Gary R. Goldstein! Gary R. Goldstein! Presentation for CIPANP 2015,! Vail, Colorado!!!

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1 Gary R. Goldstein! Gary R. Goldstein! Tufts University! Tufts University!!! Presentation for CIPANP 215,! Vail, Colorado!!! These ideas were developed in Jlab, Trento ECT*, INT, DIS211, SPIN, Frascati INF, Transversity , PANIC, POETIC, QCD215 & in consultation with many of you!! 1! Presentation for QCD Evolution 215 Workshop! Jefferson Lab, May.26-3, 215!

2 Collaborators GPDs, Extension to Chiral Odd Sector S. Liuti, O. Gonzalez Hernandez GRG, O. Gonzalez-Hernandez, S.Liuti, PRD(215) arxiv: ! GRG, O. Gonzalez-Hernandez, S.Liuti, arxiv: ! Ahmad, GRG, Liuti, PRD79, 5414, (29)! Gonzalez, GRG, Liuti PRD84, 347 (211)! GRG, Gonzalez Hernandez, Liuti, J. Phys. G: Nucl. Part. Phys (212)! Gonzalez Hernandez, Liuti, GRG, Kathuria, PRC88, 6526 (213)! QCD215 GR.Goldstein 5/25/15 2

3 Outline How to model & measure transversity, tensor charge & Chiral Odd GPDs Hadron Spatial Spin Structure from GPDs à! Our Flexible parameterization for Chiral Even GPDs! Regge diquark spectator model: R Dq! Some results for DVCS (transverse γ * à transverse γ)! EM Form factors! Extend to Chiral Odd GPDs via diquark spin relations! à Transversity! Model relations between Chiral even & odd helicity amps! π & η production & flavor separation! Tensor charge δ q! Observables: Cross sections & Asymmetries! Which processes? Exclusive π & η best candidates! QCD215 GR.Goldstein 3

4 Why look for Chiral odd GPDs? à Transversity à tensor charges δ q This paper Q 2 = 1 GeV Q 2 = 4 GeV Bacchetta et al. Q 2 = 1 GeV 2, exp. x range full x range Anselmino et al. (212) Q 2 =2 GeV 2 He and Ji (Bag model, 1997) Gamberg and Goldstein (GVMD, 23) Q 2 =1 GeV 2 Wakamatsu (CSQM, 28) Q 2 =1 GeV 2 Lattice (25) Q 2 = 4 GeV 2 Lattice (212) Q 2 = 4 GeV 2 d -.5 GG, Gonzalez, Liuti, arxiv: u QCD215 GR.Goldstein 4

5 Momentum space nucleon matrix elements of quark field correlators see, e.g. M. Diehl, Eur. Phys. J. C 19, 485 (21). Chiral even GPDs -> Ji sum rule J q x = 1 2 dx[ H(x,, ) + E(x,, ) ]x Chiral odd GPDs -> transversity How to measure and/or parameterize them? QCD215 GR.Goldstein 5 5

6 quark GPDs! 8 quark GPDs per flavor (leading twist) N q :: q N 8 independent helicity amps 2 questions: how to model them? how to measure them? DVCS accesses 4 Chiral Even dσ/dω linearly via BH X DVCS interference DVπ S accesses 2 Chiral Even + 4 Chiral Odd See F. Sabatie Jlab/ because dσ T > dσ L HallA CIPANP talk bilinearly via dσ/dω & polarization asymmetries See also - Goloskokov & Kroll EPJA47(211)112 Different approach Other methods for extracting Chiral Odd DV dihadron production - El Beiyad, et al. Phys.Lett. B688 (21) 154; M.Radici CIPANP talk DV longitudinal Vector meson production - Goloskokov & Kroll EPJC74(214)2725 QCD215 GR.Goldstein 6

7 P, Λ Factorization in exclusive processes (DVCS, DVMP ) γ * p γ (M ) p q,λ γ Longitudinal factorizes Collins, Frankfurt, Strikman PRD56, 2982 (1997) q'=q+δ, Λ γ k, λ k = k Δ. λ k, λ k = k Δ. λ P = P-Δ, Λ Convolution of hard part with quark-proton Helicity amplitudes Regge X diquark model: Chiral Even: Ahmad, Honkanen, Liuti, Taneja PRD75, 943 (27); EPJC63, 47 (29). t g! A! λ= +(-) λ chiral even (odd) see Ahmad, GG, Liuti, PRD79, 5414, (29) for first chiral odd GPD parameterization Gonzalez, GG, Liuti PRD84, 347 (211) chiral even GPD QCD215 GR.Goldstein

8 Normalizing GPDs Chiral even 1 Form factor, H q (x,ξ,t)dx = F 1 q (t), H q (x,,) = q(x) 1 E q (x,ξ,t)dx = F 2 q (t) Forward limit Integrates to charge 1 H q (x,ξ,t)dx = g q A (t), H q (x,,) = Δq(x) = q (x) q (x) 1 E q (x,ξ,t)dx = g P q (t) Integrates to axial charge QCD215 GR.Goldstein 8

9 EM Form Factors (t dependence) t 2 F Diquark Regge Total u Total d u d.25 κ q -1 t 2 F t (GeV 2 ) u d u d O.Gonzalez, GRG, S.Liuti, K.Kathuria PRC88, 6526(213) data: G.D. Cates, et al. PRL16,2523 (211). QCD215 GR.Goldstein 9

10 The question is: how do we normalize chiral-odd GPDs? Only Physical constraints on the various chiral-odd GPDs are Forward limit H T (x,,) = q (x) q (x) = h 1 (x) Form Factors H q T (x,ξ,t)dx E T (x,ξ,t)dx = = δq(t) E q (x,ξ,t)dx = ( 2H q + E q T T T )dx = κ q T (t) Transversity Integrates to tensor charge δ q Tensor form factor Integrates to transverse dipole moment κ T q T q No direct interpretation of E T lim t t 4M 2 H T (x,,t) = h 1 (x) QCD215 GR.Goldstein 1 5/26/15

11 The Model Reggeized Diquarks! The Model first for Chiral Even Reggeized Diquarks! QCD215 GR.Goldstein 11

12 Procedure to construct Chiral Odd GPDs & observables! k + =XP + S= or 1 k + =(X-ζ)P + Λ P + P X+ =(1-X)P + Λ P + =(1- ζ)p + Product of diquark l.c.w.f. s A Λλ;Λ λ =λ A Λλ;Λ λ chiral even GPDs g A exclusive process helicity amps pdf s, FF s, dσ/dω & Asymmetries: parameters & predictions vertex parity A Λλ;-Λ -λ chiral odd GPDs pdf s, QCD215 GR.Goldstein 12

13 Advantage: control over the number of parameters to be fitted at different stages so that it can be optimized Functional form: Recursive fit GRG, Gonzalez Hernandez, Liuti, PRD84, 347 (211) From DIS to DVCS, DVMP q(x,q o 2 ) = A q x α q (1 x) β q F(x,c q, d q,...) H q (x,ξ,t;q 2 o ) = N q x α q+α ' q (1 x) p t a 1 = m q, a 2 = M X q, a 3 = M Λ q,... a 1 G a 1a 2 a 3... (x,ξ,t) pdf s Form Factors dσ / dω! Asymmetries! Flexible parameterization based on the Reggeized quark-diquark model. QCD215 GR.Goldstein 5/25/15 13

14 t H u E u H ~ u =.13, Q 2 =1.1 GeV 2 -t = GeV 2 Chiral even GPDs E ~ u X H d E d H ~ d E ~ d X From GPDs with evolution to Compton Form Factors CFFs to helicity amps helicity amps to observables <-> parameters QCD215 GR.Goldstein 5/25/15 14

15 Chiral Even Observables Chiral Odd A Λ'±,Λ± H, E, H, E A Λ'±,Λ H T, E T, H T, E T Compton Form Factors H(ξ,t;Q 2 ) = P.V. dx 1 dx x ξ iε 1 x + ξ iε H(x,ξ,t;Q 2 ) H(x,ξ,t;Q 2 ) x ξ + iπ H(ξ,ξ,t;Q 2 ) (symm.term) Re H Im H QCD215 GR.Goldstein 5/25/15 15

16 Having fit other data we predicted Hermes data CIPANP215 GR.Goldstein 16

17 Other chiral even predictions Gonzalez Hernandez, Liuti, GG, Kathuria QCD215 GR.Goldstein 17

18 The Model for Chiral Odd Reggeized Diquarks! QCD215 GR.Goldstein 18

19 Vertex Structures with Diquark Spectator λ k + =XP + k + =(X-ζ)P + λ Λ P + P X+ =(1-X)P + P X+ =(1-X)P + S= or 1 Λ P + =(1- ζ)p + First focus on S= pure spectator beginning H ϕ + + * (k ', P ')ϕ ++ (k, P) + ϕ + * (k ', P ')ϕ + (k, P) E ϕ * ++ (k',p ')ϕ + (k,p) + ϕ * + (k ', P ')ϕ + + (k, P) H ϕ * ++ (k ', P')ϕ ++ (k,p) ϕ * + (k ', P')ϕ + (k, P) E ϕ * ++ (k ', P')ϕ + (k,p) ϕ + * (k ',P')ϕ ++ (k,p) Vertex form factor function QCD215 GR.Goldstein 19

20 Λ Vertex Structures with Diquark Spectator k + =XP + k + =(X-ζ)P + P + P X+ =(1-X)P + P X+ =(1-X)P + S= or 1 First focus on S= pure spectator beginning H ϕ + + * (k ', P ')ϕ ++ (k, P) + ϕ + * (k ', P ')ϕ + (k, P) E ϕ * ++ (k',p ')ϕ + (k,p) + ϕ * + (k ', P ')ϕ + + (k, P) H ϕ * ++ (k ', P')ϕ ++ (k,p) ϕ * + (k ', P')ϕ + (k, P) Vertex form factor λ E ϕ * ++ (k ', P')ϕ + (k,p) ϕ + λ * (k ',P')ϕ ++ (k,p) QCD215 GR.Goldstein Λ P + =(1- ζ)p + Parity at vertices: By switching λè - λ & Λ è -Λ (Parity) will have chiral evens go to ± chiral odds giving relations before k integrations A(Λ λ ;Λλ)è ±A(Λ,λ ;-Λ,-λ) * but then (Λ -λ )-(Λ-λ) (Λ -λ )+(Λ-λ) unless Λ=λ 2

21 odd <-> even S= Chiral even <-> odd helicity amps (+ S=1) t-channel flip flip<->nonflip nonflip flip nonflip<->nonflip flip Invert both sides to get GPDs same helicity amp sets QCD215 GR.Goldstein 21

22 RESULT: Chiral odd GPDs H T u =.13, Q 2 =1.1 GeV 2 -t = GeV 2 2 H ~ u u T+E T H ~ u T 2 H ~ d d T+E T H T d q dx H T (x,ζ,t,q 2 ) = δ q (t,q 2 ) Tensor charge q dx [2!H T (x,ζ,t,q ) + E q T (x,ζ,t,q 2 )] = κ q (t,q 2 ) Transverse dipole H ~ T d.5 moment E ~ u T X E ~ T d X QCD215 GR.Goldstein sizeable f 1 -f 4 5/25/15 22

23 4 2 Im H T Q 2 = 1.1 GeV 2 x Bj = Re H T Im 2 H ~ T +E T Re 2 H ~ T +E T Im H ~ T Re H ~ T Im E ~ T t (GeV 2 ) 4 Re E ~ T t (GeV 2 ) QCD215 GR.Goldstein 5/25/15 23

24 N +1, How to single out & measure chiral odd GPDs? Exclusive Lepto-production of π o or η, η to measure chiral odd GPDs & Transversity +1/2 π o -1/2 N e.g. f +1+,- (s,t,q 2 ) +1, +1/2 +1/2 +1/2 g +1+,- A ++,- - -1/2-1/2 q nos of C-odd exchange 1 +- exchange b 1 & h 1 π o H T +1, twist 2 twist 3-1/2 +1/2 N N t-channel J PC quantum numbers enhance chiral odd QCD215 GR.Goldstein 24 b 1 & h 1

25 6 independent helicity amps for π o or η, η (& K, D C ) 8 Quark-nucleon helicity amps for u,d (& s,c) k, λ t! k = k Δ. λ A! P, Λ P = P-Δ, Λ odd even QCD215 GR.Goldstein 5/25/15 25

26 6 helicity amps for π Compton Form Factors f 1 f 2 f 3 f 4 f 5 f 6 t t t t Also Chiral Even CFFs QCD215 GR.Goldstein 26

27 Observables Cross sections! Asymmetries! QCD215 GR.Goldstein 27

28 Cross section with φ modulations & beam/target polarized QCD215 GR.Goldstein

29 F UU (nb/gev 2 ) V.Kubarovsky, et -4 al.. Jlab/CLAS data F UU (nb/gev 2 ) Unpolarized cross sections F UU,T + F UU,L F UU cos F UU cos 2 f 1 ++ f 1 +- f 1 -+ f See F. Sabatie Jlab/HallA -t (GeV 2 ) CIPANP talk for L & T separation QCD215 GR.Goldstein x Bj =.13 Q 2 = 1.1 GeV 2 * ++ f 1 f -- 1 f 1 ++ f 1 +- f 1 -+ f 1 -- * +- f 1 f t (GeV 2 ) 5/25/15 29

30 Same, separating the GPDs contribution F UU (nb/gev 2 ) F UU,T + F UU,L F UU cos F UU cos E ~ T H ~ T, E T H T H T, H ~ T, E T -4-4 F UU (T, L) (nb/gev 2 ) E ~ T H ~ T, E T H T t (GeV 2 ) E ~ T H ~ T, E T H T /25/15 -t (GeV 2 ) 3

31 Unpolarized cross section components f 1 +- dominates small t & > f 1 ±± Jlab/HallA L & T separation Or form of - f f 1-2 Polarized beam QCD215 GR.Goldstein 31

32 Comparing to other models The t-> feature for us is that f 1 +- dominates & it is driven by H T. But f 1 ++ & f 1 -- also contribute as ~ (t -t), however weaker.! f 1 ++ & f 1 -- are not equal in magnitude, especially vs. ζ or ξ.! In A LL ~ f f f f sensitive to differences! QCD215 GR.Goldstein 32

33 Comparison between models dσ T dt H T 2 + τ E T 2 Goloskokov and Kroll τ = t o t 8M 2 dσ T dt g π (1) ( Q 2 )τ E T + (1+ ξ) E! 2 T + (2) gπ ( Q 2 )τ E T + (1 ξ) E! 2 T + (3) gπ Goldstein, Gonzalez, Liuti ( Q 2 2 ) H T dσ TT dt E T 2 Goloskokov and Kroll dσ TT dt ( ) * ( E T + (1 ξ) E! T ) E T + (1+ ξ)! E T Goldstein, Gonzalez, Liuti

34 CLAS π : Bedlinskiy, et al. PRL19, 1121 (212). GGL vs. G&K QCD215 GR.Goldstein 34

35 Important combinations of overall helicity amps natural unnatural for ξ Quite sizable effect for ξ > Goloskokov&Kroll take only H T and (2 ~ H T + E T ) non-zero EPJA47, (211) 112 for π and EPJC74 (214)2725 for V. What observables reveal this? A LU sinφ,... QCD215 GR.Goldstein 35

36 Asymmetries: Longitudinal polarizations Sensitive to f f QCD215 GR.Goldstein 36

37 Andrey Kim, Harut Avakian et al., Jefferson Lab CLAS Collaboration Sensitive to tensor charge Role of parameters QCD215 GR.Goldstein 5/25/15 37

38 Asymmetry sensitive to tensor charge x Bj =.2, Q 2 = 1.5 GeV 2 * p o p'.1 u =.91±.8, d = -.12 u =.6, d = -.12 u = 1.4, d = -.12 A UT sin s t (GeV 2 ) QCD215 GR.Goldstein 5/25/15 38

39 Chiral odd GPD s & helicity/transversity interpretation? From T invariance for ξ = QCD215 GR.Goldstein 39

40 Model dependent relations! Pretzelosity B-M Chiral odd GPDs & TMDs? Transversity transfer; Boer-Mulders; pretzelosity; worm gears Transversity pdf ξ h T 1L worm-gear **Tensor charge can be related to BSM couplings A.~Courtoy, S.~Baessler, M.~Gonzalez-Alonso and S.~Liuti, arxiv: QCD215 GR.Goldstein 4

41 Connecting tensor charge to BSM: Courtoy, Baessler, Gonzalez-Alonso and Liuti, arxiv: BSM couplings 1,γ 5,(γ µ + γ µ γ 5 ),iσ j+ γ 5 C T = G F 2 V g ud Tε T The observable is always the product of the fundamental coupling times a hadronic matrix element! g T and g S are the flavor- non-singlet/isovector hadronic matrix elements! or by using isospin symmetry:! The precision with which ε T can be measured depends on the uncertainty on g T! 5/26/15 41

42 x h 1 u x h 1 d Extraction of transversity after using DVCS data via chiral evenß à odd Transversity à pdf s: h 1q (x,q 2 ) This paper BCR Torino Q 2 = 2 GeV 2 GG, Gonzalez, Liuti, arxiv: PRD x BCR=Bacchetta, Conte, Radici Anselmino, Boglione, et al., Phys.Rev. D87 (213) 9419 δu = δd= QCD215 G.R.Goldstein 42 5/25/15

43 Extraction of tensor charge x h 1 u x h 1 d This paper BCR Torino Q 2 = 2 GeV 2 Anselmino, Boglione, et al., Phys.Rev. D87 (213) 9419 δu = δd= From our Reggeized form x δu 1.2 δd -.8 Closer to QCD sum rule values QCD215 G.R.Goldstein 43 5/25/15

44 Chiral odd GPDs à Transversity à tensor charges δ q This paper Q 2 = 1 GeV Q 2 = 4 GeV Bacchetta et al. Q 2 = 1 GeV 2, exp. x range full x range Anselmino et al. (212) Q 2 =2 GeV 2 He and Ji (Bag model, 1997) Gamberg and Goldstein (GVMD, 23) Q 2 =1 GeV 2 Wakamatsu (CSQM, 28) Q 2 =1 GeV 2 Lattice (25) Q 2 = 4 GeV 2 Lattice (212) Q 2 = 4 GeV 2 d -.5 GG, Gonzalez, Liuti, arxiv: PRD u QCD215 GR.Goldstein 44

45 Chiral odd GPDs à transverse spin-flavor dipole moments κ T q Wakamatsu (CSQM, 28) Ledwig et al. (CSQM, 21) Pasquini and Boffi (LFCQM, 28) Lattice (27) This paper defined by M. Burkardt, PRD72,942(25) d T 2 GG, Gonzalez, Liuti, arxiv: u T QCD215 GR.Goldstein 45

46 Comparing with new data from Hall A courtesy F. Sabatie, CIPANP 46

47 Comparing with new data from Hall A courtesy F. Sabatie, CIPANP 47

48 Comparing with new data from Hall A courtesy F. Sabatie, CIPANP 48

49 Ratio of unpolarized η / π η/π o F UU,T ( )/F UU,T ( ) x Bj =.2, Q 2 =1.5 GeV 2 no d quark +- without f 1 Q 2 =1.5 GeV 2 x Bj = t (GeV 2 ) QCD215 GR.Goldstein 49 5/25/15

50 Summary Flexible parameterization for chiral even from form factors, pdfs & DVCS R Dq! Extended R Dq to chiral odd sector! DVMP π many dσ s & Asymmetries! measure Transversity! QCD215 GR.Goldstein 5

51 Backup slides QCD215 GR.Goldstein 51

52 Longitudinally polarized target A UL sin sin A UL x Bj =.25, Q 2 = 1.94 GeV 2 x Bj =.4, Q 2 = 2.83 GeV 2 f +-* (f f 1 -+) f ++* (f f 1 --) t (GeV 2 ) sin2 A UL sin2 A UL x Bj =.25, Q 2 = 1.94 GeV 2 x Bj =.4, Q 2 = 2.83 GeV 2 f +-* 1 f -+ 1 f ++* 1 f t (GeV 2 ) Look for tensor charge in f 1 +- Transverse dipole moment in f 1 ++,f 1 -- QCD215 GR.Goldstein 5/25/15 52

53 Transverse target A UT sin s x Bj =.2, Q 2 = 1.5 GeV 2 * p o p' Im f 1 Re f Re f 1 Im f 1 -Im(f ++ 1 * f -+ 1 ) A UT sin s x Bj =.2, Q 2 = 1.5 GeV 2 * p p' Im f 1 Re f Re f 1 Im f 1 -Im(f ++ 1 * f -+ 1 ) A UT sin + s Im f 1 Re f 1 A UT sin + s Im f 1 Re f 1 A UT cos s Im f 1 Im f Re f 1 Re f 1 Re (f ++ 1 * f -+ 1 ) t (GeV 2 ) Look for tensor charge in f +- 1 Transverse dipole moment in f ++ 1,f -- 1 A UT cos s QCD215 GR.Goldstein t (GeV 2 ) 5/25/ Im f 1 Im f Re f 1 Re f 1 Re (f ++ 1 * f -+ 1 )

54 Reggeization via spectator diquark mass formulation Where does the Regge behavior come from? Diquark spectral function Regge ρ δ(m X2 -M X2 ) (M X2 ) α + Q 2 Evolution GRG, Gonzalez Hernandez, Liuti, J. Phys. G: Nucl. Part. Phys (212)! Following DIS work by Brodsky, Close, Gunion (1973) QCD215 GR.Goldstein 54 M X 2

55 Reggeization q, Λ γ k, λ q'=q+δ, Λ γ k = p Δ. λ P, Λ M X à k X,λ P = P-Δ, Λ Landshoff, Polkinghorn, Short 71 Brodsky, Close, Gunion 71 Regge behavior required for Compton Ahmad, Honkanen,Liuti,Taneja 7, 9 Gorshteyn & Szczepaniak (PRD, 21) Brodsky, Llanes-Estrada 7 Brodsky, Llanes, Szczepaniak 8 GRG, Gonzalez Hernandez, Liuti, J. Phys. G: Nucl. Part. Phys (212)! 55 QCD215 GR.Goldstein 5/25/15

56 Helicity amps (q +N->q+N ) are linear combinations of GPDs T-reversal at ξ = In diquark spectator models A ++;++, etc. are calculated directly. Inverted -> GPDs 56 QCD215 GR.Goldstein 56

57 S= diquark Spectator model A ++,-+ = - A ++,+- * A -+,++ = - A +-,++ * A ++,++ = A ++,- - Invert to obtain model parameterization for GPDs double flip QCD215 GR.Goldstein 57 57

58 F UU (nb/gev 2 ) Unpolarized Helicity Amplitudes F UU,T + F UU,L F UU cos F UU cos x Bj =.13 Q 2 = 1.1 GeV 2 f 1 ++ f 1 +- f 1 -+ f 1 -- F UU (nb/gev 2 ) f 1 ++ f 1 +- f 1 -+ f t (GeV 2 ) * ++ f 1 f -- 1 * +- f 1 f t (GeV 2 ) 5/25/15 58