The 9th Joint International Hadron Structure '15 Conference, Horný Smokovec, Slovak Republic, 29 June–3 July 2015; Editors: Stanislav Dubnička, Anna Zuzana Dubničková and Erik BartošOpen Access

Light-front holography and superconformal quantum mechanics: A new approach to hadron structure and color confinement

Stanley J. Brodsky

SLAC National Accelerator Laboratory, Stanford University, Stanford, California 94039, USA

E-mail Address: sjbth@slac.stanford.edu

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Alexandre Deur

Thomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA

E-mail Address: deurpam@jlab.org

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Guy F. de Téramond

Universidad de Costa Rica, San José, Costa Rica

E-mail Address: gdt@asterix.crnet.cr

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, and

Hans Günter Dosch

Institut für Theoretische Physik, Philosophenweg 16, D-6900 Heidelberg, Germany

E-mail Address: h.g.dosch@thphys.uni-heidelberg.de

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https://doi.org/10.1142/S2010194515600812Cited by:12 (Source: Crossref)

Abstract

A primary question in hadron physics is how the mass scale for hadrons consisting of light quarks, such as the proton, emerges from the QCD Lagrangian even in the limit of zero quark mass. If one requires the effective action which underlies the QCD Lagrangian to remain conformally invariant and extends the formalism of de Alfaro, Fubini and Furlan to light-front Hamiltonian theory, then a unique, color-confining potential with a mass parameter $κ$ $κ$ emerges. The actual value of the parameter $κ$ $κ$ is not set by the model – only ratios of hadron masses and other hadronic mass scales are predicted. The result is a nonperturbative, relativistic light-front quantum mechanical wave equation, the Light-Front Schrödinger Equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories with the identical slope in the radial quantum number $n$ $n$ and orbital angular momentum $L$ $L$ . The same light-front equations for mesons with spin $J$ $J$ also can be derived from the holographic mapping to QCD (3+1) at fixed light-front time from the soft-wall model modification of AdS₅ space with a specific dilaton profile. Light-front holography thus provides a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. One can also extend the analysis to baryons using superconformal algebra – $2 \times 2$ $2 \times 2$ supersymmetric representations of the conformal group. The resulting fermionic LF bound-state equations predict striking similarities between the meson and baryon spectra. In fact, the holographic QCD light-front Hamiltonians for the states on the meson and baryon trajectories are identical if one shifts the internal angular momenta of the meson ( $L_{M}$ $L_{M}$ ) and baryon ( $L_{B}$ $L_{B}$ ) by one unit: $L_{M} = L_{B} + 1$ $L_{M} = L_{B} + 1$ . We also show how the mass scale $κ$ $κ$ underlying confinement and the masses of light-quark hadrons determines the scale $Λ_{\bar{M S}}$ $Λ_{\bar{M S}}$ controlling the evolution of the perturbative QCD coupling. The relation between scales is obtained by matching the nonperturbative dynamics, as described by an effective conformal theory mapped to the light-front and its embedding in AdS space, to the perturbative QCD regime. The data for the effective coupling defined from the Bjorken sum rule $α_{g_{1}} (Q^{2})$ $α_{g_{1}} (Q^{2})$ are remarkably consistent with the Gaussian form predicted by LF holographic QCD. The result is an effective coupling defined at all momenta. The predicted value $Λ_{\bar{M S}}^{(N_{F} = 3)} = 0.440 m_{ρ} = 0.341 \pm 0.024 G e V$ $Λ_{\bar{M S}}^{(N_{F} = 3)} = 0.440 m_{ρ} = 0.341 \pm 0.024 G e V$ is in agreement with the world average $0.339 \pm 0.010 G e V$ $0.339 \pm 0.010 G e V$ . We thus can connect $Λ_{\bar{M S}}$ $Λ_{\bar{M S}}$ to hadron masses. The analysis applies to any renormalization scheme.

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Published: 26 November 2015

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Light-front holography and superconformal quantum mechanics: A new approach to hadron structure and color confinement

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