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.     

Studies of the 3D structure of the proton at Jlab

In recent years parton distributions, describing longitudinal momentum, helicity and transversity distributions of quarks and gluons, have been generalized to account also for transverse degrees of freedom. Two new sets of more general distributions, Transverse Momentum Distributions (TMDs) and Generalized Parton Distributions (GPDs) were introduced to describe transverse momentum and spatial distributions of partons. Great progress has been made since then in measurements of different Single Spin Asymmetries (SSAs) in semi-inclusive and hard exclusive processes, providing access to TMDs and GPDs, respectively. Studies of TMDs and GPDs are also among the main driving forces of the JLab 12 GeV upgrade project.     

Transversity distribution and polarized fragmentation function from semi-inclusive pion electroproduction

A method is discussed to determine the hitherto unknown u-quark transversity distribution from a planned HERMES measurement of a single target-spin asymmetry in semi-inclusive pion electroproduction off a transversely polarized target. Assuming u-quark dominance, the measurement yields the shapes of the transversity distribution and of the ratio , of polarized and unpolarized u-quark fragmentation functions. The unknown relative normalization can be obtained by identifying the transversity distribution with the well-known helicity distribution at large x and small . The systematic uncertainty of the method is dominated by the assumption of u-quark dominance. Received: 18 June 2000 / Revised version: 20 November 2000 / Published online: 5 February 2001     

Moments of isovector quark distributions in lattice QCD

We investigate the connection of lattice calculations of moments of isovector parton distributions to the physical regime through extrapolations in the quark mass. We consider the one-pion loop renormalisation of the nucleon matrix elements of the corresponding operators and thereby develop formulae with which to extrapolate the moments of the unpolarised, helicity and transversity distributions. These formulae are consistent with chiral perturbation theory in chiral limit and incorporate the correct heavy-quark limits. In the polarised cases, the inclusion of intermediate states involving the -isobar is found to be very important. The results of our extrapolations are in general agreement with the phenomenological values of these moments where they are known, and for the first time we make reliable predictions for the low moments of the isovector transversity distribution.Received: 30 September 2002, Published online: 22 October 2003PACS: 12.38.Gc Lattice QCD calculations - 11.30.Rd Chiral symmetries     

The amplitude structure of the processesK - p→ϱ-∑ (1385) andK - p→Φ ∑0 (1385) at 4.2 GeV/c

We present model-independent transversity amplitudes for the processesK ^- p→?^-∑ (1385) andK ^- p→Φ ∑⁰ (1385) at 4.2 GeV/c. We also perform a model dependent analysis and compare the resulting helicity amplitudes with the predictions of a simple exchange model. Implications for future model building are discussed.     

On the photon-drag effect of photocurrent of surface states of topological insulators

The photocurrent of surface states of topological insulator due to photon-drag effect is computed, being based on pure Dirac model of surface states. The scattering by disorder is taken into account to provide a relaxation mechanism for the photocurrent. The Keldysh–Schwinger formalism has been employed for the systematic calculation of photocurrent. The helicity dependent photocurrent of sizable magnitude transverse to the in-plane photon momentum is found, which is consistent with experimental data. Other helicity independent photocurrents with various polarization states are also calculated.     

Polarization effects in Drell-Yan processes

Effects of polarization of hadrons and constituent quarks in Drell-Yan processes are considered; they are one of the most efficient tools for investigation of the quark structure of hadrons. Special attention is paid to such important parton distribution functions as the transversity and T-odd Sivers and Boer—Mulders functions whose study is necessary for understanding the effects connected with the nonzero transverse component of the quark momentum. An original method for direct extraction of transversity and Boer—Mulders function in the proton from the data on Drell—Yan processes, in which a maximum of one hadron in the initial state is transversely polarized, is presented. This method possesses a number of important advantages. The method is applied both to Drell—Yan processes with a valence antiquark (antiproton-proton and pion-proton collisions) and with a sea antiquark (proton-proton, proton-deuteron, and deuteron-deuteron collisions). Theoretical estimates of asymmetries and cross sections for setups at RHIC (BNL, US), NICA (JINR, Russia), COMPASS (CERN, Switzerland), PAX (GSI, Germany), and J-PARC (Japan) are presented for evaluation of the measurability of transversity and T-odd distributions. These theoretical estimates are accompanied by calculations of statistical uncertainties for measured asymmetries using the new Monte Carlo generator of Drell—Yan events. The duality of Drell—Yan processes and those of production of J/Φ resonance is studied, and it may allow one to considerably reduce statistical uncertainties of parton distributions. Kinematical conditions, for which this duality can be observed, are evaluated.     

整数自旋粒子的方程和波函数

从高自旋态的Bargmann-Wigner方程出发,建立了整数自旋粒子的运动方程,通过求解方程得到了一套整数自旋粒子波函数,并建立了等效Largrange形式.     

On the Decay Analysis of Electroproduced Higher-Spin Hadrons

We study exclusive electroproduction of two hadrons where one or both of the hadrons is a higherspin resonance whose decay is analysed. Interesting electroproduction experiments of this type are discussed. A complete formal apparatus is given for the decay analysis of spin-J particles produced in this way with polarized or unpolarized electron beams and targets. The cases J = 1, 3/2, 2 and 5/2 are worked out in detail. A conventional helicity frame analysis in terms of s-channel helicity amplitudes is given. Also we rearrange the formalism for use in the Gottfried-Jackson frame with everything given in terms of t-channel helicity amplitudes. The t-channel formalism makes it possible to completely separate the contributions from longitudinal and transverse virtual photon t-channel helicity states when only the laboratory azimuthal angle between the lepton and hadron planes is variable.     

A novel method to test particle ordering and final state alignment in helicity formalism

In this study,the non-trival effect of the selection of reference particles for decay angle definitions is demonstrated when constructing the partial-wave amplitude of multi-body decays using helicity formalism.This issue is often ignored in the standard use case of helicity formalism.A new technique is proposed to test the selection of the particle ordering,and it can also be used as a generalized method to calculate the rotation operators that are used for the final-state alignment between different decay chains.Moreover,numerical validations are performed to support the arguments and to verify the effectiveness of the proposed technique.     

Transversity of quarks in a nucleon

The transversity distribution of quarks in a nucleon is one of the three fundamental distributions, that characterize nucleon's properties in hard scattering processes at leading twist (twist 2). It measures the distribution of quark transverse spin in a nucleon polarized transverse to its (infinite) momentum. It is a chiral-odd twist-two distribution function — gluons do not couple to it. Quarks in a nucleon/hadron are relativistically bound and transversity is a measure of the relativistic nature of bound quarks in a nucleon. In this work, we review some important aspects of this less familiar distribution function which has not been measured experimentally so far.     

Transversity and its accompanying T-odd distribution from Drell–Yan processes with pion-proton collisions

This paper studies the possibility of direct extraction of the transversity and its accompanying T-odd parton distribution function (PDF) from Drell–Yan (DY) processes with unpolarized pion beam and with both unpolarized and transversely polarized proton targets. At present, such an extraction can be performed with the COMPASS experiment at CERN. The preliminary estimations performed for the COMPASS kinematic region demonstrate that it is quite realistic to extract both transversity and its accompanying T-odd PDF under COMPASS conditions. PACS 13.60.Hb, 13.88.+e     

Helicity representation of the N-N bound-state problem

The two-nucleon bound-state problem described in the momentum space is presented in the helicity state formalism.     

Measurement of branching fractions and polarization in B-->phiK(*) decays

We present the first measurement of decay amplitudes in B-->phiK* and measurements of branching fractions in B-->phiK(*) decays based on 78.1 fb(-1) of data recorded at the Upsilon(4S) resonance with the Belle detector at the KEKB e+e- storage ring. The decay amplitudes for the different phiK*0 helicity states are measured from the angular distributions of final state particles in the transversity basis. The longitudinal and transverse complex amplitudes are |A0|2=0.43+/-0.09+/-0.04, |A(perpendicular)|2=0.41+/-0.10+/-0.04, arg((A(parallel))=-2.57+/-0.39+/-0.09, and arg((A(perpendicular))=0.48+/-0.32+/-0.06. The direct CP-violating asymmetries are found to be consistent with zero.     

Transversity <Emphasis Type="Italic">K</Emphasis> factors for Drell-Yan processes

The question of the K factor in transversely polarised Drell-Yan (DY) processes is examined. The transverse-spin case is peculiar for the absence of a reference point in deeply inelastic scattering (DIS). Therefore, in order to study more fully the possible effects of higher-order corrections on DY asymmetries, a DIS definition for transversity is devised using a hypothetical scalar (Higgs-like) vertex. The results show that some care may be required in interpreting experimentally extracted partonic transversity, in particular when comparing with model calculations or predictions.Received: 21 December 2004, Revised: 15 March 2005, Published online: 21 April 2005PACS: 13.88. + e, 12.38.Bx     

Polarized electron-nucleon scattering at TESLA

Measurements of polarized electron-nucleon scattering can be realized at the TESLA linear collider facility with projected luminosities that are about two orders of magnitude higher than those expected of other experiments at comparable energies. Longitudinally polarized electrons, accelerated as a small fraction of the total current in the e⁺ arm of TESLA, can be directed onto a solid state target that may be either longitudinally or transversely polarized. A large variety of polarized parton distribution and fragmentation functions can be determined with unprecedented accuracy, many of them for the first time. A main goal of the experiment is the precise measurement of the x- and Q²-dependence of the unknown transversity distributions that will provide us with the full information on the nucleon's quark spin structure as relevant for high energy processes. Comparing their Q²-evolution to that of the corresponding helicity distributions constitutes an important precision test of the predictive power of QCD in the spin sector. The additional possibilities of using unpolarized targets and of experiments with a real photon beam turn TESLA-N into a versatile next-generation facility at the intersection of particle and nuclear physics.     

First glances at the transversity parton distribution through dihadron fragmentation functions

We present first observations of the transversity parton distribution based on an analysis of pion-pair production in deep-inelastic scattering off transversely polarized targets. The extraction of transversity relies on the knowledge of dihadron fragmentation functions, which we take from electron-positron annihilation measurements. This is the first attempt to determine the transversity distribution in the framework of collinear factorization.     

Model-independent analysis of <Emphasis Type="Italic">CP</Emphasis> violation effects in decays of the Higgs boson into a Pair of the <Emphasis Type="Italic">W</Emphasis> and <Emphasis Type="Italic">Z</Emphasis> bosons

Effects of CP and T invariance violation are studied in the most general interaction of the Higgs boson with the intermediate vector W ^± and Z bosons. Various angular distributions of the cascade decay Φ → W ⁺ W ^?/ZZ → 4 of fermions in the transversity and helicity systems are calculated, and asymmetries are constructed and evaluated. It is shown that studying the azimuthal angle distribution of the process Φ → ZZ → (e ^? e ⁺)(μ^?μ⁺) in the transversity system is effective for measuring the spatial parity of the Higgs boson.     

Three-dimensional parton distribution functions g1T and $h_{1L}^{\perp}$ in the polarized proton–antiproton Drell–Yan process

We present predictions of the unweighted and weighted double spin asymmetries related to the transversal helicity distribution g _1T and the longitudinal transversity distribution h_1L^{^}h_{1L}^{\perp}, two of eight leading-twist transverse momentum dependent parton distributions (TMDs) or three-dimensional parton distribution functions (3dPDFs), in the polarized proton–antiproton Drell–Yan process at typical kinematics on the Facility for Antiproton and Ion Research (FAIR). We conclude that FAIR is ideal to access the new 3dPDFs toward a detailed picture of the nucleon structure.