Unitarized Chiral Perturbation Theory in a finite volume: scalar meson sector

We develop a scheme for the extraction of the properties of the scalar mesons f0(600), f0(980), and a0(980) from lattice QCD data. This scheme is based on a two-channel chiral unitary approach with fully relativistic propagators in a finite volume. In order to discuss the feasibility of finding the mass and width of the scalar resonances, we analyze synthetic lattice data with a fixed error assigned, and show that the framework can be indeed used for an accurate determination of resonance pole positions in the multi-channel scattering.Comment: 15 pages, 17 figure

Cosmological Magnetogenesis driven by Radiation Pressure

The origin of large scale cosmological magnetic fields remains a mystery, despite the continuous efforts devoted to that problem. We present a new model of magnetic field generation, based on local charge separation provided by an anisotropic and inhomogeneous radiation pressure. In the cosmological context, the processes we explore take place at the epoch of the reionisation of the Universe. Under simple assumptions, we obtain results (i) in terms of the order of magnitude of the field generated at large scales and (ii) in terms of its power spectrum. The amplitudes obtained (B ~ 8.10^(-6) micro-Gauss) are considerably higher than those obtained in usual magnetogenesis models and provide suitable seeds for amplification by adiabatic collapse and/or dynamo during structure formation.Comment: 9 pages, 2 figure

Scalar mesons moving in a finite volume and the role of partial wave mixing

Phase shifts and resonance parameters can be obtained from finite-volume lattice spectra for interacting pairs of particles, moving with nonzero total momentum. We present a simple derivation of the method that is subsequently applied to obtain the pi pi and pi K phase shifts in the sectors with total isospin I=0 and I=1/2, respectively. Considering different total momenta, one obtains extra data points for a given volume that allow for a very efficient extraction of the resonance parameters in the infinite-volume limit. Corrections due to the mixing of partial waves are provided. We expect that our results will help to optimize the strategies in lattice simulations, which aim at an accurate determination of the scattering and resonance properties.Comment: 19 pages, 12 figure

Observation of the Higgs Boson of strong interaction via Compton scattering by the nucleon

It is shown that the Quark-Level Linear $\sigma$ Model (QLL$\sigma$M) leads to a prediction for the diamagnetic term of the polarizabilities of the nucleon which is in excellent agreement with the experimental data. The bare mass of the $\sigma$ meson is predicted to be $m_\sigma=666$ MeV and the two-photon width $\Gamma(\sigma\to\gamma\gamma)=(2.6\pm 0.3)$ keV. It is argued that the mass predicted by the QLL$\sigma$M corresponds to the $\gamma\gamma\to\sigma\to NN$ reaction, i.e. to a $t$-channel pole of the $\gamma N\to N\gamma$ reaction. Large -angle Compton scattering experiments revealing effects of the $\sigma$ meson in the differential cross section are discussed. Arguments are presented that these findings may be understood as an observation of the Higgs boson of strong interaction while being part of the constituent quark.Comment: 17 pages, 6 figure

The K^*_0(800) scalar resonance from Roy-Steiner representations of pi K scattering

We discuss the existence of the light scalar meson K^*_0(800) (also called kappa) in a rigorous way, by showing the presence of a pole in the pi K --> pi K amplitude on the second Riemann sheet. For this purpose, we study the domain of validity of two classes of Roy-Steiner representations in the complex energy plane. We prove that one of them is valid in a region sufficiently broad in the imaginary direction. From this representation, we compute the l=0 partial wave in the complex plane with neither additional approximation nor model dependence, relying only on experimental data. A scalar resonance with strangeness S=1 is found with the following mass and width: E_kappa = 658 \pm 13 MeV and Gamma_kappa = 557 \pm 24 MeV.Comment: 16 pages, 8 figures. Domain of validity of a Roy-Steiner representation corrected and enlarged, and features of the K^*_0(800) pole discussed in more details. Conclusions unchange

Implications of unitarity and analyticity for the D\pi form factors

We consider the vector and scalar form factors of the charm-changing current responsible for the semileptonic decay D\rightarrow \pi l \nu. Using as input dispersion relations and unitarity for the moments of suitable heavy-light correlators evaluated with Operator Product Expansions, including O(\alpha_s^2) terms in perturbative QCD, we constrain the shape parameters of the form factors and find exclusion regions for zeros on the real axis and in the complex plane. For the scalar form factor, a low energy theorem and phase information on the unitarity cut are also implemented to further constrain the shape parameters. We finally propose new analytic expressions for the $D\pi$ form factors, derive constraints on the relevant coefficients from unitarity and analyticity, and briefly discuss the usefulness of the new parametrizations for describing semileptonic data.Comment: 10 pages, 7 figures, uses EPJ style files: expanded version of v1 with extended discussion, additional analysis, explanation, figure and references; corresponds to EPJA versio

Two photons into \pi^0\pi^0

We perform a theoretical study based on dispersion relations of the reaction \gamma\gamma\to \pi^0\pi^0 emphasizing the low energy region. We discuss how the f_0(980) signal emerges in \gamma\gamma\to \pi\pi within the dispersive approach and how this fixes to a large extent the phase of the isoscalar S-wave \gamma\gamma\to \pi\pi amplitude above the K\bar{K} threshold. This allows us to make sharper predictions for the cross section at lower energies and our results could then be used to distinguish between different \pi\pi isoscalar S-wave parameterizations with the advent of new precise data on \gamma\gamma\to\pi^0\pi^0. We compare our dispersive approach with an updated calculation employing Unitary Chiral Perturbation Theory (U\chiPT). We also pay special attention to the role played by the \sigma resonance in \gamma\gamma\to\pi\pi and calculate its coupling and width to gamma\gamma, for which we obtain \Gamma(\sigma\to\gamma\gamma)=(1.68\pm 0.15) KeV.Comment: 31 pages, 9 figure

Couplings of light I=0 scalar mesons to simple operators in the complex plane

The flavour and glue structure of the light scalar mesons in QCD are probed by studying the couplings of the I=0 mesons $\sigma(600)$ and $f_0(980)$ to the operators $\bar{q}q$, $\alpha_s G^2$ and to two photons. The Roy dispersive representation for the $\pi\pi$ amplitude $t_0^0(s)$ is used to determine the pole positions as well as the residues in the complex plane. On the real axis, $t_0^0$ is constrained to solve the Roy equation together with elastic unitarity up to the K\Kbar threshold leading to an improved description of the $f_0(980)$. The problem of using a two-particle threshold as a matching point is discussed. A simple relation is established between the coupling of a scalar meson to an operator $j_S$ and the value of the related pion form-factor computed at the resonance pole. Pion scalar form-factors as well as two-photon partial-wave amplitudes are expressed as coupled-channel Omn\`es dispersive representations. Subtraction constants are constrained by chiral symmetry and experimental data. Comparison of our results for the $\bar{q}q$ couplings with earlier determinations of the analogous couplings of the lightest I=1 and $I=1/2$ scalar mesons are compatible with an assignment of the $\sigma$, $\kappa$, $a_0(980)$, $f_0(980)$ into a nonet. Concerning the gluonic operator $\alpha_s G^2$ we find a significant coupling to both the $\sigma$ and the $f_0(980)$.Comment: 31 pages, 5 figure

The First Magnetic Fields

We review current ideas on the origin of galactic and extragalactic magnetic fields. We begin by summarizing observations of magnetic fields at cosmological redshifts and on cosmological scales. These observations translate into constraints on the strength and scale magnetic fields must have during the early stages of galaxy formation in order to seed the galactic dynamo. We examine mechanisms for the generation of magnetic fields that operate prior during inflation and during subsequent phase transitions such as electroweak symmetry breaking and the quark-hadron phase transition. The implications of strong primordial magnetic fields for the reionization epoch as well as the first generation of stars is discussed in detail. The exotic, early-Universe mechanisms are contrasted with astrophysical processes that generate fields after recombination. For example, a Biermann-type battery can operate in a proto-galaxy during the early stages of structure formation. Moreover, magnetic fields in either an early generation of stars or active galactic nuclei can be dispersed into the intergalactic medium.Comment: Accepted for publication in Space Science Reviews. Pdf can be also downloaded from http://canopus.cnu.ac.kr/ryu/cosmic-mag1.pd

Magnetic Field Amplification in Galaxy Clusters and its Simulation

We review the present theoretical and numerical understanding of magnetic field amplification in cosmic large-scale structure, on length scales of galaxy clusters and beyond. Structure formation drives compression and turbulence, which amplify tiny magnetic seed fields to the microGauss values that are observed in the intracluster medium. This process is intimately connected to the properties of turbulence and the microphysics of the intra-cluster medium. Additional roles are played by merger induced shocks that sweep through the intra-cluster medium and motions induced by sloshing cool cores. The accurate simulation of magnetic field amplification in clusters still poses a serious challenge for simulations of cosmological structure formation. We review the current literature on cosmological simulations that include magnetic fields and outline theoretical as well as numerical challenges.Comment: 60 pages, 19 Figure