Naturalness of the Coleman-Glashow Mass Relation in the 1/N_c Expansion: an Update

A new measurement of the Xi^0 mass verifies the accuracy of the Coleman-Glashow relation at the level predicted by the 1/N_c expansion. Values for other baryon isospin mass splittings are updated, and continue to agree with the 1/N_c hierarchy.Comment: 6 pages, revte

Baryon masses at second order in large-NN chiral perturbation theory

We consider flavor breaking in the the octet and decuplet baryon masses at second order in large-$N$ chiral perturbation theory, where $N$ is the number of QCD colors. We assume that $1/N \sim 1/N_F \sim m_s / \Lambda \gg m_{u,d}/\Lambda, \alpha_{EM}$, where $N_F$ is the number of light quark flavors, and $m_{u,d,s} / \Lambda$ are the parameters controlling $SU(N_F)$ flavor breaking in chiral perturbation theory. We consistently include non-analytic contributions to the baryon masses at orders $m_q^{3/2}$, $m_q^2 \ln m_q$, and $(m_q \ln m_q) / N$. The $m_q^{3/2}$ corrections are small for the relations that follow from $SU(N_F)$ symmetry alone, but the corrections to the large-$N$ relations are large and have the wrong sign. Chiral power-counting and large-$N$ consistency allow a 2-loop contribution at order $m_q^2 \ln m_q$, and a non-trivial explicit calculation is required to show that this contribution vanishes. At second order in the expansion, there are eight relations that are non-trivial consequences of the $1/N$ expansion, all of which are well satisfied within the experimental errors. The average deviation at this order is 7 \MeV for the \De I = 0 mass differences and 0.35 \MeV for the \De I \ne 0 mass differences, consistent with the expectation that the error is of order $1/N^2 \sim 10\%$.Comment: 19 pages, 2 uuencoded ps figs, uses revte

Current Algebras and Symmetries in Bootstrap Theory

In the first paper of this series we showed how, in the bootstrap theory, the currents associated with the hadrons could be determined from a set of self-consistency conditions. In the present paper we show that these "self-consistent" currents satisfy a current algebra. The proof is accomplished without recourse to any approximate model It includes the interesting case of nonconserved currents. The convergence of sum rules derived from current algebras is investigated in detail, and shown to be most rapid when no "nonbootstrap" terms are present. Using these convergence properties, we discuss how and when current algebras can give rise to hadron symmetries

Resolution of the strong CP problem

It is shown that the quark mass aligns QCD $\theta$ vacuum in such a way that the strong CP is conserved, resolving the strong CP problem.Comment: 9 pages;v2 slightly rewritten and expanded;v3 a few points clarified;v4 minor changes, journal versio

Nucleon-Nucleon Scattering under Spin-Isospin Reversal in Large-N_c QCD

The spin-flavor structure of certain nucleon-nucleon scattering observables derived from the large N_c limit of QCD in the kinematical regime where time-dependent mean-field theory is valid is discussed. In previous work, this regime was taken to be where the external momentum was of order N_c which precluded the study of differential cross sections in elastic scattering. Here it is shown that the regime extends down to order N_c^{1/2} which includes the higher end of the elastic regime. The prediction is that in the large N_c limit, observables describable via mean-field theory are unchanged when the spin and isospin of either nucleon are both flipped. This prediction is tested for proton-proton and neutron-proton elastic scattering data and found to fail badly. We argue that this failure can be traced to a lack of a clear separation of scales between momentum of order N_c^{1/2} and N_c^1 when N_c is as small as three. The situation is compounded by an anomalously low particle production threshold due to approximate chiral symmetry.Comment: 5 pages, 1 figur

Zero-brane approach to quantization of biscalar field theory about topological kink-bell solution

We study the properties of the topologically nontrivial doublet solution arisen in the biscalar theory with a fourth-power potential introducing an example of the spontaneous breaking of symmetry. We rule out the zero-brane (non-minimal point particle) action for this doublet as a particle with curvature. When quantizing it as the theory with higher derivatives, we calculate the quantum corrections to the mass of the doublet which could not be obtained by means of the perturbation theory.Comment: some references were adde

Self-Consistent Determination of Coupling Shifts in Broken SU(3)

The possibility that certain patterns of SU(3) symmetry breaking are dynamically enhanced in baryon-meson couplings is studied by bootstrap methods. For the strong couplings, a single dominant enhancement is found. It produces very large symmetry-breaking terms, transforming like an octet, as often conjectured. Experimental consequences are listed, such as a reduction of K-baryon couplings relative to π-baryon couplings which is in accord with the experimental weakness of K relative to π production in many circumstances, such as photoproduction and multi-BeV cosmic-ray collisions. For parity-violating nonleptonic couplings, a dominant octet enhancement is again found, as mentioned in a previous paper, which leads to an excellent fit with experiment. For parity-conserving nonleptonic couplings, on the other hand, several different enhancements compete, and the only conclusion we can draw is that terms with the "abnormal" transformation properties brought in by strong symmetry-breaking corrections are present. Our work provides a dynamical derivation of various phenomenological facts associated with SU(6), such as the dominance of the 35 representation in parity-violating nonleptonic decays

Triviality and the Precision Bound on the Higgs Mass

The triviality of the scalar sector of the standard one-doublet Higgs model implies that this model is only an effective low-energy theory valid below some cut-off scale Lambda. For a heavy higgs this scale must be relatively low (10 TeV or less). Additional interactions coming from the underlying theory, and suppressed by the scale Lambda, give rise to model-dependent corrections to precisely measured electroweak quantities. Dimension six operators arising from the underlying physics naturally contribute to the S and T parameters, and their effects should be included in a global fit to the precision data that determines any limit on the Higgs mass. Using dimensional analysis, we estimate the expected size of these corrections in a custodially-symmetric strongly-interacting underlying theory. Taking these operators' coefficients to be of natural size gives sufficiently large contributions to the T parameter to reconcile Higgs masses as large as 400-500 GeV with the precision data.Comment: 9 pages, 3 epsf figures include

Weak and electromagnetic interactions of the hadrons in bootstrap theory

This is the first of a series of papers on the properties of the weak and electromagnetic currents of the hadrons in the bootstrap theory of strong interactions. In a bootstrap theory, there are many self-consistency conditions relating these weak and electromagnetic parameters to each other. We develop a formalism designed to take the fullest advantage of such bootstrap-like relations. In fact, we conjecture that the weak and electromagnetic properties of the hadrons are determined to a large extent, and perhaps completely, by self-consistency requirements. Some simple calculations of the weak and electromagnetic parameters pertaining to the octet of baryons and decuplet of resonances are given. The comparison of the results of these calculations with the experimental numbers indicates that the above conjecture holds, at least in this case

Thermal Decays in a Hot Fermi Gas

We present a study of the decay of metastable states of a scalar field via thermal activation, in the presence of a finite density of fermions. The process we consider is the nucleation of ``{\it droplets}'' of true vacuum inside the false one. We analyze a one-dimensional system of interacting bosons and fermions, considering the latter at finite temperature and with a given chemical potential. As a consequence of a non-equilibrium formalism previously developed, we obtain time-dependent decay rates.Comment: 18 pages, REVTEX, 9 figures available upon reques