Old and new parton distribution and fragmentation functions

A short review of problems with parton distribution functions in nucleons, non-polarized and polarized, is given. The main part is devoted to the transversity distribution its possible measurement and its first experimental probe via spin asymmetry in semi-inclusive DIS. It is argued that the proton transversity distribution could be successfully measured in future DIS experiments with longitudinally polarized target.     

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     

On the T-old quark fragmentation function and on transversal handedness

The first probe of the correlation of the T-odd one-particle fragmentation function responsible for the left-right asymmetry of fragmentation of a transversely polarized quark is done by using the 1991–95 DELPHI data for Z→2-jet decay. Integrated over the fraction of longitudinal and transversal momenta, this correlation is of 1.5% order, which means order of 13% for the analyzing power.A rather large (≈ 10%) handedness transversal to the production plane was observed in the diffractive production of (π^?+π⁺π^?) triples from nuclei by the 40 GeV/c π^?-beam. It was shown that the phenomenon has a clear dynamic origin and resembles the single spin asymmetry behavior. All this makes us hope to use this effects in polarized DIS experiments for transversity measurement.     

To old and new PDF and PFF

A short review of problems with parton distribution functions in nucleons, non-polarized and polarized, is given. The main part is devoted to the T-odd Collins fragmentation function and to the proton transversity distribution its possible measurements and its first experimental probe via spin asymmetries in semi-inclusive DIS. It is argued that the proton transversity distribution is close to the prediction of chiral quark soliton model could be successfully measured in future DIS experiments with longitudinally polarized target and the Collins analyzing power is linearly growing with z.     

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     

Single-Spin asymmetries in semi-inclusive pion production

For the first time single-spin asymmetries in semi-inclusive pion production are measured by the HERMES experiment with a transversely polarised hydrogen target. Two different sine-modulations are extracted which can be related to the transversity δq(x) and Sivers $f_{1T}^{ \bot q} (x)$ quark distribution functions. The extracted sine-moments still contain small sub-leading twist contributions which can be extracted from HERMES data combining the results from the transversely polarised hydrogen target with previously measured results from a longitudinally polarised hydrogen target.     

Neutron transversity measurement at Jefferson Lab with a polarized 3He target

A first measurement of single target spin asymmetry (SSA) from semi-inclusive electroproduction of charged pions from a transversely polarized ³He target in deep-inelastic-scattering kinematics will take data in Hall A at Jefferson Lab in 2008. Such SSA will allow for an extraction of the much desired information on the Collins and Sivers asymmetry from the “neutron” in order to probe the quark transversity distributions. The experiment will be a coincidence measurement with the BigBite spectrometer detecting the scattered electrons and the left-arm HRS spectrometer detecting the charged pions. The prospect of future 11 GeV measurements at Jefferson Lab in Hall A using a solenoid magnetic detector system is also discussed in this talk. Correspondence: H. Gao, Department of Physics and the Triangle Universities Nuclear Laboratory, Duke University, Durham, NC 27708, USA     

The influence of direct <Emphasis Type="Italic">D</Emphasis>-meson production on the determination of the nucleon strangeness asymmetry via dimuon events in neutrino experiments

Experimentally, the production of oppositely charged dimuon events by neutrino and antineutrino deep inelastic scattering (DIS) is used to determine the strangeness asymmetry inside a nucleon. Here we point out that the direct production of a D-meson in DIS may have a substantial influence on the measurement of nucleon strangeness distributions. Direct D-meson production is via heavy quark recombination (HQR) and via light-quark fragmentation from perturbative QCD (LQF-P). To see the influence precisely, we compute the direct D-meson productions via HQR and LQF-P quantitatively and estimate their corrections to the analysis of the strangeness asymmetry. The results show that HQR has a stronger effect than LQF-P does, and the former may influence the experimental determination of the nucleon strangeness asymmetry.     

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     

Transversity distribution function in hard scatteringof polarized protons and antiprotons in the PAX experiment

Estimates are given for the double spin asymmetry in lepton-pair production from collisions of transversely polarized protons and antiprotons for the kinematics of the recently proposed PAX experiment at GSI on the basis of predictions for the transversity distribution from the chiral quark soliton model.Received: 30 March 2004, Published online: 11 May 2004     

COMPASS results on collins and sivers asymmetries for charged hadrons

The study of transverse spin and transverse momentum effects is an important part of the scientific program of COMPASS, a fixed target experiment at the CERN SPS taking data since 2002. The studies are carried on by measuring the hadrons produced in deep inelastic scattering (DIS) of 160 GeV/c muons off different targets. Among the possible asymmetries in the hadron azimuthal distributions, particularly interesting are the Collins and Sivers asymmetries which the COMPASS Collaboration has measured using transversely polarised deuteron and proton targets. Here new results for charged pions and kaons obtained from the 2010 run with a transversely polarised proton target are presented for the first time.     

2-jet production in polarised\vec p\vec pcollisions

Following recent interest in the subject of polarisation phenomena, we discuss the cross-sections and polarisation asymmetry in 2-jet production in polarised proton-polarised proton ( ) scattering. We set up a complete set of parametrisations for the proton spin-dependent parton densities and use them to demonstrate that this cross-section is dominated by gluonic terms. Hence, a measurement of the asymmetry in such processes will provide information on the gluon spin-dependent density. We further show that a factorisation of the hadronic cross-section a la Combridge and Maxwell's work in unpolarised 2-jet production also applies to the spin-dependent case. Hence, the cross-section can be written in terms of a genericpolarised parton density, which can then be measured in the process.     

Three methods to detect the predicted $$D\bar D$$ scalar meson X(3700)

Fixed-target unpolarized Drell-Yan experiments often feature an acceptance depending on the polar angle of the lepton tracks in the laboratory frame. Typically leptons are detected in a defined angular range, with a dead zone in the forward region. If the cutoffs imposed by the angular acceptance are independent of the azimuth, at first sight they do not appear dangerous for a measurement of the cos(2φ) asymmetry, which is relevant because of its association with the violation of the Lam-Tung rule and with the Boer-Mulders function. On the contrary, direct simulations show that up to 10 percent asymmetries are produced by these cutoffs. These artificial asymmetries present qualitative features that allow them to mimic the physical ones. They introduce some model dependence in the measurements of the cos(2φ) asymmetry, since a precise reconstruction of the acceptance in the Collins-Soper frame requires a Monte Carlo simulation, that in turn requires some detailed physical input to generate event distributions. Although experiments in the eighties seem to have been aware of this problem, the possibility of using the Boer-Mulders function as an input parameter in the extraction of transversity has much increased the requirements of precision on this measurement. Our simulations show that the safest approach to these measurements is a strong cutoff on the Collins-Soper polar angle. This reduces statistics, but does not necessarily decrease the precision in a measurement of the Boer-Mulders function.     

A new beam asymmetry measurement from pion photoproduction on the neutron using CLAS

We present a preliminary analysis of the photon beam asymmetry observable (Σ) from the pho-toproduction reaction channel γn→pπ~- in the invariant mass range 1.6-2.3 GeV. The measurement was obtained using the near-4π CEBAF Large Acceptance Spectrometer (CLAS) at Jefferson Laboratory, USA, employing a linearly polarised photon beam with an energy range 1.1-2.3 GeV, incident on a liquid deuterium target. The measurement will provide new data to address the poorly established neutron excitation spectrum and will greatly expand the sparse world data-set both in energy and angle.     

Single-spin asymmetries in semi-inclusive deep-inelastic scattering on a transversely polarized hydrogen target

Single-spin asymmetries for semi-inclusive electroproduction of charged pions in deep-inelastic scattering of positrons are measured for the first time with transverse target polarization. The asymmetry depends on the azimuthal angles of both the pion (phi) and the target spin axis (phi(S)) about the virtual-photon direction and relative to the lepton scattering plane. The extracted Fourier component sin((phi+phi(S))(pi)(UT) is a signal of the previously unmeasured quark transversity distribution, in conjunction with the Collins fragmentation function, also unknown. The component sin((phi-phi(S)(pi)(UT) arises from a correlation between the transverse polarization of the target nucleon and the intrinsic transverse momentum of quarks, as represented by the previously unmeasured Sivers distribution function. Evidence for both signals is observed, but the Sivers asymmetry may be affected by exclusive vector meson production.     

Structure functions at HERA

HERA provides the key facility for the measurement of proton structure functions. Formalism and methods are outlined for the measurement and interpretation of inclusive structure functions, including the use of polarised e ^± beams. The measurement of charm, beauty and photon structure functions is discussed, together with special runs at low proton energy for measurement of the longitudinal structure function. Finally, the functions accessed using polarised beams on polarised targets are indicated.     

Deeply virtual compton scattering at HERA – A probe of asymptotia

We demonstrate that the measurement of an azimuthal angle asymmetry in deeply virtual Compton scattering (DVCS) at HERA energies, is experimentally feasible and allows one to determine for the first time the ratio, η, of the real to imaginary part of the DIS amplitude. We further show that such measurements would discriminate between different scenarios for the energy dependence of F₂(x,Q²) at energies beyond those reachable at HERA.     

ALT in the nucleon-nucleon polarized Drell-Yan process

We present a leading order (LO) estimate for the longitidinal-transverse spin asymmetry (A ) in the nucleon-nucleon polarized Drell-Yan process at RHIC and energies in comparison with A and A . A receives contribution from g₁, the transversity distribution h₁, and the twist-3 distributions g and h . For the twist-3 contribution we use the bag model prediction evolved to a high energy scale by the large-N_c evolution equation. We found that A (normalized by the asymmetry in the parton level) is much smaller than the corresponding A . Twist-3 contribution given by the bag model turned out to be negligible.     

Probing the Flavor Asymmetric Nucleon Sea with Weak Currents

NMC has recently shown that the proton contains an excess of dd sea pairs as compared to uu sea pairs. We form appropriate combinations of quantities in v and v DIS which are sensitive to this flavor asymmetry of the sea. Estimates of the sensitivity of these quantities to the flavor asymmetry of the sea are obtained.     

Transversity Form Factors and Generalized Parton Distributions of the Pion in Chiral Quark Models

The transversity Generalized Parton Distributions (tGPDs) and related transversity form factors of the pion are evaluated in chiral quark models, both local (Nambu–Jona–Lasinio) and nonlocal, involving a momentum-dependent quark mass. The obtained tGPDs satisfy all a priori formal requirements, such as the proper support, normalization, and polynomiality. We evaluate generalized transversity form factors accessible from the recent lattice QCD calculations. These form factors, after the necessary QCD evolution, agree very well with the lattice data, confirming the fact that the spontaneously broken chiral symmetry governs the structure of the pion also in the case of the transversity observables.