Igor Halperin

Can Theta / N dependence for gluodynamics be compatible with 2 pi periodicity in Theta?

In a number of field theoretical models the vacuum angle \theta enters physics in the combination \theta/N, where N stands generically for the number of colors or flavors, in an apparent contradiction with the expected 2 \pi periodicity in \theta. We argue that a resolution of this puzzle is related to the existence of a number of different \theta dependent sectors in a finite volume formulation, which can not be seen in the naive thermodynamic limit V -> \infty. It is shown that, when the limit V -> \infty is properly defined, physics is always 2 \pi periodic in \theta for any integer, and even rational, values of N, with vacuum doubling at certain values of \theta. We demonstrate this phenomenon in both the multi-flavor Schwinger model with the bosonization technique, and four-dimensional gluodynamics with the effective Lagrangian method. The proposed mechanism works for an arbitrary gauge group.

INTEGRATING IN AND EFFECTIVE LAGRANGIAN FOR NON-SUPERSYMMETRIC YANG-MILLS THEORY

Abstract Recently a non-supersymmetric analog of Veneziano-Yankielowicz (VY) effective Lagrangian has been proposed and applied for the analysis of the θ dependence in pure Yang-Mills theory. This effective Lagrangian is similar in many respects to the VY construction and, in particular, exhibits a kind of low energy holomorphy which is absent in the full YM theory. Here we incorporate a heavy fermion into this effective theory by using the “integrating in” technique. We find that, in terms of this extended theory, holomorphy of the effective Lagrangian for pure YM theory naturally implies a holomorphic dependence on the heavy fermion mass. It is shown that this analysis fixes, under certain assumptions, a dimensionless parameter which enters the effective Lagrangian and determines the number of non-degenerate vacuum sectors in pure YM theory. We also compare our results for the vacuum structure and θ dependence to those obtained recently by Witten on the basis of AdS/CFT correspondence.

Axion potential, topological defects and CP odd bubbles in QCD

Abstract It follows on general grounds that the θ dependence in QCD is more complicated than suggested by the large N c approach or instanton arguments. Generically, the vacuum energy E vac ( θ ) is a multi-valued function of θ admitting the existence of metastable states. We discuss decays of such metastable vacua in the theory with and without the axion, and point out the potential relevance of this and related phenomena for constraining a dark matter axion. Based on the analysis of the axion potential, an idea for a new axion search experiment at RHIC is suggested. It is noted that the false vacuum decay proceeds with maximal violation of CP, even if θ =0. We further speculate that the famous Sakharov criteria for baryogenesis could be satisfied at the QCD scale.

Veneziano ghost versus isospin breaking

It is argued that an account for the Veneziano ghost pole, appearing in the resolution of the U(1) problem, is necessary for understanding isospin violation in the [pi]-[eta]-[eta][prime] system. By virtue of a perturbative expansion around the SU(2)[sub [ital V]] ([ital m][sub [ital u]]=[ital m][sub [ital d]]) symmetric Veneziano solution, we find that the ghost considerably suppresses isospin-breaking gluon and [ital s]-quark matrix elements. We further speculate on a few cases where the proposed mechanism can play an essential role. We discuss the isospin violation in meson-nucleon couplings and its relevance to the problem of charge asymmetric nuclear forces and the possible breaking of the Bjorken sum rule. It is shown that the ghost pole could yield an isospin violation of the order of 2% for the [pi][ital N] couplings and 20% for the Bjorken sum rule.

Condensates and vacuum structure of adjoint QCD2

We discuss a two-dimensional SU(N) Yang-Mills theory coupled to massive adjoint fermions for different worlds classified by the integer k = 0, 1,…,N−1. We study the fermion condensate for these unconnected worlds as a function of the parameter k. We show that the condensate as well as the spectrum of the theory do depend on this vacuum parameter k. Technically, the value of the fermion condensate is related to the value of the gluon condensate via the Operator Product Expansion. We use this to find the leading dependence (in the limit of a heavy quark) of the fermion condensate 〈k|ψψ|k〉 on the non-trivial vacuum angle k. We also determine the gluon condensate of the theory using low-energy theorems.

ON TOPOLOGICAL SUSCEPTIBILITY, VACUUM ENERGY AND THETA DEPENDENCE IN GLUODYNAMICS

We suggest that the topological susceptibility in gluodynamics can be found in terms of the gluon condensate using renormalizability and heavy fermion representation of the anomaly. Analogous relations can also be obtained for other zero-momentum correlation functions involving the topological density operator. Using these relations, we find the θ dependence of the condensates , and of the partition function for small θ and an arbitrary number of colors.

Conformal symmetry on the light cone and nonleading twist distribution amplitudes of a massive vector meson

A complete set of asymptotic three particle light cone distribution amplitudes of twist 3 and 4 for a transversely polarized massive vector meson built out of massless current quarks is constructed. The method used is based on a modified conformal projectors technique which allows one to handle kinematical corrections due to a finite hadron mass. Consequences of our finding for the

Axion potential, topological defects and θ dependence in QCD

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Inclusive B \to sg decay in QCD

-meson hard diffractive electroproduction and

ANOMALOUS EFFECTIVE LAGRANGIAN AND THETA DEPENDENCE IN QCD AT FINITE NC

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