Strong CP breaking and quark-antiquark repulsion in QCD, at finite theta

This work is devoted to the study of the CP-breaking dynamics in QCD, at finite theta-angle. By working in the semi-classical limit, in which the topology of the vacuum is clustered around instantons and anti-instantons, we show that quantum fluctuations of the theta-vacuum generate an effective flavor-dependent repulsion between matter and anti-matter, inside hadrons. As a consequence, during the tunneling between the degenerate vacua, quarks and anti-quarks in the neutron migrate in opposite directions, giving rise to an oscillating electric dipole moment. We discuss a possible phenomenological implication of this effect.Comment: Final version, accepted for publication on Phys. Rev. D (Rapid Comm.

Quarks and Anomalies

A nonperturbative understanding of neutral pion decay was an essential step towards the idea that strong interactions are governed by a color gauge theory for quarks. Some aspects of this work and related problems are still important.Comment: 18 pages, 2 figures. Contribution to "50 Years of Quarks", ed. H. Fritzsch and M. Gell-Mann, World Scientific (to be published

The Bosonic Structure of Fermions

We bosonize fermions by identifying their occupation numbers as the binary digits of a Bose occupation number. Unlike other schemes, our method allows infinitely many fermionic oscillators to be constructed from just one bosonic oscillator.Comment: 7pages, ADP-94-13/T15

Status of Chiral-Scale Perturbation Theory

Chiral-scale perturbation theory $\chi$PT$_\sigma$ has been proposed as an alternative to chiral $SU(3)_L\times SU(3)_R$ perturbation theory which explains the $\Delta I = 1/2$ rule for kaon decays. It is based on a low-energy expansion about an infrared fixed point in three-flavor QCD. In $\chi$PT$_\sigma$, quark condensation $\langle\bar q q \rangle_\mathrm{vac} \neq 0$ induces nine Nambu-Goldstone bosons: $\pi, K, \eta$ and a QCD dilaton $\sigma$ which we identify with the $f_0(500)$ resonance. Partial conservation of the dilatation and chiral currents constrains low-energy constants which enter the effective Lagrangian of $\chi$PT$_\sigma$. These constraints allow us to obtain new phenomenological bounds on the dilaton decay constant via the coupling of $\sigma/f_0$ to pions, whose value is known precisely from dispersive analyses of $\pi\pi$ scattering. Improved predictions for $\sigma \to \gamma \gamma$ and the $\sigma NN$ coupling are also noted. To test $\chi$PT$_\sigma$ for kaon decays, we revive a 1985 proposal for lattice methods to be applied to $K \to \pi$ on-shell.Comment: 10 pages, 1 figure. Presented at the 8th International Workshop on Chiral Dynamics, 29 June 2015 - 03 July 2015, Pisa, Italy. Revision: references and comment adde

Electromagnetic Contributions to the Schiff Moment

The Schiff moment, \smij, is a parity and time reversal violating fermion-fermion coupling. The nucleus-electron Schiff moment generically gives the most important contribution to the electric dipole moments of atoms and molecules with zero net intrinsic electronic spin and nuclear spin ${1 \over 2}$. Here, the electromagnetic contribution to the Schiff moment, \emij, is considered. For a nucleon, the leading chirally violating contribution to this interaction is calculable in the chiral limit in terms of the parity and time reversal violating pion-nucleon coupling. For the Schiff moment of heavy nuclei, this chiral contribution is somewhat smaller than the finite size effect discussed previously in the literature.Comment: 7 pages, 1 figure (not included), Tex file, requires phyzzx, preprint SCIPP 93/4

Chiral perturbation theory in a theta vacuum

We consider chiral perturbation theory (ChPT) with a non-zero theta term. Due to the CP violating term, the vacuum of chiral fields is shifted to a non-trivial element on the SU(N_f) group manifold. The CP violation also provides mixing of different CP eigenstates, between scalar and pseudoscalar, or vector and axialvector operators. We investigate upto O(theta^2) effects on the mesonic two point correlators of ChPT to the one-loop order. We also address the effects of fixing topology, by using saddle point integration in the Fourier transform with respect to theta.Comment: 31 pages, references added, minor corrections, version published in PR

Strong CP, Up-Quark Mass, and the Randall-Sundrum Microscope

In the Randall-Sundrum model, setting the ratio of up and down quark masses $m_u/m_d << 1$, relevant to the strong CP problem, does not require chiral symmetry or fine-tuning, due to exponential bulk fermion profiles. We point out that such geometric suppression of the mass of a fermion magnifies the masses of its corresponding Kaluza-Klein (KK) states. In this sense, these KK states act as "microscopes" for probing light quark and lepton masses. In simple realizations, this hypothesis can be testable at future colliders, like the LHC, by measuring the spectrum of level-1 KK fermions. The microscope can then provide an experimental test for the vanishing of $m_u$ in the ultraviolet, independently of non-perturbative determinations, by lattice simulations or other means, at hadronic scales. We also briefly comment on application of our microscope idea to other fermions, such as the electron and neutrinos.Comment: 7 pages. New discussions and references added. Main previous conclusions unchange

Introduction to Quantum Field Theory

Even the uninitiated will know that Quantum Field Theory cannot be introduced systematically in just four lectures. I try to give a reasonably connected outline of part of it, from second quantization to the path-integral technique in Euclidean space, where there is an immediate connection with the rules for Feynman diagrams and the partition function of Statistical Mechanics.Comment: 47 pages, no figures, plain LaTeX. Entire manuscript available as a ps file at http://www.physics.adelaide.edu.au/theory/home.html Also available via anonymous ftp at ftp://adelphi.adelaide.edu.au/pub/theory/ADP-95-30.T184.p

CP-violating theta parameter in the domain model of the QCD vacuum

A non-zero CP-violating $\theta$ parameter is treated in the domain model which assumes a cluster-like vacuum structure whose units are characterised in particular by a topological charge which is not necessarily an integer number. In the present paper we restrict consideration to rational values of the charge. The model has previously been shown to manifest confinement, spontaneous chiral symmetry breaking and the absence of an axial U(1) Goldstone boson. We find that the specific structure of the minima of the free energy density of the domain ensemble forces a $2\pi$-periodicity of observables in $\theta$ for any number of light quarks, that vacuum doubling occurs at $\theta=\pi$ for any $N_f>1$ and any value of topological charge $q$. These features are in agreement with expectations based on anomalous Ward identities and large $N_c$ effective theories. We find also additional values of $\theta$ depending on $q$ for which vacuum doubling occurs.Comment: 10 pages, 6 figures. Final version with modification of Eq.(2), additional references, minor typographical correction