Unitarity Constraints on the B and B^* Form Factors from QCD Analyticity and Heavy Meson Spin Symmetry

A method of deriving bounds on the weak meson form factors, based on perturbative QCD, analyticity and unitarity, is generalized in order to fully exploit heavy quark spin symmetry in the ground state $(L=0)$ doublet of pseudoscalar $(B)$ and vector $(B^*)$ mesons. All the relevant form factors of these mesons are taken into account in the unitarity sum. They are treated as independent functions along the timelike axis, being related by spin symmetry only near the zero recoil point. Heavy quark vacuum polarisation up to three loops in perturbative QCD and the experimental cross sections $\sigma(e^+e^- \rightarrow \Upsilon)$ are used as input. We obtain bounds on the charge radius of the elastic form factor of the $B$ meson, which considerably improve previous results derived in the same framework.Comment: 13 pages LaTex, 1 figure as a separate ps fil

Ultraviolet Complete Electroweak Model Without a Higgs Particle

An electroweak model with running coupling constants described by an energy dependent entire function is utraviolet complete and avoids unitarity violations for energies above 1 TeV. The action contains no physical scalar fields and no Higgs particle and the physical electroweak model fields are local and satisfy microcausality. The $W$ and $Z$ masses are compatible with a symmetry breaking $SU(2)_L\times U(1)_Y \rightarrow U(1)_{\rm em}$, which retains a massless photon. The vertex couplings possess an energy scale $\Lambda_W > 1$ TeV predicting scattering amplitudes that can be tested at the LHC.Comment: 19 pages, no figures, LaTex file. Equation and text corrected. Reference added. Results remain the same. Final version published in European Physics Journal Plus, 126 (2011

Non-Localizability and Asymptotic Commutativity

The mathematical formalism commonly used in treating nonlocal highly singular interactions is revised. The notion of support cone is introduced which replaces that of support for nonlocalizable distributions. Such support cones are proven to exist for distributions defined on the Gelfand-Shilov spaces $S^\beta$, where $0<\beta <1$ . This result leads to a refinement of previous generalizations of the local commutativity condition to nonlocal quantum fields. For string propagators, a new derivation of a representation similar to that of K\"{a}llen-Lehmann is proposed. It is applicable to any initial and final string configurations and manifests exponential growth of spectral densities intrinsic in nonlocalizable theories.Comment: This version is identical to the initial one whose ps and pdf files were unavailable, with few corrections of misprint

Theory of unitarity bounds and low energy form factors

We present a general formalism for deriving bounds on the shape parameters of the weak and electromagnetic form factors using as input correlators calculated from perturbative QCD, and exploiting analyticity and unitarity. The values resulting from the symmetries of QCD at low energies or from lattice calculations at special points inside the analyticity domain can beincluded in an exact way. We write down the general solution of the corresponding Meiman problem for an arbitrary number of interior constraints and the integral equations that allow one to include the phase of the form factor along a part of the unitarity cut. A formalism that includes the phase and some information on the modulus along a part of the cut is also given. For illustration we present constraints on the slope and curvature of the K_l3 scalar form factor and discuss our findings in some detail. The techniques are useful for checking the consistency of various inputs and for controlling the parameterizations of the form factors entering precision predictions in flavor physics.Comment: 11 pages latex using EPJ style files, 5 figures; v2 is version accepted by EPJA in Tools section; sentences and figures improve

Integrable Systems

Integrable systems which do not have an \u201cobvious\u201c group symmetry, beginning with the results of Poincar\ue9 and Bruns at the end of the last century, have been perceived as something exotic. The very insignificant list of such examples practically did not change until the 1960\u2019s. Although a number of fundamental methods of mathematical physics were based essentially on the perturbation-theory analysis of the simplest integrable examples, ideas about the structure of nontrivial integrable systems did not exert any real influence on the development of physics