1. Exclusive Meson Production with EIC Tanja Horn (JLab) Antje Bruell (JLab) Garth Huber (University of Regina) Christian Weiss (JLab) EIC Collaboration Meeting, Hampton University, 19-23 May 2008

2. Outline Exclusive processes: physics motivation Cross section parameterization Monte Carlo simulations: input for detector design L/T separations and the pion form factor

3. Exclusive Processes: Physics motivation Experimental challenge –Small cross sections, σ(meson+N) ~1/Q 8 –Detection of the recoil nucleon –Differential measurements in x, Q 2, t [cf. GPD White Paper for NSAC Long-Range Plan, presented at Rutgers Town Meeting Jan-07] Study of high-Q 2 exclusive processes essential part of physics program for ep collider –Reaction mechanism: QCD factorization –Information about GPDs, meson wave functions (baryon/meson structure)

4. Exclusive Processes: Collider Energies

5. Exclusive Processes: EIC Potential and Simulations

6. 1 H(e,e’ π + )n at EIC: Cross Section Parameterization

7. MC Simulations Rate predictions including simulations of the detector restrictions Input for detector design Momentum and angular distributions for various particles Case studies: H(e,e’π +)n H(e,e’π°)p H(e,e’K) Λ

8. Exclusive MC Generator Exclusive EIC Monte Carlo: Based on HERMES GMC New event generator using standard cernlib functions Includes cross section model by Ch. Weiss model for π + production Can be easily extended to other channels, e.g. π°, KΛ etc. MC agrees with fixed target data from Jlab

9. 1 H(e,e’ π + )n Momentum and Angular Distributions Kinematically, electrons and pions are separated The neutron is the highest energy particle and is emitted in the direction of the proton beam neutrons π+π+n electrons E e =5 GeVE p =50 GeV π+π+ Q 2 >1 GeV 2

10. 1 H(e,e’ π + )n – Scattered Electron Most electrons scatter at angles <25° BUT access to the high Q 2 region of interest for GPD studies requires larger electron angles Electron Lab Angle (deg) Q 2 (GeV2) Minimum angle for Q 2 =40 GeV 2 is ~70° P (GeV) Electron Lab Angle (deg) Q 2 =40 GeV 2 can be reached for electron momenta < 7 GeV E e =5 GeVE p =50 GeV

11. 1 H(e,e’ π + )n – Scattered Neutron Neutron Lab Angle (deg) -t (GeV2) Low –t neutrons are emitted at very small angles with respect to the beam line, outside the main detector acceptance A separate detector placed tangent to the proton beam line away from the intersection region is required P (GeV) Neutron Lab Angle (deg)

12. 1 H(e,e’ π + )n – Scattered Pion Pion Lab Angle (deg) P (GeV)Q 2 (GeV2) The pion cross section is peaked in the direction of the proton At larger Q 2 pion angles and momenta are smaller within the capability of the detector (p π and Q 2 are uncorrelated) provide good missing mass resolution E e =5 GeVE p =50 GeV

13. Event Topologies Q 2, x t, φ e e’ p n π The most straightforward way to assure exclusivity of the 1 H(e,e’ π + )n reaction is by detecting the recoil neutron The neutron acceptance is limited to <0.27° by a magnet aperture close to the interaction point Alternatively, the neutron can be reconstructed from missing momentum Missing mass resolution has to be good enough to exclude additional pions

14. Rates and coverage in different Event Topologies -t (GeV2) Γ dσ/dt (ub/GeV2) -t (GeV2) Γ dσ/dt (ub/GeV2) Detect the neutron Missing mass reconstruction Neutron acceptance limits the t-coverage The missing mass method gives full t-coverage for x<0.2 Assume dp/p=1% (p π <5 GeV) E e =5 GeVE p =50 GeV 0.01<x<0.02 0.02<x<0.050.05<x<0.1 10<Q 2 <15 15<Q 2 <20 35<Q 2 <40 10<Q 2 <15 15<Q 2 <20 35<Q 2 <40 0.05<x<0.1 Assume: 100 days, Luminosity=10E34

15. At higher energies, the missing mass resolution deteriorates, so need to detect the neutron At lower energies, the missing mass reconstruction works well, but neutron detection is more difficult With Ee=5 GeV and Ep= 50 GeV can ensure exclusivity over the full region in (x,-t, Q2) using a combination of the two methods: Overlap region between the two methods allows for cross checks

16. Systematic uncertainty on the rate estimate Data rates obtained using two different approaches are in reasonable agreement: Ch. Weiss: Regge model T. Horn: π + empirical parameterization 10<Q 2 <15 15<Q 2 <20 35<Q 2 <40 0.01<x<0.02 0.02<x<0.050.05<x<0.1 Assume: 100 days, Luminosity=10E34

17. Statistical uncertainty in the measurement Luminosity= 10 31 Γ dσ/dt (ub/GeV2) High luminosity is essential to achieve the experimental goals E e =5 GeVE p =50 GeVAssume: 100 days

18. 1 H(e,e’ π ° )p Momentum and Angular Distributions Similar to π +, but additional complication due to photons from π° decay π° decay photon opening angle places a constraint on the calorimetry electrons π°π°protons Photon from π° decay π°π° 2γ opening angle Q 2 >1 GeV 2 E e =5 GeVE p =50 GeVt<1GeV 2

19. 1 H(e,e’ π °)p – π° Decay Photons E e =5 GeVE p =50 GeV Opening angle is small and requires fine calorimeter granularity JLab/BigCal: 38x38mm, H1 forward calorimeter: 35x35mm High energy photons at large angles can be detected At high momentum, charged particles are difficult to measure 1° → 35mm / 2m

20. electrons K Λ proton π-π- 1 H(e,e’ K )Λ Momentum and Angle Distributions Kinematics overall similar to the pion case Some π - from Λ decay might be detected in an outbending toroidal field Λ Assume: 100 days, Luminosity=10E34

21. Rate estimate for KΛ Using an empirical fit to kaon electroproduction data from DESY and JLab 10<Q 2 <15 15<Q 2 <20 35<Q 2 <40 0.01<x<0.020.02<x<0.050.05<x<0.1

22. 1 H(e,e’π+)n L/T Separation Experiments 1.Pion Form Factor, F π (Q 2 ) –Excellent opportunity for studying the QCD transition from effective degrees of freedom to quarks and gluons. i.e. from the strong QCD regime to the hard QCD regime. 2. Longitudinal Photon, Transverse Nucleon Single-Spin Asymmetry, A ┴ π Especially sensitive to spin-flip GPD which can only be probed via hard exclusive pseudoscalar meson production. 3. QCD and GPD scaling tests –Scan vs Q 2 at fixed x B to test Hard QCD scaling predictions σ L ~1/Q 6, σ T ~1/Q 8 –Scan σ L vs x B at fixed Q 2 to distinguish pole and axial contributions in GPD framework.

23. To access higher Q 2, one must employ the p(e,e’  + )n reaction. the t-channel process dominates  L at small –t<0.02 GeV 2. At low Q 2 <0.3 GeV 2, the  + form factor can be measured exactly using high energy  + scattering from atomic electrons.  F  determined by the pion charge radius 0.657±0.012 fm. Determination of F  via Pion Electroproduction In the actual analysis, a model incorporating the  + production mechanism and the `spectator’ nucleon is used to extract F  from  L.

24. Cross Section Extraction –Determine σ T + ε σ L for high and low ε –Isolate σ L, by varying photon polarization, ε L/T separations in exclusive π + production ε=0.64 ε=0.40 Requires special low energies for at least one ε point and cannot be done with the standard EIC L/T separations require sufficiently large Δε to avoid magnification of the systematic uncertainty in the separation E e =5 GeV E p =2 GeV E e =3 GeV E p =5 GeV

25. Different accelerator mode The ability to use 5-15 GeV protons will allow many high priority L/T- separation experiments which are otherwise not possible. The proton accelerator needs a mode where the injector is not run to its full energy. –This beam is injected into the main proton accelerator, which is used as a storage ring. The costs to implement this low energy mode will be reduced if this flexibility is included at the planning stage. –Achieving the high luminosity required for this experiment may not be possible

26. Recoil Polarization Technique In parallel kinematics can relate σ L /σ T to recoil polarization observables From R and the simultaneous measurement of σ 0 one can obtain σ L Requires only one epsilon setting Polarized proton beam Additional model assumptions needed in general if the reaction is not elastic

27. 27 Kinematic Reach (Pion Form Factor) Assumptions: High ε:High ε: 5(e - ) on 50(p). Low εLow ε proton energies as noted. Δ ε~0.22. Scattered electron detection over 4 π. Recoil neutrons detected at θ<0.35 o with high efficiency.Recoil neutrons detected at θ<0.35 o with high efficiency. Statistical unc: Δσ L /σ L ~5% Systematic unc: 6%/Δε. Approximately one year at L=10 34.Approximately one year at L=10 34. strong QCDhard QCD Excellent potential to study the QCD transition nearly over the whole range from the strong QCD regime to the hard QCD regime. Preliminary

28. Projected uncertainties for Q -n scaling Transition region 5-15 GeV 2 well mapped out even with narrow fixed x and t careful with detector requirements EIC: Ee=5 GeV, Ep=50 GeV Preliminary

29. Outlook Extend studies to vector mesons Resolution studies Test additional requirements from e.g. π˚ and KΛ At high energies, calorimeter granularity needs to be better than 35x35mm Requirements on magnets, e.g. toroidal fields for KL

30. Summary High Q 2 studies of exclusive processes are an essential part of the physics program for an ep collider For beam energy 5 on 50 two methods are available to ensure exclusivity over the full range in (x,-t,Q 2 ): At high energies, need a separate detector tangent to proton direction to detect the exclusive final state – limited acceptance At low energies, missing mass reconstruction works well Overlap in certain kinematic regions allows for cross checks between the two methods High luminosity (10E34) is essential for these studies

31. Other

32. 1 H(e,e’ π + )n Momentum and Angular Distributions Kinematically, electrons and pions are separated E e /E p (GeV) p electron (GeV) p π (GeV) θ electron (deg) θ π (deg) 3/301-41-1818-45140-175 5/502-61-3011-30150-177 10/2508-111-1455-15173-179 The neutron is the highest energy particle and is emitted in the direction of the proton beam E (GeV) p neutron (GeV) Θ neutron (deg) 3/3012-30>177.8 5 /5020-50>178.6 10/25095-250>179.7 neutrons π+π+n electrons E e =5 GeVE p =50 GeV π+π+ Q 2 >1 GeV 2

33. 1 H(e,e’ π °)p – π° Decay Photons π° Lab Angle (deg) Opening Angle (deg) 6 on 15 3 on 30 5 on 50 10 on 250 Separating the π° decay photons is getting more difficult as the energy increases, but recall that pion momenta are low at high Q 2

34. Systematic uncertainty on the π° rate estimate E e =5 GeVE p =50 GeV Data rates obtained using two different approaches are in reasonable agreement: Ch. Weiss: σ T from Regge model T. Horn: σ T from π + empirical parameterization 15<Q 2 <20 10<Q 2 <15

35. Missing Mass Resolution Assume dp/p=0.5%

36. 36 Longitudinal Photon, Transverse Nucleon Single-Spin Asymmetry, A ┴ π Measure A ┴ π to access the spin-flip GPD Requires a transversely polarized proton beam, and an L/T-separation. The asymmetry vanishes in parallel kinematics, so the π + must be detected at θ π q >0, -t up to 0.2Q 2. where dσ is the exclusive p(e,e’ π + )n cross section using longitudinal photons β is the angle between the proton polarization vector and the reaction plane. A ┴ π vs x B -LO -Q 2 =4 -Q 2 =10 A.V.Belitsky, hep-ph/0307256

37. QCD Scaling Tests To access physics contained in GPDs, one is limited to the kinematic regime where hard-soft factorization applies –No single criterion for the applicability, but tests of necessary conditions can provide evidence that the Q 2 scaling regime (partonic picture) has been reached One of the most stringent tests of factorization is the Q 2 dependence of the π electroproduction cross section –σ L scales to leading order as Q -6 –σ T scales as Q -8 –As Q 2 becomes large: σ L >> σ T Factorization Factorization theorems for meson electroproduction have been proven rigorously only for longitudinal photons [Collins, Frankfurt, Strikman, 1997] Q 2 ?

38. Low ε data from Jlab12? L/T separations at EIC will benefit from Jlab12 measurements JLAB: E e =12 EIC: E e =5 GeV, E p =50 GeV ε=0.99 ε=0.3-0.7