<p>We consider SU(2) gauge theory with a scalar field in the fundamental representation. The model is known to contain electric field solutions sourced by the scalar field that are distinct from embedded Maxwell electric fields. We examine the perturbative stability of the solution and identify a region of parameter space where the solution is stable. In the regime where the scalar field has a negative mass squared, the solution has two branches, and we identify an instability in one of the branches.</p>

United States

Jude Pereira

Tanmay Vachaspati

Perturbative stability of non-Abelian electric field solutions

We study the annihilation of electroweak dumbbells and the dependence of their dynamics on initial dumbbell length and twist. Untwisted dumbbells decay rapidly while maximally twisted dumbbells collapse to form a compact sphaleron-like object, before decaying into radiation. The decay products of a dumbbell include electromagnetic magnetic fields with energy that is a few percent of the initial energy. The magnetic field from the decay of twisted dumbbells carries magnetic helicity with magnitude that depends on the twist, and handedness that depends on the decay pathway.

Teerthal Patel

CERN

Annihilation of electroweak dumbbells

We consider the creation of kink-antikink pairs of a scalar field <math><mi>ϕ</mi></math> by the scattering of classical wave packets of a second scalar field <math><mi>ψ</mi></math> when there are no direct interactions between <math><mi>ϕ</mi></math> and <math><mi>ψ</mi></math>. The creation becomes possible only due to a quantum field that interacts with both <math><mi>ϕ</mi></math> and <math><mi>ψ</mi></math>. We scan parameter space and find it favorable for kink production when the initial wave packets have large total energy and wide spatial extent but scatter at low velocities.

Omer Albayrak

Creating kinks with quantum mediation

We investigate kink-antikink scattering in the <math><mi>λ</mi><msup><mi>ϕ</mi><mn>4</mn></msup></math> model in the presence of an additional scalar field, <math><mi>ψ</mi></math>, that is in its quantum vacuum and interacts with <math><mi>ϕ</mi></math> via a <math><mi>ξ</mi><msup><mi>ϕ</mi><mn>2</mn></msup><msup><mi>ψ</mi><mn>2</mn></msup></math> term where <math><mi>ξ</mi></math> is the coupling. The final state of such a scattering is either a bound state with eventual annihilation or a reflection of the kink-antikink pair. Without the <math><mi>ψ</mi></math> field, the outcome is known to depend fractally on the initial velocity of the kink-antikink pair. In the quantum vacuum of the <math><mi>ψ</mi></math> field, the fractal dependence gets modified and disappears above a critical interaction strength, <math><mi>ξ</mi><mo>≈</mo><mn>0.1</mn></math>.

Mainak Mukhopadhyay

Resonance structures in kink-antikink scattering in a quantum vacuum

We analyze the magnetic field of electroweak dumbbells. While the magnetic field of the untwisted dumbbell is given by the usual dipole formula and falls off as <math><mrow><mn>1</mn><mo>/</mo><msup><mrow><mi>r</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></math>, dumbbells with twist have a novel twisted magnetic field that only falls off as <math><mi>cos</mi><mi>θ</mi><mo>/</mo><msup><mi>r</mi><mn>2</mn></msup></math> (in spherical coordinates). We comment on the relevance of twisted electroweak dumbbells for understanding the coherence of the magnetic field generated at the electroweak phase transition.

Structure of electroweak dumbbells

We detail the construction of electric string solutions in <math><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><mo>)</mo></mrow></math> Yang-Mills-Higgs theory with a scalar in the fundamental representation and discuss the properties of the solution. We show that Schwinger gluon pair production in the electric string background is absent. A similar construction in other models, such as with an adjoint scalar field and the electroweak model, does not yield solutions.

Construction of non-Abelian electric strings

We study the formation and evolution of topological defects that arise in the postrecombination phase transition predicted by the gravitational neutrino mass model in Dvali and Funcke [Phys. Rev. D 93, 113002 (2016)]. In the transition, global skyrmions, monopoles, strings, and domain walls form due to the spontaneous breaking of the neutrino flavor symmetry. These defects are unique in their softness and origin; as they appear at a very low energy scale, they only require standard model particle content, and they differ fundamentally depending on the Majorana or Dirac nature of the neutrinos. One of the observational signatures is the time dependence and space dependence of the neutrino mass matrix, which could be observable in future neutrino experiments. Already existing data rule out parts of the parameter space in the Majorana case. The detection of this effect could shed light onto the open question of the Dirac versus Majorana neutrino nature.

Germany

Gia Dvali

Lena Funcke

Time- and Space-Varying Neutrino Mass Matrix from Soft Topological Defects

We find electric string solutions in Yang-Mills-Higgs theory.

Electric strings in non-Abelian theories

We study the stability of fluctuations around a homogeneous non-Abelian electric field background that is of a form that is protected from Schwinger pair production. Our analysis identifies the unstable modes and we find a limiting set of parameters for which there are no instabilities. We discuss potential implications of our analysis for confining strings in non-Abelian gauge theories.

Stability analysis of non-Abelian electric fields

Electric fields in QED are known to discharge due to Schwinger pair production of charged particles. Corresponding electric fields in non-Abelian theory are known to discharge due to the production of gluons. Yet electric flux tubes in QCD ought to be stable to the production of charged gluons as they confine quarks. We resolve this conundrum by finding electric field configurations in pure non-Abelian gauge theory in which the Schwinger process is absent and the electric field is protected against quantum dissipation. We comment on the implications for QCD flux tubes.