Calculating Phases Between B => K* pi Amplitudes

A phase $\Delta \Phi$ between amplitudes for $B^0 \to K^{*0} \pi^0$ and $B^0 \to K^{*+} \pi^-$ plays a crucial role in a method for constraining Cabibbo-Kobayashi-Maskawa (CKM) parameters. We present a general argument for destructive interference between amplitudes for $B^0 \to K^{*+} \pi^-$ and $B^0 \to K^{*0} \pi^0$ forming together a smaller $I(K^* \pi) = 3/2$ amplitude. Applying flavor SU(3) and allowing for conservative theoretical uncertainties, we obtain lower limits on $|\Delta \Phi|$ and its charge-conjugate. Values of these two phases favored by the BaBar Collaboration are in good agreement with our bounds.Comment: 12 pages, 6 figures; slight revisions and clarification

Decays of Non-strange Negative Parity Baryons in the 1/Nc Expansion

The decays of non-strange negative parity baryons via the emission of single $\pi$ and $\eta$ mesons are analyzed in the framework of the $1/N_c$ expansion. A basis of spin-flavor operators for the partial wave amplitudes is established to order $1/N_c$ and the unknown effective coefficients are determined by fitting to the S- and D-wave partial widths as provided by the Particle Data Group. A set of relations between widths that result at the leading order, i.e. order $N_c^0$, is given and tested with the available data. Up to a few exceptions, a good description of the partial decays widths is already obtained at that order. Because of the rather large errors in the empirical input data the next to leading order fit fails to pin down with satisfactory accuracy the subleading effective coefficients. The hierarchy expected from the $1/N_c$ expansion is reflected in the results.Comment: 24 pages, 8 table

Masses of the 70- Baryons in Large Nc QCD

The masses of the negative parity 70-plet baryons are analyzed in large N_c QCD to order 1/N_c and to first order in SU(3) symmetry breaking. The existing experimental data are well reproduced and twenty new observables are predicted. The leading order SU(6) spin-flavor symmetry breaking is small and, as it occurs in the quark model, the subleading in 1/N_c hyperfine interaction is the dominant source of the breaking. It is found that the Lambda(1405) and Lambda(1520) are well described as three-quark states and spin-orbit partners. New relations between splittings in different SU(3) multiplets are found.Comment: 11 pages; references were added and a couple of improvements to the text were mad

Excited Baryon Decay Widths in Large N_c QCD

We study excited baryon decay widths in large N_c QCD. It was suggested previously that some spin-flavor mixed-symmetric baryon states have strong couplings of O(N_c^{-1/2}) to nucleons [implying narrow widths of O(1/N_c)], as opposed to the generic expectation based on Witten's counting rules of an O(N_c^0) coupling. The calculation obtaining these narrow widths was performed in the context of a simple quark-shell model. This paper addresses the question of whether the existence of such narrow states is a general property of large N_c QCD. We show that a general large N_c QCD analysis does not predict such narrow states; rather they are a consequence of the extreme simplicity of the quark model.Comment: 9 page

1/Nc Countings in Baryons

The $1/N_c$ power countings for baryon decays and configuration mixings are determined by means of a non-relativistic quark picture. Such countings are expected to be robust under changes in the quark masses, and therefore valid as these become light. It is shown that excited baryons have natural widths of ${\cal{O}}(N_c^0)$. These dominant widths are due to the decays that proceed directly to the ground state baryons, with cascade decays being suppressed to ${\cal{O}}(1/N_c)$. Configuration mixings, defined as mixings between states belonging to different $O(3)\times SU(2 N_f)$ multiplets, are shown to be sub-leading in an expansion in $1/\sqrt{N_c}$ when they involve the ground state baryons, while the mixings between excited states can be ${\cal{O}}(N_c^0)$.Comment: 19 pages, 1 figure An omission that changes the conclusions on configuration mixings has been correcte

Inclusive Semileptonic Decays in QCD Including Lepton Mass Effects

Starting from an Operator Product Expansion in the Heavy Quark Effective Theory up to order 1/m_b^2 we calculate the inclusive semileptonic decays of unpolarized bottom hadrons including lepton mass effects. We calculate the differential decay spectra d\Gamma/(dE_\tau ), and the total decay rate for B meson decays to final states containing a \tau lepton.Comment: 16 pages + 4 figs. appended in uuencoded form, LaTeX, MZ-TH/93-3

Excited Baryons in Large N_c QCD Revisited: The Resonance Picture Versus Single-Quark Excitations

We analyze excited baryon properties via a 1/N_c expansion from two perspectives: as resonances in meson-nucleon scattering, and as single-quark excitations in the context of a simple quark model. For both types of analysis one can derive novel patterns of degeneracy that emerge as N_c --> \infty, and that are shown to be compatible with one another. This helps justify the single-quark excitation picture and may give some insight into its successes. We also find that in the large N_c limit one of the S_{11} baryons does not couple to the pi-N channel but couples to the eta-N channel. This is empirically observed in the N(1535), which couples very weakly to the pi-N channel and quite strongly to the eta-N channel. The comparatively strong coupling of the N(1650) to the pi-N channel and weak coupling to eta-N channel is also predicted. In the context of the simple quark model picture we reproduce expressions for mixing angles that are accurate up to O(1/N_c) corrections and are in good agreement with mixing angles extracted phenomenologically.Comment: 13 pages, ReVTeX

Chiral Multiplets of Large-N Ground State Baryons

I show that in the large-N limit the ground state baryons with helicity h fall into an ((N-2h)/4,(N+2h)/4) irreducible representation of SU(2)XSU(2). This representation determines the absolute normalization of the ground state baryon axial vector couplings at large-N. Results map precisely to (spin-flavor) SU(4) results. For instance, I find g_A =(N+2)/3. As a consequence of this multiplet structure, chiral symmetry forbids pion transitions between the ground state baryons and other baryon towers in the large-N limit.Comment: 6 pages TeX and mtexsis.te

One-pion transitions between heavy baryons in the constituent quark model

Single pion transitions of S wave to S wave, P wave to S wave and P wave to P wave heavy baryons are analyzed in the framework of the Heavy Quark Symmetry limit (HQS). We use a constituent quark model picture for the light diquark system with an underlying SU(2N_{f}) X O(3) symmetry to reduce the number of the HQS coupling factors required to describe these transitions. We also use the quantum theory of angular momentum to rewrite the one-pion transitions constituent quark model results in a more general form using the 6j- and 9j-symbols. We finally estimate the decay rates of some single pion transitions between charm baryon states.Comment: Latex, 33 pages including 2 figures (Postscript). Some typos are corrected with minor changes. Two references were added to the final version which will appear in Phy. Rev.

Bosonic Operator Methods for the Quark Model

Quark model matrix elements can be computed using bosonic operators and the holomorphic representation for the harmonic oscillator. The technique is illustrated for normal and exotic baryons for an arbitrary number of colors. The computations are much simpler than those using conventional quark model wavefunctions