Transverse Spin Phenomena in Lepton Scattering Anna Martin Trieste University and INFN Trieste October 4, 2006

in this field FANTASTIC PROGRESS SINCE SPIN2004 EXPERIMENTS: Collins mechanism has been firmly established and there is a first check of universality  transversity can be measured in SIDIS Sivers mechanism is real THEORY: important developments on connection between Sivers effect and Orbital Angular Momentum assessing universality (lN vs pp) ... and many new ideas ... VERY ACTIVE FIELD: many interesting theoretical & experimental talks at a lot of material: I will not be able to show all the results Anna Martin

Content of this talk Polarised DIS and Experiments Transversity Distribution Function new results Sivers Distribution Function Other TMD Distribution Function Conclusions HERMES COMPASS CLAS verificare numero talks Anna Martin

Deep Inelastic Scattering key role in investigating the partonic structure of the necleons only the final lepton is detected inclusive DIS P inclusive hadrons Q2 >> M2, W2>> M2 q= four momentum transferred to the nucleon nu= lepton’s energy loss in the nucleon rest frame (sometimes ν = q · P). Here, E and E are the initial and final lepton energies in the nucleon rest frame x =in the parton model, fraction of the nucleon’s momentum carried by the struck quark. y=fraction of the lepton’s energy lost in the nucleon rest frame. W2=is the mass squared of the system X recoiling against the scattered lepton. W2 = (P + q)2 = M2 + 2Mν − Q2 in addition, detection of final hadrons semi-inclusive DIS (SIDIS) Anna Martin

Polarised SIDIS Experiments transverse spin effects are an important part of the program of the present experiments HERMES at DESY electron beam, energy 27.5 GeV internal H↑ gas target (2002-2005) COMPASS at CERN long pol m beam, energy 160 GeV solid state target (2002-2004 with 6LiD↑) JLAB experiments electron beam, energy 6 GeV to be upgraded to 12 GeV (long pol target, till now) Anna Martin

CLAS 0.15 < x x 0.004 < x < 0.4 0.02 < x < 0.6 50 100 50 100 Q2 [GeV/c]2 0.004 < x < 0.4 10 -3 10 -2 10 -1 1 x Anna Martin

Content: Polarised DIS and Experiments Transversity Distribution Function new results Sivers Distribution Function Other TMD Distribution Function Conclusions Anna Martin

Spin Structure of the Nucleons three quark distribution functions (DF) are necessary to describe the structure of the nucleon at LO q(x) f1q (x) unpolarised DF quark with momentum xP in a nucleon well known – unpolarised DIS helicity DF quark with spin parallel to the nucleon spin in a longitudinally polarised nucleon known – polarised DIS Dq(x) g1q(x) DTq(x) = q↑↑(x) - q↑↓(x) h1q(x), dq(x), dTq(x) transversity DF quark with spin parallel to the nucleon spin in a transversely polarised nucleon still unkown ALL 3 OF EQUAL IMPORTANCE Anna Martin

Transversity Distribution Function DTq(x), h1q(x), dq(x), dTq(x) , q=uv, vv, qsea contribution of the quarks to the transverse spin of the nucleon Properties: is chiral-odd: decouples from incl DIS because helicity of quark must flip probes the relativistic nature of quark dinamics no contribution from the gluons  simple Q2 evolution positivity (Soffer) bound first moments: tensor charge sum rule for transverse spin Bakker, Leader, Trueman, PRD 70 (04) Anna Martin

Transversity DF: how to measure it the Transversity DF is chiral-odd: observable effects are given only by the product of Tq (x) and an other chiral-odd function can be measured in SIDIS on a transversely polarised target via “quark polarimetry” “Collins” asymmetry “Collins” Fragmentation Function hadron-pair asymmetry “Interference” Fragmentation Function Λ polarisation Fragmentation Function of q↑Λ …. Anna Martin

“Collins asymmetry” in Measurement of the Transversity DF in SIDIS “Collins asymmetry” in the chiral-odd partner is the Collins Fragmentation Function the “quark polarimetry” relies on the Collins effect (J. Collins, 93) a quark moving “horizontally” and polarized “upwards” would emit the leading meson preferentially on the “left” side of the jet  the fragmentation function has a spin dependent part “Collins” FF: unknown … Anna Martin

Collins effect in SIDIS distribution of the hadrons: ± refer to the opposite orientation of the transverse spin of the nucleon PT is the target polarisation; DNN is the transverse spin transfer coefficient initial  struck quark the “Collins angle” is C = h - s’ = h + S - p C = h + S (Trento) C h,s’,S azimuthal angles of hadron momentum, of the spin of the fragmenting quark and of the nucleon from the azimuthal distribution of the hadrons one measures the “Collins Asymmetry” J. Collins, Nucl. Phys. B396 (1993) 161 F. Baldrachini, N.S. Craigie, V. Roberto, M. Socolovsky, Fortschritte der Physik 29 (1981) 505 using different targets (p, d, n) and identifying the final hadron one can perform flavour separation unique feature of SIDIS Anna Martin

What have we learnt over the past 2 years ? Collins Effect great news from BELLE measurement of the correlation between the azimuthal angles of p‘s in the near jet and in the far jet from e+e– annihilation ( … no results yet at ) j1 j2-p Q e- e+ A0 Final results A12 spin2004 ref? significant non-zero asymmetries, rising behavior with z z1 Collins effect is a real phenomenon spin dependent FF can be measured in e+e– annihilation z2 Anna Martin

What have we learnt over the past 2 years What have we learnt over the past 2 years ? Collins Asymmetry - p+ and p- asymmetries from HERMES proton target 2002-2005 NEW RESULTS (DIS2005) 2002-2003 data unexpected large p- positive p+ and negative p- asymmetries confirmed with larger statistics: the Collins FF is ≠ 0, transverity is ≠ 0 Anna Martin

What have we learnt over the past 2 years What have we learnt over the past 2 years ? Collins Asymmetry - h+ and h- asymmetries from COMPASS deuteron target PRL 94, 202002 (2005) 2002-2004 hadrons: mostly pions 2002 data cancellation between p and n ? NEW RESULTS 2002- 2004 data (DIS2006) asymmetries compatible with zero within the smaller statistical errors preliminary 2002-2004 preliminary 2002-2004 Anna Martin

What have we learnt over the past 2 years ? Collins Asymmetry naïve interpretation of the data (parton model, valence region) new proton data preliminary 2002-2004 asymmetry for p+ ~ opposite to asymmetry for p-  unfavored Collins FF ~ opposite favored Collins FF at variance with unpolarised case  u quark dominance new deuteron data preliminary 2002-2004 some (small) effect expected even if  cancellation between Tu (x) and Td (x) handle on Td (x) Anna Martin

What have we learnt over the past 2 years ? recent theoretical work Vogelsang Yuan, PRD 72, 054028 (2005) Soffer bound Efremov et al, PRD 73, 094025 (2006) chiral quark-soliton model Anselmino et al, BNL UM 2006 Soffer bound & Tq = q favored Collins FF ~ – unfavored Collins FF u-dominance agreement with Belle comparison with the new COMPASS 2002-2004 prelim data RICH + AGS annual Users’ Meeting June 6, 2006, www.bnl.gov/rhic ags/users meetings/workshops/basp , and paper in preparation. Vogelsang and Yuan preliminary COMPASS 2002-2004 Efremov et al preliminary COMPASS 2002-2004 Anselmino et al, Tq = q preliminary COMPASS 2002-2004 Anselmino et al, SB preliminary COMPASS 2002-2004 Anna Martin

Also new: Collins asymmetry for K± together with different targets, relevant for flavour decomposition there are very recent results for the Collins asymmetry on proton for K+ and K– (HERMES, DIS2006) on deuteron for p+ and p– , K+ and K– (COMPASS, GPD06) Aerogel n=1.03 C4F10 n=1.0014 C4F10 Anna Martin

Collins Asymmetry for Pions and Kaons HERMES preliminary 2002-2004 data proton COMPASS sign convention COMPASS preliminary 2003-2004 data deuteron very recent results; comparison with phenomenological calculations already available (M. Anselmino et al) Anna Martin

hadron-pair asymmetries Measurement of the Transversity DF in SIDIS hadron-pair asymmetries alternative way to access transversity measurement from HERMES using longitudinally polarised target data NEW RESULTS: measurements from HERMES and COMPASS on transversely polarised proton and deuteron targets more on Friday Session 2B R. Joosten, M. Contalbrigo, M. Radici Anna Martin

Two Hadron Asymmetries in inclusive production of hadron pairs, one can define the angle f R┴ and measure an azimuthal asymmetry from the modulation of the number of events in fRS= fR┴ - fs’ or fRS= fR┴ + fS presently unknown can be measured in e+e- (BELLE) expected to depend on the hadron pair invariant mass Anna Martin

also these data can be described by models What have we learnt over the past 2 years ? Two Hadron Asymmetries NEW RESULTS deuteron target NEW RESULTS proton target 2002-2004 data all +/- pairs x 2002-2004 data all +/- pairs preliminary A. Bacchetta, M. Radici hep-ph/0608037 model for DiFF (expected to be overestimated) proton HERMES kin deuteron COMPASS kin positive moments for all invariant mass bins first evidence for non-zero FF  small errors (order of ~%)  small asymmetries! cancellation? similar results ordering in pTh, z inspired to the string fragm. model also these data can be described by models 0.004<x<0.4 AND deuteron target 1/10 Anna Martin

Measurement of the Transversity DF in SIDIS polarimetry alternative way to access transversity no results NEW RESULTS from COMPASS presented here for the first time more on Friday Session 2A A. Ferrero Anna Martin

L polarimetry S x 10 all Q2 Anna Martin

L polarimetry NEW systematic errors not larger than statistical errors RICH ID not used yet Anna Martin

Content: Polarised DIS and Experiments Transversity Distribution Function new results Sivers Distribution Function Other TMD Distribution Function Conclusions Anna Martin

Measurement of the Sivers DF in SIDIS presently, the most studied in SIDIS together with the Transversity DF it is one of the TMD parton distribution functions is related to an intrinsic asymmetry in the parton transverse momentum distribution induced by the nucleon spin requires final/initial-state interactions quark rescattering via soft gluon exchange should change sign from SIDIS to DY it is related to the parton orbital angular momentum in a transversely polarized nucleon on its properties and the relation with angular momentum  talks by Budkart, Vogelsan, .... and several others in the next days Anna Martin

Sivers Asymmetry S = h - S S appears in SIDIS as a modulation in the “Sivers angle” S S S = h - S h azimuthal angle of hadron momentum S azimuthal angle of the spin of the nucleon J. Collins, Nucl. Phys. B396 (1993) 161 F. Baldrachini, N.S. Craigie, V. Roberto, M. Socolovsky, Fortschritte der Physik 29 (1981) 505 the “Sivers angle” S and the “Collins angle” C are independent  the Collins and Sivers asymmetries can be disentangled and extracted from the same data in SIDIS Anna Martin

What have we learnt over the past 2 years ? Sivers Asymmetry NEW RESULTS 2002-2004 data proton target 2002-2005 2002-2003 data Sivers moments as function of x, z and $P_{h\perp}$. The error band represents the maximal systematic uncertainty due to acceptance and detector smearing effects and due to a possible contribution from the $\cos\phi$ moment in the unpolarised cross section. The common overall scaling uncertainty is due to the target polarisation uncertainty. The average values of the asymmetry are pi+: A=0.0416+/-0.0046+/-0.0021 and pi-: A=0.0030+/-0.0055+/-0.0007 and for the kinematics the same as given in 05-078  significant positive asymmetry for positive pions with a factor ~4 in statistics p+ asymmetry > 0 p– asymmetry compatible with 0 the Sivers effect is a real effect Anna Martin

What have we learnt over the past 2 years ? Sivers Asymmetry deuteron target 2002-2004 2002 data PRL 94, 202002 (2005) hadrons: mostly pions cancellation between p and n ? NEW RESULTS 2002- 2004 data preliminary COMPASS 2002-2004 factor ~7 in statistics: asymmetries still compatible with zero Anna Martin

What have we learnt over the past 2 years ? Sivers Asymmetry naïve interpretation of the data (valence region) new proton data preliminary 2002-2004 asymmetry for p+ > 0, asymmetry for p- ≈ 0  Sivers DF for d-quark ≈ - 2 Sivers DF for u-quark 2 new deuteron data preliminary 2002-2004 the measured asymmetries compatible with zero suggest Anna Martin

 F. Bradamante talk, yesterday What have we learnt over the past 2 years ? Sivers Asymmetry also, the measured asymmetry on deuteron compatible with zero has been interpreted as Evidence for the Absence of Gluon Orbital Angular Momentum in the Nucleon S.J. Brodsky, S. Gardner SLAC-PUB-12062, Aug 2006. Subm. Phys.Lett.B, hep-ph/0608219  F. Bradamante talk, yesterday Anna Martin

first qualitative picture of the Sivers functions What have we learnt over the past 2 years ? Sivers Asymmetry recent theoretical work on the interpretation of the data use of the new HERMES results to exctract the Sivers DF Vogelsang Yuan (2005), Anselmino et al (2005), Collins et al (2006) good fits to the new proton from HERMES comparison (or fit) with the deuteron COMPASS 2002 data ok with Vogelsang, Yuan Anselmino et al Collins et al RICH + AGS annual Users’ Meeting June 6, 2006, www.bnl.gov/rhic ags/users meetings/workshops/basp , and paper in preparation. Anselmino et al., hep-ph/0511017 first qualitative picture of the Sivers functions to progress more data from the experiments are vital Anna Martin

Also new: Sivers Asymmetry for K± HERMES preliminary 2002-2004 K+ and K– on proton (DIS06) COMPASS preliminary 2003-2004 p+ and p– , K+ and K– on deuteron (GPD06) very recent results; phenomenological calculations already available (M. Anselmino et al) Anna Martin

Content: Polarised DIS and Experiments Transversity Distribution Function new results Sivers Distribution Function Other TMD Distribution Function Conclusions Anna Martin

other Azimuthal Asymmetries in SIDIS related to TMD PDF and/or FF (LO) inclusive DIS Boer-Mulders, 98 long. polarized target transv. polarized target polarized beam and target inclusive DIS Anna Martin

TMD Asymmetries in SIDIS (LO) AColl ~ sin(fh + fS) Collins asymmetry already seen ASiv ~ sin(fh - fS) Sivers asymmetry ~ sin(3fh - fS) inverstigated at HERMES and COMPASS ~ cos(fh - fS) g1T and FF inverstigated at COMPASS ~ cos2fh “Boer-Mullders” DF and Collins FF results from CLAS also for and other higher order TMD Asymmetries no preliminary results yet Anna Martin

(Boer – Mulders DF) can be measured in HERMES, COMPASS, CLAS, H1, ZEUS correlation between the transverse momentum and transverse spin of quarks in an unpolarised nucleon times Collins FF can be measured in HERMES, COMPASS, CLAS, H1, ZEUS Barone et al. Phys.Lett. B632,277 (2006) Anna Martin

CLAS 5.7 GeV (preliminary) (Boer – Mulders DF) difficult to measure background higher twist terms (f. i. Cahn) radiative correction, acceptance + … M.Osipenko CLAS 5.7 GeV (preliminary) Anna Martin

Content: Polarised DIS and Experiments Transversity Distribution Function new results Sivers Distribution Function Other TMD Distribution Function Conclusions Anna Martin

Future measurements in SIDIS “SHORT” TERM Collins and Sivers asymmetries more statistics from HERMES (2005 data) p0 asymmetries (HERMES) weighted asymmetries (HERMES and COMPASS) Boer-Mulders, and other hadron asymmetries from HERMES, COMPASS, JLAB Proton data from COMPASS (2007) Neutron (p, d) data from JLAB (upgrade at 12 GeV) “LONGER” TERM the present experiments can not precisely map all transverse spin effects in SIDIS COMPASS program after 2010 polarized ep collider Anna Martin