Transversity via Exclusive pion-electroproduction

Transcription

1 Transversity via Exclusive pion-electroproduction Gary R. Goldstein (Tufts U.) Simonetta Liuti & Saeed Ahmad (U.Va.) Thanks also to : Leonard Gamberg Presentation for Transversity Ferrara, Italy May 28,

2 Outline Tensor Charge and Transversity A new way of extracting the Tensor Charge from data: exclusive experiments Electroproduction of Mesons in the Multi GeV region The motivation from comparing: Hadronic d.o.f.: Regge interpretation Partonic d.o.f. : Generalized Parton Distributions Details of Observables & Regge and/or GPDs Conclusions and Outlook 2

3 Physics links What is transversity? Not here! What does transversity tell us about hadron spin & partons? Tensor charge: 1st moment of transversity distribution How is it determined? Axial vector meson couplings C-parity odd Axial vector dominance b1(1235) & h1(1170 & 1380) Regge-ized axials contribute to π0 & η exclusive photoproduction & electroproduction Helicity amps relate to GPDs HT & tensor charge Model results: tensor charge & data 3

4 Transversity & tensor charge Flavor components of nucleon tensor charge, via tensor current local operator. Master equation: Like other charges, integral of a distribution QuickTime and a TIFF (LZW) decompressor are needed to see this picture. δqa (x) or h1a (x) is transversity distribution for flavor a 4

5 Transversity 2-body scattering amps - Exclusive hadronic fa,b;c,d(s,t) with spin projections a,b;c,d What spin frame leads to simplest description of theory or data? Amps to observables? helicity has easy relativistic covariance - theory states of S p, e.g. +1/2>, -1/2>, etc. transversity: eigenstates of S (p1 p2) ± 1/2 )T = { +1/2> ±(i) -1/2>}/ 2 for spin 1/2, etc. Especially for relating to single spin asymmetries - only S n GRG & M.J.Moravcsik, Ann.Phys

6 Spin & momentum distributions δqa = dx h1a (x) 6

7 How can tensor charge be predicted? δu= 1.26, δd = Lattice (QCDSF, M. Gockeler et al., 2005) δ(u-d)= Pheno.: (Prokudin, DIS2008) δu= , δd = Pheno.: (Gamberg,Goldstein, 2001) δu= , δd = Just a sampling! First moment of transversity distribution h1(x) QCD Sum rules (H.He, X.Ji, 1995) Bounded by qa + qa 2 δqa Otherwise h1(x) extracted from SIDIS data (Anselmino, et al. 2007) 7

8 Axial (1+-) vector dominance - extrapolate from t=ma2 to 0 How to improve extrapolation? Regge for exclusive process. Which? 8

9 Tensor charge & transversity related to b1 & h1 exchanges 9

10 Important ingredients for relating transversity to exclusive π0 electroproduction Tensor charge couples via σµνγ5 to nucleons Coupled quantum numbers 1+- correspond to b1 & h1 couplings (γµ γ5 is opposite C-parity & does not contribute) γ* + π0 is C-parity eigenstate coupling to 1+- q+anti-q states (S=0, L=1 ) b10 & h q+anti-q states (S=1, L=1 ) ρ0 & ω γ*l + π0 does not couple to ρ0 & ω at small angles, but b10 & h1 do couple γ*t + π0 couples to both sets Factorization proofs: QCD γl. Applicable to γt & GPDs? Different transition form factors ρ0 π0 & b10 π0 Which picture - Regge or partons? Both connected 10

11 πo +1 +1/2 +1-1/2 +1/2 N +1/2-1/2 N f+1+,0-(s,t,q2) q nos of 1+- exchange b1 & h1-1/2 +1/2 πo g+1+,0- A++,- - mquark=0 has to flip helicity for q π+q and q q 0. +1,0 b1 & h1 HT +1/2 N -1/2 N 11

12 Generalized Parton Distributions (GPDs) & transversity distributions See also S. Liuti talk at Hadron 07 & DIS 2008 e γ(q2) One amp for Deep Elastic Scattering via X N(P) e X σ(x,q2) for DIS from squaring amp & summing over X s Handbag model is lowest order Perturbative QCD N(P) But not chiral odd > no h1(x,q2) γ(q2) q 12

13 π0 electroproduction γ(0) e γ(q2) γ(0) π0 forces quark helicity to flip q N(P) N(P) For virtual photoproduction of π0 quark helicity must flip at π vertex Questions: Amps for γl shown to factorize in DVCS. Do amps for γt factorize for π0 as 1/Q2 0? What to do about moderate Q2? Where does b1 or h1 exchange approximate t dependence of GPD? How is x dependence modeled? Small x -> large s. Regge! Many recent resurrections - Laget, et al., Sczepaniak, et al., VGG, Liuti, et al., Kroll,... 13

14 GPDs & helicity ξ=ζ/(2-ζ) Quarks do not flip helicity for these amps not quark transversity H(x,0,0)=f1(x) & H~q(x,0,0)=g1(x) M. Diehl; Boglione & Mulders 14

15 Chiral odd GPDs Eqns connecting GPD & helicity amps - M. Diehl, Eur.Phys.J.C19 (2001) 485; Boglione & Mulders, Phys.Rev.D 60 (1999) Exploit these relations to evaluate HTq with diquark spectator (scalar & axial vector -> u & d distributions) with constraints from form factors & lattice calculations. (Hägler, Schierholtz, et al. See especially S.Liuti, et al. DIS 2008 tomorrow.) 15

16 How does transversity enter? Quark helicity flip amps quark transversity HTq(x,t=0,ξ=0) =h1(x) Norm δq Also H(x,0,0)=f1(x) & H~q(x,0,0)=g1(x) Norm q M. Diehl; Boglione & Mulders 16

17 Additional connections See M.Burkardt 17

18 Exclusive πo electroproduction Transverse polarized cos 2ϕ + h1 LAB Sensitive to tensor charge! π e e' 18

19 Exclusive πo electroproduction and Transversity Connect to helicity amps- make spin behavior explicit Relate exchange picture to GPDs 2 Re(f*+1+,0+ f +1 -,0,- - f*+1+,0- f +1-,0,+ ) πo ±1,0 N ±1/2 only f+1+,0-(s,t,q2) = f2 survives at t 0 Target asymmetry for γt AUT 2Im(f*+1+,0+ f +1 -,0,+ - f*+1-,0- f +1+,0,- ) N ±1/2 dσt f+1+, f+1+,0-2 + f+1-, f+1-,0-2 19

20 FSI: Hadronic Picture Regge Model GRG & weak Regge cut model w. nonsense zeroes 20

21 Importance of b1 & h1 Photoproduction ala Regge mostly ρ&ω Many models Dip filling at -0.5 & dsigtt show importance of axial contribution Data from 1970 s Not 1++, but 1+- for π0 C-parity! b1 not a1 GG&Owens 73 Guidal, Laget, Vanderhaeghen 97 NSWSZ & Weak cut with b1&h1vs. SCRAM Electroproduction? See P.D.B.Collins & T.D.B.Wilkie [Zeits.f.Phys.C7(1981)357] need nonleading poles (daughters) to fill dip dramatically How to get Q2 dependence? Form factors for γ*+π0 21

22 Coupling exchange to γ* + π0 Kμ = For vector(q) + *(q) 0 (p=q+q) Pseudoscalar coupling to μ(q) photon & vector meson Note that photon cannot be longitudinal for small angles because two s must be orthogonal to each other & q+q Axial vector (1+-)(q) c oupling to * + 0 formed from σ(q 22

23 Tensor Charge resides in 1& h1 residue Residue at Axial vector pole determines t<0 amps & sensitive observables gg Ap gann pa A - ma2 ca /2 βa = e 4p ma 4 2 Factor out gγ π δa = cu-d δu-d + cu+d δu+d b1,h1 Γ(b1 πγ)~230 kev gbπγ ~0.25/mb Z.E.S. Uy PRD(1988) divide out b1, ρ h1, ω gbnn~8 & δb~δu-d ~1.3 modified by final state inter.w.s dependence factored out Need δh :SU(3)flavor δh~0.87 δu ~0.39 & δdtransversity ~-0.14+/-30% 2008-G.R. Goldstein 23

24 dσt/dt at Q2=0 Fixes parameters 24

25 photoproduction data & Regge-cut model (GRG&Owens,1973) 25

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27 P is polarized photon (Q2=0) asymmetry dσtt/dt P= dσt/dt 27

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31 Modeling Spin-dependent GPDs Build on spin-independent analysis of AHLT, based on data & lattice calculations of moments. 31

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35 Q2 dependence & γ* π0 form factors JPC =0-+ 35

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39 GPDs with vector & axial vector Form Factors 39

40 Cuts & form factors dsig/dt s=9 with cuts + no cut 2 dsigt/dt Q^ dsigt/dt Q^2 1.3 dsigtt/dt Q^2 1.3 dsigt/dt NO CUTS Q^2 0 1 mubarns/gev^ t 40

41 How to compare σtt with data for Q2>0? Different choices of κt q from small to large u&d SAID curve 41

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43 Regge-cut model Beam-spin asymmetry α data R. De Masi et al.,phys.rev.c77, (2008). 43

44 neutron vs. proton dσt/dt (switch isovector sign) 44

45 η Production vs. π in dσt/dt & dσtt/dt η Photon asymmetry shows more axial vector 45

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48 Variation of asymmetries with tensor charge 48

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52 Conclusions Tensor charge and Transversity are fundamental properties of spinning hadrons Methods to measure Transversity are crucial to test plethora of models (& factorization assumptions from SIDIS & theory) C-parity odd & chiral odd combinations select Transversity Exclusive π0 electroproduction (plentiful background to DVCS) observables depend on axial vector exchange quantum numbers δu & δd dσt/dt, dσtt/dt, AUT, beam asymmetry, beam-target correlations, dσ L/dt, dσlt/dt Regge with final state interactions & GPD HT yield values of δu & δd also κtu & κtd. Jlab with overlapping kinematic regions & plenty of π0 can bring enlightenment to transversity. 52