526 research outputs found
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
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- chiral perturbation theory
We consider flavor breaking in the the octet and decuplet baryon masses at
second order in large- chiral perturbation theory, where is the number
of QCD colors. We assume that , where is the number of light quark
flavors, and are the parameters controlling
flavor breaking in chiral perturbation theory. We consistently include
non-analytic contributions to the baryon masses at orders , , and . The corrections are small for
the relations that follow from symmetry alone, but the corrections to
the large- relations are large and have the wrong sign. Chiral
power-counting and large- consistency allow a 2-loop contribution at order
, 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 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 .Comment: 19 pages, 2 uuencoded ps figs, uses revte
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
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
The permutation group S_N and large Nc excited baryons
We study the excited baryon states for an arbitrary number of colors Nc from
the perspective of the permutation group S_N of N objects. Classifying the
transformation properties of states and quark-quark interaction operators under
S_N allows a general analysis of the spin-flavor structure of the mass operator
of these states, in terms of a few unknown constants parameterizing the unknown
spatial structure. We explain how to perform the matching calculation of a
general two-body quark-quark interaction onto the operators of the 1/Nc
expansion. The inclusion of core and excited quark operators is shown to be
necessary. Considering the case of the negative parity L=1 states transforming
in the MS of S_N, we discuss the matching of the one-gluon and the
Goldstone-boson exchange interactions.Comment: 38 pages. Final version to be published in Physical Review
Renormalization of the baryon axial vector current in large-N_c chiral perturbation theory
The baryon axial vector current is computed at one-loop order in heavy baryon
chiral perturbation theory in the large-N_c limit, where N_c is the number of
colors. Loop graphs with octet and decuplet intermediate states cancel to
various orders in N_c as a consequence of the large-N_c spin-flavor symmetry of
QCD baryons. These cancellations are explicitly shown for the general case of
N_f flavors of light quarks. In particular, a new generic cancellation is
identified in the renormalization of the baryon axial vector current at
one-loop order. A comparison with conventional heavy baryon chiral perturbation
theory is performed at the physical values N_c=3, N_f=3.Comment: REVTex4, 29 pages, 2 figures, 6 tables. Equations (32) and (81)
corrected. Some typos fixed. Results and conclusions remain unchange
On Kinks and Bound States in the Gross-Neveu Model
We investigate static space dependent \sigx=\lag\bar\psi\psi\rag saddle
point configurations in the two dimensional Gross-Neveu model in the large N
limit. We solve the saddle point condition for \sigx explicitly by employing
supersymmetric quantum mechanics and using simple properties of the diagonal
resolvent of one dimensional Schr\"odinger operators rather than inverse
scattering techniques. The resulting solutions in the sector of unbroken
supersymmetry are the Callan-Coleman-Gross-Zee kink configurations. We thus
provide a direct and clean construction of these kinks. In the sector of broken
supersymmetry we derive the DHN saddle point configurations. Our method of
finding such non-trivial static configurations may be applied also in other two
dimensional field theories.Comment: Revised version. A new section added with derivation of the DHN
static configurations in the sector of broken supersymmetry. Some references
added as well. 25 pp, latex, e-mail [email protected]
Resolving the Large-N Nuclear Potential Puzzle
The large nuclear potential puzzle arose because three- and
higher-meson exchange contributions to the nucleon-nucleon potential did not
automatically yield cancellations that make these contributions consistent with
the general large scaling rules for the potential. Here it is proposed
that the resolution to this puzzle is that the scaling rules only apply for
energy-independent potentials while all of the cases with apparent
inconsistencies were for energy-dependent potentials. It is shown explicitly
how energy-dependent potentials can have radically different large N behavior
than an equivalent energy-independent one. One class of three-meson graphs is
computed in which the contribution to the energy-independent potential is
consistent with the general large N rules even though the energy-dependent
potential is not.Comment: Corrections to the toy mode
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