Transversity distribution describes the quark transverse polarization inside
a transversely polarized nucleon. It is the less known leading-twist piece of
the QCD description of the partonic structure of the nucleon. Transversity can
be extracted from semi-inclusive deep inelastic scattering (SIDIS) where,
however, it couples to a new, unknown fragmentation function, called Collins
function. We present the preliminary results of the measurement of the
azimuthal asymmetries in the process e^+e^- -> qqbar -> pi pi X, where the two
pions are produced in opposite hemispheres. These preliminary results are based
on a data sample of about 45 fb^{-1}, collected by the BABAR experiment at a
center-of-mass energy of 10.54 GeV, and are compared with the Belle
measurements.Comment: 6 pages, 4 postscript figues, contributed to the Proceedings of
  Transversity 201

Garzia, I.

English

arXiv

Transversity distribution describes the quark transverse polarization inside a transversely polarized nucleon. It is the less known leading-twist piece of the QCD description of the partonic structure of the nucleon. Transversity can be extracted from semi-inclusive deep inelastic scattering (SIDIS) where, however, it couples to a new, unknown fragmentation function, called Collins function. We present the preliminary results of the measurement of the azimuthal asymmetries in the process e+e− → qq → ππX, where the two pions are produced in opposite hemispheres. These preliminary results are based on a data sample of about 45 fb−1, collected by the BABAR experiment at a center-of-mass energy of 10.54GeV, and are compared with the Belle measurements

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DOI 10.1393/ncc/i2012-11210-1Colloquia: Transversity 2011IL NUOVO CIMENTO Vol. 35 C, N. 2 Marzo-Aprile 2012Study of Collins asymmetries at BaBarI. Garzia for the BaBar CollaborationINFN and University of Ferrara - Italyricevuto il 24 Ottobre 2011; approvato l’ 11 Gennaio 2012pubblicato online il 26 Marzo 2012Summary. — Transversity distribution describes the quark transverse polarizationinside a transversely polarized nucleon. It is the less known leading-twist piece ofthe QCD description of the partonic structure of the nucleon. Transversity can beextracted from semi-inclusive deep inelastic scattering (SIDIS) where, however, itcouples to a new, unknown fragmentation function, called Collins function. Wepresent the preliminary results of the measurement of the azimuthal asymmetriesin the process e+e− → qq → ππX, where the two pions are produced in oppositehemispheres. These preliminary results are based on a data sample of about 45 fb−1,collected by the BABAR experiment at a center-of-mass energy of 10.54GeV, and arecompared with the Belle measurements.PACS 13.66.Bc – Hadron production in e−e+ interactions.PACS 13.87.Fh – Fragmentation into hadrons.1. – Motivation for extraction of Collins function in e+e− annihilationTransversity (h1) is the less known function [1] among the three parton distributionfunctions needed for a complete description of the momentum and spin distributionof the quarks inside the nucleon. We can measure h1 in semi-inclusive lepton-nucleonscattering (Semi Inclusive Deep Inelastic Scattering or SIDIS), in which the proton targetis transversely polarized. Using the factorization theorem, the SIDIS cross-section is(1) σep→ehX =∑qDF × σ(eq → eq)× FF,with DF the parton Distribution Function, and FF the Fragmentation Function. Fortransversely polarized target, DF is the transversity distribution (h1), and FF is theCollins fragmentation function (H⊥1 ). Therefore, to extract h1 we need to know H⊥1 . Themeasurement of the Collins function can be done in e+e− annihilation taking into accountthe process e+e− → qq → h1h2X, in which the two hadrons are detected in opposite jets.A non-zero value of the Collins FF produces an asymmetry in the azimuthal distributionc© Societa` Italiana di Fisica 7980 I. GARZIA for the BABAR COLLABORATION(a) RF12 (b) RF0Fig. 1. – (Color online) RF12 (a): θ = θT is the angle between the beam and thrust axis;φ1,2 are the azimuthal angles between the scattering plane and the transverse momentum Ph⊥around the thrust axis. RF0 (b): θ2 is the angle between the beam axis and the second hadronmomentum; φ0 is the azimuthal angle between the plane spanned by the beam axis and thesecond hadron momentum P2, and by the first hadron’s transverse momentum P1⊥. All tracksare boosted in the e+e− center-of-mass frame.of the two hadrons around the fragmenting qq direction. The Collins asymmetry canbe measured in two different reference frames. In the first frame, called thrust referenceframe or RF12, the azimuthal angles φ1 and φ2 shown in fig. 1(a) are calculated withrespect to the thrust axis, that is the axis that maximizes the longitudinal momentumof the event. In this frame the cross-section is [2]dσ(e+e− → h1h2X)dz1dz2d cos θ dφ1dφ2=∑q,q3α2Q2e2q4z21z22 [(1 + cos2 θ)D(0)1 (z1)D(0)1 (z2)(2)+ sin2(θ) cos(φ1 + φ2)H⊥,(1)1 (z1)H⊥,(1)1 (z2)].In the second reference frame, second hadron momentum frame or RF0, the azimuthalangle φ0 is calculated with respect to the second hadron momentum, as shown in fig. 1(b),and the differential cross-section is [2]dσ(e+e+ → h1h2X)dz1dz2d2qTd cos θ2 dφ0=(3)3α2Q2z21z22{A(y)F(D1(z1)D1(z2))+B(y) cos(2φ0)F[(2hˆ · kˆT hˆ · pˆT − kˆT · pˆT )H⊥1 (z1)H⊥1 (z2)M1M2]},where A(y) = 1/4(1+cos2 θ2) and B(y) = 1/4(sin2 θ2) in the e+e− center of mass frame.In eqs. (2) and (3), D1 is the unpolarized FF, H⊥1 is the Collins FF, z1,2 are the frac-tional energy of the hadrons (z = 2E/Q), Q2 is the center-of-mass energy, and the anglesare defined in fig. 1. In conclusion, the Collins asymmetry in e+e− annihilation is pro-portional to H⊥1 (z1)×H⊥1 (z2) and, therefore, we can obtain a independent measurementof this FF.STUDY OF COLLINS ASYMMETRIES AT BABAR 812. – Analysis strategyThe preliminary measurement of Collins asymmetries is performed using a sample ofdata collected by the BABAR experiment at the energy of 10.54GeV, that is 40MeV belowthe nominal energy of the collider, which corresponds to the peak of Υ(4S) resonance.For this reason, we refer to this data sample as off-peak sample.Assuming the thrust axis as the qq direction and selecting pions in opposite hemi-spheres with respect to the thrust axis, we measure the azimuthal angles φ1, φ2, and φ0.In order to select the two jets topology, we require a thrust higher than 0.8. In addition,we select pions coming from the primary vertex with a fractional energy higher than 0.2.The total visible energy of the event (sum of the energies of reconstructed charged andneutral particles) is required to be higher than 7GeV. The Collins asymmetries are ob-tained by measuring the cos(φ) modulation of the normalized azimuthal distributions ofthe selected pion pairs, where φ = φ1 + φ2 or φ = 2φ0 for the two reference frames. Theasymmetries resulting by these distributions are largely affected by detector acceptanceeffects, making their measurement unreliable. We therefore perform suitable double ra-tios of the asymmetries in order to eliminate the detector effects and the first order ofradiative corrections [2]. In particular we use the ratio of the normalized distributionsof unlike sign (RUL) over those of like sign (RL) pion pairs. In addition, the possibilityto select pion pairs with same charge or opposite charge allows to be sensitive to favoredand disfavored fragmentation functions. Favored FFs describe the fragmentation of aquark of flavor q into a hadron with a valence quark of the same flavor: i.e. u → π+and d → π−. Instead, we refer to u → π− and d → π+ as disfavored fragmentationprocesses. Consider, for example, the production of unlike-sign charged pions from a uupair: e+e− → uu → π±π∓X. The pion pair can be either created through two favoredfragmentation processes or through two disfavored fragmentation processes. Taking intoaccount what said above, the double ratio can be written asRULRL=1 + sin2 θ1+cos2 θ cos(φ)GUL1 + sin2 θ1+cos2 θ cos(φ)GL 1+ sin2 θ1 + cos2 θcos(φ){GUL−GL} ,(4)GUL =∑q e2qF(Hfav1 Hfav2 + Hdis1 Hdis2 )∑q e2q(Dfav1 Dfav2 + Ddis1 Ddis2 ), GL=∑q e2qF(Hfav1 Hdis2 + Hdis1 Hfav2 )∑q e2q(Dfav1 Ddis2 + Ddis1 Dfav2 );where θ is the polar angle of the thrust axis in the RF12 frame (θ = θT ) or the polarangle of the second hadron momentum in the RF0 frame (θ = θ2), as shown in fig. 1.Fitting the double ratio with a cosine function(5)RULRL=NUL(φ)/〈NUL〉NL(φ)/〈NL〉 = P0 + P1 · cos(φ),the P1 parameter contains only the Collins effect and higher order of radiative effects,since acceptance and radiative contributions do not depend on the charge combinationof the pion pairs.82 I. GARZIA for the BABAR COLLABORATIONthrust0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1Evis7891011121314(a) (b)Fig. 2. – (a) Total visible energy of the events versus the thrust value. The peak at about12GeV of energy and very high thrust values is due to BhaBha and μ+μ−(γ) events, while thesmall accumulation visible at lower energies and thrust higher than 0.94 is due to τ+τ− events.(b) Opening angle between the thrust axis and the qq axis.3. – Study of systematic effectsA crucial point for the measurement of Collins asymmetry is the identification of allthe effects that can influence the azimuthal distribution of the pion pairs. We study theinfluence of the particle identification, the possible dependence of the detector responseon the pion charge, the presence of residual polarization of the beams, and other minoreffects.Asymmetry dilution due to the charm and τ decays. – Measured asymmetries arediluted by the presence of background sources like charm and τ decays. For this reasonwe study and evaluate the correction to the asymmetries in order to obtain the trueCollins effect.– e+e− → τ+τ− contribution. Since weak decays are well described in Monte Carlo,any azimuthal asymmetries should be visible in simulated events. The study ofsimulated e+e− → τ+τ− gives an asymmetry consistent with zero. In additionwe consider a τ -enhanced data sample, sitting in the lower-right side of the Etotvs. T distribution of fig. 2(a). Taking into account the contamination of 25% frome+e− → qq in this enhanced sample, the fitted asymmetries are consistent with zeroin both reference frames. The measured asymmetry is then corrected following theequation Aα = Ameasuredα /(1−Dτ ), with the fraction of pion pairs (Dτ ) from τ+τ−events estimated using MC to vary from about 1 to 18% in the individual bins offractional energy.– e+e− → cc contribution. The fraction of pion pairs due to the cc events is muchlarger than the τ component. Furthermore, both fragmentation processes and weakdecays can introduce azimuthal asymmetries. For this reason, in addition to thecc MC sample, we select a charm-enhanced data sample requiring at least one D∗candidate from the decay D∗± → D0π±, with the D0 candidate reconstructedonly in the decay channel D0 → K−π+. We estimate the cc contribution in thisenhanced sample (d) and in the main data sample (Dcharm), and we measurethe asymmetry in both samples. In this way, we are able to extract the Collinsasymmetry (Aα) and the charm asymmetry (Acharm) solving the following systemSTUDY OF COLLINS ASYMMETRIES AT BABAR 83bin)2,z1(z2 4 6 8 10A12-0.0500.050.10.150.20.250.30.35BaBar preliminaryBelle PRL 96,232002(2006)Belle PRD 78,032011(2008)BABAR Preliminarybin)2,z1(z2 4 6 8 10A0-0.0500.050.10.150.20.250.3 BaBar preliminaryBelle PRL 96,232002(2006)Belle PRD 78,032011(2008)BABAR PreliminaryFig. 3. – (Colour on-line) Preliminary BABAR measurement of Collins asymmetries (full circlein red). By comparison the superseded Belle off-peak results (open circle in blue), and Belleresults on the full data sample (full green circles) are shown. Systematic and statistical errorsare added in quadrature.of equations:Ameasα = (1−Dcharm) ·Aα + Dcharm ·Acharmα ,AD∗α = d ·Acharmα + (1− d) ·Aα.Asymmetry dilution due to reconstruction of the thrust axis. – The deviation of thethrust axis from the real qq direction as shown in fig. 2(b) can lead to a dilution of themeasured asymmetries. This effect could be evaluated using a MC sample. However,the Collins fragmentation functions are not defined in our MC generator. Therefore,we simulate the asymmetries applying different weights to the angular distribution ofgenerated tracks. We finally fit the reconstructed azimuthal distributions and we comparethe resulting asymmetries with the weights introduced in the simulation. We find that,in RF12, the asymmetry is significantly underestimated, and we apply a correction factoraccording to the measured value.4. – Preliminary resultsThe preliminary results are presented in 10 symmetric combinations of (z1, z2) inter-vals, as described in table I. All significant systematic errors are evaluated and addedin quadrature for each bins. In fig. 3 the BABAR preliminary results are compared withTable I. – Symmetrised z-bin subdivision: we divided the asymmetry results in 10 “bins” of z1and z2 as summarized above.z214 7 9 100.73 6 8 90.52 5 6 70.31 2 3 40.20.2 0.3 0.5 0.7 1 z184 I. GARZIA for the BABAR COLLABORATION)thθ(21+cos)thθ(2sin0 0.2 0.4 0.6 0.8 1A12-0.0100.010.020.030.04 (a)BABAR Preliminary)2θ(21+cos)2θ(2sin0 0.2 0.4 0.6 0.8 1A0-0.0100.010.020.030.04 (b)BABAR PreliminaryFig. 4. – Collins asymmetry A12 (a), and A0 (b), as a function of (sin2 θ)/(1 + cos2 θ), whereθ = θT and θ = θ2 have been used in plot (a) and (b), respectively.the superseded off-peak Belle data and the off- and on-peak combined Belle data [3, 4].We should note that in the newer Belle publication [4], they estimated a new correctionfactor due to the approximation of the qq axis with the thrust axis, so that we correctthe first Belle results by the factor 1.66/1.21.Following eq. (4), we studied also the sin2 θ/(1 + cos2 θ) dependence of the Collinsasymmetries in both reference frames, as reported in fig. 4. The expected sin2 θT /(1 +cos2 θT ) linear dependence of asymmetry is observed in the thrust reference frame, butit seems not to hold in the second hadron momentum frame, where θ = θ2 is taken. Thesame dependences are observed by Belle in ref. [4], and explained by the fact that thethrust axis describes the original qq direction better than the second hadron momentum.5. – ConclusionsWe reported the preliminary BABAR results of Collins asymmetries in the pion system,performed using a data sample of about 45 fb−1 collected at the energy of 10.54GeV. Theasymmetries are studied as a function of symmetric bins (z1, z2) of the pion fractionalenergies and as a function of sin2 θ/(1+cos2 θ), and are compared with the Belle analysis.The results are in overall good agreement each other. However, the off-peak data sampleis statistically limited, and the update of the measurement with the full BABAR datasample is ongoing.REFERENCES[1] Anselmino M. et al., Phys. Rev. D, 75 (2007) 054032.[2] Boer D., Nucl. Phys. B, 806 (2009) 23; arXiv:0804.2408v2 (2008).[3] Seidl R. et al. (Belle Collaboration), Phys. Rev. Lett., 96 (2006) 232002.[4] Seidl R. et al. (Belle Collaboration), Phys. Rev. D, 78 (2008) 032011.

Study of Collins asymmetries at BaBar

Transversity distribution describes the quark transverse polarization inside a transversely polarized nucleon. It is the less known leading-twist piece of the QCD description of the partonic structure of the nucleon. Transversity can be extracted from semi-inclusive deep inelastic scattering (SIDIS) where, however, it couples to a new, unknown fragmentation function, called Collins function. We present the preliminary results of the measurement of the azimuthal asymmetries in the process e+e- → qq → φφX, where the two pions are produced in opposite hemispheres. These preliminary results are based on a data sample of about 45 fb-1, collected by the BABAR experiment at a center-of-mass energy of 10.54GeV, and are compared with the Belle measurements. © Societa Italiana di Fisica

GARZIA, Isabella

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Study of Collins Asymmetries at BaBar

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