Transverse quark spin distributions in the nucleon Hidekazu Tanaka - PowerPoint PPT Presentation

Transverse quark spin distributions in the nucleon Hidekazu Tanaka for HERMES collaboration Tokyo Institute of Technology, Department of Physics Spin puzzle Deep Inelastic Scattering Single-spin asymmetry Recent results from HERMES

Spin Puzzle Spin Puzzle Quark helicity distribution Gluon spin distribution u   ≡ u  d  d  s  s  G  ~ 0.2 − 0.3  now in measuring Known 1 = 1    G  L q  L g 2 2 Orbital angular momenta of quark and gluon L q  L g Unknown ....

Parton Distribution Functions Parton Distribution Functions PDFs describe the nucleon structure Gluon distributions Quark density (well known) Quark transversity (unmeasured!) Quark helicity (known)

What is Quark Transversity ? What is Quark Transversity ? Transversity δq describes transverse quark polarization in the transversely polarized nucleon.  q ?? =  q  q quark polarization quark polarization i in the long. pol. in the trans. pol. nucleon nucleon  q −  q = ?? Non-realtivestic limit ;  q −  q = 0

Yet Another Quark Distribution Yet Another Quark Distribution ⊥ f 1 T Other quark distribution is “Sivers function” . The Sivers function describes unpolarized quark in the transversely polarized nucleon. ?? ⊥  x  q  x  f 1 T quark momentum quark momentum distribution distribution in unpol. nucleon in trans. pol. nucleon ⊥  x  f 1 T L The Sivers function is related to quark orbital angular momentum.

The HERMES Experiment The HERMES Experiment Deep Inelastic Scattering is the best tool to access to both distribution functions  q ⊥ f 1 T L Transversity Sivers function

Deep Inelastic Scattering (DIS) Deep Inelastic Scattering (DIS) Inclusive (Only scattered lepton lepton is measured) Fragmentation *  Q  ,  q  Unmeasured Semi-inclusive q  x  D  z  (Hadron coincidence nucleon measurement with the P  M , 0  scattered lepton) x : Quark momentum fraction M : Target mass (Bjorken scaling parameter) : Virtual photon 4-momentum Q z  : Virtual photon energy : Fractional energy of produced hadron

Transversely Polarized DIS Transversely Polarized DIS Lepton Scatt. Two Azimuthal angles Plane  S  S ⊥ : Angle between and L.P.  : Angle between L.P. and H.P. k ,   ' k Hadron Prod. : Lepton momentum Plane  q : Virtual photon momentum : Hadron momentum  p had

Single Target-spin Asymmetry Single Target-spin Asymmetry   ∗ d   − d   = d  e  A U T T ransversely   d   U npolarized d  polarized  ,  π production ∗   d  d   e cross-section Collins sin  S   Sivers sin − S  ≡ A A UT A UT U T Sivers asymmetry Collins asymmetry Collins ∝  q  x  H 1 ⊥  z  Sivers ∝ ⊥  x  D 1  z  A UT A UT f 1 T Transversity Sivers function

Fragmentation Function Fragmentation Function Unpolarized FF Collins FF Collins ∝  q  x  H 1 ⊥  z  Sivers ∝ ⊥  x  D 1  z  A UT A UT f 1 T Collins FF describes Normal unpol. fragmentation of pol. quark fragmentation into unpol hadron (Well known) (Unknown) π π

Properties of the Asymmetry Properties of the Asymmetry Collins sin  S   Sivers sin − S  ≡ A A UT A UT U T Collins Asymmetry Sivers Asymmetry Collins ∝  q  x  H 1 ⊥  z  Sivers ∝ ⊥  x  D 1  z  A UT A UT f 1 T Transversity Sivers function (Polarized PDF) (Unpolarized PDF) & ↓ Collins FF Orbital angular (Polarized FF) momenta

Sivers Asymmetry Measured at HERMES Sivers Asymmetry Measured at HERMES Beam : (27.6 GeV)  e Target : Hydrogen π+ About 5 months data taking 0.023  x B  0.4 x B : Quark momentum fraction z : Fractional energy of 0.2  z  0.7 π- produced hadron 2 〉 ~ 2.5 GeV 2 〈 Q Asymmetries are small, but is slightly positive   Sivers  A UT at low x. π0 ⊥  x  ∫ dz D 1  z  A UT  x  ∝ f 1 T ⊥  x  D 1  z  A UT  z  ∝ ∫ dx f 1 T Gray band indicates possible effects of exclusive vector meson.

Collins Asymmetry Measured at HERMES Collins Asymmetry Measured at HERMES π+ Collins   ≥ 0 ; Small positive A UT π+ Collins  − ≤ 0 ; Large negative A UT π- Collins  0 ≤ 0 ; Negative π- A UT ⊥  z  A UT  x  ∝  q  x  ∫ dz H 1 π0 π0 ⊥  z  A UT  z  ∝ ∫ dx  q  x  H 1

Conclusion Conclusion Tow new quark distributions are important to understand the nucleon structure. - Transversity : a probe of a relativistic nature of the nucleon. - Sivers function : related to quark orbital angular momentum. To investigate those functions, several experiments (HERMES, COMPASS, RHIC-spin) are now running. HERMES provided their preliminary results on single spin asymmetry of π production in DIS.