Cluster decomposition of Veneziano amplitudes

A simple general rule is given for writing down the factorized form of an N-point Veneziano amplitude when it is decomposed into several clusters separated by high energies. It is hoped that while the explicit form of the cluster vertices may be useful phenomenologically, the manner in which they are obtained may also be instructive when considering the factorization of N-point functions in general. Note that factorization along trajectories as considered here differs in meaning from that of residues at resonance poles as embodied in the operator formalism.     

A fresh look at exotics

Simple quark model considerations suggest that the least massive oxotic mesons and baryons may occur close to the nucleon-antinucleon and nucleon-nucleon-antinucleon thresholds respectively. The fact that such channels are energetically open for the decay of these exotics means that both production and decay can proceed via allowed duality diagrams. We suggest three specific reactions which may permit their detection.     

A fresh look at neutrino oscillations

We analyze the present experimental situation on neutrino oscillations in the standard weak interaction theory with three neutrinos. Sizeable oscillations ν_e ? ν_τ are compatible with, and perhaps indicated by, present data.     

On the freund-witten adelic formula for Veneziano amplitudes

On the basis of the analysis of the adele group (Tate's formula), a regularization for the divergent infinite product ofp-adic Г-functions $$\Gamma _p (\alpha ) = \frac{{1 - p^{\alpha - 1} }}{{[ - p^{ - \alpha } }}$$ is proposed, and the adelic formula is proved $$reg\coprod\limits_{p = 2}^\infty {\Gamma _p (\alpha )} = \frac{{\zeta (\alpha )}}{{\zeta (1 - \alpha )}}$$ whereζ(α) is the Riemannζ-function.     

A fresh look at the statistical bootstrap model

A new interpretation of the statistical bootstrap model is proposed, on the basis of which the statistical bootstrap equation is modified. A deep relationship between the statistical bootstrap model and the Pomeranchuk model for multiple hadron production is established and as a result the significance of the volume V in the statistical bootstrap model is elucidated.     

New strings for old Veneziano amplitudes: I. Analytical treatment

The bosonic string theory evolved as an attempt to find a physical/quantum mechanical model capable of reproducing Euler’s beta function (Veneziano amplitude) and its multidimensional analogue. The multidimensional analogue of beta function was studied mathematically for some time from different angles by mathematicians such as Selberg, Weil and Deligne, among many others. The results of their studies apparently were not taken into account in physics literature on string theory. In a recent publication [IJMPA 19 (2004) 1655] an attempt was made to restore the missing links. The results of this publication are incomplete, however, since no attempts were made at reproduction of known spectra of both open an closed bosonic strings or at restoration of the underlying model(s) reproducing such spectra. Nevertheless, as discussed in this publication the existing mathematical interpretation of the multidimensional analogue of Euler’s beta function as one of the periods associated with the corresponding differential form “living” on the Fermat-type (hyper)surfaces, happens to be crucial for restoration of the quantum/statistical mechanical model reproducing such generalized beta function. Unlike the traditional formulations, this model is supersymmetric. Details leading to restoration of this model will be presented in the forthcoming Parts 2–4 of our work. They are devoted, respectively, to the group-theoretic, symplectic and combinatorial treatments of this model. In this paper the discussion is restricted mainly to the study of analytical properties of the multiparticle Veneziano and Veneziano-like (tachyon-free) amplitudes. In the last case, we demonstrate that the Veneziano-like amplitudes alone (with parameters adjusted accordingly) are capable of reproducing known spectra of both open and closed bosonic strings. The choice of parameters is subject to some constraints dictated by the mathematical interpretation of these amplitudes as periods of Fermat-type (hyper)surfaces considered as complex manifolds of Hodge-type.     

A fresh look at the electric-field dependence of surface-atom binding energy

This paper aims to clarify the theoretical concepts associated with the field dependence of surface-atom binding energy. The various coefficients involved are defined, and orbital-polarization and charge-transfer effects are distinguished. It is demonstrated that the latter, as well as the former, may have an F² form. A new empirical method of estimating the polarization-energy coefficient for a field-evaporating surface atom is described: this is based on the joint measurements of activation energy and onset appearance energy made by Ernst. His data for rhodium are reanalysed to give the value 1.05 ± 0.3 meV V^?2 nm². This value is then used to show that polarization-type effects will influence the interpretation of field-sensitivity data. Further experiments are called for.     

Probing quark-distribution amplitudes through generalized parton distributions at large momentum transfer

In the large momentum transfer limit, generalized parton distributions can be calculated through a QCD factorization theorem which involves perturbatively calculable hard kernels and light-cone parton distribution amplitudes of hadrons. We illustrate this through the H(q)(x,xi,t) distribution for the pion and the proton, presenting the hard kernels at leading order. As a result, experimental data on the generalized parton distributions in this regime can be used to determine the functional form of the parton distribution amplitudes which has thus far been quite challenging to obtain. Our result can also be used as a constraint in phenomenological generalized parton distribution parametrizations.     

A fresh look at diffraction from a nonabsorbing perfect crystal in the Bragg-Laue configuration

The Bragg diffraction from a thick, nonabsorbing perfect crystal theory of dynamical diffraction. The intensities of two beams, one in the incident and the other in the diffracted direction, exciting the side face of the crystal are characterised. The implications of such beams for neutron diffraction experiments are indicated.     

New techniques for new sources: A fresh look at energy-dispersive diffraction for high-pressure studies

Abstract

Energy-dispersive diffraction is the most frequently used technique for high-pressure studies with synchrotron radiation. For optimum performance it requires high-energy radiation and few existing sources are able to meet this requirement. This is also important with large volume devices which demand even higher energies in order to obtain sufficient transmission. When working with diamond-anvil cells, the main experimental difficulties arise from the very small sample sizes. The use of a conical diffraction geometry increases the diffracted intensities, improves the signal-to-noise ratio and largely overcomes the crystallite statistics problem. This technique can also be used to greatly simplify high-pressure single-crystal studies. Combining these developments with recent progress in detectors and electronics will open up the field of high-pressure kinetics, but it is only with the operation of third generation synchrotron sources such as the ESRF that the present experimental limitations will be overcome.

Presented at the IUCr Workshop on ‘Synchrotron Radiation Instrumentation for High Pressure Crystallography’. Daresbury Laboratory 20-21 July 1991     

A generalized leading-term approximation of high-energy scattering amplitudes in Yang-Mills theory

In this paper, the high-energy vector meson-vector meson elastic scattering amplitudes of a Yang-Mills theory of an SU(2) model are calculated in a generalized leading-term approximation (s→∞ with t fixed). The resulting amplitude, through the 10th order, coincides with the expansion of an eikonal formula. The present method is generalizable to other non-Abelian gauge theories.     

A fresh look into the neutron EDM and magnetic susceptibility

We reexamine the estimate of the neutron electric dipole moment (NEDM) from chiral and QCD spectral sum rules (QSSR) approaches. In the former, we evaluate the pion mass corrections which are about 5% of the leading Log results. However, the chiral estimate can be affected by the unknown value of the renormalizaton scale ν  . For QSSR, we analyze the effect of the nucleon interpolating currents on the existing predictions. We conclude that previous QSSR results are not obtained within the optimal choice of these operators, which lead to an overestimate of these results by about a factor 4. The weakest upper bound |θ|?2×¹⁰⁻⁹$|\theta |?2\times {10}^{\mathrm{-9}}$ for the strong CP  -violating angle is obtained from QSSR, while the strongest upper bound |θ|?1.3×¹⁰⁻¹⁰$|\theta |?1.3\times {10}^{\mathrm{-10}}$ comes from the chiral approach evaluated at the scale ν=MN$\nu =M_N$. We also re-estimate the proton magnetic susceptibility, which is an important input in the QSSR estimate of the NEDM.     

A fresh look at hadronic light-by-light scattering in the muon g - 2 with the Dyson-Schwinger approach

Using the Dyson-Schwinger and Bethe-Salpeter equations, we calculate the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon a_m\ensuremath a_\mu , using a phenomenological model for the gluon and quark-gluon interaction. We find a_m=(84 ±13)×10^-11\ensuremath a_\mu=(84 \pm 13)\times 10^{-11} for meson exchange, and a_m = (107 ±2 ±46)×10^-11\ensuremath a_\mu = (107 \pm 2 \pm 46)\times 10^{-11} for the quark loop. The former is commensurate with past calculations; the latter much larger due to dressing effects. This leads to a revised estimate of a_m=116 591 865.0(96.6)×10^-11\ensuremath a_\mu=116 591 865.0(96.6)\times 10^{-11} , reducing the difference between theory and experiment to ≃ 1.9s \sigma .     

A Veneziano amplitude for four spinning pions

A Veneziano formula for four spinning particles, previously obtained by factorization of many point functions, is modified in order to kill the spin 0 particles on the leading trajectories. The formula obtained may now refer to particles on the pion trajectory, and we verify that it has Adler zeros when any one of the particles is spinless and soft.     

A new look at Hamilton's principle

Hamilton's principle and Hamilton's law are discussed. Hamilton's law is then applied to achieve direct solutions to time-dependent, nonconservative, initial value problems without the use of the theory of differential or integral equations. A major question has always plagued competent investigators who use “energy methods,” viz., “Why is it that one can derive the differential equations for a system from Hamilton's principle and then solve these equations (at least in principle) subject to applicable initial and boundary conditions; but one cannot obtain a solution directly from Hamilton's principle except in very special cases?” This paper provides the answer to that question. In Hamilton's own words, “... the peculiar combination it [i.e., Hamilton's law] involves, of the principles of variations with those of partial differentials, for the determination and use of an important class of integrals, may constitute, when it shall be matured by the future labors of mathematicians, a separate branch of analysis.”     

A new look at nuclear glory

It is shown that the surface transparency of the nuclear optical potential is responsible for the rise of the elastic cross section at large angles. We suggest the interpretation that by decreasing the radius of the imaginary potential, the formation of surface waves is supported. Numerical results applied to the elastic scattering of-particles on⁴⁰Ca are compared fairly well with experiment over a large range of c.m. angles.