Single Spin Asymmetry at large x F and k T

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1 1 Single Spin Asymmetry at large x F and k T Paul Hoyer University of Helsinki Workshop on Transverse momentum, spin, and position distributions of partons in hadrons ECT*, June 2007 PH and M. Järvinen, JHEP 02 (2007) 039

2 Question: Does the large AN measured in p p π(xf, kt) + X at high xf and kt arise from multiparton coherence? Consider two distinct asymptotic limits: E704 p p π +X 2 π + π 0 Berger Brodsky kt with xf fixed (Bj limit) 2 (1 xf) kt fixed (BB limit) k > 0.7 GeV π Bj limit: Leading twist dominates. Only hard partons are coherent BB limit: All twists contribute. Coherence between soft and hard partons In the BB limit, soft scattering influences the hard dynamics at leading order in kt. This enables an unsuppressed single spin asymmetry at high kt. Berger Brodsky Paul Hoyer ECT* 13 June 2007 Cf. talk by G. Bunce

3 Hard-Soft Coherence in large x Fock States 3 The (Light-Front) energy of a Fock state with total momentum P is P = i p 2 i + m2 i x i P + Hence contributions to P P + of order Q 2 can arise in two ways: From hard partons, with p 2 Q 2 From soft partons with p 2 m 2 Λ 2 QCD but with low x Λ 2 QCD/Q 2 Both give commensurate, short life-times 1/P i x i = 1 In the limit where a hard parton takes nearly all the hadron momentum: x 1 with (1 x)q 2 Λ 2 QCD fixed the full Fock state interacts coherently.

4 [ Example: Coherent dynamics of DIS in lab frame : 4 γ* q γ (2ν, mx B, 0 ) LI r ~1 fm p + q = zq + q Soft rescattering in target p + q q = (1 z)q + const. The antiquark takes a fraction 1-z 1/Q 2 of the photon energy Soft scattering of the slow antiquark within L I 1/2mx B is coherent with and determines the cross section of the hard γ* scattering process.

5 Example: π N µ + µ - X at high x F 5 In the limit where (1-xF)Q 2 is fixed as Q 2 : Entire pion wf contributes to hard process π N x 1 q 1-x 0 xf 1 Soft scattering of stopped quark in target affects hard process µ + µ - Virtual photon is longitudinally polarized Berger and Brodsky, PRL 42 (1979) 940 The polarization of the virtual photon is revealed by the angular distribution of the muon pair: Paul Hoyer ECT* 13 June 2007

6 dσ/dω µµ 1 + λ cos 2 θ 6 π N µ + µ - X plab = 252 GeV Evidence for virtual photon becoming longitudinally polarized (λ -1) as xf 1 Paul Hoyer ECT* 13 June 2007 J. S. Conway et al, PRD 39 (1989) 92

7 The inclusive - exclusive connection 7 As xb 1, inclusive DIS becomes semi-exclusive, and finally exclusive. This gives insights into the dynamics of inclusive and exclusive processes S. D. Drell and T. M. Yan, PRL 24 (1970) 181 G. B. West, PRL 24 (1970) 1206 γ* γ* γ* Q 2 Q 2 Q 2 xb p X p p p e p e X DIS N* e p e N* xb 1 xb Semi-exclusive, = 1 or Transition FF e p e p Elastic FF Paul Hoyer ECT* 13 June 2007 M 2 N = m 2 N + (1 x B)Q 2 x B A given resonance appears, with increasing Q 2, at fixed Q 2 (1-xB)

8 Jlab Hall C Bloom Gilman duality 8 Q 2 ~ 1.5 GeV 2 F 2 Q Q S. Alekhin, PRD 68 (2003) NNLO Jlab Hall C ξ xb Duality suggests that the photon scatters from the same target Fock states in ep ex (DIS) and ep en* (FF) Bloom and Gilman, PRL 25 (1970) 1140 W. Melnitchouk et al, Phys. Rep. 406 (2005) 127 The formation time of resonances in the final state is long and is incoherent with the hard scattering: Unitarity preserves the cross section Paul Hoyer ECT* 13 June 2007

9 Consequences of Duality 9 γ* Q 2 γ* Q 2 r > 1/Q! p xb r > 1/Q xb X p N* σ q e 2 q e p e X e p e N* In the above interpretation of duality, the virtual photon couples incoherently to single quarks in DIS as well as in exclusive form factors Endpoint contribution: 1-xB 1/Q 2 Protons remain noncompact in wide angle scattering No color transparency for ep ep in nuclear targets

10 A N = dσ dσ dσ + dσ = Single Spin Asymmetry [ ] 2Σ {σ}im M,{σ} M,{σ} [ M,{σ} Σ {σ} 2 ] + M,{σ} 2 10 An SSA (AN 0) requires: A dynamical, helicity-dependent phase Helicity flip In hard perturbative diagrams both features are suppressed Kane, Pumpkin and Repko, PRL 41 (1978) 1689 Hence the observed AN reveals important aspects of the dynamics of scattering at large transverse momentum

11 SSA suppression at high k T : The BHS model 11 The helicity may flip at either of the vertices 1, 2 or 3. If the large kt is generated at the flip vertex, AN mq/kt, where mq is the current quark mass Flip at 1, large kt at 2: Due to incoherence, AN ΛQCD/kT, from trigger bias (Sivers effect) P q 1 k 1 2 k 2 k 3 3 k Flip at 3, large kt at 2: AN mq/ν, anomalous moment of bare quark is not formed (perturbatively) within coherence time. (This might possibly be upset due to QCD vacuum effects, see PH and M. Järvinen, JHEP 10 (2005) 080) Similar arguments for p p π(xf, kt) + X give AN ΛQCD/kT for kt at fixed xf (twist-3 in the Bj limit).

12 p p Λ(x F, k ) +X 12 Lundberg et al., PRD 40 (1989) 3557

13 13

14 2 SSA analysis at fixed k (1-xF) 14 For k at fixed k 2 (1-xF): soft spectator interactions remain coherent with the hard process, enabling unsuppressed spin flip contributions and a helicity dependent phase, as required for AN 0. p x 0 Spin flip x 0 π (xf 1) x 1 k t soft 1 Λ QCD (1 x F )p + Λ QCD p Paul Hoyer ECT* 13 June 2007 X p+ k 2 1 k p + k t hard

15 A Model Demonstration 15 On-shell intermediate state p ± Proton helicities (1-y)p + + ± yp + Large transverse momentum ~ (1-x F )p + ~(1-y)p + k ~ k Longitudinal momentum transfer ± + + l ± l 1 l 2 π Soft helicity flip PH and M. Järvinen, JHEP 0702 (2007) 039

16 Phase difference between flip and non-flip amplitudes 16 A non-vanishing SSA requires a phase difference exp(iθ) between the helicity flip and non-flip amplitudes. In the above Feynman diagram, after some simplifying assumptions, AB tan θ =, which vanishes if either A/B or B/A 0 and where A + 2B A = l2 2 + M 2 (1 w)(1 x) + l2 + M 2 1 z B = k 2 This verifies that AN 0 only in the BB limit: k 2 (1 x) fixed

17 Conclusions on SSA 17 The data suggest that the SSA dynamics of p p π +X and pp Λ +X is distinct from that of ep π +X (SIDIS): A leading twist effect requires AN 1/k AN in p p at high xf is 10 times larger than AN in SIDIS These features suggest a limit where k 2 (1-xF) is fixed as k The SSA in p p is an edge-of-phase-space effect Cf. talk by G. Bunce Via Bloom-Gilman duality, this dynamics is relevant also for hard exclusive processes

18 Quark helicity flip in γp ρ Y 18 Partonic subprocess in perturbative QCD: n = ±.02 ±.12 Expect: dσ dt 1 t 3 r %p &>!Y! 0 ZEUS 1995 ZEUS 0 4 r 0 0 # T($! = 0)! 0 ZEUS (Prel.) 1-d " ZEUS (Prel.) 1-d 2 and λ ρ = 0 but find λ ρ = ±1 (SCHC) Paul Hoyer ECT* 13 June t (GeV 2 )

19 Size of Perturbative Subprocesses at large t The effective size of the perturbative photoproduction amplitude for γ + u π + d at large momentum transfer -t is measured by giving the photon a small virtuality Q γ ( ) u q zq' q x s p t zq' (1 z)q' d π + The amplitude is very sensitive to Q 2, even for ϕ π (x) = x(1-x) dσ/dt 1 γ 2 (Q ) + e > γ + e The singular behavior is due to the endpoints. More generally, quark helicity flip and rescattering enhance endpoint contributions Paul Hoyer ECT* 13 June γ (Q ) + u > π + d Q /-t PH, J. T. Lenaghan, K. Tuominen and C. Vogt, PRD 70 (2004) T +

20 Perspective: Q 2 (1-x) fixed? 20 Bloom-Gilman duality, FF Phenomenology, SSA in p p π +X,... Suggest that endpoints (x 0,1) may be relevant for physical observables The limit where Q 2 (1-x) is held fixed as Q 2 needs more attention: What can be said about soft/hard factorization in this limit? Q 2 Q 2 π x 1 π π x 1 π Spectators and struck quark have similar p. Soft spectator interactions cannot be ignored Form factors cannot be factorized into a product of hadron wave functions