Measurements of Transverse Spin Effects in SIDIS

Outlook Introduction Asymmetries Near/Far Future Conclusions Transversity DF from Single Hadron from Two Hadrons from Hyperons Sivers DF Other TMD Near/Far Future Conclusions

What you will w/not find Review of all Deuteron Results w/not 2007 proton results They are on their way… ½ PB of data processed Data quality checks ongoing Late Spring

Spectrometer longitudinally polarised muon beam longitudinally or transversely polarised target momentum and calorimetry measurements particle identification MuonWall SM2 E/HCAL E/HCAL Straws SDC MWPC W45 SciFi Silicon Micromegas GEMs SM1 Polarised Target Muon Wall RICH m beam Beam: Luminosity 5 . 1032 cm-2 s-1 intensity 2 108 µ+/spill (4.8s/16.8s) momentum 160 GeV/c

Target solid state target operated in frozen spin mode 2002-2004: 6LiD superconductive Solenoid (2.5 T) 3He – 4He Dilution refrigerator (T~50mK) Dipole (0.5 T) solid state target operated in frozen spin mode 2002-2004: 6LiD dilution factor f = 0.38 polarization PT = 50% ~20% of the time transversely polarised during data taking with transverse polarization dipole field always  polarization reversal in the 2 cells after ~ 5 days two 60 cm long cells with opposite polarisation (systematics) dN/dz 4000 2000 zvtx (mm) -1000 1000

Event Selection DIS cuts: Q2 > 1 (GeV/c)2 Statistics 2002 - 2004: 0.1 < y < 0.9 W > 5 GeV/c2 All hadron selection: z > 0.20 pt > 0.1 GeV/c Plus for leading hadron: zl > 0.25 No signals in the CALOs from neutral particles with z > zl Statistics 2002 - 2004: 8.5 * 106 positive hadrons 7.0 * 106 negative hadrons

Hadron Identification Hadron identification is based on RICH response: several studies performed on the stability in time of the detector. Cherenkov thresholds: π ~ 2 GeV/c K ~ 9 GeV/c p ~ 17 GeV/c 2 σ π/K separation at 43 GeV/c In the leading hadron sample: ~76% pions ~12% kaons positive negative leading  3.4M 2.8M leading K 0.7M 0.4M

Kinematics – inclusive

Kinematics - SI

K0 Reconstruction Z(V0) – Z(prim. vtx.) > 10 cm ● angle of target pointing < 0.01 rad ● |Mpp– MK0| < 20 MeV/c² ● pt, arm > 0.025 GeV/c ● pt, K0 > 0.1 GeV/c K0 target pointing Armenteros S/B ~ 15

TRANSVERSITY

Bakker, Leader, Trueman, PRD 70 (04) Transversity DF q=uv, dv, qsea quark with spin parallel to the nucleon spin in a transversely polarised nucleon DTq(x) = q↑↑(x) - q↑↓(x) h1q(x), dq(x), dTq(x) Properties: probes the relativistic nature of quark dynamics no contribution from the gluons  simple Q2 evolution Positivity: Soffer bound…………….. first moments: tensor charge………. sum rule for transverse spin in Parton Model framework………… it is related to GPD’s is chiral-odd: decouples from inclusive DIS Soffer, PRL 74 (1995) Bakker, Leader, Trueman, PRD 70 (04)

How To L Nl’ h X Collins Asymmetry (Collins FF) L Nl’ L X the Transversity DF is chiral-odd: survives only by the product with another chiral-odd function can be measured in SIDIS on a transversely polarised target via “quark polarimetry” L Nl’ h X Collins Asymmetry (Collins FF) L Nl’ L X L polarization (FF of q L) L Nl’ hh X Two hadrons asymmetry (Interference FF)

Single hadron asymms. Collins and Sivers terms in SIDIS cross sections depend on different combination of angles: C = h - s’ Collins angle S = h - s Sivers angle h azimuthal angle of the hadron s azimuthal angle of the transverse spin of the initial quark s’ azimuthal angle of the transverse spin of the fragmenting quark s’ = p - s (spin flip)

Collins Effect Collins effect: a quark with an upward (downward) polarization, perpendicular to the motion, prefers to emit the leading meson to the left (right) side with respect to the quark direction i.e. the fragmentation function of a transversely polarized quark has a spin dependent part And the resulting measured asymmetry

Unidentified Hadrons only statistical errors shown (~1%), systematic errors considerably smaller small asymmetries compatible with 0 for both + and – hadrons [NP B765 (2007) 31-70]

Identified Hadrons

Naïve Interpretation proton data (parton model, valence region) proton data  unfavored Collins FF ~ – favored Collins FF at variance with unpol case u quark dominance (d quark DF ~ unconstrained) deuteron data refs! some (small) effect expected even if  cancellation between Tu (x) and Td (x) access to Td (x) F. Bradamante Genova, 27 febbraio 2008

Two Hadrons R= angle between lepton S= azimuthal angle of initial z-axis = virtual photon direction x-z plane = lepton scattering plane R= angle between lepton scattering plane and two-hadron plane S= azimuthal angle of initial quark versus lepton scattering plane S´= π - S (fragmenting quark) R RS= R - S´ = R + S - π (A. Bacchetta, M. Radici, hep-ph/0407345) (X. Artru, hep-ph/0207309)

Azimuthal Asymmetries z=z1+z2 Target single spin asymmetry ARS(x,z,Mh2): and N±(RS): Number of events for target spin up (+) and down (-) f: Dilution factor ≈ 0.38 D: Depolarisation factor D=(1-y)/(1-y+y2/2) PT: Target polarisation ≈ 0.5 Under measurement in e+e- (BELLE) expected to depend on the hadron pair invariant mass (X. Artru, hep-ph/0207309)

Selection DIS cuts: Q2 > 1 GeV2/c2 0.1 < y < 0.9 W > 5 GeV/c2 Hadron selection: z1,2 > 0.1 (current fragmentation) xF1,2 > 0.1 z1+z2 < 0.9 (exclusive rho) RICH identification of π, K

Two hadron asymm.s Expected Small (Radici/Bacchetta, PRD74(2006)114007)

Identified 2 Hadrons

z-order two identified hadrons Motivations: Hadrons with higher relative energy carry more information about the fragmenting quark polarization For leading hadron pairs signal enhancement is predicted PID with 2003-04 rich

z-order two identified hadrons

L Polarimetry

Results

SIVERS DF

SIVERS Mechanism The Sivers DF is probably the most famous between TMDs… gives a measure of the correlation between the transverse momentum and the transverse spin Requires final/initial state interactions of the struck quark with the spectator system and the interference between different helicity Fock states to survive time-reversal invariance Time-reversal invariance implies: …to be checked In SIDIS:

Unidentified hadrons only statistical errors shown (~1%), systematic errors considerably smaller small asymmetries compatible with 0 for both + and – hadrons [NP B765 (2007) 31-70]

Identified Hadrons

Naïve Interpretation proton data deuteron data asymmetry for p+ > 0, asymmetry for p- ≈ 0  Sivers DF for d-quark ≈ - 2 Sivers DF for u-quark 2 deuteron data preliminary 2002-2004 the measured asymmetries compatible with zero suggest F. Bradamante

Small SIVERS on D: hint for small Lg 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 and S. Gardner, PLB643 (2006) 22

Other TMD’s

Sidis Xsection From A. Bacchetta et al., JHEP 0702:093,2007. e-Print: hep-ph/0611265

Results - LO g1T is the only parton DF which is chiral-even, T-even, leading twist function in addition to the unpolarised DF and to the helicity DF

Results - LO

Transverse Target SSA for exclusive r (Q2>1) Motivations: Hard exclusive meson production (HEMP) is a way, complementary to DVCS, to access GPDs Vector mesons Transverse Target Single Spin Asymmetry AUT(fh,fS) connected to GPD E E allows flip of proton helicity, while quark helicity is not flipped → overall helicity is not conserved angular momentum conservation implies transfer of orbital angular momentum Ji Sum Rule

Selection Besides standard DIS cuts: Q2 > 1 GeV2/c2 0.1 < y < 0.9 W > 5 GeV/c2 Exclusive r selection: only 3 outgoing particles m, p+, p- 0.01 < pT2 < 0.5 [(GeV/c)2] missing energy -2.5 GeV< Emiss<2.5 GeV Inv. Mass -0.3 MeV/c2 < Mpp – Mr < 0.3 MeV/c2

Results

2007 RUN

Target in 2007 solid state target operated in frozen spin mode 2007: NH3 dilution factor f = 0.14 polarization PT = 90% 2  3 cells Beam line Cavity 1 Cavity 2 Cavity 3 Thermal screen Microwave power Coupling hole

Projected errors for full statistics (45x1012 m)

Summary precise deuteron data from COMPASS are now available Collins and Sivers asymmetries h±, p±, K± + other 6 TMDs [sin(3fh-fS), sin(fS), sin(2fh-fS), cos(fh-fS), cos(2fh-fS), cos(fh)] Two hadron asymmetries pp, pK, KK Transverse Lamba polarization all the measured deuteron asymmetries are very small, and compatible with zero COMPASS data on deuteron allows to determine the d-quark contribution present phenomenological studies can describe at the same time the BELLE (FF), the HERMES (proton) and COMPASS (deuteron)…and have allowed a first extraction of the transversity distribution DTq At the same way COMPASS and HERMES data have allowed a first extraction of the Sivers DF

Coming Soon Future programs Deuteron Cahn and Boer-Mulders asymmetries  unpol g2 Proton Collins + Sivers… Little further in time… all the rest Future programs Drell-Yan [see … M. Chiosso talk] Precision measurement … for better flavour separation and measurements of first moments…

THAT’S ALL… (FOR NOW!)