Aspects Of Heavy Quark Theory

Recent achievements in the heavy quark theory are critically reviewed. The emphasis is put on those aspects which either did not attract enough attention or cause heated debates in the current literature. Among other topics we discuss (i) basic parameters of the heavy quark theory; (ii) a class of exact QCD inequalities; (iii) new heavy quark sum rules; (iv) virial theorem; (v) applications (|V_cb| from the total semileptonic width and from the B->D* transition at zero recoil). In some instances new derivations of the previously known results are given, or new aspects addressed. In particular, we dwell on the exact QCD inequalities. Furthermore, a toy model is considered that may shed light on the controversy regarding the value of the kinetic energy of heavy quarks obtained by different methods.Comment: 67 pages, 6 Figures; plain LaTeX. Changes: Some equations in Sect.4 related to spin-nonsinglet sum rules are corrected. The references are updated

Calculation of 1/m^3 terms in the total semileptonic width of D mesons.

We calculate the 1/$m^3_c$ corrections in the inclusive semileptonic widths of $D$ mesons. We show that these are due to the novel penguin type operators that appear at this level in the transition operator. Taking into account the nonperturbative corrections leads to the predicted value of the semileptonic width significantly lower than the experimental value. The $1/m^3_c$ worsen the situation or at the very least, within uncertainty, give small contribution. We indicate possible ways out. It seems most probable that violations of duality are noticeable in the energy range characteristic to the inclusive decays in the charm family. Theoretically these deviations are related to divergence of the high-order terms in the power expansion in the inverse heavy quark mass.Comment: Final version accepted for publication in Physical Review D (19 pages, 5 figures appended as two PS files at the end of the LATEX file

Determining V(ub) from B+ --> D*+(s) e+ e- and B+ --> D*+ e+ e-

It was recently pointed out that the decays B^+ --> D^{*+}_s gamma and B^+ --> D^{*+} gamma can be used for an extraction of |V_{ub}|. The theory of these decays is poorly understood. It was shown that in a world of almost degenerate b and c-quarks the decay would be computable. The severe difficulties that are encountered in the realistic calculation stem primarily from the very hard photon produced in the two body decay. We point out that in the decays B^+ --> D^{*+}_s e^+e^- and B^+ --> D^{*+} e^+e^- the photon vertex is soft when the charmed meson is nearly at rest (in the B^+ rest frame). This allows us to compute with some confidence the decay rate in a restricted but interesting kinematic regime. Given enough data the extraction of V_{ub} with reasonably small uncertainties could proceed through an analysis of these exclusive decays much as is done in the determination of V_{cb}.Comment: 9 pages, latex (revtex), replaced with published versio

Multivalued Fields on the Complex Plane and Conformal Field Theories

In this paper a class of conformal field theories with nonabelian and discrete group of symmetry is investigated. These theories are realized in terms of free scalar fields starting from the simple $b-c$ systems and scalar fields on algebraic curves. The Knizhnik-Zamolodchikov equations for the conformal blocks can be explicitly solved. Besides of the fact that one obtains in this way an entire class of theories in which the operators obey a nonstandard statistics, these systems are interesting in exploring the connection between statistics and curved space-times, at least in the two dimensional case.Comment: (revised version), 30 pages + one figure (not included), (requires harvmac.tex), LMU-TPW 92-1

Hierarchical wave function, Fock cyclic condition and spin-statistics relation in the spin-singlet fractional quantum Hall effect

We construct the hierarchical wave function of the spin-singlet fractional quantum Hall effect, which turns out to satisfy Fock cyclic condition. The spin-statistics relation of the quasi-particles in the spin-singlet fractional quantum Hall effect is also discussed. Then we use particle-hole conjugation to check the wave function.Comment: 23 pages, PHYZZ

Updated Analysis of a_1 and a_2 in Hadronic Two-body Decays of B Mesons

Using the recent experimental data of $B\to D^{(*)}(\pi,\rho)$, $B\to D^{(*)} D_s^{(*)}$, $B\to J/\psi K^{(*)}$ and various model calculations on form factors, we re-analyze the effective coefficients a_1 and a_2 and their ratio. QCD and electroweak penguin corrections to a_1 from $B\to D^{(*)}D_s^{(*)}$ and a_2 from $B\to J/\psi K^{(*)}$ are estimated. In addition to the model-dependent determination, the effective coefficient a_1 is also extracted in a model-independent way as the decay modes $B\to D^{(*)}h$ are related by factorization to the measured semileptonic distribution of $B\to D^{(*)}\ell \bar\nu$ at $q^2=m_h^2$. Moreover, this enables us to extract model-independent heavy-to-heavy form factors, for example, $F_0^{BD}(m_\pi^2)=0.66\pm0.06\pm0.05$ and $A_0^{BD^*}(m_\pi^2)=0.56\pm0.03\pm0.04$. The determination of the magnitude of a_2 from $B\to J/\psi K^{(*)}$ depends on the form factors $F_1^{BK}$, $A_{1,2}^{BK^*}$ and $V^{BK^*}$ at $q^2=m^2_{J/\psi}$. By requiring that a_2 be process insensitive (i.e., the value of a_2 extracted from $J/\psi K$ and $J/\psi K^*$ states should be similar), as implied by the factorization hypothesis, we find that $B\to K^{(*)}$ form factors are severely constrained; they respect the relation $F_1^{BK}(m^2_{J/\psi})\approx 1.9 A_1^{BK^*}(m^2_{J/\psi})$. Form factors $A_2^{BK^*}$ and $V^{BK^*}$ at $q^2=m^2_{J/\psi}$ inferred from the measurements of the longitudinal polarization fraction and the P-wave component in $B\to J/\psi K^*$ are obtained. A stringent upper limit on a_2 is derived from the current bound on \ov B^0\to D^0\pi^0 and it is sensitive to final-state interactions.Comment: 33 pages, 2 figures. Typos in Tables I and IX are corrected. To appear in Phys. Rev.

Hadronic Spectral Moments in Semileptonic B Decays With a Lepton Energy Cut

We compute the first two moments of the final hadronic invariant mass in inclusive semileptonic B decay, in the presence of a cut on the charged lepton energy. These moments may be measured directly by experiments at the Upsilon(4S) using the neutrino reconstruction technique, which requires such a cut. Measurement of these moments will place constraints on the nonperturbative parameters \bar\Lambda and \lambda_1, which are relevant for extracting the quark masses m_b and m_c, as well as the CKM angle V_cb. We include terms of order \alpha_s^2\beta_0 and 1/m_b^3 in the operator product expansion, and use the latter to estimate the theoretical uncertainty in the extraction of \bar\Lambda and \lambda_1.Comment: 13 pages, 5 figures, REVTe

The Baryonic Tully-Fisher Relation

We explore the Tully-Fisher relation over five decades in stellar mass in galaxies with circular velocities ranging over 30 < Vc < 300 km/s. We find a clear break in the optical Tully-Fisher relation: field galaxies with Vc < 90 km/s fall below the relation defined by brighter galaxies. These faint galaxies are however very gas rich; adding in the gas mass and plotting baryonic disk mass Md = M* + Mg in place of luminosity restores a single linear relation. The Tully-Fisher relation thus appears fundamentally to be a relation between rotation velocity and total baryonic mass of the form Md = A Vc^4.Comment: 10 pages including 1 color figure. Accepted for publication in ApJ Letter

Stability of Chiral Luttinger Liquids and Abelian Quantum Hall States.

A criterion is given for topological stability of Abelian quantum Hall states, and of Luttinger liquids at the boundaries between such states; this suggests a selection rule on states in the quantum Hall hierarchy theory. The linear response of Luttinger liquids to electromagnetic fields is described: the Hall conductance is quantized, irrespective of whether edge modes propagate in different directions.Comment: 12 pages, LaTeX (RevTeX 3.0

Annihilation, Rescattering, and CP Asymmetries in B Meson Decays

A number of $B$ meson decays may proceed only through participation of the spectator quark, whether through amplitudes proportional to $f_B/m_B$ or via rescattering from other less-suppressed amplitudes. An expected hierarchy of amplitudes in the absence of rescattering will be violated by rescattering corrections. Such violations could point the way toward channels in which final-state interactions could be important. Cases in which final state phases can lead to large CP asymmetries are pointed out.Comment: 9 page