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

Observational constraint on the fourth derivative of the inflaton potential

We consider the flow-equations for the 3 slow-roll parameters n_S (scalar spectral index), r (tensor to scalar ratio), and dn_S/dlnk (running of the spectral index). We show that the combination of these flow-equations with the observational bounds from cosmic microwave background and large scale structure allows one to put a lower bound on the fourth derivative of the inflationary potential, M_P^4(V''''/V) > -0.02.Comment: 3 pages, 3 figure

CMB temperature anisotropy at large scales induced by a causal primordial magnetic field

We present an analytical derivation of the Sachs Wolfe effect sourced by a primordial magnetic field. In order to consistently specify the initial conditions, we assume that the magnetic field is generated by a causal process, namely a first order phase transition in the early universe. As for the topological defects case, we apply the general relativistic junction conditions to match the perturbation variables before and after the phase transition which generates the magnetic field, in such a way that the total energy momentum tensor is conserved across the transition and Einstein's equations are satisfied. We further solve the evolution equations for the metric and fluid perturbations at large scales analytically including neutrinos, and derive the magnetic Sachs Wolfe effect. We find that the relevant contribution to the magnetic Sachs Wolfe effect comes from the metric perturbations at next-to-leading order in the large scale limit. The leading order term is in fact strongly suppressed due to the presence of free-streaming neutrinos. We derive the neutrino compensation effect dynamically and confirm that the magnetic Sachs Wolfe spectrum from a causal magnetic field behaves as l(l+1)C_l^B \propto l^2 as found in the latest numerical analyses.Comment: 31 pages, 2 figures, minor changes, matches published versio

Gravitational wave production: A strong constraint on primordial magnetic fields

We compute the gravity waves induced by anisotropic stresses of stochastic primordial magnetic fields. The nucleosynthesis bound on gravity waves is then used to derive a limit on the magnetic field amplitude as function of the spectral index. The obtained limits are extraordinarily strong: If the primordial magnetic field is produced by a causal process, leading to a spectral index $n\ge 2$ on super horizon scales, galactic magnetic fields produced at the electroweak phase transition or earlier have to be weaker than B_\la \le 10^{-27}Gauss! If they are induced during an inflationary phase (reheating temperature $T\sim 10^{15}$GeV) with a spectral index $n\sim 0$, the magnetic field has to be weaker than B_\la \le 10^{-39}Gauss! Only very red magnetic field spectra, $n\sim -3$ are not strongly constrained. We also find that a considerable amount of the magnetic field energy is converted into gravity waves. The gravity wave limit derived in this work rules out most of the proposed processes for primordial seeds for the large scale coherent magnetic fields observed in galaxies and clusters

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

Gravitational wave generation from bubble collisions in first-order phase transitions: an analytic approach

Gravitational wave production from bubble collisions was calculated in the early nineties using numerical simulations. In this paper, we present an alternative analytic estimate, relying on a different treatment of stochasticity. In our approach, we provide a model for the bubble velocity power spectrum, suitable for both detonations and deflagrations. From this, we derive the anisotropic stress and analytically solve the gravitational wave equation. We provide analytical formulae for the peak frequency and the shape of the spectrum which we compare with numerical estimates. In contrast to the previous analysis, we do not work in the envelope approximation. This paper focuses on a particular source of gravitational waves from phase transitions. In a companion article, we will add together the different sources of gravitational wave signals from phase transitions: bubble collisions, turbulence and magnetic fields and discuss the prospects for probing the electroweak phase transition at LISA.Comment: 48 pages, 14 figures. v2 (PRD version): calculation refined; plots redone starting from Fig. 4. Factor 2 in GW energy spectrum corrected. Main conclusions unchanged. v3: Note added at the end of paper to comment on the new results of 0901.166

αs\alpha_s from τ\tau decays: contour-improved versus fixed-order summation in a new QCD perturbation expansion

We consider the determination of $\alpha_s$ from $\tau$ hadronic decays, by investigating the contour-improved (CI) and the fixed-order (FO) renormalization group summations in the frame of a new perturbation expansion of QCD, which incorporates in a systematic way the available information about the divergent character of the series. The new expansion functions, which replace the powers of the coupling, are defined by the analytic continuation in the Borel complex plane, achieved through an optimal conformal mapping. Using a physical model recently discussed by Beneke and Jamin, we show that the new CIPT approaches the true results with great precision when the perturbative order is increased, while the new FOPT gives a less accurate description in the regions where the imaginary logarithms present in the expansion of the running coupling are large. With the new expansions, the discrepancy of 0.024 in $\alpha_s(m_\tau^2)$ between the standard CI and FO summations is reduced to only 0.009. From the new CIPT we predict $\alpha_s(m_\tau^2)= 0.320 ^{+0.011}_{-0.009}$, which practically coincides with the result of the standard FOPT, but has a more solid theoretical basis

Gravitational Waves from Warped Spacetime

We argue that the RSI model can provide a strong signature in gravitational waves. This signal is a relic stochastic background generated during the cosmological phase transition from an AdS-Schwarschild phase to the RS1 geometry that should occur at a temperature in the TeV range. We estimate the amplitude of the signal in terms of the parameters of the potential stabilizing the radion and show that over much of the parameter region in which the phase transition completes, a signal should be detectable at the planned space interferometer, LISA.Comment: 18 pages, 15 figures; v2: discussion improved, in particular on the justification of the thick wall approximation. 6 figures added. 4 pi factor corrected in perturbativity bound. N-dependence displayed. Conclusions unchanged. JHEP versio

Quark-Hadron Duality, Factorization and Strong Phases in Bd0→π+π−B^0_d \to \pi^+\pi^- Decay

We consider the hadronic description of the $B^0_d\to \pi^+\pi^-$ decay, with the aim to investigate the strong phases generated by the final state interactions. The derivation of the dispersion relations using the Lehmann-Symanzik-Zimmermann formalism and the Goldberger-Treiman method to include inelastic effects in the spectral function are presented. We discuss the problem of quark-hadron duality and estimate in the hadronic formalism the corrections to the factorized amplitude in the heavy quark limit.Comment: 16 pages, revised version, introduction of a scale dependenc