Nuclear Physics Seminar

New Perspectives for QCD: Light-Front Holography and the Principle of Maximum Conformality

Stanley Brodsky (SLAC)

A remarkable holographic feature of dynamics in AdS space in five dimensions is that it is dual to Hamiltonian theory in physical space-time quantized at fixed light-front time. This light-front holographic principle provides a precise relation between the bound-state amplitudes in AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. The resulting valence Fock-state wavefunction eigensolutions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schrödinger equation. The quark-antiquark potential is determined uniquely using a method based on conformally invariant quantum mechanics. The resulting potential is color-confining and reproduces the observed linear Regge behavior of the light-quark hadron spectrum in both the orbital angular momentum, and the radial node number. The pion mass vanishes in the chiral limit and other features of chiral symmetry are satisfied. The running QCD coupling displays an infrared fixed point. The elastic and transition form factors of the pion and the nucleons are also found to be well described in this framework. The light-front AdS/QCD holographic approach thus gives a frame-independent, analytic, first approximation of the color-confining dynamics, spectroscopy, and excitation spectra of relativistic light-quark bound states in QCD, including results conventionally attributed to spontaneous symmetry breaking.

The renormalization scale uncertainty in perturbative QCD predictions can be eliminated by using the Principle of Maximum Conformality (PMC). Using the PMC, all non-conformal contributions in the perturbative expansion series are summed into the running coupling, and one obtains unique, scale-fixed, scheme-independent predictions at any finite order. We introduce a generalization of conventional dimensional regularization which illuminates the renormalization scheme and scale ambiguities of pQCD predictions, exposes the general pattern of nonconformal terms., and allows us to systematically determine the argument of the running coupling order by order in a form which can be readily automatized. The resulting PMC scales and finite-order predictions are both to high accuracy independent of the choice of initial renormalization scale. We find that PMC scale-setting leads to a scheme-independent PQCD prediction for the top-quark forward-backward asymmetry which is within one sigma of the Tevatron measurements. The PMC procedure satisfies all of the principles of the renormalization group: reflectivity, symmetry, and transitivity, and it thus eliminates an unnecessary source of systematic error in pQCD predictions.

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