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

OutlineOutline

• Exclusive processes: physics motivation

• Cross section parameterization

• Monte Carlo simulations: input for detector design

• L/T separations and the pion form factor

Exclusive Processes: Physics Exclusive Processes: Physics motivationmotivation

• Experimental challenge– Small cross sections, σ(meson+N) ~1/Q8

– Detection of the recoil nucleon– Differential measurements in x, Q2, t

[cf. GPD White Paper for NSAC Long-Range Plan, presented at Rutgers Town Meeting Jan-07]

• Study of high-Q2 exclusive processes essential part of physics program for ep collider

– Reaction mechanism: QCD factorization– Information about GPDs, meson wave functions

(baryon/meson structure)

pγe'pe

Nmesone'

222 GeV1Q,W 2GeV1|| t

Exclusive Processes: Collider Exclusive Processes: Collider EnergiesEnergies

Exclusive Processes: EIC Potential Exclusive Processes: EIC Potential and Simulationsand Simulations

11H(e,e’H(e,e’ππ++)n at EIC: Cross Section )n at EIC: Cross Section ParameterizationParameterization

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

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

1H(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+ n

electrons

Ee=5 GeVEp=50 GeV

π+

Q2>1 GeV2

1H(e,e’π+)n – Scattered Electron

• Most electrons scatter at angles <25° • BUT access to the high Q2 region of interest for GPD studies requires

larger electron angles

Electron Lab Angle (deg)

Q2

(GeV

2)

Minimum angle for Q2=40 GeV2 is ~70°

P (G

eV)

Electron Lab Angle (deg)

Q2=40 GeV2 can be reached for electron momenta < 7 GeV

Ee=5 GeVEp=50 GeV

1H(e,e’π+)n – Scattered Neutron

Neutron Lab Angle (deg)-t

(GeV

2)• 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 (G

eV)

Neutron Lab Angle (deg)

1H(e,e’π+)n – Scattered Pion

Pion Lab Angle (deg) Pion Lab Angle (deg)P

(GeV

)

Q2

(GeV

2)

• The pion cross section is peaked in the direction of the proton• At larger Q2 pion angles and momenta are smaller

• within the capability of the detector (pπ and Q2 are uncorrelated)• provide good missing mass resolution

Ee=5 GeVEp=50 GeV

Event Topologies

Q2, x

t, φ

e e’

p n

π

• The most straightforward way to assure exclusivity of the 1H(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

Rates and coverage in different Event Topologies

-t (GeV2)

Γ dσ

/dt (

ub/G

eV2)

-t (GeV2)

Γ dσ

/dt (

ub/G

eV2)

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% (pπ<5 GeV)

Ee=5 GeVEp=50 GeV

0.01<x<0.02 0.02<x<0.05 0.05<x<0.1

10<Q2<1515<Q2<2035<Q2<40

10<Q2<1515<Q2<2035<Q2<40

0.05<x<0.1

Assume: 100 days, Luminosity=10E34

• 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

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<Q2<1515<Q2<2035<Q2<40

0.01<x<0.02 0.02<x<0.05 0.05<x<0.1

Assume: 100 days, Luminosity=10E34

Statistical uncertainty in the measurement

Luminosity= 1031

Γ dσ

/dt (

ub/G

eV2)

• High luminosity is essential to achieve the experimental goals

Ee=5 GeVEp=50 GeV Assume: 100 days

1H(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° protons

Photon from π° decay

π°

2γ opening angle

Q2>1 GeV2

Ee=5 GeVEp=50 GeV t<1GeV2

1H(e,e’π°)p – π° Decay PhotonsEe=5 GeVEp=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

electrons K Λ

protonπ-

1H(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

Rate estimate for KΛ

• Using an empirical fit to kaon electroproduction data from DESY and JLab

10<Q2<1515<Q2<20

35<Q2<40

0.01<x<0.02 0.02<x<0.05 0.05<x<0.1

1H(e,e’π+)n L/T Separation Experiments

1. Pion Form Factor, Fπ(Q2)– 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 Q2 at fixed xB to test Hard QCD scaling predictions

σL~1/Q6, σT~1/Q8

1. Scan σL vs xB at fixed Q2 to distinguish pole and axial contributions in GPD framework.

E~

To access higher Q2, one must employ the p(e,e’+)n reaction.

• the t-channel process dominates L at small –t<0.02 GeV2.

At low Q2<0.3 GeV2, the + form factor can be measuredexactly 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.

πNNg

),()()(

2222

2

tQFtgmttQ

dtd

NNL

• Cross Section Extraction– Determine σT+ ε σL for high and low ε– Isolate σL, by varying photon

polarization, ε

dφdtdσεdφdt

σ2d T dφdtdσL

22

-121

-1εε

dσL )ε(R)ε(Rdσ

21

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

Ee=5 GeVEp=2 GeV

Ee=3 GeVEp=5 GeV

)( lossenergy fractional the where

)1(1)1(2

2

2

2Ntot Msx

Qyyy

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

Recoil Polarization Technique

1

ε1hP

ε1

σσR

2z

T

L

• In parallel kinematics can relate σL/σT to recoil polarization observables

εσσR10

L

• From R and the simultaneous measurement of σ0 one can obtain σL

dRσdσ 0L

• Requires only one epsilon setting• Polarized proton beam• Additional model assumptions needed in general if the reaction is not elastic

27

Kinematic Reach (Pion Form Factor)

Assumptions:• High High εε:: 5(e-) on 50(p).• Low Low εε proton energies as

noted.• Δε~0.22.• Scattered electron detection

over 4π.• Recoil neutrons detected at Recoil neutrons detected at

θθ<0.35<0.35oo with high efficiency. with high efficiency.• Statistical unc: ΔσL/σL~5%• Systematic unc: 6%/Δε.• Approximately one year at Approximately one year at

LL=10=103434..

Excellent potential to study the QCD transition nearly over the whole range from the strong QCDstrong QCD regime to the hard QCDhard QCD regime.

Preliminary

Projected uncertainties for Q-n scaling

• Transition region 5-15 GeV2 well mapped out even with narrow fixed x and t • careful with detector requirements

EIC: Ee=5 GeV, Ep=50 GeV

Preliminary

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

Summary

• High Q2 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,Q2):• 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

Other

1H(e,e’π+)n Momentum and Angular Distributions

• Kinematically, electrons and pions are separated

Ee/Ep

(GeV)pelectron

(GeV)pπ

(GeV)θelectron

(deg)θπ

(deg)

3/30 1-4 1-18 18-45 140-175

5/50 2-6 1-30 11-30 150-177

10/250 8-11 1-145 5-15 173-179

• The neutron is the highest energy particle and is emitted in the direction of the proton beam

E(GeV)

pneutron (GeV)

Θneutron

(deg)

3/30 12-30 >177.8

5 /50 20-50 >178.6

10/250 95-250 >179.7

neutrons

π+ n

electrons

Ee=5 GeVEp=50 GeV

π+

Q2>1 GeV2

1H(e,e’π°)p – π° Decay Photons

π° Lab Angle (deg)O

peni

ng A

ngle

(de

g)

Ope

ning

Ang

le (

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 Q2

Systematic uncertainty on the π° rate estimate

Ee=5 GeVEp=50 GeV

• Data rates obtained using two different approaches are in reasonable agreement:

• Ch. Weiss: σT from Regge model

• T. Horn: σT from π+ empirical parameterization

15<Q2<2010<Q2<15

Missing Mass Resolution

Assume dp/p=0.5%

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 θπq>0, -t up to 0.2Q2.

E~

12 2

0 0

L L Ld d dA d d dd d d

where dσ is the exclusive p(e,e’π+)n cross section using longitudinal photonsβ is the angle between the proton polarization vector and the reaction plane.

A┴π vs xB

-LO-Q2=4-Q2=10

A.V

.Bel

itsky

, hep

-ph/

0307

256

QCD Scaling TestsQCD 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 Q2 scaling regime (partonic picture) has been reached

• One of the most stringent tests of factorization is the Q2 dependence of the π electroproduction cross section– σL scales to leading order as Q-6

– σT scales as Q-8

– As Q2 becomes large: σL >> σT

Factorization

H H~ E E~

• Factorization theorems for meson electroproduction have been proven rigorously only for longitudinal photons [Collins, Frankfurt, Strikman, 1997]

Q2 ?

Low ε data from Jlab12?

• L/T separations at EIC will benefit from Jlab12 measurements

JLAB: Ee=12 EIC: Ee=5 GeV, Ep=50 GeV

ε=0.99

ε=0.3-0.7