Stephen D.H. Hsu

Solutions to the strong CP problem in a world with gravity

We examine various solutions of the strong-CP problem to determine their sensitivity to possible violations of global symmetries by Plauck scale physics. While some solutions remain viable even in the face of such effects. Violations of the Peccei-Quinn (PQ) symmetry by non-renormalizable operators of dimension less than 10 will generally shift the value of {bar {theta}} to values inconsistent with the experimental bound {bar {theta}} {approx_lt} 10{sup {minus}}9. We show that it is possible to construct axion models where gauge symmetries protect PQ symmetry to the requisite level.

Walking technicolor and electroweak radiative corrections

Abstract We examine the effect of walking technicolor dynamics on the electroweak S -parameter and contrast it with the effect of QCD-like technicolor dynamics. Our main tools are the operator product expansion for the high-momentum behavior of the electroweak gauge boson vacuum polarizations and the analyticity of these polarizations which relate their low and high momentum behaviors. We show that whereas in large QCD-like technicolor models S is large and positive, in walking technicolor models a negative contribution is emphasized, related to the large anomalous dimension of the technifermion condensate. Thus in walking technicolor S is determined by a large cancellation of two competing effects. This may result in much smaller values of S than in QCD-like technicolor, although considerable uncertainties are involved. We conclude that it is impossible to rule out walking technicolor based on the present experimental limits on S and the present theoretical technology.

Long-range forces from two-neutrino exchange reexamined.

The exchange of two massless neutrinos gives rise to a long-range force which couples to weakly charged matter. The form of this force was first computed by Feinberg and Sucher using dispersion-theoretic techniques. Here we give a simple derivation using Fourier transforms. Our result agrees with that of Feinberg and Sucher.

Metastable cosmic strings in realistic models

The stability of the electroweak Z-string is investigated at high temperatures. The results show that, while finite temperature corrections can improve the stability of the Z-string, their effect is not strong enough to stabilize the Z-string in the standard electroweak model. Consequently, the Z-string will be unstable even under the conditions present during the electroweak phase transition. Phenomenologically viable models based on the gauge group SU(2)[sub L] [times] SU(2) [sub R] [times] U(1)[sub B-L] are then considered, and it is shown that metastable strings exist and are stable to small perturbations for a large region of the parameter space for these models. It is also shown that these strings are superconducting with bosonic charge carriers. The string superconductivity may be able to stabilize segments and loops against dynamical contraction. Possible implications of these strings for cosmology are discussed.

Quantum scattering from classical field theory

Abstract We show that scattering amplitudes between initial wave packet states and certain coherent final states can be computed in a systematic weak coupling expansion about classical solutions satisfying initial-value conditions. The initial-value conditions are such as to make the solution of the classical field equations amenable to numerical methods. We propose a practical procedure for computing classical solutions which contribute to high energy two-particle scattering amplitudes. We consider in this regard the implications of a recent numerical simulation in classical SU(2) Yang-Mills theory for multiparticle scattering in quantum gauge theories and speculate on its generalization to electroweak theory. We also generalize our results to the case of complex trajectories and discuss the prospects for finding a solution to the resulting complex boundary value problem, which would allow the application of our method to any wave packet to coherent state transition. Finally, we discuss the relevance of these results to the issues of baryon number violation and multiparticle scattering at high energies.

Anomalous violation of conservation laws in Minkowski space

Abstract We consider the evolution of quantum Fermi fields in Minkowski gauge field backgrounds. Our motivation is the study of anomalous fermion number violating processes. We derive selection rules for fermion scattering amplitudes which relate the violation of fermionic charge to the change in winding between early and late times of the vacuum part of the gauge field. We find that the amount of fermion number violation is always integer, even when the topological charge of the gauge field is fractional. As an explicit example, we apply our results to spherically symmetric Minkowski solutions.

Quantum Scattering and Classical Solutions

The behavior of quantum scattering amplitudes at large center of mass energies, E ∼ E* = m/g 2, is an open question currently under investigation. Here, m is a mass scale characterizing the particle excitations of the theory, and g is a small coupling constant controlling the nonlinear interactions. It has been speculated that multiparticle scattering from initial states with only a small number of particles could be unsup-pressed at these energies. A second related issue is whether anomalous processes, such as baryon number violation in electroweak theory where E* ≃ O (M ω /αω) ∼ 10 TeV, are unsuppressed at energies of the same order1.

Complementarity and chiral fermions in SU(2) gauge theories.

Complementarity, the absence of a phase boundary separating the Higgs and confinement phases of a gauge theory, can be violated by the addition of chiral fermions. We utilize chiral-symmetry-violating fermion correlators such as

On tunneling at finite energies and temperatures

〈\overline{\ensuremath{\psi}}\ensuremath{\psi}〉

Nonperturbative decoupling and effective field theory.

as order parameters to investigate this issue. Using inequalities similar to those of Vafa and Witten and Weingarten, we show that SU(2) gauge theories with Higgs and fermion fields in the fundamental representation exhibit chiral symmetry breaking in the confined phase and therefore do not lead to massless composite fermions. We discuss the implications for the Abbott-Farhi strongly interacting standard model.