Interference Fragmentation Functions Research Articles

Exploring the spin structure of the nucleon at STAR

Understanding the internal spin structure of the nucleon remains a challenge in strong interaction physics. The unique capability of RHIC opened new avenues in studying the internal structure of the proton with unprecedented depth and precision. Significant progress has been made in the last few years through various measurements at STAR. The longitudinal spin measurements have contributed significantly to our understanding of the quark and gluon helicity distributions inside the proton. The longitudinal double-spin asymmetry, ALL, from STAR inclusive jet and dijet measurements provides the first evidence of a positive gluon polarization with partonic momentum fraction x > 0.05. The reconstruction of W±/Z in longitudinally polarized proton-proton collisions indicates that there is a flavor separation of the light sea quark helicity distributions. In transversely polarized proton collisions, W±/Z-bosons provide the first constraint on the sea-quark Sivers function and contributes to the tests of the predicted sign change. The tilt of the dijet opening angle provides a direct access to the first Mellin momentum of the Sivers function and avoids the spin-correlated fragmentation contributions. The novel measurements of the azimuthal distributions of identified hadrons in jets and spin-dependent dihadron correlations directly probe the collinear quark transversity in the proton, with the former coupled to the transverse momentum dependent (TMD) Collins fragmentation function and the latter to the dihadron interference fragmentation function. These measurements shed lights on Sivers function, quark transversity and spin-dependent fragmentation functions in both collinear and TMD formalism. In this proceeding, recent jet results on both the longitudinal and transverse spin structure of the proton from STAR are presented.

Transverse-spin-dependent azimuthal asymmetries of pion and kaon pairs produced in muon-proton and muon-deuteron semi-inclusive deep inelastic scattering

A set of measurements of azimuthal asymmetries in the production of pairs of identified hadrons in deep-inelastic scattering of muons on transversely polarised 6LiD (deuteron) and NH3 (proton) targets is presented. All available data collected in the years 2003–2004 and 2007/2010 with the COMPASS spectrometer using a muon beam of 160GeV/c at the CERN SPS were analysed. The asymmetries provide access to the transversity distribution functions via a fragmentation function that in principle may be independently obtained from e+e− annihilation data. Results are presented, discussed and compared to existing measurements as well as to model predictions. Asymmetries of π+π− pairs measured with the proton target as a function of the Bjorken scaling variable are sizeable in the range x>0.032, indicating non-vanishing transversity distribution and di-hadron interference fragmentation functions. As already pointed out by several authors, the small asymmetries of π+π− measured on the 6LiD target can be interpreted as indication for a cancellation of u and d-quark transversity distributions.

Exploring universality of transversity in proton-proton collisions

We consider the azimuthal correlations of charged hadron pairs with large total transverse momentum and small relative momentum, produced in proton-proton collisions with one transversely polarized proton. One of these correlations directly probes the chiral-odd transversity parton distribution in connection with a chiral-odd interference fragmentation function. We present predictions for this observable based on previous extractions of transversity (from charged pion pair production in semi-inclusive deep-inelastic scattering) and of the interference fragmentation function (from the production of back-to-back charged pion pairs in electron-positron annihilations). All analyses are performed in the framework of collinear factorization. We compare our predictions to the recent data on proton-proton collisions released by the STAR collaboration at RHIC, and we find them reasonably compatible. This comparison confirms for the first time the predicted role of transversity in proton-proton collisions and it allows to test its universality.

High Precision Measurement of Transversity Using Di-hadron Correlations in p↑+p Collisions at sNN = 500 GeV

The transversity distribution, which describes transversely polarized quarks in a transversely polarized nucleon, is a fundamental component of the current picture of the spin structure of the nucleon, and is only loosely constrained by existing semi-inclusive deep inelastic scattering data. The di-hadron interference fragmentation function (IFF), which describes the fragmentation of transversely polarized quarks, is expected to give rise to spin-dependent di-hadron correlations in p[Formula: see text]+p collisions. Significant di-hadron correlations have recently been measured at RHIC in p[Formula: see text]+p collisions at [Formula: see text] = 200 GeV at mid-rapidity. In 2011, STAR collected p[Formula: see text]+p data at [Formula: see text] = 500 GeV, allowing STAR to extend these di-hadron asymmetries into a previously unexplored kinematic region. The status of the charge-ordered pion pair asymmetry measurement from [Formula: see text] = 500 GeV p[Formula: see text]+p collisions will be presented.

Improved extraction of valence transversity distributions from inclusive dihadron production

We present an updated extraction of the transversity parton distribution based on the analysis of pion-pair production in deep-inelastic scattering off transversely polarized targets in collinear factorization. Data for proton and deuteron targets make it possible to perform a flavor separation of the valence components of the transversity distribution, using di-hadron fragmentation functions taken from the semi-inclusive production of two pion pairs in back-to-back jets in e + e − annihilation. The e + e − data from Belle have been reanalyzed using the replica method and a more realistic estimate of the uncertainties on the chiral-odd interference fragmentation function has been obtained. Then, the transversity distribution has been extracted by using the most recent and more precise COMPASS data for deep-inelastic scattering off proton targets. Our results represent the most accurate estimate of the uncertainties on the valence components of the transversity distribution currently available.

COMPASS results on the transverse spin asymmetry in hadron-pair production in SIDIS

The parton distribution function h q (x) of a transversely polarized quark q inside a transversely po- larized nucleon, is chiral-odd and therefore not accessible in inclusive deep-inelastic scattering. It can however be observed in semi-inclusive deep-inelastic scattering (SIDIS) in combination with another chiral-odd func- tion, for instance the dihadron interference fragmentation function (DiFF) H /q 1 . The 160 GeV=c polarized muon beam of CERN's M2 beamline allows COMPASS to investigate transverse spin e ects using polarized solid- state targets. In this contribution an overview of COMPASS results for the azimuthal asymmetry in identified dihadron production is given. Pions and kaons were identified by a RICH detector. Recently, the full set of this asymmetry from the COMPASS data on the deuteron and the proton target became available. All data, includ- ing early data sets, were analyzed using the same methods and requirements. The results are compared to model predictions and HERMES data. Also a point-by-point extraction of the Transversity distribution functions h1(x) for u and d quarks was carried out with this full data set. Further investigations on the correlation between the dihadron asymmetry and the Collins asymmetries of the two hadrons of the pair have revealed an interesting dependence of these three asymmetries on the di erence of the azimuthal angles of the two hadrons.

Dihadron Fragmentation Functions and Transversity

We present preliminary results for an updated extraction of the transversity parton distribution based on the analysis of pion-pair production in deep-inelastic scattering off transversely polarized targets in collinear factorization. Data for proton and deuteron targets by HERMES and COMPASS allow for a flavor separation of the valence components of transversity, while di-hadron fragmentation functions are taken from the semi-inclusive production of two pion pairs in back-to-back jets in $e^+ e^-$ annihilation. The latter data from Belle have been reanalyzed using the replica method and a more realistic estimate of the uncertainties on the chiral-odd interference fragmentation function has been obtained. After encoding this piece of information into the deep-inelastic scattering cross section, the transversity has been re-extracted by using the most recent and more precise COMPASS data for proton target. This picture represents the current most realistic estimate of the uncertainties on our knowledge of transversity. The preliminary results indicate that the valence up component seems smaller and with a narrower error band than in previous extraction.

First extraction of interference fragmentation functions frome+e−data

We report on the first extraction of interference fragmentation functions from the semi-inclusive production of two hadron pairs in back-to-back jets in e+e- annihilation. A nonzero asymmetry in the correlation of azimuthal orientations of opposite \pi+\pi- pairs is related to the transverse polarization of fragmenting quarks through a significant polarized dihadron fragmentation function. Extraction of the latter requires the knowledge of its unpolarized counterpart, the probability density for a quark to fragment in a \pi+\pi- pair. Since data for the unpolarized cross section are missing, we extract the unpolarized dihadron fragmentation function from a Monte Carlo simulation of the cross section.

Transverse spin effects in hadron-pair production from semi-inclusive deep inelastic scattering

First measurements of azimuthal asymmetries in hadron-pair production in deep-inelastic scattering of muons on transversely polarised LiD6 (deuteron) and NH3 (proton) targets are presented. The data were taken in the years 2002–2004 and 2007 with the COMPASS spectrometer using a muon beam of 160 GeV/c at the CERN SPS. The asymmetries provide access to the transversity distribution functions, without involving the Collins effect as in single hadron production. The sizeable asymmetries measured on the NH3 target indicate non-vanishing u-quark transversity and two-hadron interference fragmentation functions. The small asymmetries measured on the LiD6 target can be interpreted as indication for a cancellation of u- and d-quark transversities.

Forward Transverse Single Spin Asymmetries at PHENIX

Recent measurements of single transverse spin asymmetries in proton-proton collisions measured by the PHENIX experiment at RHIC are presented. The focus is on the single particle left-right asymmetry AN for π0 at √s = 200 GeV and √s = 62.4 GeV and the measurement of di-hadron correlations at √s = 200 GeV which are produced by the fragmentation of a transversely polarized quark via the Interference Fragmentation Function (IFF) H1< and thus provide a probe for the quark transversity distribution function.

Observation of Transverse Polarization Asymmetries of Charged Pion Pairs ine+e−Annihilation nears=10.58 GeV

The interference fragmentation function translates the fragmentation of a quark with a transverse projection of the spin into an azimuthal asymmetry of two final-state hadrons. In e(+)e(-) annihilation the product of two interference fragmentation functions is measured. We report nonzero asymmetries for pairs of charge-ordered π(+)π(-) pairs, which indicate a significant interference fragmentation function in this channel. The results are obtained from a 672 fb(-1) data sample that contains 711 × 10(6) π(+)π(-) pairs and was collected at and near the Υ(4S) resonance, with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider.

Dihadron Fragmentation Functions for Large Invariant Mass

Using perturbative quantum chromodynamics, we compute dihadron fragmentation functions for a large invariant mass of the dihadron pair. The main focus is on the interference fragmentation function H(1)(∢), which plays an important role in spin physics of the nucleon. Our calculation also reveals that H(1)(∢) and the Collins fragmentation function have closely related underlying dynamics. By considering semi-inclusive deep-inelastic scattering, we further show that collinear factorization in terms of dihadron fragmentation functions and collinear factorization in terms of single-hadron fragmentation functions provide the same result in the region of intermediate invariant mass.

Transverse Spin Physics at COMPASS

The investigation of transverse spin and transverse momentum effects in deep inelastic scattering is one of the key physics programs of the COMPASS collaboration. Three channels have been analyzed at COMPASS to access the transversity distribution function: The azimuthal distribution of single hadrons, involving the Collins fragmentation function, the azimuthal dependence of the plane containing hadron pairs, involving the two-hadron interference fragmentation function, and the measurement of the transverse polarization of Lambda hyperons in the final state. Azimuthal asymmetries in unpolarized semi-inclusive deep-inelastic scattering give important information on the inner structure of the nucleon as well, and can be used to estimate both the quark transverse momentum k_T in an unpolarized nucleon and to access the so-far unmeasured Boer-Mulders function. COMPASS has measured these asymmetries using spin-averaged 6LiD data.

Transverse spin effects at COMPASS

The investigation of transverse spin and transverse momentum effects in deep inelastic scattering is one of the key physics programs of the COMPASS collaboration. In the years 2002–2004 COMPASS took data scattering 160 GeV muons on a transversely polarized 6 LiD target. In 2007, a transversely polarized NH 3 target was used. Three different channels to access the transversity distribution function have been analyzed: The azimuthal distribution of single hadrons, involving the Collins fragmentation function, the azimuthal dependence of the plane containing hadron pairs, involving the two-hadron interference fragmentation function, and the measurement of the transverse polarization of λ hyperons in the final state. Transverse quark momentum effects in a transversely polarized nucleon have been investigated by measuring the Sivers distribution function. Azimuthal asymmetries in unpolarized semi-inclusive deep-inelastic scattering give important information on the inner structure of the nucleon as well, and can be used to estimate both the quark transverse momentum k T in an unpolarized nucleon and to access the so-far unmeasured Boer-Mulders function. COMPASS has measured these asymmetries using spin-averaged 6 LiD data.

Measurement of transversity signals in two hadron production at COMPASS

The quark structure of the nucleon at the twist two level can be completely described with three quark distribution functions: the spin averaged distribution function q(x), the helicity distribution Δq(x) and the transverse spin distribution ΔTq(x). This last function, referred to as transversity, is chiral-odd and can only be measured in combination with another chiral-odd function. COMPASS is a fixed target experiment at the CERN SPS M2 beamline. Its target (6LiD) can be both longitudinally and transversely polarized with respect to the polarized 160 GeV/c µ+-beam. In transverse configuration ΔTq(x) can be measured in semi-inclusive deep-inelastic scattering (SIDIS), requiring the detection of hadronic products. A rather new probe of the transverse spin distribution function ΔTq(x) is the measurement of two hadron production, introducing the chiral odd interference fragmentation function H1∢(z, Mh2). Results are presented for the years 2003–2004 including particle identification by using the information of the RICH detector. The analysis was performed using all positive/negative charged pairs and z-ordered pairs.

Transversity from two pion interference fragmentation

We present calculation on the azimuthal spin asymmetries for pion pair production in semi-inclusive deep inelastic scattering (SIDIS) process at both HERMES and COMPASS kinematics, with transversely polarized proton, deuteron, and neutron targets. We calculate the asymmetry by adopting a set of parametrization of the interference fragmentation functions and two different models for the transversity. We find that the result for the proton target is insensitive to the approaches of the transversity but more helpful to understand the interference fragmentation functions. However, for the neutron target, which can be obtained through using deuteron and $^{3}\mathrm{He}$ targets, we find different predictions for different approaches to the transversity. Thus probing the two pion interference fragmentation from the neutron can provide us more interesting information on the transversity.

Dihadron interference fragmentation functions in proton-proton collisions

We study the production of hadron pairs in proton-proton collisions, selecting pairs with large total transverse momentum with respect to the beam, and small relative transverse momentum, i.e., belonging to a single jet with large transverse momentum. We describe the process in terms of dihadron fragmentation functions. We consider the production of one pair in polarized collisions (with one transversely polarized proton) and the production of two pairs in unpolarized collisions. In the first case, we discuss how to observe the quark transversity distribution in connection with a specific class of dihadron fragmentation functions, named interference fragmentation functions. In the second case, we suggest how to determine the latter and also how to observe linearly polarized gluons.

Interference fragmentation functions in electron-positron annihilation

We study the process of electron-positron annihilation into back-to-back jets, where in each jet a pair of hadrons is detected. The orientation of these two pairs with respect to each other can be used to extract the interference fragmentation functions in a clean way, for instance from BELLE or BABAR experiment data. This is of relevance for studies of the transversity distribution function. In particular, we focus on two azimuthal asymmetries. The first one has already been studied by Artru and Collins, but is now expressed in terms of interference fragmentation functions. The second asymmetry is new and involves a function that is related to longitudinal jet handedness. This asymmetry offers a different way of studying handedness correlations.

Partial-wave analysis of two-hadron fragmentation functions

We reconsider the option of extracting the transversity distribution by using interference fragmentation functions into two leading hadrons inside the same current jet. To this end, we perform a new study of two-hadron fragmentation functions. We derive new positivity bounds on them. We expand the hadron pair system in relative partial waves, so that we can naturally incorporate in a unified formalism specific cases already studied in the literature, such as the fragmentation functions arising from the interference between the s- and p-wave production of two mesons, as well as the production of a spin-one hadron. In particular, our analysis clearly distinguishes two different ways to access the transversity distribution in two-hadron semi-inclusive leptoproduction.

Accessing transversity with interference fragmentation functions

We discuss in detail the option to access the transversity distribution function $h_1(x)$ by utilizing the analyzing power of interference fragmentation functions in two-pion production inside the same current jet. The transverse polarization of the fragmenting quark is related to the transverse component of the relative momentum of the hadron pair via a new azimuthal angle. As a specific example, we spell out thoroughly the way to extract $h_1(x)$ from a measured single spin asymmetry in two-pion inclusive lepton-nucleon scattering. To estimate the sizes of observable effects we employ a spectator model for the fragmentation functions. The resulting asymmetry of our example is discussed as arising in different scenarios for the transversity.