Quark-binding effects in inclusive decays of heavy mesons

We present a new approach to the analysis of quark-binding effects in inclusive decays of heavy mesons within the relativistic dispersion quark model. Various differential distributions, such as electron energy spectrum, $q^2$- and $M_X$-distributions, are calculated in terms of the $B$ meson soft wave function which also determines long-distance effects in exclusive transition form factors. Using the quark-model parameters and the $B$ meson wave function previously determined from the description of the exclusive $b \to u$ transitions within the same dispersion approach, we provide numerical results on various distributions in the inclusive $B \to X_c l\nu$ decays.Comment: revtex, 18 pages, preprint HD-THEP-99-50 (Heidelberg) and RM3-TH/99-13 (Roma

Pressure Waves due to Rapid Evaporation of Water Droplet in Liquid Lead Coolant

Flash evaporation of a superheated water droplet in heavy liquid metal coolant (lead) is considered, in application to the analysis of a lead-cooled fast reactor steam generator tube rupture accident. The model is based on thermodynamic equilibrium formulation for the expanding water-steam mixture and inviscid compressible formulation for the surrounding liquid lead, with the interface conditions determined from the solution of the Riemann problem. Numerical solution is performed in the spherically symmetric geometry using a conservative numerical scheme with a moving sharp interface. Transient pressure and velocity profiles in each phase are presented for the parameters typical of the steam generator tube rupture accidents, demonstrating the process of boiling water expansion and pressure wave formation in the coolant. The results obtained are compared with a simplified model which considers the volume-averaged parameters of boiling water droplets and considers coolant as an incompressible liquid. Good agreement between the full and simplified models is demonstrated. Impacts of coolant flow on structures caused by pressure wave propagation and subsequent coolant flow are discussed

Non-local anomaly of the axial-vector current for bound states

We demonstrate that the amplitude $<\rho\gamma|\partial_\nu (\bar q\gamma_\nu \gamma_5 q)|0>$ does not vanish in the limit of zero quark masses. This represents a new kind of violation of the classical equation of motion for the axial current and should be interpreted as the axial anomaly for bound states. The anomaly emerges in spite of the fact that the one loop integrals are ultraviolet-finite as guaranteed by the presence of the bound-state wave function. As a result, the amplitude behaves like $\sim 1/p^2$ in the limit of a large momentum $p$ of the current. This is to be compared with the amplitude $$ which remains finite in the limit $p^2\to\infty$. The observed effect leads to the modification of the classical equation of motion of the axial-vector current in terms of the non-local operator and can be formulated as a non-local axial anomaly for bound states.Comment: revtex, 4 pages, numerical value for $\kappa$ in Eq. (19) is corrected, Eqs. (22) and (23) are modified. New references added. Results remain unchange

Accuracy of the pion elastic form factor extracted from a local-duality sum rule

We analyze the accuracy of the pion elastic form factor predicted by a local-duality (LD) version of dispersive sum rules. To probe the precision of this theoretical approach, we adopt potential models with interactions that involve both Coulomb and confining terms. In this case, the exact form factor may be obtained from the solution of the Schroedinger equation and confronted with the LD sum rule results. We use parameter values appropriate for hadron physics and observe that, independently of the details of the confining interaction, the deviation of the LD form factor from the exact form factor culminates in the region Q^2~4-6 GeV^2. For larger Q^2, the accuracy of the LD description increases rather fast with Q^2. A similar picture is expected for QCD. For the pion form factor, existing data suggest that the LD limit may be reached already at the relatively low values Q^2=4-10 GeV^2. Thus, large deviations of the pion form factor from the behaviour predicted by LD QCD sum rules for higher values of Q^2, as found by some recent analyses, appear to us quite improbable. New accurate data on the pion form factor at Q^2=4-10 GeV^2 expected soon from JLab will have important implications for the behaviour of the pion form factor in a broad Q^2 range up to asymptotically large values of Q^2.Comment: 12 pages, extended version, conclusions remain unchange

Possible Supersymmetric Effects on Angular Distributions in B→K∗(→Kπ)ℓ+ℓ−B \to K^* (\to K \pi) \ell^+ \ell^- Decays

We investigate the angular distributions of the rare B decay, $B \to K^* (\to K \pi) \ell^+ \ell^-$, in general supersymmetric extensions of the standard model. We consider the new physics contributions from the operators $O_{7,8,9,10}$ in small invariant mass region of lepton pair. We show that the azimuthal angle distribution of the decay can tell us the new physics effects clearly from the behavior of the distribution, even if new physics does not change the decay rate substantially from the standard model prediction

Rare exclusive semileptonic b -> s transitions in the Standard Model

We study long-distance effects in rare exclusive semileptonic decays B -> (K, K*) (l+ l-, nu bar{nu}) and analyze dilepton spectra and asymmetries within the framework of the Standard Model. The form factors, describing the meson transition amplitudes of the effective Hamiltonian are calculated within the lattice-constrained dispersion quark model: the form factors are given by dispersion representations through the wave functions of the initial and final mesons, and these wave functions are chosen such that the B -> K* transition form factors agree with the lattice results at large q**2. We calculate branching ratios of semileptonic B -> K, K* transition modes and study the sensitivity of observables to the long-distance contributions. The shape of the forward-backward asymmetry and the longitudinal lepton polarization asymmetry are found to be independent of the long-distance effects and mainly determined by the values of the Wilson coefficients in the Standard Model.Comment: revtex, 17 pp., 5 figures with epsfig.st

Good covers are algorithmically unrecognizable

A good cover in R^d is a collection of open contractible sets in R^d such that the intersection of any subcollection is either contractible or empty. Motivated by an analogy with convex sets, intersection patterns of good covers were studied intensively. Our main result is that intersection patterns of good covers are algorithmically unrecognizable. More precisely, the intersection pattern of a good cover can be stored in a simplicial complex called nerve which records which subfamilies of the good cover intersect. A simplicial complex is topologically d-representable if it is isomorphic to the nerve of a good cover in R^d. We prove that it is algorithmically undecidable whether a given simplicial complex is topologically d-representable for any fixed d \geq 5. The result remains also valid if we replace good covers with acyclic covers or with covers by open d-balls. As an auxiliary result we prove that if a simplicial complex is PL embeddable into R^d, then it is topologically d-representable. We also supply this result with showing that if a "sufficiently fine" subdivision of a k-dimensional complex is d-representable and k \leq (2d-3)/3, then the complex is PL embeddable into R^d.Comment: 22 pages, 5 figures; result extended also to acyclic covers in version

Decay constants of heavy pseudoscalar mesons from QCD sum rules

We revisit the sum-rule extraction of the decay constants of the D, Ds, B, and Bs mesons from the two-point correlator of heavy-light pseudoscalar currents. We use the operator product expansion for this correlator expressed in terms of the MSbar heavy-quark mass, for which the perturbative expansion exhibits a reasonable convergence. Our main emphasis is laid on the control over the uncertainties in the decay constants, related both to the input QCD parameters and to the limited accuracy of the method of sum-rules. This becomes possible due to the application of our procedure of extracting hadron observables that involves as novel feature dual thresholds depending on the Borel parameter. For charmed mesons, we find the decay constants f_D=206.2\pm 7.3(OPE)\pm 5.1(syst) MeV and f_Ds=245.3\pm 15.7(OPE)\pm 4.5(syst) MeV. For beauty mesons, the decay constants turn out to be extremely sensitive to the precise value of mb(mb). By requiring our sum-rule estimate to match the average of the lattice results for f_B, a very accurate value mb(mb)=4.245\pm 0.025 GeV is extracted, leading to f_B=193.4\pm 12.3(OPE)\pm 4.3(syst) MeV and f_Bs=232.5\pm 18.6(OPE)\pm 2.4(syst) MeV.Comment: 12 page

New results on the limit for the width of the exotic Theta^+ resonance

We investigate the impact of the \Theta^+(1540) resonance on differential and integrated cross sections for the reaction K^+d{\to}K^0pp, where experimental information is available at kaon momenta below 640 MeV/c. The calculation utilizes the J\"ulich KN model and extensions of it that include contributions from a \Theta^+(1540) state with different widths. The evaluation of the reaction K^+d{\to}K^0pp takes into account effects due to the Fermi motion of the nucleons within the deuteron and the final three-body kinematics. We conclude that the available data constrain the width of the \Theta^+(1540) to be less than 1 MeV.Comment: 5 pages, 5 figures, updated version, accepted for publication in Phys. Lett.