QCD Constituent Counting Rules for Neutral Vector Mesons

QCD constituent counting rules define the scaling behavior of exclusive hadronic scattering and electromagnetic scattering amplitudes at high momentum transfer in terms of the total number of fundamental constituents in the initial and final states participating in the hard subprocess. The scaling laws reflect the twist of the leading Fock state for each hadron and hence the leading operator that creates the composite state from the vacuum. Thus, the constituent counting scaling laws can be used to identify the twist of exotic hadronic candidates such as tetraquarks and pentaquarks. Effective field theories must consistently implement the scaling rules in order to be consistent with the fundamental theory. Here we examine how one can apply constituent counting rules for the exclusive production of one or two neutral vector mesons $V^0$ in $e^+ e^-$ annihilation, processes in which the $V^0$ can couple via intermediate photons. In case of a (narrow) real $V^0$, the photon virtuality is fixed to a precise value $s_1 = m_{V^0}^2$, in effect treating the $V^0$ as a single fundamental particle. Each real $V^0$ thus contributes to the constituent counting rules with $N_{V_0} = 1$. In effect, the leading operator underlying the $V^0$ has twist 1. Thus, in the specific physical case of single or double on-shell $V^0$ production via intermediate photons, the predicted scaling from counting rules coincides with Vector Meson Dominance (VMD), an effective theory that treats $V^0$ as an elementary field. However, the VMD prediction fails in the general case where the $V^0$ is not coupled through an elementary photon field, and then the leading-twist interpolating operator has twist $N_{V_0} = 2$. Analogous effects appear in $pp$ scattering processes.Comment: 15 page

QCD Compositeness as Revealed in Exclusive Vector Boson Reactions through Double-Photon Annihilation: e+e−→γγ∗→γV0e^+ e^- \to \gamma \gamma^\ast \to \gamma V^0 and e+e−→γ∗γ∗→V0V0e^+ e^- \to \gamma^\ast \gamma^\ast \to V^0 V^0

We study the exclusive double-photon annihilation processes, $e^+ e^- \to \gamma \gamma^\ast\to \gamma V^0$ and $e^+ e^- \to \gamma^\ast \gamma^\ast \to V^0_a V^0_b,$ where the $V^0_i$ is a neutral vector meson produced in the forward kinematical region: $s \gg -t$ and $-t \gg \Lambda_{\rm QCD}^2$. We show how the differential cross sections $\frac{d\sigma}{dt}$, as predicted by QCD, have additional falloff in the momentum transfer squared $t$ due to the QCD compositeness of the hadrons, consistent with the leading-twist fixed-$\theta_{\rm CM}$ scaling laws. However, even though they are exclusive channels and not associated with the conventional electron-positron annihilation process $e^+ e^- \to \gamma^\ast \to q \bar q,$ these total cross sections $\sigma(e^+ e^- \to \gamma V^0)$ and $\sigma(e^+ e^- \to V^0_a V^0_b),$ integrated over the dominant forward- and backward-$\theta_{\rm CM}$ angular domains, scale as $1/s$, and thus contribute to the leading-twist scaling behavior of the ratio $R_{e^+ e^-}$. We generalize these results to exclusive double-electroweak vector-boson annihilation processes accompanied by the forward production of hadrons, such as $e^+ e^- \to Z^0 V^0$ and $e^+ e^- \to W^-\rho^+$. These results can also be applied to the exclusive production of exotic hadrons such as tetraquarks, where the cross-section scaling behavior can reveal their multiquark nature.Comment: 10 page

Optimization methods for topological design of interconnected ring networks

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1994.Includes bibliographical references (leaves 177-179).by Valery Brodsky.M.S

Quantum Chromodynamics Resolution of the ATOMKI Anomaly in 4He{\rm {^4He}} Nuclear Transitions

Recent observations of the angular correlation spectra in the decays ${\rm ^4He}^*\to {\rm ^4He}+ e^+e^-$ and ${\rm ^8Be}^*\to {\rm ^8Be}+ e^+e^-$ have been suggested as due to the creation and subsequent decay to an electron-positron pair of a new light particle with a mass of $\sim 17$ MeV. In this work, we present a calculation of the invariant $m_{e^+e^-}$ mass spectrum of the electromagnetic transition of an excited state of helium and estimate the differential and total width of the decay. We investigate the possibility that the source of the signal is an $e^+ e^-$ pair created by a new electromagnetic decay of $\rm ^4He$ caused by a proposed 12-quark hidden-color Fock state in the ${\rm {^4He}}$ nuclear wavefunction, the "hexadiquark.'' We find that we can fit the shape of the signal with the QCD Fock state at excitation energy ${\rm E^*}\simeq 17.9$ MeV and a Gaussian form factor for the electromagnetic decay. We address the physical issues with the fit parameters using properties of the hexadiquark state. In light of this work, we emphasize the need for independent experimental confirmation or refutation of the ATOMKI results as well as further experiments to detect the proposed new excitation of ${\rm ^4He}$.Comment: Condensed version, 8 pages, 3 figures, comments welcom

Nucleon Generalized Parton Distributions and Holographic Models

Using ideas from Light Front Holography, we discuss the calculation of the nucleon helicity-independent generalized parton distributions of quarks in the zero skewness case.Comment: Prepared for LIGHTCONE 2011, 23 - 27 May, 2011, Dalla

QED-Induced Rapidity-Gap Events at the Z Peak

We study rapidity-gap events in $e^+e^-$ annihilation at the Z boson peak initiated by the emission of a virtual photon. This mechanism is suppressed by the QED coupling constant, but it is enhanced due to a large propagator term from the virtual photon. For typical kinematics, we find a smaller event rate than analogous QCD type gap events. In the small jet-pair invariant mass limit, the QED type events follow a $1+\cos^2\theta$ distribution in the jet-pair scattering angle, instead of the $\sin^2\theta$ distribution of the QCD case.Comment: 13 pages, plain TeX (needs the PHYZZX macros), 4 figures in PostScript. SLAC-PUB-6116, DOE/ER/40762-009, U of Md. PP \#93-19

Estimates of the higher-order QCD corrections: Theory and Applications

We consider the further development of the formalism of the estimates of higher-order perturbative corrections in the Euclidean region, which is based on the application of the scheme-invariant methods, namely the principle of minimal sensitivity and the effective charges approach. We present the estimates of the order $O(\alpha^{4}_{s})$ QCD corrections to the Euclidean quantities: the $e^+e^-$-annihilation $D$-function and the deep inelastic scattering sum rules, namely the non-polarized and polarized Bjorken sum rules and to the Gross--Llewellyn Smith sum rule. The results for the $D$-function are further applied to estimate the $O(\alpha_s^4)$ QCD corrections to the Minkowskian quantities $R(s) = \sigma_{tot} (e^{+}e^{-} \to {\rm hadrons}) / \sigma (e^{+}e^{-} \to \mu^{+} \mu^{-})$ and $R_{\tau} = \Gamma (\tau \to \nu_{\tau} + {\rm hadrons}) / \Gamma (\tau \to \nu_{\tau} \overline{\nu}_{e} e)$. The problem of the fixation of the uncertainties due to the $O(\alpha_s^5)$ corrections to the considered quantities is also discussed.Comment: revised version and improved version of CERN.TH-7400/94, LATEX 10 pages, six-loop estimates for R(s) in Table 2 are revised, thanks to J. Ellis for pointing numerical shortcomings (general formulae are non-affected). Details of derivations of six-loop estimates for R_tau are presente

Hadron properties in AdS/QCD

We discuss a holographic soft-wall model developed for the description of mesons and baryons with adjustable quantum numbers n, J, L, S. This approach is based on an action which describes hadrons with broken conformal invariance and which incorporates confinement through the presence of a background dilaton field. Results obtained for heavy-light meson masses and decay constants are consistent with predictions of HQET. In the baryon sector applications to the baryon masses, nucleon electromagnetic form factors and generalized parton distributions are discussed.Comment: 7 pages, 2 figures, Presented by Valery E. Lyubovitskij at the International School of Nuclear Physics "33rd Course: From Quarks and Gluons to Hadrons and Nuclei" 16-24 September 2011, Erice-Sicily, Ital

Mesons and baryons in a soft-wall holographic approach

We discuss a holographic soft-wall model developed for the description of mesons and baryons with adjustable quantum numbers n, J, L, S. This approach is based on an action which describes hadrons with broken conformal invariance and which incorporates confinement through the presence of a background dilaton field.Comment: 6 pages, Presented by Valery E. Lyubovitskij at LIGHTCONE 2011, 23 - 27 May, 2011, Dalla