QCD on the Light-Front

Light-front Hamiltonian theory, derived from the quantization of the QCD Lagrangian at fixed light-front time x ⁺ = x ⁰ + x ³, provides a rigorous frame-independent framework for solving nonperturbative QCD. The eigenvalues of the light-front QCD Hamiltonian H _LF predict the hadronic mass spectrum, and the corresponding eigensolutions provide the light-front wavefunctions which describe hadron structure, providing a direct connection to the QCD Lagrangian. In the semiclassical approximation 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 and the color confinement scale also arises when one extends the formalism of de Alfaro, Fubini and Furlan to light-front Hamiltonian theory. In the case of mesons, the valence Fock-state wavefunctions of H _LF for zero quark mass satisfy a single-variable relativistic equation of motion in the invariant variable \({\zeta^2=b^2_\perp x(1-x)}\) , which is conjugate to the invariant mass squared \({{M^2_{q\bar q}}}\) . 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 \({M^2(n, L, S) = 4\kappa^2( n+L +S/2)}\) with the same slope in the radial quantum number n and orbital angular momentum L. Only one mass parameter \({\kappa}\) appears. The corresponding light-front Dirac equation provides a dynamical and spectroscopic model of nucleons. The same light-front equations arise from the holographic mapping of the soft-wall model modification of AdS₅ space with a unique dilaton profile to QCD (3 + 1) at fixed light-front time. 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. 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.     

Light-Front Holography,Color Confinement,and Supersymmetric Features of QCD

Light-Front Quantization—Dirac’s “Front Form”—provides a physical, frame-independent formalism for hadron dynamics and structure. Observables such as structure functions, transverse momentum distributions, and distribution amplitudes are defined from the hadronic light-front wavefunctions. One obtains new insights into the hadronic spectrum, light-front wavefunctions, and the functional form of the QCD running coupling in the nonperturbative domain using light-front holography—the duality between the front form and AdS₅, the space of isometries of the conformal group. In addition, superconformal algebra leads to remarkable supersymmetric relations between mesons and baryons of the same parity. The mass scale \({\kappa}\) underlying confinement and hadron masses can be connected to the parameter \({\Lambda_{\overline {MS}}}\) in the QCD running coupling by matching the nonperturbative dynamics, as described by the effective conformal theory mapped to the light-front and its embedding in AdS space, to the perturbative QCD regime. The result is an effective coupling defined at all momenta. This matching of the high and low momentum transfer regimes determines a scale Q₀ which sets the interface between perturbative and nonperturbative hadron dynamics. The use of Q₀ to resolve the factorization scale uncertainty for structure functions and distribution amplitudes, in combination with the principle of maximal conformality for setting the renormalization scales, can greatly improve the precision of perturbative QCD predictions for collider phenomenology. The absence of vacuum excitations of the causal, frame-independent front form vacuum has important consequences for the cosmological constant. I also discuss evidence that the antishadowing of nuclear structure functions is non-universal; i.e., flavor dependent, and why shadowing and antishadowing phenomena may be incompatible with the momentum and other sum rules for nuclear parton distribution functions.     

New Results in Light-Front Phenomenology

The light-front quantization of gauge theories in light-cone gauge provides a frame-independent wavefunction representation of relativistic bound states, simple forms for current matrix elements, explicit unitarity, and a trivial vacuum. In this talk I review the theoretical methods and constraints which can be used to determine these central elements of QCD phenomenology. The freedom to choose the light-like quantization four-vector provides an explicitly covariant formulation of light-front quantization and can be used to determine the analytic structure of light-front wave functions and define a kinematical definition of angular momentum. The AdS/CFT correspondence of large N_C supergravity theory in higher-dimensional anti-de Sitter space with supersymmetric QCD in four-dimensional space-time has interesting implications for hadron phenomenology in the conformal limit, including an all-orders demonstration of counting rules for exclusive processes. String/gauge duality also predicts the QCD power-law behavior of light-front Fock-state hadronic wavefunctions with arbitrary orbital angular momentum at high momentum transfer. The form of these near-conformal wavefunctions can be used as an initial ansatz for a variational treatment of the light-front QCD Hamiltonian. The light-front Fock-state wavefunctions encode the bound state properties of hadrons in terms of their quark and gluon degrees of freedom at the amplitude level. The nonperturbative Fock-state wavefunctions contain intrinsic gluons, and sea quarks at any scale Q with asymmetries such as . Intrinsic charm and bottom quarks appear at large x in the light-front wavefunctions since this minimizes the invariant mass and off-shellness of the higher Fock state. In the case of nuclei, the Fock state expansion contains “hidden color” states which cannot be classified in terms of nucleonic degrees of freedom. I also briefly review recent analyses which show that some leading-twist phenomena such as the diffractive component of deep inelastic scattering, single-spin asymmetries, nuclear shadowing and antishadowing cannot be computed from the LFWFs of hadrons in isolation.Work supported by Department of Energy contract DE-AC02-76SF00515     

AdS/QCD and Applications of Light-Front Holography

Light-front holography leads to a rigorous connection between hadronic amplitudes in a higher dimensional anti-de Sitter(AdS) space and frame-independent light-front wavefunctions of hadrons in(3 + 1)-dimensional physical space-time,thus providing a compelling physical interpretation of the AdS/CFT correspondence principle and AdS/QCD,a useful framework which describes the correspondence between theories in a modified AdS 5 background and confining field theories in physical space-time.To a first semiclassical approximation,where quantum loops and quark masses are not included,this approach leads to a single-variable light-front Schro¨dinger equation which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum.The coordinate z in AdS space is uniquely identified with a Lorentz-invariant coordinate ζ which measures the separation of the constituents within a hadron at equal light-front time.The internal structure of hadrons is explicitly introduced and the angular momentum of the constituents plays a key role.We give an overview of the light-front holographic approach to strongly coupled QCD.In particular,we study the photon-to-meson transition form factors(TFFs) FMγ(Q 2) for γ→ M using light-front holographic methods.The results for the TFFs for the η and η ' mesons are also presented.Some novel features of QCD are discussed,including the consequences of confinement for quark and gluon condensates.A method for computing the hadronization of quark and gluon jets at the amplitude level is outlined.     

Exclusive Rare B (s,c) Decays in Light-Front Quark Model

We investigate the exclusive rare ${B_s\to (K,\eta^{(\prime)})(\nu_{\ell}\bar{\nu_{\ell}}, \ell^+\ell^-)}$ and ${B_c\to D_{(s)}(\nu_{\ell}\bar{\nu_{\ell}}, \ell^+\ell^-)}$ (? = e, μ, τ) decays within the standard model and the light-front quark model constrained by the variational principle for the QCD motivated effective Hamiltonian. The branching ratios and the longitudinal lepton polarization asymmetries are calculated and compared with other theoretical model predictions.     

Second order QCD corrections toq\bar q-anihilation into a lepton pair at large transverse momentum

The \(\mathcal{O}{\text{(}}\alpha _{\text{s}}^{\text{2}} )\) correction is presented to \(q\bar q\) -annihilation into a lepton pair at large transverse momentum. I calculate the corresponding hadron cross section difference \(\frac{{d\sigma }}{{d^4 q}}(p\bar p - pp) \to e^ + e^ - + x(q\) is the momentum of the lepton pair system). The correction to this cross section difference is found to be large. This essentially agrees with recently published results by Ellis, Martinelli and Petronzio. Two improtant approximations are used: the invariant mass of the two-gluon-system is put to zero, and only valence-valence quark scattering is considered.     

Holographic screening length in a hot plasma of two sphere

We study the screening length \(L_{\mathrm{max}}\) of a moving quark–antiquark pair in a hot plasma, which lives in a two sphere, \(S^2\), using the AdS/CFT correspondence in which the corresponding background metric is the four-dimensional Schwarzschild–AdS black hole. The geodesic of both ends of the string at the boundary, interpreted as the quark–antiquark pair, is given by a stationary motion in the equatorial plane by which the separation length L of both ends of the string is parallel to the angular velocity \(\omega \). The screening length and total energy H of the quark–antiquark pair are computed numerically and show that the plots are bounded from below by some functions related to the momentum transfer \(P_c\) of the drag force configuration. We compare the result by computing the screening length in the reference frame of the moving quark–antiquark pair, in which the background metrics are “Boost-AdS” and Kerr–AdS black holes. Comparing both black holes, we argue that the mass parameters \(M_{\mathrm{Sch}}\) of the Schwarzschild–AdS black hole and \(M_{\mathrm{Kerr}}\) of the Kerr–AdS black hole are related at high temperature by \(M_{\mathrm{Kerr}}=M_{\mathrm{Sch}}(1-a^2l^2)^{3/2}\), where a is the angular momentum parameter and l is the AdS curvature.     

Form factors of η c in light-front quark model

We study the form factors of the η _c meson in the light-front quark model. We explicitly show that the transition form factor of η _c →γ ^? γ as a function of the momentum transfer is consistent with the experimental data by the BaBar collaboration, while the decay constant of η _c is found to be $f_{\eta_{c}}=230.5^{+52.2}_{-61.0}$ and $303.6^{+115.2}_{-116.4}~\mathrm{MeV}$ for $\eta_{c}\sim c\bar{c}$ by using two η _c →γγ decay widths of 5.3±0.5 and 7.2±2.1 keV, given by Particle Data Group and Lattice QCD calculation, respectively.     

On strange quark scalar condensate in the nucleon

A well known difficulty with a large value of the σ term in πN scattering is analysed from positions of the QCD sum rules approach. The matrix element \(\left\langle {p\left| {\bar ss} \right|p} \right\rangle\) is related to flavour singlet correlation function of two quark condensates at zero momentum. The splittings \(\left\langle {p\left| {\bar uu - \bar ss} \right|p} \right\rangle\) and \(\left\langle {p\left| {\bar dd - \bar ss} \right|p} \right\rangle\) are calculated and turn to be in agreement withSU ₃ relations.     

K→π form factors with reduced model dependence

Using partially twisted boundary conditions we compute the K→π semi-leptonic form factors in the range of momentum transfers $0\lesssim q^{2}\leq q^{2}_{\max}=(m_{K}-m_{\pi})^{2}$ in lattice QCD with N _f =2+1 dynamical flavours. In this way we are able to determine $f_{+}^{K\pi}(0)$ without any interpolation in the momentum transfer, thus eliminating one source of systematic error. This study confirms our earlier phenomenological ansatz for the strange quark mass dependence of the scalar form factor. We identify and estimate potentially significant NNLO effects in the chiral expansion that guides the extrapolation of the data to the physical point. Our main result is $f_{+}^{K\pi}(0)=0.9599(34)(^{+31}_{-47})(14)$ , where the first error is statistical, the second error is due to the uncertainties in the chiral extrapolation of the lattice data and the last error is an estimate of potential discretisation effects.     

Universality of identified hadron production in pp collisions

The shapes of invariant differential cross section for identified $\pi ^{\pm },K^{\pm }, p$ and $\overline{p}$ production as a function of transverse momentum measured in $pp$ collisions by the PHENIX detector are analyzed in terms of a recently introduced approach. Simultaneous fits of these data to the sum of exponential and power-law terms show a significant difference in the exponential term contributions. This effect qualitatively explains the observed shape of the experimental $K/\pi $ and $p/\pi $ yield ratios measured as a function of transverse momentum of produced hadrons. A picture with two types of mechanisms for hadron production is presented. Universality of the power-law term behavior for $\pi ^{\pm },K^{\pm }, p$ , and $\overline{p}$ production is shown.     

Lattice QCD Towards Nuclear Forces

Recent studies of nuclear forces based on lattice QCD are presented. Not only the central potential but also the tensor potential is deduced from the Nambu?CBethe?CSalpeter wave function measured with lattice QCD. This method is applied to various kinds of nuclear potentials, such as ${V_{NN}, V_{\Lambda N}, V_{p{\Xi}^0},V_{\Lambda\Lambda-N\Xi-\Sigma\Sigma}}$ (coupled-channel potential), and ${V^{\{{\bf {27},{8}_s,{1},{10},\overline{10},{8}_a}\}}}$ (flavor representation potential). The energy dependence and the angular momentum dependence of the quenched V _NN is studied. A challenge for three-nucleon force from lattice QCD is also presented.     

Testing the Concept of Quark–Hadron Duality with the ALEPH τ Decay Data

We propose a modified procedure for extracting the numerical value for the strong coupling constant α _s from the τ lepton hadronic decay rate into non-strange particles in the vector channel. We employ the concept of the quark–hadron duality specifically, introducing a boundary energy squared s _p > 0, the onset of the perturbative QCD continuum in Minkowski space (Bertlmann et al. in Nucl Phys B 250:61, 1985; de Rafael in An introduction to sum rules in QCD. In: Lectures at the Les Houches Summer School. arXiv: 9802448 [hep-ph], 1997; Peris et al. in JHEP 9805:011, 1998). To approximate the hadronic spectral function in the region s > s _p, we use analytic perturbation theory (APT) up to the fifth order. A new feature of our procedure is that it enables us to extract from the data simultaneously the QCD scale parameter ${\Lambda_{\overline{\rm MS}}}$ and the boundary energy squared s _p. We carefully determine the experimental errors on these parameters which come from the errors on the invariant mass squared distribution. For the ${\overline{\rm MS}}$ scheme coupling constant, we obtain ${\alpha_s(m^{2}_{\tau})=0.3204\pm 0.0159_{exp.}}$ . We show that our numerical analysis is much more stable against higher-order corrections than the standard one. Additionally, we recalculate the “experimental” Adler function in the infrared region using final ALEPH results. The uncertainty on this function is also determined.     

Resummed multiplicity moments

The multiplicity distribution of hadrons in a jet is reanalysed. The \(\mathcal{O}(1/\sqrt {\ln (W^2 /\Lambda _{QCD}^2 )} )\) correction to the double-log summation is so large that its addition makes the value of the multiplicity moments unphysical at the current energies ofe ⁺ e ^? annihilation. This implies the necessity of systematic resummation of the whole series in powers of \(1/\sqrt {\ln (W^2 /\Lambda _{QCD}^2 )} \) . In this article we perform this resummation. In fact, a formal exact solution of the integral equation, which gives recursion relations among the multiplicity moments, takes the form of a geometric series. The resummation reduces the correction substantially.     

Hypothesis of Quark Binding by Condensation of Gluons in Hadrons

Hypothesis of quark binding through condensation of gluons inside hadrons is formulated in the context of a renormalization group procedure for effective particles (RGPEP) in the light-front (LF) Hamiltonian approach to QCD. At the momentum scales of relative motion of hadronic constituents that are comparable with Λ _QCD , the hypothetical boost-invariant constituent dynamics is identified using gauge symmetry. The resulting picture of mesons and baryons closely resembles constituent quark models with harmonic oscillator potentials, shares some features of AdS/QCD, and can be systematically studied using RGPEP in QCD.     

Mass level of heavy flavored hadrons in the heavy-quark effective theory

We have studied the heavy flavored hadron spectroscopy, which is motivated by the heavy quark effective theory. TheQ \(\bar q\) ,Qqq andQQq hadrons have been investigated systematically. Regarding thes-quark as a member of heavy quarks, the predicted mass levels of both theQqq andQQq baryons are quite consistent with experimental ones.     

Single slepton production associated with a top quark at LHC in NLO QCD

Single slepton production in association with a top quark at the CERN Large Hadron Collider (LHC) is one of the important processes in probing the R-parity violation couplings. We calculate the QCD next-to-leading order (NLO) corrections to the $pp \to t\tilde{\ell}^{-}(\bar{t}\tilde{\ell}^{+})+X$ process at the LHC and discuss the impacts of the QCD corrections on kinematic distributions. We investigate the dependence of the leading order (LO) and the NLO QCD corrected integrated cross section on the factorization/renormalization energy scale, slepton, stop-quark and gluino masses. We find that the uncertainty of the LO cross section due to the energy scale is obviously improved by the NLO QCD corrections, and the exclusive jet event selection scheme keeps the convergence of the perturbative series better than the inclusive scheme. The results show that the polarization asymmetry of the top-quark will be reduced by the NLO QCD corrections, and the QCD corrections generally increase with the increment of the $\tilde{t}_{1}$ or $\tilde {g}$ mass value.     

Coupling constant in dispersive model

The average of the moments for event shapes in e ^?+? e??→hadrons within the context of next-to-leading order (NLO) perturbative QCD prediction in dispersive model is studied. Moments used in this article are $\langle {1-T}\rangle$ , $\langle \rho\rangle$ , $\langle {B_{\rm T}}\rangle$ and $\langle {B_{\rm W} }\rangle$ . We extract α _s, the coupling constant in perturbative theory and α ₀ in the non-perturbative theory using the dispersive model. By fitting the experimental data, the values of $\alpha_{\rm s} ({M_{\rm Z^0} })=0.1171\pm 0.00229$ and $\alpha_0 \left( {\mu_{\rm I} =2\,{\rm GeV}} \right)=0.5068\pm 0.0440$ are found. Our results are consistent with the above model. Our results are also consistent with those obtained from other experiments at different energies. All these features are explained in this paper.     

Light-Front Quark Model Analysis of Meson-Photon Transition Form Factor

We discuss \({(\pi^{0}, \eta, \eta') \to \gamma^{*}\gamma}\) transition form factors using the light-front quark model. Our discussion includes the analysis of the mixing angles for \({\eta-\eta'}\). Our results for \({Q^{2} F_{(\pi^0,\eta,\eta')\to\gamma^*\gamma}(Q^2)}\) show scaling behavior for high Q² consistent with pQCD predictions.     

Charm Mass Determination from QCD Sum Rules: A Revision of the Classical Method

In this work we take a revised look at the charm quark mass determination from QCD sum rules analyses. On the theoretical side we use the most up to date calculations (amounting to up ${O(\alpha_s^3)}$ expressions) and on the experimental side, to our knowledge, the most complete data set (maximum coverage of the energy spectrum). We reconsider the estimate of perturbative uncertainties (due to truncation of the series in ?? _s ) proposing four alternative methods (equivalent in perturbation theory) to determine the ${\rm{\overline{MS}}}$ charm quark mass. We also use a very robust method to combine data from different experiments when systematic correlated errors are mainly due to normalization. This allows to use experimental data up to 10.5GeV, and to quantify statistic and systematic experimental errors in a meaningful way.