Exclusive Processes at HERMES

Transcription

1 Exclusive Processes at HERMES Arne Vandenbroucke Gent University, Belgium On behalf of the HERMES Collaboration 22nd Winter Workschop on Nuclear Dynamics La Jolla, California, USA March 17th, 26

2 Outline 1 Introduction 2 DVCS 3 Pseudoscalar Mesons 4 Vector Mesons 5 Outlook 6 Summary

3 Exclusive processes Initial and Final State fully known HERA Lepton Beam with fixed internal gas target. Scattered Lepton and produced meson in Hermes acceptance Select Exclusive reactions by putting constraints on the missing mass, or missing energy e p q γ g e _ q M Y Spectrometer Not Detected

4 Exclusive Leptoproduction of Mesons/Photons - Collins, hep-ph/ Collins, Frankfurt, Strikman, hep-ph/ Factorization can be applied for exclusive processes: a hard part a meson distribution amplitude a soft part providing information about the nucleon in terms of Generalized Parton Distributions Factorization valid for large Q 2, low t (and γ L ) H,E, H,Ẽ(x,ξ,t) e p γ t g e M q(x ξ) q(x+ ξ) GPD GPD(x,ξ,t) Y Hermes Constraints

5 DIS structure func s: forward limit (ξ =, t = ) q(x) = H q (x,ξ =,t = ) Δq(x) = H q (x,ξ =,t = ) Connection to many observables Elastic form factors: first moments in x F q 1 (t) = Z 1 1 dx H q (x,ξ,t) Z 1 g q A (t) = dx H q (x,ξ,t) 1 F q 2 (t) = Z 1 1 g q P (t) = Z 1 1 dx E q (x,ξ,t) dx Ẽ q (x,ξ,t) Ji sum rule: J q = 1 ΔΣ + Lq 2 H(x, ξ,) J q = 1 2 Z 1 1 xdx[h q (x,ξ,t = ) + E q (x,ξ,t = )] model-independent access to L! Note connection of H, E to Dirac, Pauli form factors... and their connection to nucleon magnetic moment: F N 1 () + F N 2 () = µ N N.C.R. Makins, INT Workshop on Synergy between Lattice and Experiment, Apr 24-25, 26

6 Observing Generalized Parton Distributions Both different final states and different observables select different combinations of GPD s: Exclusive Pseudoscalar Meson Production: H,Ẽ Exclusive Vector Meson Production:H,E Deeply Virtual Compton Scattering: H,E, H, Ẽ Target or Beam related asymmetries access a product of GPD s. Cross Section Measurements give access to quadratic combination.

7 Deeply Virtual Compton Scattering Probe E and H (and Ẽ, H)

8 e + p e + p + γ DVCS final state indistinguishable from the Bethe-Heithler final state, where a Brehmsstrahlung photon is created.

9 e + p e + p + γ DVCS final state indistinguishable from the Bethe-Heithler final state, where a Brehmsstrahlung photon is created. Select Final state by putting constraints on the Missing Mass Amplitudes add up coherently: dσ = τ BH + τ DVCS 2 = τ BH 2 + τ DVCS 2 + (τ BH τ DVCS + τ BH τ DVCS) }{{} c +Σ n c n cos (nφ)+λσ n s n sin (nφ) z y k k q p γ x φ uli N/(1*N DIS ) M x 2 (GeV 2 ) A. Vandenbroucke, WWND26, A. Vandenbroucke, La Jolla, WWND26, March La 17th

10 e + p e + p + γ DVCS final state indistinguishable from the Bethe-Heithler final state, where a Brehmsstrahlung photon is created. Select Final state by putting constraints on the Missing Mass Amplitudes add up coherently: dσ = τ BH + τ DVCS 2 = τ BH 2 + τ DVCS 2 + (τ BH τ DVCS + τ BH τ DVCS) }{{} c +Σ n c n cos (nφ)+λσ n s n sin (nφ) Beam Related Asymmetries: BSA: dσ( e + p) dσ( e + p) sin (φ) ImMunp 1,1 BCA: dσ(e + p) dσ(e p) cos (φ) ReMunp 1,1

11 Beam Spin Asymmetry A LU = 1 < P B > N + (φ) N (φ) N + (φ)+n (φ) Σ ns n sin (nφ) A LU e + p e + γ X HERMES PREL. (M x < 1.7 GeV) 2 (refined) P1 + P2 sin φ + P3 sin 2φ P1 = -.4 ±.2 (stat) P2 = -.18 ±.3 (stat) P3 =. ±.3 (stat) expected sin (φ) behavior! <-t > =.18 GeV 2, <x B > =.12, <Q 2 > = 2.5 GeV φ (rad)

12 Beam Charge Asymmetry A C = N+ (φ) N (φ) N + (φ)+n (φ) c + Σ n c n cos (nφ) + λσ n s n sin (nφ) A C.6.4 HERMES PRELIMINARY (<-t c > =.12 GeV 2 ) e ± p e ± γ X (M x < 1.7 GeV) c + c1 cos φ + s1 sin φ χ 2 / ndf : 11.47/ 8 c =.9 ±.2 (stat) c1 =.59 ±.28 (stat) s1 =.94 ±.28 (stat) φ (rad) expected cos (φ) behaviour sin (φ) moment due to polarized beam

13 Beam Charge Asymmetry cosφ A C t (GeV 2 ) A C (t) can distinguish between models GPD model with factorized t-dependence (dotted) with D-term (dash-dotted) GPD model with Regge-inspired t-dependence (solid) with D-term (dashed)

14 From Asymmetries to GPD s M 1,1 unp = F 1 (t)h 1 (ξ, t)+ x B 2 X B (F 1 (t) + F 2 (t)) H 1 (ξ, t) F 1 (t) and F 2 (t) Dirac and Pauli Form Factors H 1, H 1 and E 1 Compton Form Factors t 4M 2 p F 2 (t)e 1 (ξ, t) < x B >.1 and < t >.1GeV 2 BSA : ImH 1 BCA : ReH 1 q e2 q (H q (ξ, ξ, t) H q ( ξ, ξ, t)) ( q e2 q P ( ) 1 1 Hq (x, ξ, t) 1 x ξ + 1 x+ξ ) dx Access to GPD H!

15 Transverse Target Asymmetry During Hermes run with a transversily polarised target: < P T > 75% z y k k q p γ x φ S φ uli 1 A UT (φ, φ S ) = N (φ,φ S ) N (φ,φ S ) P T N (φ,φ S )+N (φ,φ S ) Im(F 2 H F 1 E) sin (φ φ S ) cos (φ)+ Im(F 2 H F 1 ξẽ) cos (φ φ S ) sin (φ)

16 Transverse Target Asymmetry sin(φ-φ A s )cos(φ) UT HERMES PRELIMINARY (in HERMES acceptance) e + p e + γ X (M x < 1.7 GeV) cos(φ-φ A s )sin(φ) UT t (GeV 2 ) x B Q 2 (GeV 2 )

17 Transverse Target Asymmetry sin(φ-φ A s )cos(φ) UT HERMES PRELIMINARY (in HERMES acceptance) e + p e + γ X (M x < 1.7 GeV) cos(φ-φ A s )sin(φ) UT J u = J u =.2 J u =.4 (hep-ph/56264) t (GeV 2 ) x B Q 2 (GeV 2 ) A sin (φ φ S) cos (φ) UT Im(F 2 H F 1 E) Access to GPD E!

18 Pseudoscalar Mesons Probe Ẽ and H

19 e + p e + n + π + Cross Section: σ γ p n+π + (x, Q 2 ) = N π+ excl L x Q 2 κ(x, Q 2 ) Γ(< x >, < Q 2 >) L: Integrated luminosity : 283 pb 1 κ(x, Q 2 ): Detection probability (estimated from MC) Γ(< x >, < Q 2 >): virtual photon flux factor σ π+ ( H + Ẽ)2

20 Extracting a Cross Section Acceptance correction is model dependent, therefore a comparison with 2 different GPD models was made Mankiewicz, Piller & Radyushkin (1999) Vanderhaeghen, Guichon & Guidal (1999) Detection probability has to be taken into account Detection probability <x<.18.18<x<.26.26<x< Q (GeV 2 )

21 σ tot : Q 2 dependence in x bins: ( H + Ẽ)2 Q 2 behavior with respect to σ L σ T γ * p π + n HERMES PRELIMINARY 1 2 uncorrected for radiative effects σ tot (nb) 1.2 < x < < x < < x <.8 σ L σ L VGG: LO VGG: LO+power corrections Q 2 ( GeV 2 ) Q 2 dependence is consistent with LO expectations, however Vanderhaeghen, Guidal, Guichon model too small Power corrections (k T, soft overlap) overestimate data

22 Testing factorisation theorem predictions σ red Factorization theorem predicts a 1 Q 6 fixed x and t dependence for σ L at Cross Section can be written as σ = 1 x π 1 x Q m2 x 2 Q }{{ 2 } Kinematical Factor A(γ p pm) 2 spin } {{ } σ reduced pure γ L + LO dσ red 1 Q 2

23 Testing factorisation theorem predictions σ red ) 4 Reduced total cross section (nb.gev γ* p π n.2<x<.18.18<x<.26.26<x<.8 HERMES PRELIMINARY uncorrected for radiative effects Fit To data of a 1 Q p Q (GeV ) function: p = 1.9 ±.5 p = 1.7 ±.6 p = 1.5 ± 1.

24 Vector Mesons Probe E and H

25 e+ p e + p + ρ ρ reconstructed from h + h pairs Exclusivity constraints by requiring Missing Energy E to be, describe background shape by MC Evidence of exclusive ρ production

26 Target Spin Asymmetry A UT for e+ p e + p + ρ Goeke et al., Prog. Part. Nucl. Phys. 47 (21) A = 1 S π σ(β)dβ 2π Sensitivity to J u π 2π σ(β)dβ σ(β)dβ At Hermes asymmetry slope predicted to be positive sin(ϕ ϕs) amplitude of asymmetry: A sin(φ φ S) UT A E H

27 A UT for exclusive ρ production A UT (φ,φ s ) HERMES PRELIMINARY e p e ρ p sin (φ-φ A s ) =.46 ±.37 UT < x > =.9 < Q 2 > = 2. GeV 2 < -t > =.13 GeV φ-φ s (rad) Increasing statistics by including all transverse data will allow for an σ L σ T separation

28 A UT for exclusive ρ production sin (φ φ A s ) UT.5 HERMES PRELIMINARY e p e ρ p.5. < t <.1 (GeV 2 ).1 < t <.2 (GeV 2 ).2 < t <.4 (GeV 2 ) x Increasing statistics by including all transverse data will allow for an σ L σ T separation Data consistent with theory predictions

29 Transverse spin asymmetry Stay Tuned! Transverse Target Asymmetry for exclusive π + Theoretical prediction Frankfurt et Al., Phys. Rev. D6 (1999), 2 models with different pion form factor Data under analysis! Exclusive π production analysis ongoing information.6 about H only Transverse spin asymmetry.7 no pion-pole contribution t =.1 GeV t =.3 GeV t =.5 GeV 2 Q ~ 2 4 GeV t =.1 GeV t =.3 GeV t =.5 GeV 2 Q ~ 2 4 GeV x_bj 2 x_bj Mankiewicz et. al. Eur. Phys. J. C1 (1999) 2 HERMES

30 December The Noble ABS Target Goodbye, Cruel World! N.C.R. Makins, INT Workshop on Synergy between Lattice and Experiment, Apr 24-25, 26

31 N.C.R. Makins, INT Workshop on Synergy between Lattice and Experiment, Apr 24-25, 26

32 Run 2b: Recoil Detector Installation Iron Shielding Purpose: detect recoiling nucleons or resonances for measurement of hard exclusive processes Cryostat SC Coils SciFi Connector Plate catch decays Δ + pπ pγγ C3 Collimator Si Detector Cooling Si Detector Connectors Hybrid Photon Detector SciFi Detector Silicon Detector Target Cell Flange tracking, in 1 T solenoidal field with de/dx capability N.C.R. Makins, INT Workshop on Synergy between Lattice and Experiment, Apr 24-25, 26

33 rate cosφ A C 2 4 M 2 x [GeV 2 ] present Mx 2 rate Run 1 published Run 1 precision (nearly done) Run 2 projection recoil det Mx M 2 x [GeV 2 ] A B C D -t (GeV 2 ) sinφ A LU Recoil Detector Advantages Exclusivity: current missing-mass resolution Δ contamination t-resolution: greatly improved Statistics: order of magnitude more statistics for ALU and AC (high-density unpol d targets!) A/B C/D E -t (GeV 2 ) N.C.R. Makins, INT Workshop on Synergy between Lattice and Experiment, Apr 24-25, 26

34 Summary 1 Factorization theorem for hard exclusive processes allows GPD s to be probed 2 DVCS probes the GPD s H and E via asymmetries BCA and BSA give access to H A UT allows E to be parametrized, giving access to J u 3 Cross Section for exclusive π + production Comparison with GPD based model Q 2 dependence in agreement with theory 4 A UT for exclusive ρ production gives additional constraints on H and E Last Word: Thanks for Listening!