arXiv subjects

Stanley J. Brodsky

Publications and source records attributed to Stanley J. Brodsky.

At least 127 records · Page 7Linked to original sources

arXiv2014

Effective confining potentials for QCD

We observe that the linear potential used as a leading approximation for describing color confinement in the instant form of dynamics corresponds to a quadratic confining potential in the front form of dynamics. In particular, the instant-form potentials obtained from lattice gauge theory and string models of hadrons agree with the potentials determined from models using front-form dynamics and light-front holography, not only in their shape, but also in their numerical strength.

hep-ph↗

arXiv2014

A New Picture for the Formation and Decay of the Exotic $XY \! Z$ Mesons

We present a new dynamical picture that identifies the formation of the exotic $\bar c c$-containing states $XY \! Z$ with the confinement-induced hadronization of a rapidly separating pair of a compact diquark and antidiquark. This picture combines the advantages of diquark-based models, which can accommodate much of the known $XY \! Z$ spectrum, with the experimental fact that such states are both relatively narrow and are produced promptly. It also naturally explains the preference of some of the exotic states to decay to $ψ(2S)$, rather than $J/ψ$, in terms of a simple wave-function overlap effect.

hep-ph↗

arXiv2014

Reanalysis of the Higher Order Perturbative QCD corrections to Hadronic $Z$ Decays using the Principle of Maximum Conformality

A complete calculation of the ${\cal O}(α_s^4)$ perturbative QCD corrections to the hadronic decay width of the $Z$-boson has recently been performed by Baikov et al.[1]. In their analysis, Baikov et al. relied on the conventional practice of simply guessing the renormalization scale and taking an arbitrary range to estimate the pQCD uncertainties. This procedure inevitably introduces an arbitrary, scheme-dependent theoretical systematic error in the predictions. In this paper, we show that the renormalization scale uncertainties for hadronic $Z$ decays can be greatly reduced by applying the principle of maximum conformality (PMC), a rigorous extension of the BLM method. The PMC prediction is independent of the choice of renormalization scheme; i.e., it respects renormalization group invariance, and thus it provides an optimal and theoretically rigorous method for setting the renormalization scale. We show that the convergence of the pQCD prediction for the $Z$ hadronic width is greatly improved using the PMC since the divergent renormalon series does not appear. The magnitude of the high-order corrections quickly approach a steady point. The PMC predictions also have the property that any residual dependence on the choice of initial scale is highly suppressed, even for low-order predictions. Thus, one obtains optimal fixed-order predictions for the $Z$-boson hadronic decay rates thus enabling high precision tests of the Standard Model.

hep-ph↗

arXiv2014

Applications of Basis Light-Front Quantization to QED

Hamiltonian light-front quantum field theory provides a framework for calculating both static and dynamic properties of strongly interacting relativistic systems. Invariant masses, correlated parton amplitudes and time-dependent scattering amplitudes, possibly with strong external time-dependent fields, represent a few of the important applications. By choosing the light-front gauge and adopting an orthonormal basis function representation, we obtain a large, sparse, Hamiltonian matrix eigenvalue problem for mass eigenstates that we solve by adapting ab initio no-core methods of nuclear many-body theory. In the continuum limit, the infinite matrix limit, we recover full covariance. Guided by the symmetries of light-front quantized theory, we adopt a two-dimensional harmonic oscillator basis for transverse modes that corresponds with eigensolutions of the soft-wall anti-de Sitter/quantum chromodynamics (AdS/QCD) model obtained from light-front holography. We outline our approach and present results for non-linear Compton scattering, evaluated non-perturbatively, where a strong and time-dependent laser field accelerates the electron and produces states of higher invariant mass i.e. final states with photon emission.

nucl-th↗

arXiv2014

Light-Front Holography in QCD and Hadronic Physics

We describe a procedure to extend the light-front holographic approach to hadronic physics to include light-quark masses. The proposed framework allows us to extend the formalism of de Alfaro, Fubini and Furlan to the frame-independent light-front Hamiltonian theory in the approximation where the dynamics in the invariant transverse variable is unchanged to first order in the quark masses. The confinement potential follows from an effective theory which encodes the fundamental conformality of the classical QCD Lagrangian and leads to a semiclassical relativistic light-front wave equation for arbitrary spin. In particular, the K meson spectrum is successfully described without modifying the emerging confinement scale. The Wilson loop criteria for confinement is maintained, since for light quark masses a harmonic potential and linear Regge trajectories in the light-front form of dynamics corresponds to a linear potential in the usual instant-form.

hep-ph↗

arXiv2014

Light-Front Holographic QCD and Color Confinement

One of the most fundamental problems in Quantum Chromodynamics is to understand the origin of the mass scale which controls the range of color confinement and the hadronic spectrum. We show that a mass gap and a fundamental color confinement scale arise when one extends the formalism of de Alfaro, Fubini and Furlan to frame-independent light-front Hamiltonian theory. Remarkably, the resulting light-front potential has a unique form of a harmonic oscillator in the light-front invariant impact variable if one requires that the action remains conformally invariant. The result is a single-variable relativistic equation of motion for $q \bar q$ bound states, a "Light-Front Shrödinger Equation", analogous to the nonrelativistic radial 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 same slope in the radial quantum number and orbital angular momentum. The same equations with the correct hadron spin dependence arise from the holographic mapping of modified AdS$_5$ space with a specific dilaton profile. A fundamental mass parameter $κ$ appears, determining the hadron masses and the length scale which underlies hadron structure. Quark masses can be introduced to account for the spectrum of strange hadrons. This Light-Front Holographic approach predicts not only hadron spectroscopy successfully, but also hadronic form factors, the QCD running coupling at small virtuality, and the light-front wavefunctions of hadrons. Thus the combination of light-front dynamics, its holographic mapping to gravity in a higher-dimensional space and the dAFF procedure provides new insight into the physics underlying color confinement, chiral invariance, and the QCD mass scale.

hep-th↗

arXiv2014

Modified Anti-de-Sitter Metric, Light-Front Quantized QCD, and Conformal Quantum Mechanics

We briefly review the remarkable connections between light-front QCD, gravity in AdS space, and conformal quantum mechanics. We discuss, in particular, the group theoretical and geometrical aspects of the underlying one-dimensional quantum field theory. The resulting effective theory leads to a phenomenologically successful confining interaction potential in the relativistic light-front wave equation which incorporates relevant non-perturbative dynamical aspects of hadron physics.

hep-ph↗

arXiv2014

Novel Heavy Quark Phenomena in QCD

Heavy quarks provide a new dimension to QCD, allowing tests of fundamental theory, the nature of color confinement, and the production of new exotic multiquark states. I also discuss novel explanations for several apparently anomalous experimental results, such as the large $t \bar t$ forward-backward asymmetry observed in $p \bar p$ colisions at the Tevatron, the large rates for $γ$ or $Z$ plus high-$p_T$ charm jets observed at the Tevatron, the strong nuclear absorption of the $J/ψ$ observed in $pA$ collisions at the LHC, as well as fixed target experiments at high $x_F$. Precision measurements of the heavy quark distribution in hadrons at high $x$ are needed since intrinsic heavy quarks can play an important role in high $x$ phenomenology as well as predicting a new mechanism for high-$x_F$ Higgs production. The role of multi-parton interactions, such as di-gluon initiated subprocesses for forward quarkonium hadroproduction, is discussed. I also briefly discuss a new approach to the QCD confinement potential and the origin of the QCD mass scale based on AdS/QCD, light-front holography and a unique extension of conformal theory. The renormalization scale ambiguity can be eliminated at finite orders in pQCD using the scheme-independent PMC procedure, thus increasing the precision of predictions and eliminating an unnecessary source of theoretical systematic error.

hep-ph↗

arXiv2014

Hadron Spectroscopy and Dynamics from Light-Front Holography and Conformal Symmetry

To a first semiclassical approximation one can reduce the multi-parton light-front problem in QCD to an effective one-dimensional quantum field theory, which encodes the fundamental conformal symmetry of the classical QCD Lagrangian. This procedure leads to a relativistic light-front wave equation for arbitrary spin which incorporates essential spectroscopic and non-perturbative dynamical features of hadron physics. The mass scale for confinement and higher dimensional holographic mapping to AdS space are also emergent properties of this framework.

hep-ph↗

arXiv2014

Systematic Scale-Setting to All Orders: The Principle of Maximum Conformality and Commensurate Scale Relations

We present in detail a new systematic method which can be used to automatically eliminate the renormalization scheme and scale ambiguities in perturbative QCD predictions at all orders. We show that all of the nonconformal β-dependent terms in a QCD perturbative series can be readily identified by generalizing the conventional renormalization schemes based on dimensional regularization. We then demonstrate that the nonconformal series of pQCD at any order can be resummed systematically into the scale of the QCD coupling in a unique and unambiguous way due to a special degeneracy of the β-terms in the series. The resummation follows from the principal of maximum conformality (PMC) and assigns a unique scale for the running coupling at each perturbative order. The final result is independent of the initial choices of renormalization scheme and scale, in accordance with the principles of the renormalization group, and thus eliminates an unnecessary source of systematic error in physical predictions. We exhibit several examples known to order α_s^4; i.e. i) the electron-positron annihilation into hadrons, ii) the tau-lepton decay to hadrons, iii) the Bjorken and Gross-Llewellyn Smith (GLS) sum rules, and iv) the static quark potential. We show that the final series of the first three cases are all given in terms of the anomalous dimension of the gluon field, in accordance with conformality, and with all non-conformal properties encoded in the running coupling. The final expressions for the Bjorken and GLS sum rules directly lead to the generalized Crewther relations, exposing another relevant feature of conformality. The static quark potential shows that PMC scale setting in the Abelian limit is to all orders consistent with QED scale setting. Finally, we demonstrate that the method applies to any renormalization scheme and [...]

hep-ph↗

arXiv2013

Threefold Complementary Approach to Holographic QCD

A complementary approach, derived from (a) higher dimensional anti--de Sitter (AdS) space, (b) light-front quantization and (c) the invariance properties of the full conformal group in one dimension leads to a nonperturbative relativistic light-front wave equation which incorporates essential spectroscopic and dynamical features of hadron physics. The fundamental conformal symmetry of the classical QCD Lagrangian in the limit of massless quarks is encoded in the resulting effective theory. The mass scale for confinement emerges from the isomorphism between the conformal group and SO(2,1). This scale appears in the light-front Hamiltonian by mapping to the evolution operator in the formalism of de Alfaro, Fubini and Furlan, which retains the conformal invariance of the action. Remarkably, the specific form of the confinement interaction and the corresponding modification of AdS space are uniquely determined in this procedure.

hep-th↗

arXiv2013

QCD on the Light-Front -- A Systematic Approach to Hadron Physics

Light-Front Hamiltonian theory provides a rigorous frame-independent framework for solving nonperturbative QCD. The valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schrödinger equation, with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. Remarkably, the potential U has a unique form of a harmonic oscillator potential if one requires that the chiral QCD action remains conformally invariant. A mass gap arises when one extends the formalism of de Alfaro, Fubini and Furlan to light-front Hamiltonian theory. The valence LF meson wavefunctions for zero quark mass satisfy a single-variable relativistic equation of motion in the invariant variable $ζ^2=b^2_\perp x(1-x)$, which is conjugate to the invariant mass squared. The result is a nonperturbative relativistic light-front quantum mechanical wave 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 same slope in the radial quantum number n and orbital angular momentum L. The corresponding light-front Dirac equation provides a model of nucleons. The same light-front equations arise from the holographic mapping of the soft-wall model modification of AdS_5 space with a unique dilaton profile to QCD (3+1) at fixed light-front time. Light-front holography thus provides a precise relation between amplitudes in the fifth dimension of AdS space and light-front wavefunctions. We also discuss the implications of the underlying conformal template of QCD for renormalization scale-setting, and the implications of light-front quantization for the value of the cosmological constant.

hep-ph↗

arXiv2013

Novel Six-Quark Hidden-Color Dibaryon States in QCD

The recent observation of a hadronic resonance $d^*$ in the proton-neutron system with isospin $I = 0$ and spin-parity $J^P = 3^+$ raises the possibility of producing other novel six-quark dibaryon configurations allowed by QCD. A dramatic example of an exotic six-quark color-singlet system is the charge $Q=+4$, isospin I=3, $I^z=+3$ $|uuuuuu>$ state which couples strongly to $Δ^{++}$ + $Δ^{++} .$ The width and decay properties of such six-quark resonances could be regarded as manifestations of "hidden-color" six-quark configurations, a first-principle prediction of QCD -- SU(3)-color gauge theory for the deuteron distribution amplitude. Other implications and possible future experiments are discussed.

hep-ph↗

arXiv2013

Light-Front Holographic Quantum Chromodynamics

Anti-de Sitter space in five dimensions provides an exact geometrical representation of the conformal group. Remarkably, gravity in AdS$_5$ space is holographically dual to frame-independent light-front Hamiltonian theory, derived from the quantization of the QCD Lagrangian at fixed light-front time $τ= x^0+x^3$. Light-front holography also leads to a precise relation between the bound-state amplitudes in the fifth dimension $z$ of AdS space and the variable $ζ$, where $ζ^2 = b^2_\perp x(1-x)$ is the argument of the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. The holographic mapping of AdS space with a specific "soft-wall" dilaton yields a confining potential $U(ζ^2)$ for the light-front Schrödinger equation for hadrons with arbitrary spin $J$. Remarkably, $U(ζ^2)$ has a unique form of a harmonic oscillator potential if one requires that the chiral QCD action remains conformally invariant. One thus obtains an effective light-front effective theory for general spin which respects the conformal symmetry of the four-dimensional classical QCD Lagrangian. The predictions of the LF equations of motion include a zero-mass pion in the chiral $m_q\to 0$ limit, and linear Regge trajectories $M^2(n,L) \propto n+L$ with the same slope in the radial quantum number $n$ and the orbital angular momentum $L$. The light-front AdS/QCD holographic approach gives a frame-independent representation of color-confining dynamics, Regge spectroscopy, as well as the excitation spectra of relativistic light-quark meson and baryon bound states in QCD in terms of a single mass parameter. We also briefly discuss the implications of the underlying conformal template of QCD for renormalization scale-setting, and the implications of light-front quantization for the value of the cosmological constant.

hep-th↗

arXiv2013

Possible multiparticle ridge-like correlations in very high multiplicity proton-proton collisions

The CMS collaboration at the LHC has reported a remarkable and unexpected phenomenon in very high-multiplicity high energy proton-proton collisions: a positive correlation between two particles produced at similar azimuthal angles, spanning a large range in rapidity. We suggest that this "ridge"-like correlation may be a reflection of the rare events generated by the collision of aligned flux tubes connecting the valence quarks in the wave functions of the colliding protons. The "spray" of particles resulting from the approximate line source produced in such inelastic collisions then gives rise to events with a strong correlation between particles produced over a large range of both positive and negative rapidity. We suggest an additional variable that is sensitive to such a line source which is related to a commonly used measure, ellipticity.

hep-ph↗

arXiv2013

Light-Front Holographic QCD and the Confinement Potential

Light-Front Hamiltonian theory, derived from the quantization of the QCD Lagrangian at fixed light-front time τ= t+z/c, provides a rigorous frame-independent framework for solving nonperturbative QCD. The eigenvalues of the light-front QCD Hamiltonian predict the hadronic mass spectrum, and the eigensolutions provide the light-front wavefunctions describing hadron structure. The valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schrodinger equation, with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. The potential U has a unique form if one requires that the action for zero quark mass remains conformally invariant. The holographic mapping of gravity in AdS space to QCD with a specific soft-wall dilaton yields the same light-front Schrodinger equation. It also gives a precise relation between the bound-state amplitudes in the fifth dimension z of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. The elastic and transition form factors of the pion and the nucleons are found to be well described in this framework. The predictions include a zero-mass pion in the chiral limit, and linear Regge trajectories with the same slope in the radial quantum number n and orbital angular momentum L. The light-front AdS/QCD holographic approach thus gives a frame-independent representation of color-confining dynamics and the excitation spectra of light-quark hadrons in terms of a single mass parameter. We also discuss the implications of the underlying conformal template of QCD for renormalization scale-setting and the implications of light-front quantization for the value of the cosmological constant.

hep-th↗

arXiv2013

Linear polarization of gluons and photons in unpolarized collider experiments

We study azimuthal asymmetries in heavy quark pair production in unpolarized electron-proton and proton-proton collisions, where the asymmetries originate from the linear polarization of gluons inside unpolarized hadrons. We provide cross section expressions and study the maximal asymmetries allowed by positivity, for both charm and bottom quark pair production. The upper bounds on the asymmetries are shown to be very large depending on the transverse momentum of the heavy quarks, which is promising especially for their measurements at a possible future Electron-Ion Collider or a Large Hadron electron Collider. We also study the analogous processes and asymmetries in muon pair production as a means to probe linearly polarized photons inside unpolarized protons. For increasing invariant mass of the muon pair the asymmetries become very similar to the heavy quark pair ones. Finally, we discuss the process dependence of the results that arises due to differences in color flow and address the problem with factorization in case of proton-proton collisions.

hep-ph↗

arXiv2013

A Systematic All-Orders Method to Eliminate Renormalization-Scale and Scheme Ambiguities in PQCD

We introduce a generalization of the conventional renormalization schemes used in dimensional regularization, which illuminates the renormalization scheme and scale ambiguities of pQCD predictions, exposes the general pattern of nonconformal {β_i}-terms, and reveals a special degeneracy of the terms in the perturbative coefficients. It allows us to systematically determine the argument of the running coupling order by order in pQCD in a form which can be readily automatized. The new method satisfies all of the principles of the renormalization group and eliminates an unnecessary source of systematic error.

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