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Concept# Chiral anomaly

Résumé

In theoretical physics, a chiral anomaly is the anomalous nonconservation of a chiral current. In everyday terms, it is equivalent to a sealed box that contained equal numbers of left and right-handed bolts, but when opened was found to have more left than right, or vice versa.
Such events are expected to be prohibited according to classical conservation laws, but it is known there must be ways they can be broken, because we have evidence of charge–parity non-conservation ("CP violation"). It is possible that other imbalances have been caused by breaking of a chiral law of this kind. Many physicists suspect that the fact that the observable universe contains more matter than antimatter is caused by a chiral anomaly. Research into chiral symmetry breaking laws is a major endeavor in particle physics research at this time.
Informal introduction
The chiral anomaly originally referred to the anomalous decay rate of the neutral pion, as computed in the current algebra of the c

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PHYS-416: Particle physics II

Presentation of the electroweak and strong interaction theories that constitute the Standard Model of particle physics. The course also discusses the new theories proposed to solve the problems of the Standard Model.

PHYS-415: Particle physics I

Presentation of particle properties, their symmetries and interactions.
Introduction to quantum electrodynamics and to the Feynman rules.

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The chiral Abelian Higgs model contains an interesting class of solitons found by Rubakov and Tavkhelidze. These objects carry non-zero fermion number NF (or Chern-Simons number NCS, what is the same because of the chiral anomaly) and are stable for sufficiently large NF. In this paper we study the properties of these anomalous solitons. We find that their energy-versus-fermion-number ratio is given by E ∼ NCS 3 / 4 or E ∼ NCS 2 / 3 depending on the structure of the scalar potential. For the former case we demonstrate that there is a lower bound on the soliton energy, which reads E ≥ c NCS 3 / 4, where c is some parameter expressed through the masses and coupling constants of the theory. We construct the anomalous solitons numerically accounting both for Higgs and gauge dynamics and show that they are not spherically symmetric. The thin wall approximation valid for macroscopic solutions with NCS ≫ 1 is discussed as well. © 2007 Elsevier B.V. All rights reserved.

2007Yann David Cado, Eray Sabancilar

We show that both the baryon asymmetry of the Universe and the dark matter abundance can be explained within a single framework that makes use of maximally helical hypermagnetic fields produced during pseudoscalar inflation and the chiral anomaly in the Standard Model. We consider a minimal asymmetric dark matter model free from anomalies and constraints. We find that the observed baryon and the dark matter abundances are achieved for a wide range of inflationary parameters, and the dark matter mass ranges between 7-15 GeV. The novelty of our mechanism stems from the fact that the same source of CP violation occurring during inflation explains both baryonic and dark matter in the Universe with two inflationary parameters, hence addressing all the initial condition problems in an economical way.

Solitons are stable, non-singular solutions to the classical equations of motion of non-linear field theory. Their energy is localized and finite and their shape remains unaltered during propagation. For this reason they represent particle-like states in field theory. Their mass and their size can be very large compared to those of the elementary particles in the theory. Therefore, a soliton can be viewed as a single particle-like object containing a large number of individual particles. The chiral Abelian Higgs model contains an interesting class of non-topological solitons, that carry a non-zero fermion number NF or Chern-Simons number NCS, which is the same because of the chiral anomaly. They consist of a bosonic configuration of gauge and Higgs fields characterized by NCS and are stable for sufficiently large NCS. In the first part of this thesis we study the properties of these anomalous solitons. We find that their energy-versus-fermion-number ratio is given by E ∼ NCS3/4 or E ∼ NCS2/3 depending on the structure of the scalar potential. For the former case we prove, using some inequalities from functional analysis, that there is a lower bound on the soliton energy, which reads E ≥ c NCS3/4 , where c is some parameter expressed through the masses and coupling constants of the theory. We construct the anomalous solitons numerically for two different choices for the potential accounting both for Higgs and gauge dynamics. Solutions are obtained as a function of NCS and the Higgs mass mH and we find that they are not spherically symmetric. In addition, we outline a relation between the structure of anomalous Abelian solitons and the intermediate state observed in type-I superconductors in external magnetic fields. In the limit of large NCS anomalous solitons can be described in the thin wall approximation, which allows us to remove the Higgs field from consideration. For absolute stability of anomalous solitons, it is essential that the gauge group is Abelian. If the gauge group is non-Abelian, fermions can always be converted to a gauge vacuum configuration with an arbitrary integer NCS. Therefore, if anomalous non-Abelian solitons exist, they could only be metastable. Interestingly, anomalous solitons can potentially exist in the electroweak theory, because this theory contains all necessary ingredients, namely chiral fermions and an Abelian gauge symmetry. In the second part of this thesis we investigate this possibility. Using the numerical solutions for anomalous Abelian solitons as a starting point, we construct the corresponding numerical solutions in electroweak theory. These solutions have a similar structure as the Abelian solitons with the Abelian gauge field replaced by the Z boson field. The charged boson fields W± vanish identically. However, for weak mixing angle θω > 0, the solutions have an associated magnetic field as well, that can be characterized by a magnetic dipole moment mem. Furthermore, the shape of the solutions and the structure of the gauge fields depend on θω. In the last part of this work we analyze the classical stability of the numerical solutions in the electroweak case. It is clear that the solutions are stable in the semilocal limit sin θω → 1, where the Abelian case is reproduced exactly. For arbitrary θω, we consider perturbations in the Higgs field and in the gauge fields Z and A and show that the solutions are stable with respect to these perturbations. For small θω however, the solutions are unstable with respect to the formation of a condensate of charged boson fields W± in the centre of the solution. This W-condensation instability is essentially the same, which also destabilizes the Z-string solution of electroweak theory.