The reactions \gwl\ and \gzl\ in SU(N)SU(N) strongly interacting theories

Building on recent phenomenology of \gpi, we discuss the expectation for two photon production of longitudinal gauge boson pairs in $SU(N)$ technicolor theories. The treatment involves a matching of dispersive techniques with the methodology of chiral perturbation theory.Comment: 25 LaTeX pages (incl. 10 figures on 7 pages, also in plain LaTeX, also available from the authors in PostScript form via regular E_mail), UMHEP-39

The γγ→π0π0\gamma\gamma\to\pi^0\pi^0 and η→π0γγ\eta\to\pi^0\gamma\gamma Transitions in the Extended NJL Model

We calculate within the Extended Nambu--Jona-Lasinio model the leading in $1/N_c$ contribution to $\gamma\gamma\to\pi^0\pi^0$ to all orders in the external momenta and quark masses. This result is then combined with the known two-loop Chiral Perturbation Theory and compared with the data and other calculations. A technical difficulty in the same calculation beyond order $p^6$ for $\eta\to\pi^0\gamma\gamma$ is identified and for this decay results up to order $p^6$ are presented.Comment: 13 pages, LaTeX, uses epsf.sty, 3 postscript figures included, complete postscript file available at http://www.nordita.dk/locinfo/preprints/95084.ps.g

The Reaction γγ→π0π0\gamma\gamma\to\pi^0\pi^0 in Generalized Chiral Perturbation Theory

The cross section for $\gamma\gamma\to\pi^0\pi^0$ and the pion polarizabilities are computed, within generalized chiral perturbation theory, in the full one loop approximation, {\it i.e.} up to and including order $O({p^5})$. The result depends on the parameter ${\alpha}_{\pi\pi}$ defining the tree level $\pi - \pi$ scattering amplitude and on an additional low energy constant. The latter is shown to be related by an exact sum-rule to the $e^+ e^-$ data. The parameter ${\alpha}_{\pi\pi}$ is related to the quark mass ratio $r = m_s /{\hat m}$ via the expansion of pseudoscalar meson masses. The generalized one loop $\gamma\gamma\to\pi^0\pi^0$ amplitude agrees with the experimental data in the threshold region provided r= {m_s}/{\hat m}\lapprox 10. Higher order corrections are estimated comparing our calculation with the dispersive approach.Comment: 21 pages (plain latex)+1 fig (using feynman.tex)+ 6 figs (ps file appended), IPNO/TH 94-0

A Multilevel Analysis of Implicit and Explicit CSR in French and UK Professional Sport

Research question: This paper examines the ways in which French and UK professional sports clubs implement and communicate their CSR policies. In addition to identifying similarities and differences between CSR practices in the two countries, our analysis extends and adapts the implicit-explicit CSR framework to the field of sport. Research methods: We used a mixed methods approach to analyse qualitative and quantitative data on the CSR strategies of 66 professional rugby union (Top 14, Aviva Premiership Rugby) and football (Ligue 1, Premier League) clubs over the 2017-2018 season. Results and findings: We found major differences in CSR communication between France and the UK. Communication by French clubs tends to highlight sport’s values, involve few media channels, whereas communication by UK clubs explicitly vaunts their social responsibility and involves numerous channels. In the case of CSR implementation, there are similarities between French and UK clubs, especially in the fields their CSR initiatives cover (e.g., health, diversity), as well as differences. However, the scope of initiatives varies more between sports than between countries, with football demonstrating a more international outlook than rugby. Implications: This article expands Matten and Moon’s (2008) implicit-explicit CSR framework by identifying the influence of interactions between sectorial/field-level factors and national/macro-level factors on CSR practices, and by distinguishing between CSR communication and CSR implementation. Our results throw light on the shift from implicit to explicit CSR in French professional sport

Remarks on the f_0(400-1200) scalar meson as the dynamically generated chiral partner of the pion

The quark-level linear sigma model is revisited, in particular concerning the identification of the f_0(400-1200) (or \sigma(600)) scalar meson as the chiral partner of the pion. We demonstrate the predictive power of the linear sigma model through the pi-pi and pi-N s-wave scattering lengths, as well as several electromagnetic, weak, and strong decays of pseudoscalar and vector mesons. The ease with which the data for these observables are reproduced in the linear sigma model lends credit to the necessity to include the sigma as a fundamental q\bar{q} degree of freedom, to be contrasted with approaches like chiral perturbation theory or the confining NJL model of Shakin and Wang.Comment: 15 pages, plain LaTeX, 3 EPS figure

Low-Energy Photon-Photon Collisions to Two-Loop Order

We evaluate the amplitude for $\gamma \gamma \rightarrow \pi^0 \pi^0$ to two loops in chiral perturbation theory. The three new counterterms which enter at this order in the low-energy expansion are estimated with resonance saturation. We find that the cross section agrees rather well with the available data and with dispersion theoretic calculations even substantially above threshold. Numerical results for the Compton cross section and for the neutral pion polarizabilities are also given to two-loop accuracy.Comment: 48 pages, LaTex, 11 figs. (figures not included; available upon request from [email protected]),BUTP-93/18,LNF-93/077(P),PSI-PR-93-1

Study of gamma gamma -> W_L W_L and gamma gamma -> Z_L Z_L reactions with Chiral Lagrangians

We analyze the effects of a strongly interacting symmetry breaking sector of the Standard Model in $\gamma \gamma -> W_L^+ W_L^-$ and $\gamma \gamma -> Z_L Z_L$ reactions at TeV energies by using Chiral Lagrangians and Chiral Perturbation Theory. We find significant deviations from the Standard Model predictions for the differential cross sections at high invariant mass of the gauge bosons pair. We study the experimental signals that could be obtained in a high energy and high luminosity dedicated $\gamma\gamma$ collider and estimate the sensitivity that such experiments could reach to the values of the effective lagrangian parameters.Comment: 14 pages, LaTeX, 4 figures (not included), FTUAM92/2

Photon-Photon Scattering, Pion Polarizability and Chiral Symmetry

Recent attempts to detect the pion polarizability via analysis of $\gamma\gamma\rightarrow\pi\pi$ measurements are examined. The connection between calculations based on dispersion relations and on chiral perturbation theory is established by matching the low energy chiral amplitude with that given by a full dispersive treatment. Using the values for the polarizability required by chiral symmetry, predicted and experimental cross sections are shown to be in agreement.Comment: 21 pages(+10 figures available on request), LATEX, UMHEP-38