One-loop factorization for inclusive hadron production in p-A collisions in the saturation formalism

We demonstrate the QCD factorization for inclusive hadron production in p-A collisions in the saturation formalism at one-loop order, with explicit calculation of both real and virtual gluon radiation diagrams. In particular, we find that the cross section can be written into a factorization form in the coordinate space at the next-to-leading order, while the naive form of the convolution in the transverse momentum space does not hold. The collinear divergences associated with the incoming parton distribution of the nucleon and the outgoing fragmentation function of the final-state hadron, as well as the rapidity divergence with small-x dipole gluon distribution of the nucleus are factorized into the splittings of the associated parton distribution and fragmentation functions and the energy evolution of the dipole gluon distribution function. The hard coefficient function is evaluated at one-loop order, and contains no divergence.     

The spectral density of the QCD Dirac operator and patterns of chiral symmetry breaking

We study the spectrum of the QCD Dirac operator for two colors with fermions in the fundamental representation and for two or more colors with adjoint fermions. For N_f flavors, the chiral flavor symmetry of these theories is spontaneously broken according to SU (2N_f → Sp (2N_f) and SU (N_f → O (N_f), respectively, rather than the symmetry breaking pattern SU (N_f) × SU (N_f) → SU (N_f) for QCD with three or more colors and fundamental fermions. In this paper we study the Dirac spectrum for the first two symmetry breaking patterns. Following previous work for the third case we find the Dirac spectrum in the domain λ Λ_QCD by means of partially quenched chiral perturbation theory. In particular, this result allows us to calculate the slope of the Dirac spectrum at λ = 0. We also show that for λ 1/L₂ Λ_QCD (wing L the linear size fo the system) the Dirac spectrum is given by a chiral Random Matrix Theory with the symmetries of the Dirac operator.     

Forward Z-boson production and the unintegrated sea quark density

Drell–Yan production in the forward region at the Large Hadron Collider is sensitive to multiple radiation of QCD partons not collinearly ordered, emitted over large rapidity intervals. We propose a method to take account of these radiative contributions via a factorization formula which depends on the unintegrated, or transverse momentum dependent, splitting function associated with the evolution of the initial-state sea quark distribution. We analyze this formula numerically, and point out kinematic effects from the initial-state transverse momentum on the vector boson spectrum.     

Transverse momentum distribution in Drell-Yan pair and W and Z boson production

We exhibit and discuss the QCD prediction for the transverse momentum distribution of W bosons, Z bosons and high-mass virtual photons produced in high-energy hadron-hadron collisions. Recent work has shown that this prediction is consistent with the structure of leading twist initial state interactions.

The expression we present is expected to give results correct up to order _s^N(Q) for any Q_T when the boson mass Q is very large (> 10⁸ GeV!), given only input from perturbative calculations at order _s^N+2 and deeply inelastic scattering structure functions. We specify the required N = 0 coefficients, employing the order _s² results of Kodaira and Trentadue and of Davies and Stirling. We then show how the expression should be modified to deal with current energy scales. We also discuss the connection between low-Q_T and high-Q_T formulae.     

Perturbative universality in soft particle production b

The spectrum of partons in a QCD jet becomes independent of the primary energy in the low momentum limit. This follows within the perturbative QCD from the colour coherence in soft gluon branching. Remarkably, the hadrons follow such behaviour closely, suggesting the parton hadron duality picture to be appropriate also for the low momentum particles. More generally, this scaling property holds for particles of low transverse and arbitrary longitudinal momentum, which explains an old experimental observation (“fan invariance”). Further tests of the perturbatively based picture for soft particle production are proposed for three-jet events in annihilation and di-jet production events in , and collisions. They are based upon the difference in the intensity of the soft radiation from primary and antennae. Received: 19 November 1997 / Published online: 26 February 1998     

Reggeon interactions in perturbative QCD

We study the pairwise interaction of reggeized gluons and quarks in the Regge limit of perturbative QCD. The interactions are represented as integral kernels in the transverse momentum space and as operators in the impact parameter space. We observe conformal symmetry and holomorphic factorization in all cases.     

New non-Abelian effects on D-branes

We extend the Myers dielectric effect to configurations with angular momentum. The resulting time-dependent N D0 brane bound states can be interpreted as describing rotating fuzzy ellipsoids. A similar solution exists also in the presence of a RR magnetic field, that we study in detail. We show that, for any finite N, above a certain critical angular momentum is energetically more favorable for the bound state system to dissociate into an Abelian configuration of N D0 branes moving independently. We have investigated this problem in the low-energy expansion of the non-Abelian D brane action for generic N. In the case N=2 we find explicit solutions of the full non-Abelian Born–Infeld D brane dynamics, which remarkably have the same structure and confirm the features of the low-energy approximation. We further study D string configurations representing fuzzy funnels deformed by the magnetic field and by the rotational motion.     

Evolution of the helicity and transversity. Transverse-momentum-dependent parton distributions

We examine the QCD evolution of the helicity and transversity parton distribution functions when including also their dependence on transverse momentum. Using an appropriate definition of these polarized transverse momentum distributions (TMDs), we describe their dependence on the factorization scale and rapidity cutoff, which is essential for phenomenological applications.     

Angular momentum mixing in single flavor color superconductivity with transverse pairing

Because of the equal strength of the pairing potential mediated by one-gluon exchange for all partial waves to the leading order QCD running coupling constant and the nonlinearity of the gap equation, the non-spherical pairing in single flavor color superconductivity (CSC) cannot be restricted in a single non-s-wave channel and the mixing among different angular momenta will occur. In this paper, we examine the angular momentum mixing in single flavor CSC of massless quarks with transverse pairing, in which the pairing quarks have opposite helicity. We find that the free energy of all non-spherical pairing states are lowered by angular momentum mixing compared with that contain p-wave only, though the amount of the free energy drop is numerically small. Consequently the most stable pairing state in the ultra-relativistic limit remains the spherical color-spin-locked state (CSL).     

Heavy quarkonium production and polarization

We present a perturbative QCD factorization formalism for the production of heavy quarkonia of large transverse momentum p(T) at collider energies, which includes both the leading-power (LP) and next-to-leading-power (NLP) contributions to the cross section in the m(Q)(2)/p(T)(2) expansion for heavy quark mass m(Q). We estimate fragmentation functions in the nonrelativistic QCD formalism and reproduce the bulk of the large enhancement found in explicit next-to-leading-order calculations in the color-singlet model. Heavy quarkonia produced from NLP channels prefer longitudinal polarization.     

1/N expansion and the correlation energy of nuclear matter in the relativistic σω model

We propose the 1/N expansion method, where N can be identified with 2 due to the isospin SU(2), as a systematic expansion scheme for the relativistic meson-nucleon many-body theory. We derive a general formula for the computation of the effective action in the σω model based on the 1/N expansion, utilizing the functional integral method. In this scheme the leading contribution coincides with the familiar Hartree approximation. The elimination of the Landau ghost from the meson propagators in the subgraphs, which appears to be essential for our formulation, is also established.

As an application we compute the energy density of nuclear matter beyond the Hartree approximation including the next-to-leading order contributions in the 1/N expansion. In this order, one should include the ring energy contribution as a correlation energy addition to the exchange energy contribution. We find that we can describe the nuclear matter saturation properties without drastic changes of the overall physical picture which emerged in the Hartree approximation. The important role of the repulsive contribution due to the vacuum polarization effects in the ring energy is emphasized.     

The Thomas-Fermi atom in a strong magnetic field: The weak ionization limit

It is proved that the binding energy, radius and chemical potential of the N-electron Thomas-Fermi atom with the nuclear charge Z in a strong magnetic field at q = 1 − N/Z 1 may be expressed as a power series in q^1/3 and In q. The exact values of the first expansion coefficients are found. A comparison with numerical data shows these expansions to be applicable up to q = 0.2.     

QCD1+1 in the limit of a large number of colors and flavors

QCD in 1+1 dimensions is examined in the limit of a large number of colors and flavors. The Hamiltonian matrix is given in a Fock space spanned by 't Hooft meson states and, for the case of zero fermion mass, a submatrix is diagonalized numerically to give the low-lying spectrum as a function of N_F/N_C. Pair creation effects generate bound states which are complicated mixtures of components of different meson number. There are a number of nontrivial zero modes; in the massive part of the spectrum some states tend to a well-defined N_F N_C limit while others become unstable and disappear. The masses of most states remain remarkably constant over a large range of N_F/N_C.     

Proton–neutron structure of the N=52 nucleus Zr

Following the successful identification of mixed-symmetric one- and two-phonon states in the N=52 nuclei ⁹⁴Mo and ⁹⁶Ru, we have performed a photon scattering experiment on the N=52 isotone ⁹²Zr. Experimental data and shell model calculations show that both, single particle and collective degrees of freedom are present in the low-lying levels of ⁹²Zr. The second excited quadrupole state shows the signatures of the one-phonon mixed-symmetric 2⁺ state, while calculations and data indicate an almost pure neutron configuration for the 2⁺₁ state, in contradiction with the F-spin symmetric limit. Furthermore, two strong dipole excitations, which are candidates for the two-phonon quadrupole–octupole coupled E1 excitation and for the mixed-symmetric 1⁺ two-phonon state, were observed.     

在RHIC和LHC中光子-核子碰撞产生的大横动量双轻子

研究了RHIC和LHC能区的Au-Au和Pb-Pb周边重离子碰撞中,来自光子-核子相互作用产生的大横动量双轻子。利用微扰QCD 参数化和Weizs?cker-Williams近似计算了双轻子的产率。经过与领头阶和碎裂过程的双轻子产生数值计算结果相比较,光-核碰撞过程产生的大横动量双轻子在RHIC能区是可忽略的。但是在LHC能区,光-核碰撞在大横动量区域是周边重离子碰撞的一个重要的双轻子源。     

Mesons and baryons at large N and strong coupling

The spectrum of the lattice gauge theory in the limit N → ∞ is studied. We calculate exactly the first two terms in the strong coupling expansion of the masses for the theory with naive fermions.     

Predictions for high-energy real and virtual photon–photon scattering from color dipole BFKL–Regge factorization

High-energy virtual photon–virtual photon scattering can be viewed as an interaction of small size color dipoles from the beam and target photons, which makes scattering at high energies (LEP, LEP200 and NLC) an indispensable probe of the short distance properties of the QCD pomeron exchange. Based on the color dipole representation, we investigate the consequences for the scattering of the incorporation of asymptotic freedom into the BFKL equation which makes the QCD pomeron a series of isolated poles in the angular momentum plane. The emerging color dipole BFKL–Regge factorization allows us to relate in a model-independent way the contributions of each BFKL pole to scattering and DIS off protons. Numerical predictions based on our early works on the color dipole BFKL phenomenology of DIS on protons are in good agreement with the experimental data on the photon structure function and the most recent data on the cross section from the OPAL and L3 experiments at LEP200. We discuss the role of non-perturbative dynamics and predict a pronounced effect of the Regge-factorization breaking due to large unfactorizable non-perturbative corrections to the perturbative vacuum exchange. We comment on the salient features of the BFKL–Regge expansion for scattering including the issue of the decoupling of subleading BFKL poles and the soft plus rightmost hard BFKL pole dominance. Received: 9 January 2001 / Revised version: 25 September 2001 / Published online: 7 December 2001     

Multiple collisions and induced gluon bremsstrahlung in QCD

Induced soft gluon bremsstrahlung associated with multiple collisions is calculated via perturbative QCD. We derive the non-abelian analog of the Landau-Pomeranchuk effect that suppresses induced soft radiation with formation times exceeding the mean free path. The dependence of the suppression effect on the SU(N) representation of the jet parton as well as the kinematic variables is expressed through a radiation formation factor. The soft radiation with k < μ, where μ is the infrared screening scale in the medium, is shown to lead to an approximately constant radiative energy loss per unit length.     

Higher-order QCD corrections in prompt photon production

We exhibit a method for simultaneously treating recoil and threshold corrections in single-photon inclusive cross sections, working within the formalism of collinear factorization. This approach conserves both the energy and transverse momentum of resummed radiation. At moderate p(T), we find the potential for substantial enhancements from higher-order perturbative and power-law nonperturbative corrections.