arXiv subjects
Publications and source records attributed to W. Schäfer.
We discuss applications of the color dipole approach to hard processes on nuclei. We focus on the relation to k_t--factorisation and the role of a nuclear unintegrated gluon distribution in single-- and two-- particle inclusive spectra in γ^*A and pA collisions. Linear k_t factorisation is broken for a wide class of observables, which we exemplify on the case of heavy quark p_t--spectra.
Based on an approach to non-Abelian propagation of color dipoles in a nuclear medium we formulate a nonlinear k_t-factorization for the breakup of photons and pions into forward hard dijets in terms of the collective Weizsäcker-Williams (WW) glue of nuclei. We find quite distinct practical consequences of nonlinear nuclear k_t-factorization for interactions of pointlike photons and non-pointlike pions. In the former case the large transverse momentum p_t of jets comes from the intrinsic momentum of quarks and antiquarks in the photon and nuclear effects manifest themselves as an azimuthal decorrelation with an acoplanarity momentum of the order of the nuclear saturation momentum Q_A. In the breakup of pions off free nucleons to the leading order in pQCD the spectator parton has a small transverse momentum and the hard dijet cross section is suppressed. In the breakup of pions off heavy nuclei the forward hard jets are predicted to be entirely decorrelated. We comment on the sensitivity of the pionic dijet cross section to the pion distribution amplitude. The predicted distinction between the breakup of photons and pions can be tested by the sphericity and thrust analysis of the forward hadronic system in the COMPASS experiment at CERN.
As Glauber has shown in 1959, the spin-flip phenomena caused by the conventional spin-orbit interaction do vanish in the scattering off heavy, strongly absorbing nuclei. On the other hand, the origin of the s-channel helicity nonconservation (SCHNC) in diffractive DIS is of the origin different from simple spin-orbit interaction, and here we demonstrate that SCHNC in vector meson production survives strong absorption effects in nuclear targets. The intranuclear absorption often discussed in terms of the saturation effects introduces a new large scale $Q_A^2$ into the calculation of diffractive vector meson production amplitudes. Based on the color dipole approach, we show how the impact of the saturation scale $Q_A^2$ changes from the coherent to incoherent/quasifree diffractive vector mesons.
The Lorentz contraction of ultrarelativistic nuclei entails a spatial overlap and fusion (recombination, saturation) of partons belonging to different nucleons at the same impact parameter. In these lectures we present a consistent description of the fusion of partons in terms of nuclear attenuation of color dipole states of the photon and collective Weizsäcker-Williams (WW) gluon structure function of a nucleus. The point that all observables for DIS off nuclei are uniquely calculable in terms of the nuclear WW glue amounts to a new form of factorization in the saturation regime. We start with the theory of multichannel propagation of color dipoles in a nuclear medium including the color-singlet to color-octet to color-octet transitions. We show how the Glauber-Gribov formulas are recovered from the multichannel formalism. Then we derive the two-plateau momentum distribution of final state (FS) quarks produced in deep inelastic scattering (DIS) off nuclei in the saturation regime. Then we comment on the signatures of saturation in exclusive diffractive DIS. A large body of these lectures is on the recent theory of jet-jet inclusive cross sections. We show that for hard dijets the decorrelation momentum is of the order of the nuclear saturation momentum $Q_A$. For minijets with the transverse momentum below the saturation scale we predict a complete disappearance of the azimuthal jet-jet correlation. We conclude with comment on a possible relevance of the decorrelation of jets to the experimental data from the STAR-RHIC Collaboration.
We develop the QCD description of the breakup of photons into forward dijets in small-x deep inelastic scattering off nuclei in the saturation regime. Based on the color dipole approach, we derive a multiple scattering expansion for intranuclear distortions of the jet-jet transverse momentum spectrum. A special attention is paid to the non-Abelian aspects of the propagation of color dipoles in a nuclear medium. We report a nonlinear $k_{\perp}$-factorization formula for the breakup of photons into dijets in terms of the collective Weizsäcker-Williams (WW) glue of nuclei as defined in ref. \cite{Saturation,NSSdijet}. For hard dijets with the transverse momenta above the saturation scale the azimuthal decorrelation (acoplanarity) momentum is of the order of the nuclear saturation momentum QA. For minijets with the transverse momentum below the saturation scale the nonlinear kT-factorization predicts a complete disappearance of the jet-jet correlation. We comment on a possible relevance of the nuclear decorrelation of jets to the experimental data from the STAR-RHIC Collaboration.
We review a consistent description of the fusion and saturation of partons in the Lorentz-contracted ultrarelativistic nuclei in terms of a nuclear attenuation of color dipole states of the photon and collective Weizsäcker-Williams (WW) gluon structure function of a nucleus. Diffractive DIS provides a basis for the definition of the WW nuclear glue. The point that all observables for DIS off nuclei are uniquely calculable in terms of the nuclear WW glue amounts to a new form of factorization in the saturation regime.
We review the recent finding of the two-plateau momentum distribution of sea quarks in deep inelastic scattering off nuclei in the saturation regime. The diffractive plateau which dominates for small $\bp$ measures precisely the momentum distribution of quarks in the beam photon, the rôle of the nucleus is simply to provide an opacity. The plateau for truly inelastic DIS exhibits a substantial nuclear broadening of the momentum distribution. Despite this nuclear broadening, the observed final state and initial state sea quark densities do coincide exactly. We emphasize how the saturated sea is generated from the nuclear-diluted Weizsäcker-Williams because of the anti-collinear splitting of gluons into sea quarks.
We derive the two-plateau momentum distribution of final state (FS) quarks produced in deep inelastic scattering (DIS) off nuclei in the saturation regime. The diffractive plateau which dominates for small transverse momentum p measures precisely the momentum distribution of quarks in the beam photon, the role of the nucleus is simply to provide an opacity. The plateau for truly inelastic DIS exhibits a substantial nuclear broadening of the FS momentum distribution. We discuss the relationship between the FS quark densities and the properly defined initial state (IS) nuclear quark densities.The Weizsäcker-Williams glue of a nucleus exhibits a substantial nuclear dilution, still soft IS nuclear sea saturates because of the anti-collinear splitting of gluons into sea quarks.
Diffraction plays an exceptional role in DIS off heavy nuclei. First, diffraction into hard dijets is an unique probe of the unintegrated glue in the target. Second, because diffraction makes 50 per cent of total DIS off a heavy target, understanding diffraction in a saturation regime is crucial for a definition of saturated nuclear parton densities. After brief comments on the Nikolaev-Zakharov (NZ) pomeron-splitting mechanism for diffractive hard dijet production, I review an extension of the Nikolaev-Schafer-Schwiete (NSS) analysis of diffractive dijet production off nuclei to the definition of nuclear partons in the saturation regime. I emphasize the importance of intranuclear final state interactions for the parton momentum distributions.
We analyze the fate of the unbroken SU(2) color gauge interactions for 2 light flavors color superconductivity at non zero temperature. Using a simple model we compute the deconfining/confining critical temperature and show that is smaller than the critical temperature for the onset of the superconductive state itself. The breaking of Lorentz invariance, induced already at zero temperature by the quark chemical potential, is shown to heavily affect the value of the critical temperature and all of the relevant features related to the deconfining transition. Modifying the Polyakov loop model to describe the SU(2) immersed in the diquark medium we argue that the deconfinement transition is second order. Having constructed part of the equation of state for the 2 color superconducting phase at low temperatures our results are relevant for the physics of compact objects featuring a two flavor color superconductive state.
We discuss the condensation of relativistic spin-one fields at high chemical potential. This phenomenon leads to the spontaneous breaking of rotational invariance, together with the breaking of internal symmetries.
We discuss how the dijet azimuthal correlations in DIS and real photoproduction at HERA probe the differential (unintegrated) gluon distribution in the proton. We find a strong dependence of the azimuthal correlation pattern on Bjorken-$x$, photon virtuality and the cut on the jet transverse momenta. A rise of the azimuthal decorrelations is observed with decreasing Bjorken-x due to the interplay of perturbative and nonperturbative effects. We predict a strong rise of the same-side jet rate with photon energy for real photoproduction. We discuss conditions for the correlation function to be dominated by hard perturbative gluons and ways of constraining the size of the nonperturbative soft component. We make some predictions for the THERA energy range. The analysis of the energy dependence of the isolated jet and two-jet cross sections in photoproduction would be a new way to study the not yet well constrained unintegrated gluon distributions and to explore the onset of the pQCD regime.
We formulate the perturbative QCD approach to coherent diffractive dijet production in pion-nucleon and pion-nucleus collisions at high energy. For hard dijets the Pomeron splitting mechanism in which both helicity amplitudes are proportional to the unintegrated gluon structure function of the proton and the pion distribution amplitude is shown to dominate. In nuclear diffraction multiple Pomeron splitting components are found to give antishadowing contributions at large jet momentum. To leading twist there is an exact cancelation of effects of nuclear attenuation and antishadowing/broadening of multiple Pomeron splitting contributions. The next-to-leading higher twist correction driven by nuclear rescatterings is calculable in hard QCD and proves to be numerically very large. We argue that large higher twist effects do not preclude the determination of gross features of the pion distribution amplitude. Our results on the atomic mass number and momentum dependence of dijet cross sections agree well with the preliminary findings from the E791 experiment.
We revisit the evaluation of the pionic mechanism of the $\bar{u}-\bar{d}$-asymmetry in the proton structure function. Our analysis is based on the unitarity relation between contributions of different mechanisms to the inclusive particle production and the total photoabsorption cross-section (i.e. the proton structure function). We reanalyze the role of isovector reggeons in inclusive production of nucleons and Delta isobars in hadronic reactions. A rather large contribution of reggeon-exchange induced production of Delta isobars is found. This leaves much less room for the pion-exchange induced mechanism of $Δ$ production and provides a constraint on the $πN Δ$ form factor. The production of leading pions in proton-proton collisions puts additional constraints on the $πNN$ vertex form factors. All these constraints are used then to estimate the pion content of the nucleon and allow to calculate parameter-free the x-dependence of $\bar d - \bar u$. We discuss the violation of the Gottfried Sum Rule and $\bar d$-$\bar u$ asymmetry and compare to the one obtained from the E866 experiment at Fermilab.
We derive a unitarity relationship between the spin structure function $g_{LT}(x,Q^{2})=g_{1}(x,Q^{2})+g_{2}(x,Q^{2})$, the LT interference diffractive structure function and the spin-flip coupling of the pomeron to nucleons. Our diffractive mechanism gives rise to a dramatic small-$x$ rise $g_{LT}(x,Q^{2}) \sim g^{2}(x,\bar{Q}^{2}) \sim (1/x)^{2(1+δ_{g})}$, where $δ_{g}$ is an exponent of small-$x$ rise of the unpolarized gluon density in the proton $g(x,\bar{Q}^{2})$ at a moderate hard scale $\bar{Q}^{2}$ for light flavour contribution and large hard scale $\bar{Q}^{2} \sim m_{f}^{2}$ for heavy flavour contribution. It invalidates the Burkhardt-Cottingham sum rule. The found small-$x$ rise of diffraction driven $g_{LT}(x,Q^{2})$ is steeper than given by the Wandzura-Wilczek relation under conventional assumptions on small-$x$ behaviour of $g_{1}(x,Q^{2})$.
We revisit the evaluation of the pionic mechanism of the $\bar{u}-\bar{d}$-asymmetry in the proton structure function. Our analysis is based on the extended AGK unitarity relation between contributions of different mechanisms to the inclusive particle production and the total photoabsorption cross-section (i.e. the proton structure function). We reanalyze the role of isovector reggeons in inclusive production of nucleons and Delta isobars in hadronic reactions. We find rather large contribution of reggeon-exchange induced production of Delta isobars. This leaves much less room for the pion-exchange induced mechanism of $Δ$ production and provides a constraint on the $πN Δ$ form factor. The production of leading pions in proton-proton collisions at ISR puts additional constraints on the $πNN$ vertex form factors. An extension of the AGK-rules to reggeon exchange suggests a negligible contribution to the proton structure function from DIS off the exchanged $ρ,a_2$ reggeons. All these constraints are used then to estimate the pion content of the nucleon and allow to calculate parameter-free the $x$-dependence of $\bar d - \bar u$. We discuss the violation of the Gottfried Sum Rule and $\bar d$-$\bar u$ asymmetry and compare to the one obtained from the E866 experiment at Fermilab. We estimate the background to the pion structure function being determined by the ZEUS and H1 collaborations at HERA from leading neutron experiments.