Transverse Spin Phenomena and Their Impact on QCD In Honor of Gary Goldstein's 70th Birthday October 28-29, October 2010 Jefferson Lab

Transcription

1 Transverse Spin Phenomena and Their Impact on QCD In Honor of Gary Goldstein's 70th Birthday October 28-29, October 2010 Jefferson Lab

2 Transverse SPIN Observables SSA (TSSA) P P πx Single Spin Asymmetry Rotational invariance σ (x F, p ) = σ (x F, p ) Left-Right Asymmetry P Parity Conserving interactions: SSAs Transverse Scattering plane σ is T (P P π ) S T L P R A N = σ (x F,p ) σ (x F, p ) σ (x F,p )+σ (x F, p ) σ P S T π P P π π P π

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4 Present here aspects of transversity and transverse spin polarization phenomena Gary Goldstein and Mike Moravcsik, Ann. Phys. 98, 128 (1976); Ann. Phys. 142, 219 (1982) John Ralston & Davison Soper NPB 152 (1979) Dennis Sivers, Phys. Rev. D 41, 83 (1990); 43, 261 (1991) Bob Jaffe & Xiangdong Ji, Phys. Rev. Lett. 67, 552 (1991) Jacques Soffer, Phys. Rev. Lett. 74, 1292 (1995) Gary Goldstein, Bob Jaffe and Xiangdong Ji, Phys. Rev. D52, 5006 (1995)

5 Aspects of transversity and transverse spin polarization phenomena

6 Present here who have been instrumental in Gary s Career Kamesh Wali, Ph.D advisor of Gary Lou Cavellie Jeff Owens

7 Special Thanks to JLAB David Richards JLAB for support encouragement guiding us through Theory Group-Mike Pennington, Wally Melnitchouk and Christain Weiss Staff support Mary Fox, Ruth Bizot

8 Simonetta Liuti who s conceived of the idea to celebrate GaryFEST as a workshop at JLAB Proceedings...!!!

9 Outline Transverse structure spin Effects in TSSAs Gauge links-color Gauge Inv.- T-odd TMDs T-odd PDFs via FSIs... Summing gauge link QCD calc FSIs Gauge Links-Color Gauge Inv. T-odd TMDs Generalizing the Generalized Parton Model (GPM)--effects of FSI and ISI on color structure Connection to twist three & Gluonic Poles Universality and gluonic poles in fragmentation

10 Transverse Polarization in Inclusive Reactions P P πx e.g. Goldstein & Owens NPB 76 f Transv. polarization cross section interference of helicity flip and non-flip amps. M D M quark-quark scattering f Elastic scattering of 2 quarks of different flavor 6 independent helicity Amps M λ q1,λ q 2 ;λ q1,λ q2 M ++,++ Φ 1 M,++ Φ 2 M +,+ Φ 3 M +,+ Φ 4 M +,++ Φ 5 M ++,+ Φ 6 A N = ˆσ ˆσ ˆσ +ˆσ Im [Φ 6(Φ 1 +Φ 3 ) Φ 5 (Φ 2 Φ 4 ) ] Interference of helicity flip and non-flip amps 1) requires breaking of chiral symmetry mq /E 2) phases require higher order corrections

11 Collinear factorized QCD parton dynamics σ pp πx f a f b ˆσ D q π ˆσ ˆσ ˆσ f / =( + ± i ) D M M â N = ˆσ ˆσ ˆσ +ˆσ Im ( M + M ) M M 2 f TSSA requires relative phase btwn different helicity amps ± ˆ

12 Factorization Theorem & SSAs at Partonic level ˆσ Im[M +M ] Im m q X Born amps are real -- need loops ----> phases QCD interactions conserve helicity up to corrections O ( mq E q ) Twist three and trivial in chiral limit A N m q E α s at the partonic level Kane & Repko, PRL: 1978

13 Large Transverse Polarization in Inclusive Reactions 4"51(657(25(8*+9(:$'"+*'%;( pbeam=12 Gev/c pbeam=22 Gev/c pbeam=200 Gev/c D<6((!%=E?E(A'B(( Fixed target F8GH((!%=EI?>(A'B(( Collider,'J( "*+92( C(

14 Modern Era Transverse SSAʼs at s = 62.4 & 200 GeV at RHIC P S T L P R STAR PRL101, (2008) BRAHMS Preliminary GeV 62.4 GeV 0.1 A N (!) 0! + -! E704 E <p (!)<0.8 GeV/c T x F

15 Combining Eqs. 3 ^ n p!p pe m Bea "cosm θp # = Target The extraction perimental data i ments "cosm θp # c over the experime p# PRD 89 "! FIG. 1: Schematic diagram of inclusive Λ production and decay. The angle θp of the decay proton with respect to the normal n to the production plane is defined in the Λ rest frame. QCD test-λ Production pp Λ X dn0 dn = (1 + αpnλ cos θp ). dωp dωp quark to polarize a Λ PΛ = tein PRD 1990 σ pp Λ X σ pp Λ X Here, k p is the proton momentum unit vector in the Λ rest frame, P! Λ is the polarization of the Λ, and α = ± is the analyzing power of the parityviolating weak decay [20]. Assuming CP -invariance of the decay, the analyzing power for the Λ is of opposite sign (αλ = 0.642) [20]. The quantity dn0 /dωp denotes the decay distribution of unpolarized Λ particles. As described above, only the normal component PnΛ of the Λ polarization may be non-zero in the present analysis, and so Eq. 2 may be rewritten as σ + pp Λ X σ pp Λ X (3) For unpolarized Λ particles the distribution of the decay particles is isotropic and dn0 /dωp is simply a normalization factor, independent of angle. In the case of limited spectrometer acceptance, however, it acquires a dependence on cos θp. To extract the polarization of a sample of Λ hyperons from the angular distribution of their decay products in the acceptance, one may determine the following moments:!! dn dn dω dωp cosm θp dω cosm θp dω p p p m! dn "cos θp #, Λ N dω p acc dωp (4) and!! 0 0 dω cosm θp dn cosm θp dn p dω dωp dωp p m! dn0 "cos θp #0, Λ N dω p 0,acc dωp (5) where m = 1, 2,... The symbol "...# represents an aver- (1) "cosm The unpolariz tracted directly f larized Λ hyperon the extraction of HERMES data is ror symmetry of t case of limited ac this geometric sym "cosm where top and bot momentum was d the spectrometer. moments of the f are zero, and all the unpolarized "cosm θp The first mom rately for the top possible difference tor half. Using th one obtains from E for αpnλ and "cos αpnλ = "c where 2c+ (2c ) and "cos θp #bot. T solved iteratively. takes αpnλ = c+ /

16 Comment Largest TSSA least understood