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

Heavy-quark axial charges to non-leading order

We combine Witten's renormalization group with the matching conditions of Bernreuther and Wetzel to calculate at next-to-leading order the complete heavy-quark contribution to the neutral-current axial-charge measurable in neutrino-proton elastic scattering. Our results are manifestly renormalization group invariant.Comment: 5 pages, revtex styl

The Neutron Electric Dipole Moment in the Instanton Vacuum: Quenched Versus Unquenched Simulations

We investigate the role played by the fermionic determinant in the evaluation of the CP-violating neutron electric dipole moment (EDM) adopting the Instanton Liquid Model. Significant differences between quenched and unquenched calculations are found. In the case of unquenched simulations the neutron EDM decreases linearly with the quark mass and is expected to vanish in the chiral limit. On the contrary, within the quenched approximation, the neutron EDM increases as the quark mass decreases and is expected to diverge as (1/m)**Nf in the chiral limit. We argue that such a qualitatively different behavior is a parameter-free, semi-classical prediction and occurs because the neutron EDM is sensitive to the topological structure of the vacuum. The present analysis suggests that quenched and unquenched lattice QCD simulations of the neutron EDM as well as of other observables governed by topology might show up important differences in the quark mass dependence, for mq < Lambda(QCD).Comment: 8 pages, 3 figures, 2 table

Spin and orbital angular momentum of the proton

Since the announcement of the proton spin crisis by the European Muon Collaboration there has been considerable progress in unravelling the distribution of spin and orbital angular momentum within the proton. We review the current status of the problem, showing that not only have strong upper limits have been placed on the amount of polarized glue in the proton but that the experimental determination of the spin content has become much more precise. It is now clear that the origin of the discrepancy between experiment and the naive expectation of the fraction of spin carried by the quarks and anti-quarks in the proton lies in the non-perturbative structure of the proton. We explain how the features expected in a modern, relativistic and chirally symmetric description of nucleon structure naturally explain the current data. The consequences of this explanation for the presence of orbital angular momentum on quarks and gluons is reviewed and comparison made with recent results from lattice QCD and experimental data.Comment: Lectures at Aligarh University (4th DAE-BRNS Workshop on Hadron Physics, Feb 18-21, 200

Poincar\'e recurrence theorem and the strong CP-problem

The existence in the physical QCD vacuum of nonzero gluon condensates, such as $$, requires dominance of gluon fields with finite mean action density. This naturally allows any real number value for the unit ``topological charge'' $q$ characterising the fields approximating the gluon configurations which should dominate the QCD partition function. If $q$ is an irrational number then the critical values of the $\theta$ parameter for which CP is spontaneously broken are dense in $\mathbb{R}$, which provides for a mechanism of resolving the strong CP problem simultaneously with a correct implementation of $U_{\rm A}(1)$ symmetry. We present an explicit realisation of this mechanism within a QCD motivated domain model. Some model independent arguments are given that suggest the relevance of this mechanism also to genuine QCD.Comment: 8 pages, RevTeX, 3 figures. Revised after referee suggestions. Now includes model independent argument

Interplay of Spin and Orbital Angular Momentum in the Proton

We derive the consequences of the Myhrer-Thomas explanation of the proton spin problem for the distribution of orbital angular momentum on the valence and sea quarks. After QCD evolution these results are found to be in very good agreement with both recent lattice QCD calculations and the experimental constraints from Hermes and JLab

Gluon topology and the spin structure of the constituent quark

Gluon topology makes a potentially important contribution to the spin of the constituent quark.Comment: 3 pages, LaTeX, talk at DIS99, Zeuthen, April 199

Running couplings for the simultaneous decoupling of heavy quarks

Scale-invariant running couplings are constructed for several quarks being decoupled together, without reference to intermediate thresholds. Large-momentum scales can also be included. The result is a multi-scale generalization of the renormalization group applicable to any order. Inconsistencies in the usual decoupling procedure with a single running coupling can then be avoided, e.g. when cancelling anomalous corrections from t,b quarks to the axial charge of the proton.Comment: 12 pages, 1 figure, version to appear in PLB. Pages 8-11 and Fig. 1 are new, with consequent changes to the abstract, page 2, and the references. We show that our multi-scale renormalization group is needed to achieve anomaly cancellation in t,b decoupling from the weak neutral current, and extend it to include large moment

The Measure of Strong CP Violation

We investigate a controversial issue on the measure of CP violation in strong in teractions. In the presence of nontrivial topological gauge configurations, the $\theta$-term in QCD has a profound effect: it breaks the CP symmetry. The CP-violating amplitude is shown to be determined by the vacuum tunneling process, where the semiclassical method makes most sense. We discuss a long-standing dispute on whether the instanton dynamics satisfies or not the anomalous Ward identity (AWI). The strong CP violation measure, when complying with the vacuum alignment, is proportional to the topological susceptibility. We obtain an effective CP-violating lagrangian different from that provided by Baluni. To solve the IR divergence problem of the instanton computation, We present a ``classically gauged'' Georgi-Manohar model and derive an effective potential which uniquely determines an explicit $U(1)_A$ symmetry breaking sector. The CP violation effects are analyzed in this model. It is shown that the strong CP problem and the $U(1)$ problem are closely related. Some possible solutions to both problems are also discussed with new insights.Comment: 37 pages in LateX, SFU-Preprint-92-