Subleading-twist effects in single-spin asymmetries in semi-inclusive DIS on a longitudinally polarized hydrogen target

Transcription

1 Subleading-twist effects in single-spin asymmetries in semi-inclusive DIS on a longitudinally polarized hydrogen target G Schnell, H Ohsuga, H Tanaka, T Hasegawa, T Kobayashi, Y Miyachi, T-A Shibata Tokyo Institute of Technology gunarschnell@desyde Gunar Schnell, HERMES Coloration JPS Spring Meeting 2005 March 26 th, 2005 p 1/10

2 HERMES at DESY Gunar Schnell, HERMES Coloration JPS Spring Meeting 2005 March 26 th, 2005 p 2/10

3 hermes The HERMES Spectrometer m 2 FRONT MUON HODO FIELD CLAMPS TRIGGER HODOSCOPE H1 DRIFT CHAMBERS 270 mrad PRESHOWER (H2) 170 mrad 1 DRIFT CHAMBERS 140 mrad 0 TARGET CELL SILICON DVC FC 1/2 PROP CHAMBERS MC 1-3 LUMINOSITY MONITOR 275 GeV e+ -1 HODOSCOPE H0 BC 1/2 STEEL PLATE BC 3/4 TRD CALORIMETER 140 mrad -2 RICH 270 mrad IRON WALL 170 mrad MAGNET WIDE ANGLE MUON HODOSCOPE MUON HODOSCOPES m Internal storage cell: pure gas target (polarized or unpolarized) Forward acceptance spectrometer: 40 mrad Θ 220 mrad Tracking: 57 tracking planes: δp/p = (07 13)%, δθ 06 mrad PID: Cherenkov (RICH after 1997), TRD, Preshower, Calorimeter Gunar Schnell, HERMES Coloration JPS Spring Meeting 2005 March 26 th, 2005 p 3/10

4 Lepton Deep Inelastic Scattering use well-known probe to study hadronic structure: (E, p ) Q 2 = 4EE sin 2 ( Θ 2 ) e (E, p) γ * d q u u h π π ν W 2 y x = E E = M 2 + 2Mν Q 2 = ν E = Q 2 2Mν π z = E h ν Gunar Schnell, HERMES Coloration JPS Spring Meeting 2005 March 26 th, 2005 p 4/10

5 Lepton Deep Inelastic Scattering use well-known probe to study hadronic structure: (E, p ) Q 2 = 4EE sin 2 ( Θ 2 ) e (E, p) γ * d q u u h K π ν W 2 y x = E E = M 2 + 2Mν Q 2 = ν E = Q 2 2Mν π z = E h ν Gunar Schnell, HERMES Coloration JPS Spring Meeting 2005 March 26 th, 2005 p 4/10

6 Lepton Deep Inelastic Scattering use well-known probe to study hadronic structure: (E, p ) Q 2 = 4EE sin 2 ( Θ 2 ) e (E, p) γ * d q u u h K π ν W 2 y x = E E = M 2 + 2Mν Q 2 = ν E = Q 2 2Mν π z = E h ν Factorization σ ep ehx = q DF p q σ eq eq F F q h (quark distribution hard scattering hadron formation) Gunar Schnell, HERMES Coloration JPS Spring Meeting 2005 March 26 th, 2005 p 4/10

7 Azimuthal Angles in SIDIS Cross Section SIDIS cross section depends on x, y (Q 2 ), and z Gunar Schnell, HERMES Coloration JPS Spring Meeting 2005 March 26 th, 2005 p 5/10

8 Azimuthal Angles in SIDIS Cross Section SIDIS cross section depends on x, y (Q 2 ), and z azimuthal distribution of produced hadrons: k S k q φ S z y x P h p had P h φ uli Gunar Schnell, HERMES Coloration JPS Spring Meeting 2005 March 26 th, 2005 p 5/10

9 Azimuthal Angles in SIDIS Cross Section SIDIS cross section depends on x, y (Q 2 ), and z azimuthal distribution of produced hadrons: k S k q φ S z y x P h p had P h φ uli additional degrees of freedom: φ S and P h (φ, P h ) Gunar Schnell, HERMES Coloration JPS Spring Meeting 2005 March 26 th, 2005 p 5/10

10 SIDIS Cross Section up to Subleading Order in 1/Q dσ = dσuu 0 + cos 2φ dσuu Q cos φ 1 dσ2 UU + λ e Q sin φ dσ3 LU { +S L sin 2φ dσul Q sin φ dσ5 UL + λ e [dσll ]} Q cos φ dσ7 LL +S T { sin(φ + φ S ) dσ 8 UT + sin(φ φ S ) dσ 9 UT + sin(3φ φ S ) dσ 10 UT + 1 Q +λ e [ cos(φ φ S ) dσ 13 LT + 1 Q ( ) sin(2φ φs ) dσut 11 + sin φ S dσut 12 1 Q ( cos φs dσlt 14 + cos(2φ φ S ) dσlt 15 ) ]} σ XY Beam Target Polarization Mulders and Tangermann, Nucl Phys B 461 (1996) 197 Boer and Mulders, Phys Rev D 57 (1998) 5780 Gunar Schnell, HERMES Coloration JPS Spring Meeting 2005 March 26 th, 2005 p 6/10

11 SIDIS Cross Section up to Subleading Order in 1/Q dσ = dσuu 0 + cos 2φ dσuu Q cos φ 1 dσ2 UU + λ e Q sin φ dσ3 LU { +S L sin 2φ dσul Q sin φ dσ5 UL + λ e [dσll ]} Q cos φ dσ7 LL +S T { sin(φ + φ S ) dσ 8 UT + sin(φ φ S ) dσ 9 UT + sin(3φ φ S ) dσ 10 UT + 1 Q +λ e [ cos(φ φ S ) dσ 13 LT + 1 Q ( ) sin(2φ φs ) dσut 11 + sin φ S dσut 12 1 Q ( cos φs dσlt 14 + cos(2φ φ S ) dσlt 15 ) ]} σ XY Beam Target Polarization Terms with 1/Q are so-called subleading twist Gunar Schnell, HERMES Coloration JPS Spring Meeting 2005 March 26 th, 2005 p 6/10

12 SIDIS Cross Section up to Subleading Order in 1/Q dσ = dσuu 0 + cos 2φ dσuu Q cos φ 1 dσ2 UU + λ e Q sin φ dσ3 LU { +S L sin 2φ dσul Q sin φ dσ5 UL + λ e [dσll ]} Q cos φ dσ7 LL +S T { sin(φ + φ S ) dσ 8 UT + sin(φ φ S ) dσ 9 UT + sin(3φ φ S ) dσ 10 UT + 1 Q +λ e [ cos(φ φ S ) dσ 13 LT + 1 Q ( ) sin(2φ φs ) dσut 11 + sin φ S dσut 12 1 Q ( cos φs dσlt 14 + cos(2φ φ S ) dσlt 15 ) ]} σ XY Beam Target Polarization Terms with 1/Q are so-called subleading twist Gunar Schnell, HERMES Coloration JPS Spring Meeting 2005 March 26 th, 2005 p 6/10

13 Azimuthal Single-Spin Asymmetries ep e hx study azimuthal distribution of hadrons: (eg Unpolarized beam & Transversely polarized target) A UT (φ, φ S ) 1 S σ + (φ, φ S ) σ (φ, φ S ) σ + (φ, φ S ) + σ (φ, φ S ) = 2 sin(φ+φ S ) UT sin(φ + φ S ) y k k q p had S φ S + 2 sin(φ φ S ) UT sin(φ φ S ) + z x φ uli sin(φ+φ ) S UT Collins Moment sin(φ φ ) S UT Sivers Moment Gunar Schnell, HERMES Coloration JPS Spring Meeting 2005 March 26 th, 2005 p 7/10

14 Longitudinally Polarized Target l y l q S x z θ γ S P h P h φ Experiment: Target Polarization wrt Beam Direction! experimental asymmetries (which have polarization along beam) related to theory asymmetries (polarization along virtual photon direction) via: [Diehl and Sapeta, in preparation] sin φ UL sin(φ φ ) S UT sin(φ+φ ) S UT (cos θ γ = cos θ γ sin θ γ sin θ γ 1 2 sin θ γ cos θ γ sin θ γ 0 cos θ γ 1, sin θ γ up to 15% at HERMES energies) sin φ UL sin(φ φ S ) UT sin(φ+φ S ) UT Gunar Schnell, HERMES Coloration JPS Spring Meeting 2005 March 26 th, 2005 p 8/10

15 Contributions to Measured A UL sin φ UL = sin φ UL + sin θ γ ( sin(φ+φs ) UT + sin(φ φ S) UT sin φ UL M Q I [ ˆP h k T M h + ˆP h p T M ( ( xh L m ) q M g 1 H1 + M h ( )] Mh zm h H 1L xfl D 1 Bacchetta et al, Phys Lett B 595 (2004) 309 they are all subleading-twist expressions! ) zm g 1G I[ ] Convolution integral over intrinsic transverse momenta sin φ UL Airapetian et al, Phys Rev Lett 84 (2000) 4047 sin(φ±φ ) S UT Airapetian et al, Phys Rev Lett 94 (2005) ) Gunar Schnell, HERMES Coloration JPS Spring Meeting 2005 March 26 th, 2005 p 9/10

16 Contributions to Measured A UL sin φ UL = sin φ UL + sin θ γ ( sin(φ+φs ) UT + sin(φ φ S) UT ) 2 sinφ 005 π + -2sinθ γ ( sin(φ+φ S ) UT ' + sin(φ-φ S ) ) UT ' HERMES Preliminary 2 sinφ 005 π - 2 sinφ UL' 2 sinφ UL x z twist-3 dominates A UL! Gunar Schnell, HERMES Coloration JPS Spring Meeting 2005 March 26 th, 2005 p 9/10

17 Conclusion semi-inclusive DIS cross section depends not only on x, y, and z but also on φ S and P h different terms can be isolated through azimuthal single (double) spin asymmetries HERMES has data with (un)polarized beam and targets = for first time subleading-twist contribution, ie sin φ UL to experimental longitudinal target-spin asymmetries extracted subleading-twist contribution dominates in experimental longitudinal asymmetries clean signal for subleading twist in SIDIS Gunar Schnell, HERMES Coloration JPS Spring Meeting 2005 March 26 th, 2005 p 10/10