Is the strong-interaction proton-proton scattering length renormalization scale dependent in effective field theory?

It is shown that the strong-interaction ¹S₀ proton-proton scattering length in very low-energy effective field theory does not depend on the renormalization scale, if the electromagnetic interaction is switched off consistently.Received: 3 July 2003, Revised: 26 September 2003, Published online: 20 January 2004PACS: 03.65.Nk Scattering theory - 13.75.Cs Nucleon-nucleon interactions (including antinucleons, deuterons, etc.)     

Perturbative thermalisation in nuclear collisions at very high energies?

According to lowest order perturbation theory more than one hundred gluons and quarks with p_T > p₀ ≈2 GeV are produced per unit rapidity within a time of 0.1 fm in an average collision of two large nuclei at a CMS energy/particle in the few 100 GeV range. We show, including longitudinal expansion and QCD branching, that before a time of about 0.4 fm each of these will experience more than one collision with one of the other gluons and quarks. Without any assumptions concerning soft QCD one thus concludes that the quark-gluon subsystem is driven towards thermalisation.     

B→K*ℓ+ℓ- decay in soft-collinear effective theory

We study the rare B decay B→K^*ℓ⁺ℓ^- using soft-collinear effective theory (SCET). At leading power in 1/m_b, a factorization formula is obtained valid to all orders in α_s. For phenomenological application, we calculate the decay amplitude including order α_s corrections, and resum the logarithms by evolving the matching coefficients from the hard scale down to the scale . The branching ratio for B→K^*ℓ⁺ℓ^- is uncertain due to the imprecise knowledge of the soft form factors ζ_⊥(q²) and ζ_∥(q²). Constraining the soft form factor ζ_⊥(q²=0) from data on B→K^*γ yields ζ_⊥(q²=0)=0.32±0.02. Using this input, together with the light-cone sum rules to determine the q²-dependence of ζ_⊥(q²) and the other soft form factor ζ_∥(q²), we estimate the partially integrated branching ratio in the range 1 GeV²≤q²≤7 GeV² to be (2.92^+0.67 _-0.61)×10^-7. We discuss how to reduce the form factor related uncertainty by combining data on B→ρ(→ππ)ℓν_ℓ and B→K^*(→Kπ)ℓ⁺ℓ^-. The forward-backward asymmetry is less sensitive to the input parameters. In particular, for the zero-point of the forward-backward asymmetry in the standard model, we get q₀ ²=(4.07^+0.16 _-0.13) GeV². The scale dependence of q₀ ² is discussed in detail. PACS 13.25.Hw, 12.39.St, 12.38.Bx     

Tensor polarized γ-deuteron Compton scattering in effective field theory

The differential cross section for γ-deuteron Compton scattering from a tensor polarized deuteron is computed in an effective field theory. The first non-vanishing contributions to this differential cross section are the interference terms between the leading electric coupling diagrams and the subleading single potential pion exchange diagrams or the subleading magnetic moment coupling diagrams. At 90° photon scattering angle, only the pion term contributes at this order to the tensor polarized differential cross section. This provides a clean way to study the photon pion dynamics in the two nucleon sector. The effect is measurable for photon energies between 40 and 80 MeV provided the uncertainty in the measured cross sections are ≲ 7%.     

Does string theory predict an open universe?

It has been claimed that the string landscape predicts an open universe, with negative curvature. The prediction is a consequence of a large number of metastable string vacua, and the properties of the Coleman–De Luccia instanton which describes vacuum tunneling. We examine the robustness of this claim, which is of particular importance since it seems to be one of string theory's few claims to falsifiability. We find that, due to subleading tunneling processes, the prediction is sensitive to unknown properties of the landscape. Under plausible assumptions, universes like ours are as likely to be closed as open.     

Triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis

A triaxially deformed relativistic Hartree–Bogoliubov theory in the Woods–Saxon basis is developed with the aim of treating the triaxial deformation, pairing correlations and continuum in a unified way.In order to consider the triaxial deformation, the deformed potentials are expanded in terms of spherical harmonic functions in the coordinate space. In order to take the pairing correlations into account and treat the continuum properly, by using the Dirac Woods–Saxon basis, which has correct asy...     

n + p → d + γ in effective field theory

The radiative capture process n + p → d + γ provides clear evidence for meson exchange currents in nuclear physics. We compute this process at low energies using a recently developed power counting for the effective field theory that describes nucleon-nucleon interactions. The leading order contribution to this process comes from the photon coupling to the nucleon magnetic moments. At subleading order there are other contributions. Among these are graphs where the photon couples directly to pions, i.e. meson exchange currents. These diagrams are divergent and require the presence of a local four-nucleon-one-photon counterterm. The coefficient of this operator is determined by the measured cross section, σ^expt = 334.2±0.5 mb, for incident neutrons with speed |v| = 2200 m/s.     

On the ππ-scattering lengths in the theory with effective Lagrangian

Use of the effective Lagrangian incorporating both the scalar and pseudoscalar mesons gives a possibility to calculate the ππ-scattering lengths without attraction of the ChPT theory.     

Quantum field theory as effective BV theory from Chern–Simons

The general procedure for obtaining explicit expressions for all cohomologies of Berkovits' operator is suggested. It is demonstrated that calculation of BV integral for the classical Chern–Simons-like theory (Witten's OSFT-like theory) reproduces BV version of two-dimensional gauge model at the level of effective action. This model contains gauge field, scalars, fermions and some other fields. We prove that this model is an example of “singular” point from the perspective of the suggested method for cohomology evaluation. For arbitrary “regular” point the same technique results in AKSZ (Alexandrov, Kontsevich, Schwarz, Zaboronsky) version of Chern–Simons theory (BF theory) in accord with [N. Berkovits, Covariant quantization of the superparticle using pure spinors, JHEP 0109 (2001) 016, hep-th/0105050; N. Berkovits, ICTP lectures on covariant quantization of the superstring, hep-th/0209059; M. Movshev, A. Schwarz, On maximally supersymmetric Yang–Mills theories, Nucl. Phys. B 681 (2004) 324, hep-th/0311132; M. Movshev, A. Schwarz, Algebraic structure of Yang–Mills theory, hep-th/0404183].     

Convergent perturbation theory for a q–deformed anharmonic oscillator

A q–deformed anharmonic oscillator is defined within the framework of q–deformed quantum mechanics. It is shown that the Rayleigh–Schr?dinger perturbation series for the bounded spectrum converges to exact eigenstates and eigenvalues, for q close to 1. The radius of convergence becomes zero in the undeformed limit. Received: 6 August 1998 / Published online: 16 September 1998     

Random response of an oscillator with hysteresis damping

The response behaviour of an oscillator with Reid hysteresis damping un-der stationary Gauss white excitation is studied.By means of numerical simulationconducted on computer,the mean square response,probability density function andpower spectral density function for the response are given.These response character-istics are compared with those predicted by equivalent linearization treatment.