Timelike Compton Scattering

Transcription

1 Timelike Compton Scattering and transversely polarized targets Jakub Wagner Theoretical Physics Department National Centre for Nuclear Research, Warsaw JLab, November 9, 204 E. R. Berger,M. Diehl, B. Pire - Eur.Phys.J. C23 (2002) B. Pire, L. Szymanowski and JW - Phys.Rev. D79 (2009), B. Pire, L. Szymanowski and JW - Phys. Rev. D83 (20), D. Mueller, B. Pire, L. Szymanowski and JW - Phys. Rev. D86 (202), H. Moutarde, B. Pire, F. Sabatié, L. Szymanowski and JW - Phys. Rev. D87 (203), A. Goritschnig, B. Pire and JW - Phys.Rev. D89 (204) / 47

2 Processes Universality of GPDs, Meson production - additional difficulties, 2 / 47

3 So, in addition to spacelike DVCS... e e q γ N N GPD ( a ) Figure : Deeply Virtual Compton Scattering (DVCS) : ln l N γ 3 / 47

4 we can also study timelike DVCS γ q e e+ N N GPD ( b ) Figure : Timelike Compton Scattering (TCS): γn l + l N Why TCS: universality of the GPDs another source for GPDs (special sensitivity on real part of GPD H), spacelike-timelike crossing (very different analytic structure, dispersion relations - work in progress with C.Weiss) 4 / 47

5 General Compton Scattering: γ (q in)n(p) γ (q out)n (p ) variables, describing the processes of interest in this generalized Bjorken limit, are the scaling variable ξ and skewness η > 0: ξ = q2 out + qin 2 qout 2 qin 2 η, η = qout 2 qin 2 (p + p ) (q in + q. out) DDVCS: q 2 in < 0, q 2 out > 0, η ξ DVCS: q 2 in < 0, q 2 out = 0, η = ξ > 0 TCS: q 2 in = 0, q 2 out > 0, η = ξ > 0 5 / 47

6 Coefficient functions and Compton Form Factors CFFs are the GPD dependent quantities which enter the amplitudes. They are defined through relations: [ A µν (ξ, η, t) = e 2 ( (P + P ) ū(p ) g µν + T H(ξ, η, t) γ + + E(ξ, η, t) iσ+ρ ) ρ 2M,where: + iɛ µν T ( H(ξ, η, t) γ + γ 5 + Ẽ(ξ, η, t) + γ ) ] 5 u(p ), 2M ( ) H(ξ, η, t) = + dx T q (x, ξ, η)h q (x, η, t) + T g (x, ξ, η)h g (x, η, t) q ( ) H(ξ, η, t) = dx T q (x, ξ, η) H q (x, η, t) + T g (x, ξ, η) H g (x, η, t). q 6 / 47

7 LO DVCS vs TCS DV CS T q DV CS T q DV CS Re(H) P = e 2 q = e 2 q x+η iε x+η iε x ± η Hq (x, η, t), (x x) = (T + (x x) = (T CS T q ) CS T q ) DV CS Im(H) iπh q (±η, η, t) DDVCS DDV CS T q = e 2 q (x x) x + ξ iε DDV CS Re(H) P x ± ξ Hq DV (x, η, t), CS Im(H) iπh q (±ξ, η, t) But this is only true at LO. At NLO all GPDs hidden in the convolutions. Digression: log( Q2 Q 2 ) in DDVCS? µ 2 F 7 / 47

8 Coefficient functions Renormalized coefficient functions for DVCS are given by [ ( ) ] T q (x) = C0(x) q + C(x) q Q 2 + ln C q coll (x) (x x), T g (x) = T q (x) = T g (x) = [ C g (x) + ln ( Q 2 µ 2 F [ C q 0(x) + C q (x) + ln [ C g (x) + ln ( Q 2 µ 2 F µ 2 F ) C g coll (x) ] + (x x), ( Q 2 µ 2 F ) C q coll (x) ] + (x x), ) C g coll (x) ] (x x). The results for DVCS and TCS cases are simply related: ( ) T CS T (x, η) = ± DV CS T (x, ξ = η) + iπ C coll (x, ξ = η), D.Mueller, B.Pire, L.Szymanowski, J.Wagner, Phys.Rev.D86, 202. where + ( ) sign corresponds to vector (axial) case. 8 / 47

9 Models H. Moutarde, B. Pire, F. Sabatié, L. Szymanowski and JW - Phys. Rev. D87 (203), In our analysis we use two GPD models based on double distibution: β ( ) F i(x, ξ, t) = dβ dα δ(β+ξα x) f i(β, α, t)+di F x ξ, t Θ(ξ 2 x 2 ), The DD f i reads where: D F i + β f i(β, α, t) = g i(β, t) h i(β) Γ(2n i + 2) [( β ) 2 α 2 ] n i, 2 2n i+ Γ 2 (n i + ) ( β ) 2n i+ h g(β) = β g( β ), hg(β) = β g( β ), h q sea(β) = q sea( β ) sign(β), hq sea (β) = q sea( β ), h q val (β) = q val(β) Θ(β), hq val (β) = q val(β) Θ(β). denotes the Polyakov-Weiss D-term. In our estimates we will use parametrizations obtained by a fit to the chiral soliton model. 9 / 47

10 Factorized: based on MSTW08 PDFs with simple factorizing ansatz for t - dependence g u(β, t) = 2 F u (t), F u (t) = 2F p (t) + F n (t), g d (β, t) = F d (t), F d (t) = F p (t) + 2F n (t), g s(β, t) = g g(β, t) = F D(t), F D(t) = ( t/m 2 V ) 2, with M V = 0.84 GeV, F p and F n are electromagnetic Dirac form factors of the proton and neutron. We use that model to construct only H. Goloskokov-Kroll: based on CTEQ6m PDFs, and g i(β, t) = e b it β α i t and simple parametrization of the sea quarks: H u sea = H d sea = κ sh s sea, with κ s = /( ln Q 2 /Q 2 0), with the initial scale of the CTEQ6m PDFs Q 2 0 = 4 GeV 2. H is constructed using the Blümlein - Böttcher (BB) polarized PDF parametrization to fix the forward limit. Meson electroproduction data from HERA and HERMES have been considered to fix parameters for this GPD in the GK model. / 47

11 Compton Form Factors - DVCS - Re(H) Figure : The real part of the spacelike Compton Form Factor H(ξ) multiplied by ξ, as a function of ξ in the double distribution model based on Kroll-Goloskokov (upper left) and MSTW08 (upper right) parametrizations, for µ 2 F = Q2 = 4 GeV 2 and t = 0. GeV 2, at the Born order (dotted line), including the NLO quark corrections (dashed line) and including both quark and gluon NLO corrections (solid line). / 47

12 Compton Form Factors - DVCS - Im(H) Figure : The imaginary part of the spacelike Compton Form Factor H(ξ) multiplied by ξ, as a function of ξ in the double distribution model based on Kroll-Goloskokov (upper left) and MSTW08 (upper right) parametrizations, for µ 2 F = Q2 = 4 GeV 2 and t = 0. GeV 2, at the Born order (dotted line), including the NLO quark corrections (dashed line) and including both quark and gluon NLO corrections (solid line). 2 / 47

13 Few words about factorization scale (PRELIMINARY) Figure : Left column - Re(H(ξ)), right column - Im(H(ξ)), Q 2 = 4 GeV 2, µ 2 F = Q2, Q 2 /2, Q 2 /3 3 / 47

14 Few words about factorization scale (PRELIMINARY) Figure : Full NLO result. Left column - ξ Re(H(ξ)), right column - ξ Im(H(ξ)), Q 2 = 4 GeV 2, µ 2 F = Q2, Q 2 /2, Q 2 / Figure : Left column - ξ Re(H(ξ)), right column - ξ Im(H(ξ)). Dotted - LO with Q 2 = mu 2 F, Solid NLO with Q2 = µ 2 F /2. 4 / 47

15 Compton Form Factors - TCS - Re(H) Figure : The real part of the timelike Compton Form Factor H multiplied by η, as a function of η in the double distribution model based on Kroll-Goloskokov (upper left) and MSTW08 (upper right) parametrizations, for µ 2 F = Q2 = 4 GeV 2 and t = 0. GeV 2. Below the ratios of the NLO correction to LO result of the corresponding models. 5 / 47

16 Compton Form Factors - TCS - Im(H) Figure : The imaginary part of the timelike Compton Form Factor H multiplied by η, as a function of η in the double distribution model based on Kroll-Goloskokov (upper left) and MSTW08 (upper right) parametrizations, for µ 2 F = Q2 = 4 GeV 2 and t = 0. GeV 2. Below the ratios of the NLO correction to LO result of the corresponding models. 6 / 47

17 DVCS vs TCS Figure : The ratio of the timelike to spacelike NLO corrections in the real (left) and imaginary (right) part of the CFF H, in the GK (dashed) and factorized MSTW08 (solid) 7 / 47

18 "Model (in)dependence" Figure : The dotted line shows the LO result and shaded bands around solid lines show the effect of a one sigma uncertainty of the input MSTW08 fit to the full NLO result. 8 / 47

19 Few words about factorization scale (PRELIMINARY) Figure : Left column - Re(H(ξ)), right column - Im(H(ξ)), Q 2 = 4 GeV 2, µ 2 F = Q2, Q 2 /2, Q 2 /3 9 / 47

20 Few words about factorization scale (PRELIMINARY) Figure : Full NLO result. Left column - ξ Re(H(ξ)), right column - ξ Im(H(ξ)), Q 2 = 4 GeV 2, µ 2 F = Q2, Q 2 /2, Q 2 /3 20 / 47

21 Digression: J/ψ photoproduction cross section NLO/LO for large W : α S(µ R )N c π work in progress with D.Yu.Ivanov and L.Szymanowski ( ln ξ What to do??? (PMS??, BLM??, resummation?,...?) Σ nb ) ( 4 ln M ) 2 V µ 2 F Figure : Photoproduction cross section as a function of W = s γp for µ 2 F = M J/ψ 2 {0.5,, 2}- LO and NLO. Thick lines for LO and NLO for µ 2 F = /4M 2 J/ψ. 2 / 47

22 Numerical studies Marie Boër, M.Guidal and M. Vanderhaeghen Presented on the PANIC Conference 204 Numerical studies of some higher twist effects - mass corrections, "gauge" corrections Evaluation of beam and target asymmetries in VGG model Studies of the GPDs dependence of observables in VGG model 22 / 47

23 TCS and Bethe-Heitler contribution to exlusive lepton pair photoproduction. γ l l + p p Figure : The Feynman diagrams for the Bethe-Heitler amplitude. Figure : Handbag diagrams for the Compton process in the scaling limit. 23 / 47

24 TCS Berger, Diehl, Pire, 2002 T q p e (2) e () e (3) q p k k ϕ boost p k k θ ϕ e (2) e () e (3) γ p c.m. + l l c.m. Figure : Kinematical variables and coordinate axes in the γp and l + l c.m. frames. 24 / 47

25 Interference B-H dominant for not very high energies: The interference part of the cross-section for γp l + l p with unpolarized protons and photons is given by: dσ INT cos ϕ Re H(η, t) dq 2 dt d cos θ dϕ Linear in GPD s, odd under exchange of the l + and l momenta angular distribution of lepton pairs is a good tool to study interference term. 25 / 47

26 JLAB 6 GeV data Rafayel Paremuzyan PhD thesis Figure : e + e invariant mass distribution vs quasi-real photon energy. For TCS analysis M(e + e ) >. GeV and s γp > 4.6 GeV 2 regions are chosen. Left graph represents e-6 data set, right one is from ef data set. 26 / 47

27 Theory vs experiment R.Paremuzyan and V.Guzey: R = dφ cos φ dσ dφ dσ R 2 2 Q =.3 GeV E γ = GeV SC_D= 0.00 SC_D=.00 SC_D= 2.00 BH Dual Data t GeV Figure : Thoeretical prediction of the ratio R for various GPDs models. Data points after combining both e-6 and ef data sets. 27 / 47

28 Approved experiment at Hall B, and LOI for Hall A. 28 / 47

29 29 / 47

30 TCS R(η) = 2 2π dϕ cos ϕ 0 2π 0 dϕ ds dq 2 dtdϕ ds dq 2 dtdϕ, Figure : Ratio R as a function of η, for Q 2 = µ 2 F = 4 GeV2 and t = 0. GeV 2. The dotted line represents LO contribution and the solid line represents NLO result. 30 / 47

31 TCS The photon beam circular polarization asymmetry: A = σ+ σ σ + + σ, Figure : (Left) Photon beam circular polarization asymmetry as a function of φ, for t = 0. GeV 2, Q 2 = µ 2 = 4 GeV 2, integrated over θ (π/4, 3π/4) and for E γ = GeV (η 0.). (Right) The η dependence of the photon beam circular polarization asymmetry for Q 2 = µ 2 = 4 GeV 2, and t = 0.2 GeV 2 integrated over θ (π/4, 3π/4). The LO result is shown as the dotted line, the full NLO result by the solid line. 3 / 47

32 Linear polarization A. Goritschnig, B. Pire and JW - arxiv: [hep-ph] In the case of a linearly polarized photon we now have a distinguished transverse direction given by the polarization vector, which we choose to point in the x-direction: ɛ(q) µ = δ µ Momenta of other particles in γ p c.m. frame are given by: q µ = (q 0, 0, 0, q 0 ) p µ = (p 0, 0, 0, q 0 ) q µ = (q 0, T cos Φ h, T sin Φ h, q 3 ) p µ = (p 0, T cos Φ h, T sin Φ h, q 3 ) where Φ h is the angle between polarization vector and hadronic plane: sin Φ h = ɛ(q) n = ɛ(q) where n is the vector normal to the hadronic plane. p p p p 32 / 47

33 Let us now turn to the contribution of the interference between the TCS and BH mechanisms to the differential γp l + l p cross section. For incoming photons with polarization vector as in Eq. (3) it, up to our accuracy, reads: dσ (INT ) dq 2 dtdω l + l dφ = h 2 π 5 s ( ) M 2 T CS(ɛ)MBH(ɛ) + c.c. 2 where: dσ (INT ) unpol dσ (INT ) unpol dσ (INT ) linpol dq 2 dtdω l + l dφ + h dq 2 dtdω l + l dφ, h ( + cos 2 θ ) [ cos φ Re HF t ] 4M EF2 η H(F 2 + F 2), dq 2 dtdω l + l dφ h sin θ dσ (INT ) ( ) [ linpol sin θ cos(2φ dq 2 h + 3φ) Re HF dtdω l + l dφ h t ] 4M EF2+η H(F 2 + F 2). 33 / 47

34 We define two observables sensitive to the unpolarized and linearly polarized part of interference cross section. First one is similar (up to the terms formally of the order t/q 2 or M 2 /Q 2 ) to the R ratio defined in BDP in the case of an unpolarized photon beam : R = 2π dφ 0 h 2 2π dφ cos(φ) 3π/4 sin θdθ 0 π/4 2π 2π dφ 0 h dφ 3π/4 sin θdθ 0 π/4 The second observable projects out the dσ (INT ) linpol section: dσ dtdq 2 dωdφ h. dσ dtdq 2 dωdφ h R 3 = 2 2π dφ 0 h cos(2φ h )2 2π dφ cos(3φ) 3π/4 sin θdθ 0 π/4 2π 2π dφ 0 h dφ 3π/4 dσ sin θdθ 0 π/4 part of the interference cross dσ dtdq 2 dωdφ h. dtdq 2 dωdφ h Making use of R and R 3 we can define the following observable which is sensitive only to the interference term and which provides us with information about H: C = R R 3 = 2 3π 2 + π [ Re HF t EF 4M 2 η H(F ] 2 + F 2) [ Re HF t EF 4M 2+η H(F ]. 2 + F 2) 34 / 47

35 How sensitive is C on the values of H? We take H GK g = {, 0,, 2, 3} H g C Η Figure : C as a function of η, for Q 2 = 4 GeV 2 and t = t C t Figure : C as a function of t, for Q 2 = 4 GeV 2 and η = / 47

36 Experimental possibilities Hall D - flux of linearly polarized photons, are rates big enough? Hall B - low-q 2 tagger, In the unpolarized electron scattering process, the virtual photon polarization is: ] ɛ = [ + 2 Q2 + ν 2 tan 2 (θ Q 2 e /2) where ν is the photon energy and θ e the electron scattering angle. The longitudinal polarization is given by ɛ L = Q2 ɛ, and the polarization density ν 2 matrix: ( + ɛ) 0 ɛ/2 2 L ρ = 0 ( ɛ) 0 2 ɛ /2 L 0 ɛ L and the matrix describes real transverse photons. 36 / 47

37 Effective photon approximation so: dσ ep dq 2 γdν dσ ep Mλ, dq 2 γdν F (Q2 γ, ν) M λ ρ λλ ( + ɛ) 0 0 ρ λλ 2 0 ( ɛ) 0 2, = F (Q 2 γ, ν) = F (Q 2 γ, ν) [ ( + ɛ)σxx γp + ( ɛ)σyy γp 2 2 ] [ ( ɛ)σ unp γp + ɛ σ linpol γp ] C ep = R ep R ep 3 = ɛ ɛ C 37 / 47

38 Approved CLAS2 experiment - "Meson Spectroscopy with low Q 2 electron scattering in CLAS2". 38 / 47

39 Approved experiment - E : "Timelike Compton Scattering and J/psi photoproduction on the proton in e+e- pair production with CLAS2 at GeV." Approved experiment - E : "Meson spectroscopy with low Q 2 electron scattering in CLAS2" Both in the same run group. Idea:extend the first one, by use of the low-q 2 tagger from the second one. 39 / 47

40 Transverse target asymmetries in DVCS. 40 / 47

41 Transverse target asymmetries in DVCS. Asymmetries: A DVCS UT (φ, φ S) A I UT (φ, φ S) dσ+ (φ, φ S ) dσ + (φ, φ S + π) + dσ (φ, φ S ) dσ (φ, φ S + π) S dσ + (φ, φ S ) + dσ + (φ, φ S + π) + dσ (φ, φ S ) + dσ (φ, φ S + π), () dσ+ (φ, φ S ) dσ + (φ, φ S + π) dσ (φ, φ S ) + dσ (φ, φ S + π) S dσ + (φ, φ S ) + dσ + (φ, φ S + π) + dσ (φ, φ S ) + dσ (φ, φ S + π). (2) Moments: A DVCS UT (φ, φ S) c DVCS 0,UT sin(φ φ S) (3) [ ] A I UT (φ, φ S) c I,UT sin(φ φ S) cos φ + s I,UT cos(φ φ S) sin(φ) (4) 4 / 47

42 Transverse target asymmetries in DVCS. Connection to the Compton form Factors: c DVCS t { 0,UT M Im HE EH + ξẽ H H ξẽ }, (5) c I,UT M { [ t Q Im (2 x 4M 2 B )F E 4 ] xb F 2H 2 x B [ +x Bξ F (H + E) (F + F 2)( H + t ]} 4M Ẽ), (6) 2 c I t 0,UT Q ci,ut, (7) s I,UT M { [ t Q Im 4 ] xb F 4M 2 2 H (F + ξf 2)x B Ẽ (8) 2 x B ( ) + x B [(F + F 2) ξh + ξf ( H + xb2 ]} Ẽ), t 4M 2 E 42 / 47

43 HERMES data 43 / 47

44 Comparison with GK model P. Kroll, H. Moutarde,F. Sabatié 44 / 47

45 Numerical predictions for TCS Marie Boër, M.Guidal and M. Vanderhaeghen 45 / 47

46 Numerical predictions for TCS Marie Boër, M.Guidal and M. Vanderhaeghen 46 / 47

47 Summary TCS is complementary measurement to DVCS, cleanest way to test universality of GPDs. Inclusion of NLO corrections to the coefficient function is an important issue, understood in JLAB kinematics, more work needed for small ξ s. TCS already measured at JLAB 6 GeV, but much richer and more interesting kinematical region available after upgrade to 2 GeV, Linear polarization in TCS may give some information on H. Approved experiment for Hall B. LOI for Hall A. Run group proposal in preparation for linear polarization in Hall B. Transverse target asymmetries in DVCS give an important information on GPD E. First numerical studies on transverse target polarization in TCS (Marie Boër, M.Guidal and M. Vanderhaeghen). 47 / 47