnetic field. If these states contribute sizably to the local dark matter density, they can extract significant energy from the galactic magnetic field if their decay occurs on a galactic timescale or less. We revise and extend this Parker Bound on galactic magnetic energy loss to milli-monopoles which leads to the strongest existing constraints on these states, satisfying our halo ellipticity bounds, over a wide range of monopole masses.
Schwinger showed that electrically-charged particles can be produced in a strong electric field by quantum tunnelling through the Coulomb barrier. By electromagnetic duality, if magnetic monopoles (MMs) exist, they would be produced by the same mechanism in a sufficiently strong magnetic field. Unique advantages of the Schwinger mechanism are that its rate can be calculated using semiclassical techniques without relying on perturbation theory, and the finite MM size and strong MM-photon coupling are expected to enhance their production. Pb-Pb heavy-ion collisions at the LHC produce the strongest known magnetic fields in the current Universe, and this article presents the first search for MM production by the Schwinger mechanism. It was conducted by the MoEDAL experiment during the 5.02 TeV/nucleon heavy-ion run at the LHC in November 2018, during which the MoEDAL trapping detectors (MMTs) were exposed to 0.235 nb$^{-1}$ of Pb-Pb collisions. The MMTs were scanned for the presence of magnetic charge using a SQUID magnetometer. MMs with Dirac charges 1$g_D$ $leq$ $g$ $leq$ 3$g_D$ and masses up to 75 GeV/c$^2$ were excluded by the analysis. This provides the first lower mass limit for finite-size MMs from a collider search and significantly extends previous mass bounds.
A quasiclassical approximation is constructed to describe the eigenvalues of the magnetic Laplacian on a compact Riemannian manifold in the case when the magnetic field is not given by an exact 2-form. For this, the multidimensional WKB method in the form of Maslov canonical operator is applied. In this case, the canonical operator takes values in sections of a nontrivial line bundle. The constructed approximation is demonstrated for the Dirac magnetic monopole on the two-dimensional sphere.
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