4,899 research outputs found
New Relations for Excited Baryons in Large N_c QCD
We show that excited baryons in large N_c QCD form multiplets, within which
masses are first split at O(1/N_c). The dominant couplings of resonances to
various mesons are highly constrained: The N(1535) decays at leading 1/N_c
order exclusively to eta-N rather than pi-N, and vice versa for the N(1650).
This multiplet structure is reproduced by a simple large N_c quark model, well
studied in the literature, that describes resonances as single-quark
excitations.Comment: 4 pages, no figures, ReVTeX 4. Includes new discussion of previous
work on excited baryon tower
Model-Independent Bounds on
We present a model-independent bound on . This bound is constructed by constraining the form
factors through a combination of dispersive relations, heavy-quark relations at
zero-recoil, and the limited existing determinations from lattice QCD. The
resulting 95\% confidence-level bound, , agrees
with the recent LHCb result at , and rules out some previously
suggested model form factors.Comment: 19 pages, 4 figures, JHEP format, revised to match published versio
At what sample size do correlations stabilize?
Sample correlations converge to the population value with increasing sample size, but the estimates are often inaccurate in small samples. In this report we use Monte-Carlo simulations to determine the critical sample size from which on the magnitude of a correlation can be expected to be stable. The necessary sample size to achieve stable estimates for correlations depends on the effect size, the width of the corridor of stability (i.e., a corridor around the true value where deviations are tolerated), and the requested confidence that the trajectory does not leave this corridor any more. Results indicate that in typical scenarios the sample size should approach 250 for stable estimates
Baryons in QCD_{AS} at Large N_c: A Roundabout Approach
QCD_{AS}, a variant of large N_c QCD in which quarks transform under the
color two-index antisymmetric representation, reduces to standard QCD at N_c =
3 and provides an alternative to the usual large N_c extrapolation that uses
fundamental representation quarks. Previous strong plausibility arguments
assert that the QCD_{AS} baryon mass scales as N_c^2; however, the complicated
combinatoric problem associated with quarks carrying two color indices impeded
a complete demonstration. We develop a diagrammatic technique to solve this
problem. The key ingredient is the introduction of an effective multi-gluon
vertex: a "traffic circle" or "roundabout" diagram. We show that arbitrarily
complicated diagrams can be reduced to simple ones with the same leading N_c
scaling using this device, and that the leading contribution to baryon mass
does, in fact, scale as N_c^2.Comment: 9 pages, 9 pdf figures, ReVTeX with pdflate
Interplay of the Chiral and Large N_c Limits in pi N Scattering
Light-quark hadronic physics admits two useful systematic expansions, the
chiral and 1/N_c expansions. Their respective limits do not commute, making
such cases where both expansions may be considered to be especially
interesting. We first study pi N scattering lengths, showing that (as expected
for such soft-pion quantities) the chiral expansion converges more rapidly than
the 1/N_c expansion, although the latter nevertheless continues to hold. We
also study the Adler-Weisberger and Goldberger-Miyazawa-Oehme sum rules of pi N
scattering, finding that both fail if the large N_c limit is taken prior to the
chiral limit.Comment: 10 pages, ReVTe
Phenomenology of the Baryon Resonance 70-plet at Large N_c
We examine the multiplet structure and decay channels of baryon resonances in
the large N_c QCD generalization of the N_c = 3 SU(6) spin-flavor 70. We show
that this ``70'', while a construct of large N_c quark models, actually
consists of five model-independent irreducible spin-flavor multiplets in the
large N_c limit. The preferred decay modes for these resonances fundamentally
depend upon which of the five multiplets to which the resonance belongs. For
example, there exists an SU(3) ``8'' of resonances that is eta-philic and
pi-phobic, and an ``8'' that is the reverse. Moreover, resonances with a strong
SU(3) ``1'' component prefer to decay via a K-bar rather than via a pi.
Remarkably, available data appears to bear out these conclusions.Comment: 26 pages, ReVTe
SU(3) Clebsch-Gordan Coefficients for Baryon-Meson Coupling at Arbitrary N_c
We present explicit formulae for the SU(3) Clebsch-Gordan coefficients that
are relevant for the couplings of large N_c baryons to mesons. In particular,
we compute the Clebsch-Gordan series for the coupling of the octet (associated
with mesons, and remains the correct representation at large N_c) to the large
N_c analogs of the baryon octet and decuplet representations.Comment: 8 pages, no figures, ReVTe
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