Diffraction at HERA, Color Opacity and Nuclear Shadowing in DIS off nuclei

The QCD factorization theorem for diffractive processes in DIS is used to derive formulae for the leading twist contribution to the nuclear shadowing of parton distributions in the low thickness limit (due to the coherent projectile (photon) interactions with two nucleons). Based on the current analyzes of diffraction at HERA we find that the average strength of the interactions which govern diffraction in the gluon sector at x≤ 10⁻³, Q ₀= 2 GeV is ∼50mb. This is three times larger than in the quark sector and suggests that applicability of DGLAP approximation requires significantly larger Q ₀ in the gluon sector. We use this information on diffraction to estimate the higher order shadowing terms due to the photon interactions with N≥ 3 nucleons which are important for the scattering of heavy nuclei and to calculate nuclear shadowing and Q ² dependence of gluon densities. For the heavy nuclei the amount of the gluon shadowing: G _A(x,Q ₀ ²) /AG _N(x,Q ₀ ²)_{|x ≤ 10−3}∼ 0.25–0.4 is sensitive to the probability of the small size configurations within wave function of the gluon “partonometer” at the Q ₀ scale. At this scale for A∼ 200 the nonperturbative contribution to the gluon density is reduced by a factor of 4–5 at x≤ 10⁻³ unmasking PQCD physics in the gluon distribution of heavy nuclei. We point out that the shadowing of this magnitude would strongly modify the first stage of the heavy ion collisions at the LHC energies, and also would lead to large color opacity effects in eA collisions at HERA energies. In particular, the leading twist contribution to the cross section of the coherent J/ψ production off A≥ 12 nuclei at s ⁻²≥ 70 GeV is strongly reduced as compared to the naive color transparency expectations. The Gribov black body limit for F _2A(x,Q ²) is extended to the case of the gluon distributions in nuclei and shown to be relevant for the HERA kinematics of eA collisions. Properties of the final states are also briefly discussed. Received: 12 March 1999     

Expanding color flux tubes and instabilities

We present an analytic study of the physics of the glasma which is a strong classical gluon field created at early stage of high-energy heavy-ion collisions. Our analysis is based on the picture that the glasma just after the collision is made of color electric and magnetic flux tubes extending in the longitudinal direction with their diameters of the order of 1/Q_s (Q_s is the saturation scale of the colliding nuclei). We find that both the electric and magnetic flux tubes expand outwards and the field strength inside the flux tube decays rapidly in time. Next we investigate whether there exist instabilities against small rapidity-dependent perturbations for a fixed color configuration. We find that the magnetic background field exhibits an instability induced by the fluctuations in the lowest Landau level, and it grows exponentially in the time scale of 1/Q_s. For the electric background field we find no apparent instability while the possible relation to the Schwinger mechanism for particle pair creations is suggested.     

A new numerical method for inverse Laplace transforms used to obtain gluon distributions from the proton structure function

We recently derived a very accurate and fast new algorithm for numerically inverting the Laplace transforms needed to obtain gluon distributions from the proton structure function F₂^gp(x,Q²)F_{2}^{\gamma p}(x,Q^{2}). We numerically inverted the function g(s), s being the variable in Laplace space, to G(v), where v is the variable in ordinary space. We have since discovered that the algorithm does not work if g(s)→0 less rapidly than 1/s as s→∞, e.g., as 1/s ^β for 0<β<1. In this note, we derive a new numerical algorithm for such cases, which holds for all positive and non-integer negative values of β. The new algorithm is exact if the original function G(v) is given by the product of a power v ^β−1 and a polynomial in v. We test the algorithm numerically for very small positive β, β=10⁻⁶ obtaining numerical results that imitate the Dirac delta function δ(v). We also devolve the published MSTW2008LO gluon distribution at virtuality Q ²=5 GeV² down to the lower virtuality Q ²=1.69 GeV². For devolution, β is negative, giving rise to inverse Laplace transforms that are distributions and not proper functions. This requires us to introduce the concept of Hadamard Finite Part integrals, which we discuss in detail.     

Gluon spectrum in the glasma from JIMWLK evolution

The JIMWLK equation with a “daughter dipole” running coupling is solved numerically, starting from an initial condition given by the McLerran-Venugopalan model. The resulting Wilson line configurations are then used to compute the spectrum of gluons comprising the glasma initial state of a high energy heavy ion collision. The development of a geometrical scaling region makes the spectrum of produced gluons harder. Thus the ratio of the mean gluon transverse momentum to the saturation scale grows with energy. Also the total gluon multiplicity increases with energy slightly faster than the saturation scale squared.     

Energy dependence of the saturation scale and the charged multiplicity in pp and AA collisions

A natural framework to understand the energy dependence of bulk observables from lower energy experiments to the LHC is provided by the Color Glass Condensate, which leads to a “geometrical scaling” in terms of an energy-dependent saturation scale Q _s. The measured charged multiplicity, however, seems to grow faster ( ~ ?s^0.3{\sim}\sqrt{s}^{0.3}) in nucleus–nucleus collisions than it does for protons ( ~ ?s^0.2{\sim} \sqrt{s}^{0.2}), violating the expectation from geometric scaling. We argue that this difference between pp and AA collisions can be understood from the effect of DGLAP evolution on the value of the saturation scale, and is consistent with gluon saturation observations at HERA.     

Looking at saturation effects with production in pA collisions

We compute the inclusive differential cross section production of the pseudo-scalar meson η^′ in high-energy proton-nucleus (pA) collisions. We use an effective coupling between gluons and η^′ meson to derive a reduction formula that relates the η^′ production to a field-strength tensor correlator. We take into account saturation effects on the nucleus side by using the Color Glass Condensate formalism to evaluate this correlator. We derive new results for Wilson line - color charges correlators in the McLerran-Venugopalan model needed in the computation of η^′ production. The unintegrated parton distribution functions are used to characterize the gluon distribution inside the proton. We show that the cross section is sensitive to saturation effects so it can be utilized to estimate the value of the saturation scale.     

Vector correlators in lattice QCD: Methods and applications

We discuss the calculation of the leading hadronic vacuum polarization in lattice QCD. Exploiting the excellent quality of the compiled experimental data for the e ⁺ e ⁻ → hadrons cross-section, we predict the outcome of large-volume lattice calculations at the physical pion mass, and design computational strategies for the lattice to have an impact on important phenomenological quantities such as the leading hadronic contribution to (g − 2) _μ and the running of the electromagnetic coupling constant. First, the R(s) ratio can be calculated directly on the lattice in the threshold region, and we provide the formulae to do so with twisted boundary conditions. Second, the current correlator projected onto zero spatial momentum, in a Euclidean time interval where it can be calculated accurately, provides a potentially critical test of the experimental R(s) ratio in the region that is most relevant for (g − 2) _μ . This observation can also be turned around: the vector correlator at intermediate distances can be used to determine the lattice spacing in fm, and we make a concrete proposal in this direction. Finally, we quantify the finite-size effects on the current correlator coming from low-energy two-pion states and provide a general parametrization of the vacuum polarization on the torus.     

A new approach to calculate the gluon polarization

We derive the Leading-Order (LO) master equation to extract the polarized gluon distribution G(x,Q ²)=xδg(x,Q ²) from polarized proton structure function, g^p₁(x,Q²)g^{p}_{1}(x,Q^{2}). By using a Laplace-transform technique, we solve the master equation and derive the polarized gluon distribution inside the proton. The test of accuracy which is based in our calculations on two different methods, confirms that we achieve to the correct solution for the polarized gluon distribution. To determine the polarized gluon distribution xδg(x,Q ²) more accurately, we only need to have more experimental data on the polarized structure functions, g₁^p(x,Q²)g_{1}^{p}(x,Q^{2}). Our result for polarized gluon distribution is in good agreement with some phenomenological models.     

Unpolarized structure functions and the parton distributions for nucleon in an independent quark model

Considering the nucleon as consisting entirely of its valence quarks confined independently in a scalar-vector harmonic potential; unpolarized structure functions F ₁(x, μ ²) and F ₂(x, μ ²) are derived in the Bjorken limit under certain simplifying assumptions; from which valence quark distribution functions u _v(x, μ ²) and d _v(x, μ ²) are appropriately extracted satisfying the normalization constraints. QCD-evolution of these input distributions from a model scale of μ ²=0.07 GeV² to a higher Q ² scale of Q ₀ ² =15 GeV² yields xu _v(x, Q ₀ ² ) and xd _v(x, Q ₀ ² ) in good agreement with experimental data. The gluon and sea-quark distributions such as G(x, Q ₀ ² ) and q _s(x, Q ₀ ² ) are dynamically generated with a reasonable qualitative agreement with the available data; using the leading order renormalization group equations with appropriate valence-quark distributions as the input.     

The superconducting properties of YBa2(Cu1−xMx)3O7 for M=Zn and Ni

Transverse and zero-field μSR measurements were made on YBa₂(Cu_1−xNi_x)₃O_7−y withx=0.1 and 0.2, and YBa₂(Cu_1−x Zn _x )₃O_7−y withx=0.03, 0.06, 0.1, and 0.16, wherey≈0.1. Since doping may lead to magnetic ordering this was searched for with both zero and transverse field μSR, but no evidence was found over the temperature range studied: 10–100 K. However, depolarization rates as functions of temperature were obtained, and the low temperature values of these are σ=3.2 μs⁻¹.1.6μs⁻¹, and 1 μs⁻¹ forx=0.01, and 0.2 Ni, respectively, and σ=0.8 μs⁻¹, 0.75 μs⁻¹, 0.65 μs⁻¹, and 0.4 μs⁻¹ forx=0.03, 0.06, 0.1, and 0.16 Zn, respectively. Estimates for the effect of decreasing electron concentration for Zn are made, but these alone do not account for the drop in σ. Estimates for the effect of scattering on λ and hence σ are made. The reduction in σ for Ni dopant is in surprisingly good agreement with these estimates. For Zn the order of magnitude is correct, but the relative lack of further change in σ after the effect of the first 0.03 addition seems to imply a saturation of the effect of scattering.     

Variation of multiplicities of the secondary charged particles on the geometry of collision

The total charge of the projectile spectator fragments, Q_pf is taken as a measure of the degree of centrality of collision thus defining the collision geometry. In this paper the mean multiplicities of the different charged secondaries emitted in the interaction of ²⁴Mg-Em at 4.5A GeV have been investigated as a function of the total charge Q_pf of the projectile spectator fragments. It has been observed that the average number of the produced particles, 〈N^s〉 and the heavily ionizing particles, 〈N_h> decreases exponentially with the increase of Q_pf showing strong correlation with the geometry of the collision. An attempt has also been made to compare these results with ⁸⁴Kr-Em interaction at 0.95A GeV.     

Application of FIRE for the calculation of photon matrix elements

The next-to-next-to-leading order (the order αα _s ²) corrections to the first moment of the polarized virtual photon structure function g ₁ ^γ (x,Q ², P ²) are studied in perturbative QCD for the kinematical region Λ² ≪ P ² ≪ Q ², where −Q ² (−P ²) is the mass square of the probe (target) photon and Λ is the QCD scale parameter. In order to evaluate the two-loop Feynman diagrams for the photon matrix element of the gluon operator, I apply the recently developed algorithm FIRE which reduces a complicated sum of scalar Feynman integrals to a linear combination of a few master integrals. The details of the calculation are presented.     

Lepton-pair production from deep inelastic scatteringin peripheral relativistic heavy ion collisions

We calculate the inelastic electron- and muon-pair production in peripheral relativistic heavy ion collisions in the region of large Q² of one of the photons. This offers a possibility to study the quark distribution functions in ions in "ultraperipheral heavy ion collisions". The calculations are compared with those making use of the equivalent photon and the equivalent lepton approximation. We compare the results for Pb-Pb and Pb-p collisions at RHIC (γ ≈ 100) and LHC (γ ≈ 3000) energies. Furthermore we include nuclear modifications to the parton distribution functions in our calculations to study their effect on the cross sections.     

Growth velocity and the topography of Ni-Zn binary alloy electrodeposits

We show that the electrodeposition of Ni-Zn alloys at the lowest growth velocities, v < 0.5μm/s, exclusively proceeds from an abnormal co-deposition phenomenon. The growth process in this v region greatly depends on the initial [Co²⁺] concentration of the film deposition bath. A theoretical approach of this process including the role of the saturation surface roughness of the alloy, , leads to an estimation of the transport properties of the ad-atoms involved during the deposit formation. Their surface diffusion coefficient varying between 1.76×10^-10 and 2.40×10^-8 cm^-2/s exhibits a minimal value, D _s = 2.10×10^-10 cm^-2/s located between v = 0.17 and 0.35μm/s. The spatial scaling analysis of the local roughness, σ, examined according to the power-law σ≈L ^α reveals that the resulting roughness exponents concurs with the Kardar-Parisi-Zhang dynamics including the restricted surface diffusion. Two main v regions leads to different fractal textural features of the alloy film surface. Below 0.10 μm/s, the roughness exponent obtained is α≈ 0.6, depicting a limited ad-atom mobility. Over v = 0.30μm/s, this exponent stabilises at α≈ 0.82, indicating an increase of the surface diffusion. Received 16 August 2000 and Received in final form 20 June 2001     

Evolution of the population of outer 6s and 5d shells in rare-earth metals

The shifts of the Kα ₁ and Kβ ₁ lines of all rare-earth (RE) metals (from La to Lu) have been measured experimentally by the x-ray shift method. The population of the RE-metal 6s and 5d shells has been determined by comparing the experimental and theoretical shifts obtained within the Dirac-Fock (Koopmans) model. Trivalent metals exhibit a monotonic cross-over from the 6s ^≈25d ^≈1 to 6s ^≈15d ^≈2 configuration with increasing atomic number. Fiz. Tverd. Tela (St. Petersburg) 41, 1361–1362 (August 1999)     

Probing the quark-gluon phase transition using energy and system-size dependence of long-range multiplicity correlations in heavy ion collisions from the STAR experiment

Long-range forward-backward multiplicity correlations have been measured in heavy ion collisions at RHIC. Results for short and long-range multiplicity correlations (forward-backward) are presented for several systems (Au+Au, Cu+Cu, and pp) and energies (e.g. ?{s_NN }\sqrt {s_{NN} } = 200 and 62.4 GeV). A strong, long-range correlation is seen for central heavy ion collisions at ?{s_NN }\sqrt {s_{NN} } = 200 GeV that vanishes in semi-peripheral events and pp collisions. There is no apparent scaling with the number of participants (N _part) involved in the collision. These correlations provide information about the longitudinal behavior of the system formed in heavy ion collisions. To access the transverse behavior, the clusters produced in the same heavy ion collisions have been characterized by a study of the energy and system size dependence of the percolation density parameter (ρ). The relationship between the long-range correlation and percolation has been explored to characterize the hadron-quark/gluon phase transition and rapid thermalization of the system.     

Colour effects in Drell-Yan process

We examine the predictions of gauge theories with colour excitation for the processpp →μ ⁺ μ ⁻ X. Relative to the predictions of quark parton model (with three colours) we find enhancements as large as a factor 3 – 4 for the cross-sectionM ³ d ² σ/dMdy|_y=0 in the region 0·03 ≲M/√s ≲ 0·2 at √s=62 GeV,M being the invariant mass andy the rapidity of the muon pair. We study the sensitivity of this result to the colour gluon mass and the underlying parametrisation of the quark and gluon distribution functions.     

The glasma initial state and JIMWLK factorization

We review recent work on understanding the next to leading order corrections to the classical fields that dominate the initial stages of a heavy ion collision. We have recently shown that the leading ln 1/x divergences of these corrections to gluon multiplicities can be factorized into the JIMWLK evolution of the color charge density distributions.     

Signals of a Weibel instability in the melting color glass condensate

Based on our work hep-ph/0510121, we discuss further the numerical study of classical SU(2) 3+1-D Yang-Mills equations for matter produced in a high-energy heavy-ion collision. The growth of the amplitude of fluctuations as exp(Γ ) (where g ²μ is a scale arising from the saturation of gluons in the nuclear wave function) is shown to be robust over a wide range of initial amplitudes that violate boost invariance. We argue that this growth is due to a non-Abelian Weibel instability, the scale of which is set by a dynamically generated plasmon mass. We discuss the relation of Γ to the prediction from kinetic theory.     

色玻璃凝聚近似下极端相对论重离子碰撞中的双轻子和光子产生(英文)

在色玻璃凝聚胶子饱和框架下,研究了相对论重离子碰撞中的双轻子和光子产生。在胶子饱和区域,在微扰近似(kT-因子化近似) 下低转移动量双轻子和光子的主要产生机制是胶子-胶子相互作用。在RHIC 和LHC 能量区域的相对论重离子碰撞中,饱和动量的值远远大于量子色动力学禁闭标度ΛQCD,这使得αs?1。此时,当转移动量小于饱和动量Qs 时质子和原子核的胶子密度值就会很高,双轻子和光子的不变产生横截面会由于饱效应而得到增强。数值结果给出在RHIC 和LHC 能量区域的pp, pA 和AA碰撞中,来源于色玻璃凝聚的低转移动量双轻子和光子产生贡献是显著的。We investigate inclusive dileptons and photons production in relativistic heavy ion collisions based on the idea of gluon saturation in the color glass condensate (CGC) framework. In the gluon saturation region, the dominant mechanism for low-pT dileptons and photons production in the perturbative approach (the kT-factorization approach) is gluon-gluon interaction. At Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) energies, the value of saturation momentum becomes larger than the Quantum Chromodynamics (QCD) confinement scale ΛQCD for relativistic heavy ion collisions, which implies that αs?1. In this state, the gluon density for proton and nucleus with transverse momentum less than the saturation momentum Qs will reach a high value, and the invariant cross-section for dileptons and direct photons is further enhanced by saturation effects. The numerical results indicate that the production of low-pT dileptons and photons from the color glass condensate becomes prominent in pp, pA, and AA collisions at RHIC and LHC  Energies.