Analytic structure in the coupling constant plane in perturbative QCD

We investigate the analytic structure of the Borel-summed perturbative QCD amplitudes in the complex plane of the coupling constant. Using the method of inverse Mellin transform, we show that the prescription dependent Borel-Laplace integral can be cast, under some conditions, into the form of a dispersion relation in the a-plane. We also discuss some recent works relating resummation prescriptions, renormalons and nonperturbative effects, and show that a method proposed recently for obtaining QCD nonperturbative condensates from perturbation theory is based on special assumptions about the analytic structure in the coupling plane that are not valid in QCD.Comment: 14 pages, revtex4, 1 eps-figur

Synchonisation of Resonances with Thresholds

The mechanism by which a resonance may be attracted to a sharp threshold is described with several examples. It involves a threshold cusp interfering constructively with either or both (i) a resonance produced via confinement, (ii) attractive t- and u-channel exchanges. More generally, it is suggested that resonances are eigenstates generated by mixing between confined states and long-range meson and baryon exchanges.Comment: 8 pages, 4 figures. For Meson08 Proceedings. One important typo correcte

Convergence of the expansion of the Laplace-Borel integral in perturbative QCD improved by conformal mapping

The optimal conformal mapping of the Borel plane was recently used to accelerate the convergence of the perturbation expansions in QCD. In this work we discuss the relevance of the method for the calculation of the Laplace-Borel integral expressing formally the QCD Green functions. We define an optimal expansion of the Laplace-Borel integral in the principal value prescription and establish conditions under which the expansion is convergent.Comment: 10 pages, no figure

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

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 waves from stochastic relativistic sources: primordial turbulence and magnetic fields

The power spectrum of a homogeneous and isotropic stochastic variable, characterized by a finite correlation length, does in general not vanish on scales larger than the correlation scale. If the variable is a divergence free vector field, we demonstrate that its power spectrum is blue on large scales. Accounting for this fact, we compute the gravitational waves induced by an incompressible turbulent fluid and by a causal magnetic field present in the early universe. The gravitational wave power spectra show common features: they are both blue on large scales, and peak at the correlation scale. However, the magnetic field can be treated as a coherent source and it is active for a long time. This results in a very effective conversion of magnetic energy in gravitational wave energy at horizon crossing. Turbulence instead acts as a source for gravitational waves over a time interval much shorter than a Hubble time, and the conversion into gravitational wave energy is much less effective. We also derive a strong constraint on the amplitude of a primordial magnetic field when the correlation length is much smaller than the horizon.Comment: Replaced with revised version accepted for publication in Phys Rev

Detection of gravitational waves from the QCD phase transition with pulsar timing arrays

If the cosmological QCD phase transition is strongly first order and lasts sufficiently long, it generates a background of gravitational waves which may be detected via pulsar timing experiments. We estimate the amplitude and the spectral shape of such a background and we discuss its detectability prospects.Comment: 7 pages, 5 figs. Version accepted by PR

Improvements to the Method of Dispersion Relations for B Nonleptonic Decays

We bring some clarifications and improvements to the method of dispersion relations in the external masses variables, that we proposed recently for investigating the final state interactions in the B nonleptonic decays. We first present arguments for the existence of an additional term in the dispersion representation, which arises from an equal-time commutator in the LSZ formalism and can be approximated by the conventional factorized amplitude. The reality properties of the spectral function and the Goldberger-Treiman procedure to perform the hadronic unitarity sum are analyzed in more detail. We also improve the treatment of the strong interaction part by including the contributions of both t and u-channel trajectories in the Regge amplitudes. Applications to the $B^0\to \pi^+\pi^-$ and $B^+\to \pi^0 K^+$ decays are presented.Comment: 16 pages, 4 new figures. modifications of the dispersion representatio

Stringent constraints on the scalar K pi form factor from analyticity, unitarity and low-energy theorems

We investigate the scalar K pi form factor at low energies by the method of unitarity bounds adapted so as to include information on the phase and modulus along the elastic region of the unitarity cut. Using at input the values of the form factor at t=0 and the Callan-Treiman point, we obtain stringent constraints on the slope and curvature parameters of the Taylor expansion at the origin. Also, we predict a quite narrow range for the higher order ChPT corrections at the second Callan-Treiman point.Comment: 5 pages latex, uses EPJ style files, 3 figures, replaced with version accepted by EPJ