Two-Loop Helicity Amplitudes for Quark-Gluon Scattering in QCD and Gluino-Gluon Scattering in Supersymmetric Yang-Mills Theory

We present the two-loop QCD helicity amplitudes for quark-gluon scattering, and for quark-antiquark annihilation into two gluons. These amplitudes are relevant for next-to-next-to-leading order corrections to (polarized) jet production at hadron colliders. We give the results in the `t Hooft-Veltman and four-dimensional helicity (FDH) variants of dimensional regularization. The transition rules for converting the amplitudes between the different variants are much more intricate than for the previously discussed case of gluon-gluon scattering. Summing our two-loop expressions over helicities and colors, and converting to conventional dimensional regularization, gives results in complete agreement with those of Anastasiou, Glover, Oleari and Tejeda-Yeomans. We describe the amplitudes for 2 to 2 scattering in pure N=1 supersymmetric Yang-Mills theory, obtained from the QCD amplitudes by modifying the color representation and multiplicities, and verify supersymmetry Ward identities in the FDH scheme.Comment: 77 pages. v2: corrected errors in eqs. (3.7) and (3.8) for one-loop assembly; remaining results unaffecte

Nonlinear effects in tunnelling escape in N-body quantum systems

We consider the problem of tunneling escape of particles from a multiparticle system confined within a potential trap. The process is nonlinear due to the interparticle interaction. Using the hydrodynamic representation for the quantum equations of the multiparticle system we find the tunneling rate and time evolutions of the number of trapped particles for different nonlinearity values.Comment: 10 pages, 3 figure

Single transverse spin asymmetry of forward neutrons

We calculate the single transverse spin asymmetry $A_N(t)$, for inclusive neutron production in $pp$ collisions at forward rapidities relative to the polarized proton in the energy range of RHIC. Absorptive corrections to the pion pole generate a relative phase between the spin-flip and non-flip amplitudes, leading to a transverse spin asymmetry which is found to be far too small to explain the magnitude of $A_N$ observed in the PHENIX experiment. A larger contribution, which does not vanish at high energies, comes from the interference of pion and $a_1$-Reggeon exchanges. The unnatural parity of $a_1$ guarantees a substantial phase shift, although the magnitude is strongly suppressed by the smallness of diffractive $\pi p\to a_1 p$ cross section. We replace the Regge $a_1$ pole by the Regge cut corresponding to the $\pi\rho$ exchange in the $1^+S$ state. The production of such a state, which we treat as an effective pole $a$, forms a narrow peak in the $3\pi$ invariant mass distribution in diffractive $\pi p$ interactions . The cross section is large, so one can assume that this state saturates the spectral function of the axial current and we can determine its coupling to nucleons via the PCAC Goldberger-Treiman relation and the second Weinberg sum rule. The numerical results of the parameter-free calculation of $A_N$ are in excellent agreement with the PHENIX data.Comment: 8 pages, 6 figures. Based on the talk given by B.K. at the Third International Workshop on Transverse Polarization Phenomena, Veli Losinj, Croatia, 29 August - 2 September 201

Hydrodynamic electron flow in high-mobility wires

Hydrodynamic electron flow is experimentally observed in the differential resistance of electrostatically defined wires in the two-dimensional electron gas in (Al,Ga)As heterostructures. In these experiments current heating is used to induce a controlled increase in the number of electron-electron collisions in the wire. The interplay between the partly diffusive wire-boundary scattering and the electron-electron scattering leads first to an increase and then to a decrease of the resistance of the wire with increasing current. These effects are the electronic analog of Knudsen and Poiseuille flow in gas transport, respectively. The electron flow is studied theoretically through a Boltzmann transport equation, which includes impurity, electron-electron, and boundary scattering. A solution is obtained for arbitrary scattering parameters. By calculation of flow profiles inside the wire it is demonstrated how normal flow evolves into Poiseuille flow. The boundary-scattering parameters for the gate-defined wires can be deduced from the magnitude of the Knudsen effect. Good agreement between experiment and theory is obtained.Comment: 25 pages, RevTeX, 9 figure

Experimental Evidence for Simple Relations between Unpolarized and Polarized Parton Distributions

The Pauli exclusion principle is advocated for constructing the proton and neutron deep inelastic structure functions in terms of Fermi-Dirac distributions that we parametrize with very few parameters. It allows a fair description of the recent NMC data on $F^p_2(x,Q^2)$ and $F^n_2(x,Q^2)$ at $Q^2=4 GeV^2$, as well as the CCFR neutrino data at $Q^2=3$ and $5 GeV^2$. We also make some reasonable and simple assumptions to relate unpolarized and polarized quark parton distributions and we obtain, with no additional free parameters, the spin dependent structure functions $xg^p_1(x,Q^2)$ and $xg^n_1(x,Q^2)$. Using the correct $Q^2$ evolution, we have checked that they are in excellent agreement with the very recent SMC proton data at $Q^2=10 GeV^2$ and the SLAC neutron data at $Q^2=2 GeV^2$.Comment: 17 pages,CPT-94/P.3032,latex,6 fig available on cpt.univ-mrs.fr directory pub/preprints/94/fundamental-interactions /94-P.303

The Generalized Gerasimov-Drell-Hearn Integral and the Spin Structure of the Nucleon

The spin structure functions g1 and g2 have been calculated in the resonance region and for small and intermediate momentum transfer. The calculation is based on a gauge-invariant and unitary model for one-pion photo- and electroproduction. The predictions of the model agree with the asymmetries and the spin sturcture functions recently measured at SLAC, and the first moments of the calculated spin structure functions fullfil the Gerasimov-Drell-Hearn and Burkhardt-Cottingham sum rules within an error of typically 5-10 %.Comment: 22 pages LATEX including 5 postscript figures, replaced with 2 new figure

The spin dependence of high energy proton scattering

Motivated by the need for an absolute polarimeter to determine the beam polarization for the forthcoming RHIC spin program, we study the spin dependence of the proton-proton elastic scattering amplitudes at high energy and small momentum transfer.We examine experimental evidence for the existence of an asymptotic part of the helicity-flip amplitude phi_5 which is not negligible relative to the largely imaginary average non-flip amplitude phi_+. We discuss theoretical estimates of r_5, essentially the ratio of phi_5 to phi_+, based upon extrapolation of low and medium energy Regge phenomenological results to high energies, models based on a hybrid of perturbative QCD and non-relativistic quark models, and models based on eikonalization techniques. We also apply the model-independent methods of analyticity and unitarity.The preponderence of evidence at available energy indicates that r_5 is small, probably less than 10%. The best available experimental limit comes from Fermilab E704:those data indicate that |r_5|<15%. These bounds are important because rigorous methods allow much larger values. In contradiction to a widely-held prejudice that r_5 decreases with energy, general principles allow it to grow as fast as ln(s) asymptotically, and some models show an even faster growth in the RHIC range. One needs a more precise measurement of r_5 or to bound it to be smaller than 5% in order to use the classical Coulomb-nuclear interference technique for RHIC polarimetry. As part of this study, we demonstrate the surprising result that proton-proton elastic scattering is self-analysing, in the sense that all the helicity amplitudes can, in principle, be determined experimentally at small momentum transfer without a knowledge of the magnitude of the beam and target polarization