Particle decay in false vacuum

We revisit the problem of decay of a metastable vacuum induced by the presence of a particle. For the bosons of the `master field' the problem is solved in any number of dimensions in terms of the spontaneous decay rate of the false vacuum, while for a fermion we find a closed expression for the decay rate in (1+1) dimensions. It is shown that in the (1+1) dimensional case an infrared problem of one-loop correction to the decay rate of a boson is resolved due to a cancellation between soft modes of the field. We also find the boson decay rate in the `sine-Gordon staircase' model in the limits of strong and weak coupling.Comment: 19 pages, 2 figure

New analysis of semileptonic B decays in the relativistic quark model

We present the new analysis of the semileptonic B decays in the framework of the relativistic quark model based on the quasipotential approach. Decays both to heavy D^{(*)} and light \pi(\rho) mesons are considered. All relativistic effects are systematically taken into account including contributions of the negative-energy states and the wave function transformation from the rest to moving reference frame. For heavy-to-heavy transitions the heavy quark expansion is applied. Leading and subleading Isgur-Wise functions are determined as the overlap integrals of initial and final meson wave functions. For heavy-to-light transitions the explicit relativistic expressions are used to determine the dependence of the form factors on the momentum transfer squared. Such treatment significantly reduces theoretical uncertainties and increases reliability of obtained predictions. All results for form factors, partial and total decay rates agree well with recent experimental data and unquenched lattice calculations. From this comparison we find the following values of the Cabibbo-Kobayashi-Maskawa matrix elements: |V_{cb}|=(3.85\pm0.15\pm 0.20)*10^{-2} and |V_{ub}|=(3.82\pm0.20\pm0.20)*10^{-3}, where the first error is experimental and the second one is theoretical.Comment: 25 pages, 11 figure

Quark structure of hadrons and high energy collisions

There exists a large field for phenomenological models in which the knowledge of the structure of hadrons in terms of QCD constituents obtained from deep inelastic scatterings is related to their behaviour in soft processes. One of the simplest and oldest models is the additive quark model, with the rules of quark statistics following from it. Originally, the relations of quark combinatorics for hadron yields were based on the qualitative description of a multiparticle production process as a process of the production of non-correlated quarks and antiquarks followed by their subsequent fusion into hadrons [20],[21]. As a large amount of new precision measurements appear, and, on the other hand, our understanding of QCD becomes deeper, a new level of understanding of quark-gluon physics in the region of soft interactions forces us to review the relations of quark combinatorics. To do so, an especially good possibility is provided by the experimental data for hadronic Z^0 decays which allow us to check the relations of quark combinatorics for a new type of processes: quark jets in the decays Z^0 -> q\bar{q} -> hadrons [32].Comment: 55 pages, 23 figure

Catalyzed decay of false vacuum in four dimensions

The probability of destruction of a metastable vacuum state by the field of a highly virtual particle with energy $E$ is calculated for a (3+1) dimensional theory in the leading WKB approximation in the thin-wall limit. It is found that the induced nucleation rate of bubbles, capable of expansion, is exponentially small at any energy. The negative exponential power in the rate reaches its maximum at the energy, corresponding to the top of the barrier in the bubble energy, where it is a finite fraction of the same power in the probability of the spontaneous decay of the false vacuum, i.e. at $E=0$.Comment: 9 pages (standard LaTeX)+ 3 figures (one figure in LaTeX, two are appended in PostScript). TPI-MINN-92/31-

The interaction of slow J/psi and psi' with nucleons

The interaction of the charmonium resonances J/psi and psi' with nucleons at low energies is considered using the multipole expansion and low-energy theorems in QCD. A lower bound is established for the relevant gluonic operator average over the nucleon. As a result we find the discussed interaction to be significantly stronger than previously estimated in the literature. In particular we conclude that the cross section of the J/psi - nucleon elastic scattering at the threshold is very likely to exceed 17 millibarn and that existence of bound states of the J/psi in light nuclei is possible. For the psi' resonance we estimate even larger elastic scattering cross section and also a very large cross section of the process psi'+N -> psi+N giving rise to the decay width of tens of MeV for the psi' resonance in heavy nuclei.Comment: 7 page

Functional Determinants in Quantum Field Theory

Functional determinants of differential operators play a prominent role in theoretical and mathematical physics, and in particular in quantum field theory. They are, however, difficult to compute in non-trivial cases. For one dimensional problems, a classical result of Gel'fand and Yaglom dramatically simplifies the problem so that the functional determinant can be computed without computing the spectrum of eigenvalues. Here I report recent progress in extending this approach to higher dimensions (i.e., functional determinants of partial differential operators), with applications in quantum field theory.Comment: Plenary talk at QTS5 (Quantum Theory and Symmetries); 16 pp, 2 fig

Exponentiation of Multiparticle Amplitudes in Scalar Theories

It is argued that the amplitudes of the production of $n$ soft scalar particles by one or a few energetic ones in theories like $\lambda\phi^4$ has the exponential form, $A_n\propto\sqrt{n!}\exp[{1\over\lambda}F(\lambda n,\epsilon)]$, in the regime $\lambda\to 0$, $\lambda n={fixed}$, $\epsilon={fixed}$, where $\epsilon$ is the typical kinetic energy of outgoing particles. Existing results support this conjecture. Several new analytical and numerical results in favor of the exponential behavior of multiparticle amplitudes are presented.Comment: Revtex 3.0, 45 pages, 11 figures (some requires bezier.sty, two postscript figures appended after \end{document}), INR-866/9

Deriving the existence of BBˉ∗B\bar{B}^* bound states from the X(3872) and Heavy Quark Symmetry

We discuss the possibility and the description of bound states between $B$ and $\bar{B}^*$ mesons. We argue that the existence of such a bound state can be deduced from (i) the weakly bound X(3872) state, (ii) certain assumptions about the short range dynamics of the $D\bar{D}^*$ system and (iii) heavy quark symmetry. From these assumptions the binding energy of the possible $B\bar{B}^*$ bound states is determined, first in a theory containing only contact interactions which serves as a straightforward illustration of the method, and then the effects of including the one pion exchange potential are discussed. In this latter case three isoscalar states are predicted: a positive and negative C-parity $^3S_1-{}^3D_1$ state with a binding energy of $20\,{\rm MeV}$ and $6\,{\rm MeV}$ below threshold respectively, and a positive C-parity $^3P_0$ shallow state located almost at the $B\bar{B}^*$ threshold. However, large uncertainties are generated as a consequence of the $1/m_Q$ corrections from heavy quark symmetry. Finally, the newly discovered isovector $Z_b(10610)$ state can be easily accommodated within the present framework by a minor modification of the short range dynamics.Comment: 21 pages, 3 figures; a sign error in the potential has been corrected and new predictions have been compute

Multiparticle tree amplitudes in scalar field theory

Following an argument advanced by Feynman, we consider a method for obtaining the effective action which generates the sum of tree diagrams with external physical particles. This technique is applied, in the unbroken \lambda \phi^4 theory, to the derivation of the threshold amplitude for the production of $n$ scalar particles by $n$ initial particles. The leading contributions to the tree amplitude, which become singular in the threshold limit, exhibit a factorial growth with n.Comment: uuencoded gz-compressed file created by csh script uufile

Two-particle decays of B_c meson into charmonium states

The factorization of hard and soft contributions into the hadronic decays of B_c meson at large recoils is explored in order to evaluate the decay rates into the S, P and D-wave charmonia associated with rho and pi. The constraints of approach applicability and uncertainties of numerical estimates are discussed. The mode with the J/psi in the final state is evaluated taking into account the cascade radiative electromagnetic decays of excited P-wave states, that enlarges the branching ratio by 20-25%.Comment: 13 pages, LaTeX axodraw-style, 1 figure, 2 table