1. L-T Separated Kaon production Cross Sections from 5-11 GeV
P. Bosted, S. Covrig, H. Fenker, R. Ent, D. Gaskell, T. Horn*, M. Jones,
J. LeRose, D. Mack, G.R. Smith, S. Wood, G. Huber, A. Semenov,
Z. Papandreou, W. Boeglin, P. Markowitz, B. Raue, J. Reinhold, F. Klein,
P. Nadel-Turonski, A. Asaturyan, A. Mkrtchyan, H. Mkrtchyan, V. Tadevosyan, D. Dutta, M. Kohl, P. Monaghan, L. Tang, D. Hornidge, A. Sarty,
E. Beise, G. Niculescu, I. Niculescu, K. Aniol, E. Brash, V. Punjabi,
C. Perdrisat, Y. Ilieva, F. Cusanno, F. Garibaldi, M. Iodice, S. Marrone,
P. King, J. Roche
JLab, Regina, FIU, CUA, Yerevan, Mississippi, Hampton, Mount Allison, Saint Mary’s, UMd, JMU, California State, CNU, Norfolk, W&M, South Carolina, INF, Ohio
Hall C User’s meeting
30 January 2009

2. Meson Reaction Dynamics
N(p) W t Q2
N(p’)
π, K, etc.
Meson production can be described by the t-channel exchange meson pole term in the limit of small –t and large W
Pole term is dominated by longitudinally polarized photons
Meson form factor describes the spatial distribution of the nucleon
t-channel process
π, K, etc.
hard
At sufficiently high Q2, the process should be understandable in terms of the “handbag” diagram
The non-perturbative (soft) physics is represented by the GPDs
Shown to factorize from QCD perturbative processes for longitudinal photons [Collins, Frankfurt, Strikman, 1997]
Picture behind the mechanism
pointlike
handbag

3. Form Factors and GPDs - Fπ,K
Form factors and GPDs are essential to understand the structure of nucleons, which make up nucleons and mesons (q-q systems) -
Fπ,K
π, K, etc φ
But measurements of form factors and GPDs have certain prerequisites:
Before we can start looking at form factors, we must make sure that σL is dominated by the meson pole term at low -t
Before we can learn about GPDs, we must demonstrate that factorization applies
π,K
π, K, etc. φ
A comparison of pion and kaon production data may shed further light on the reaction mechanism, and intriguing 6 GeV pion results
Why we need to understand the mechanism to measure things
Hard Scattering
GPD

4. Context
Understanding of the kaon production mechanism is important in our study of hadron structure
GPD studies require evidence of soft-hard factorization
Flavor degrees of freedom provide important information for QCD model building and understanding of basic coupling constants
K+Λ and K+Σ° have been relatively unexplored because of lack of the necessary experimental facilities
There are practically no precision L-T separated data for exclusive K+ production from the proton above the resonance region
Limited knowledge of L/T ratio at higher energies limits the interpretability of unseparated cross sections in kaon production
Relative σL and σT contributions are also needed for GPD extractions since they rely on the dominance of σL

5. Transverse Contributions
Hall C 6 GeV data (W=1.84 GeV) σL σT
0.5<Q2<2.0 GeV2
In the resonance region at Q2=2.0 GeV2 σT is not small
In pion production, σT is also much larger than predicted by the VGL/Regge model [PRL97: (2006)]
Why is σT so large? Difficult to draw a conclusion from current data
Limited W and Q2 range
Significant uncertainty due to scaling in xB and –t
K+Λ
K+Σ˚
VGL/Regge
K+Λ
K+Σ˚
High quality σL and σT data for both kaon and pion would provide important information for understanding the meson reaction mechanism

6. R=σL/σT: Kaon form factor prerequisite
Meson form factor extraction requires a good reaction model
Need high quality data to develop these models
Current knowledge of σL and σT above the resonance region is insufficient
Role of the t-channel kaon exchange in amplitude unclear
Not clear how to understand reaction mechanism through current models
VGL/Regge (Λ2K=0.68 GeV2)
Nucleon resonance data scaled to W=1.84 GeV
L/T separations above the resonance region are essential for building reliable models, which are also needed for form factor extractions

7. High Q2: Q-n scaling of σL and σT
T. Horn et al., Phys. Rev. C78, (2008)
Hall C p+ production data at 6 GeV
Q2= GeV2
Q2= GeV2 σL σT
To access physics contained in GPDs, one is limited to the kinematic regime where hard-soft factorization applies
A test is the Q2 dependence of the cross section:
σL ~ Q-6 to leading order
σT ~Q-8
As Q2 gets large: σL >> σT
The QCD scaling prediction is reasonably consistent with recent JLab π+ σL data, BUT σT does not follow the scaling expectation
Kaon production data would allow for a quasi model-independent comparison that is more robust than calculations based on QCD factorization and present GPD models

8. Bonus: Fπ,K - a factorization puzzle?
T. Horn et al., Phys. Rev. Lett. 97 (2006)
T. Horn et al., arXiv: (2007).
The Q2 dependence of Fπ is also consistent with hard-soft factorization prediction (Q-2) at values Q2>1 GeV2
BUT the observed magnitude of Fπ is larger than the hard QCD prediction
Could be due to QCD factorization not being applicable in this regime
Or insufficient knowledge about additional soft contributions from the meson wave function
A.P. Bakulev et al, Phys. Rev. D70 (2004)]
Comparing the observed Q2 dependence of σL,T and FF magnitude with kaon production would allow for better understanding of the onset of factorization

9. Motivation Summary
The charged kaon L/T cross section is of significant interest to the study of GPDs and form factors at 12 GeV
Can only learn about GPDs if soft-hard factorization applies
If transverse contributions are large, the accessible phase space may be limited
If σL not dominated by the K+ pole term at low -t, we cannot extract the form factor from the data and interpretation of unseparated data questionable
Our theoretical understanding of hard exclusive reactions will benefit from L/T separated kaon data over a large kinematic range
Constraints for QCD model building using both pion and kaon data
Understanding of basic coupling constants (Σ°/Λ ratio)
Quasi model-independent comparison of pion and kaon data would allow a better understanding of the onset of factorization

10. Experiment Overview
Measure the separated cross sections at varying –t and xB
If K+ pole dominates σL allows for extraction of the kaon ff (W>2.5 GeV)
Measure separated cross sections for the p(e,e’K+)Λ(Σ°) reaction at two fixed values of –t and xB
Q2 coverage is a factor of 2-3 larger compared to 6 GeV at much smaller –t
Facilitates tests of Q2 dependence even if L/T ratio less favorable than predicted x Q2
(GeV2) W
(GeV) -t
(GeV/c)2
0.25
0.2
0.40
0.5
Q2=3.0 GeV2 was optimized to be used for both t-channel and Q-n scaling tests

11. Cross Section Separation
The virtual photon cross section can be written in terms of contributions from transversely and longitudinally polarized photons.
Separate σL, σT, σLT, and σTT by simultaneous fit using measured azimuthal angle (φK) and knowledge of photon polarization (ε)

12. Separation in a Multi-Dimensional Phase Space
Low ε
High ε
Cuts are placed on the data to equalize the Q2-W range measured at the different ε-settings
Multiple SHMS settings (±3° left and right of the q vector) are used to obtain good φ coverage over a range of –t
Measuring 0<φ<2π allows to determine L, T, LT and TT
SHMS+3°
SHMS-3°
Radial coordinate (-t),
Azimuthal coordinate (φ)

13. Kaon PID
π+/K+ separation provided by heavy gas Cerenkov for pSHMS>3.4 GeV/c
For reliable K+/p separation above 3 GeV/c an aerogel Cerenkov is essential
Provision has been made in the SHMS detector stack for two threshold aerogel detectors
Heavy Gas Cherenkov and 60 cm of empty space
TOF
Momentum (GeV/c)
π/K Discrimination power
Kaon 12 GeV Kinematics
Heavy Gas Cerenkov
Four sets of aerogel would provide reliable K+/p separation over the full momentum range ( GeV/c)
Alternate PID methods (such as RICH) are also possible

14. Expected Missing Mass Resolution
Missing mass resolution (~30 MeV) is clearly sufficient to separate Λ and Σ° final states
Acceptance allows for simultaneous studies of both Λ and Σ° channels
Total effect of the Λ tail and possible collimator punch-through to K+Σ° projected to be <1/10 of the size of the tail
e+p→e’+K+Λ(Σ°) Λ
SHMS+HMS Σ°
Simulation at Q2=2.0 GeV2 , W=3.0 and high ε

15. Projections of R=σL/σT
VGL/Regge calculation
Empirical kaon parameterization based on Hall C data was used in rate estimates
Conservative assumptions on the evolution of L/T ratio
Projected Δ(L/T)=28-60% (10-33% using VGL/Regge) for typical kinematics
PR may indicate larger values of R, with associated smaller uncertainties
Reaching Q2=8 GeV2 may ultimately be possible
Hall C parameterization
VGL/Regge
Fπ param

16. Projected Uncertainties for σL and σT
High quality kaon L/T separation above the resonance region
Projected uncertainties for σL and σT use the L/T ratio from Hall C parameterization
PR :
Precision data for W > 2.5 GeV

17. Projected Uncertainties for the Kaon FF
If the K+ pole dominates low -t σL, we would for the first time extract FK above the resonance region (W>2.5 GeV)
Projected uncertainties for σL use the L/T ratio from Hall C parameterization

18. Projected Uncertainties for Q-n scaling
p(e,e’K+)Λ
xB=0.25
QCD scaling predicts σL~Q-6 and σT~Q-8
Projected uncertainties use R from the Hall C parameterization
1/Q4
1/Q6 x Q2
(GeV2) W
(GeV) -t
(GeV/c)2
0.25
0.2
0.40
0.5
Fit: 1/Qn
1/Q8
Is onset of scaling different for kaon than pion?
Kaons and pions together provide quasi model-independent study

19. PR Summary
L/T separated K+ cross sections will be essential for our understanding of the reaction mechanism at 12 GeV
If transverse contributions are found to be large, the accessible phase space for GPD studies may be limited
Basic coupling constants in kaon production (Σ°/Λ ratio)
If t-channel exchange dominates σL, we can perform the first reliable extraction of the kaon form factor above the resonance region
L/T separated K+ data over a wide kinematic range will have a significant impact on our understanding of hard exclusive reactions
Constraints on QCD model building using both pion and kaon data
Quasi model-independent comparison of kaon and pion data would allow better understanding of the onset of factorization
Request 47 days to provide first precision L/T separated kaon production data above the resonance region. Excellent candidate for early running.

20. Backup material

21. PR12-09-011 Beam Time Total 1123.6 (46.8 days) Q2 (GeV2) xB LH2 (hrs)
Dummy
Overhead (hrs)
Total (hrs)
0.40
0.072
189.4
12.9 8
210.3
Subtotal low Q2
210.3 (18.7%)
1.25
0.122
29.5
2.1
39.6
2.00
0.182
113.4
7.9 12
133.3
Subtotal react mech
172.9 (15.4% )
1.70
0.25
39.4
2.8
50.2
3.00
159.3
11.2
178.5
3.50
103.5
0.7
112.2
19.2
1.3
28.5
4.40
62.6
4.4
75.0
5.50
179.5
12.5
200.0
Subtotal Q-n scaling
644.4 (57.3%)
Subtotal LH2/K+
895.8
55.8 76
1027.6
Calibrations
96.0 (8.5%)
Total
(46.8 days)

22. Systematic Uncertainties
Source
pt-to-pt
(%)
t-correlated
Scale earlier (%)
Scale later (%)
Acceptance
0.4
2.0
1.0
PID
0.5
Coincidence Blocking
0.2
Tracking Efficiency
0.1
1.5
Charge
Target Thickness
0.8
Kinematics
Kaon Absorption
Kaon Decay
3.0
Radiative Corrections
Monte Carlo Model
Total
0.6
4.7
4.2

23. Overlap with pion data
No significant improvement in statistics through overlap with the approved p(e,e’π+)n experiments
Covers only a small region at very high –t, which is not interesting for studies of form factors or GPDs
Most events are off the focal plane
exclusive K+ peak lies at -5.5%<δSHMS<-2%
Missing Mass tail cut off by SHMS acceptance
Would require that aerogels installed during pion experiments as well
Proposed kaon experiment
Approved pion experiments x Q2
(GeV2) W
(GeV) -t
(GeV/c)2
0.25
0.2
0.40
0.5 x Q2
(GeV2) W
(GeV) -t
(GeV/c)2
0.16
1.6
3.0
0.03
0.21
2.45
3.2
0.05
0.31
2.73
2.6
0.12
4.0
3.1

24. Transverse Contributions in Pion production
VGL σL
VGL σT
In pion production, magnitude of σT has been controversial for a long time
VGL/Regge model systematically underestimates σT, for which it seems to have limited predictive power
T. Horn et al., Phys. Rev. Lett. 97, (2006)

25. Bonus: Interference Terms
K+Λ(Σ°) as calculated in VGL/Regge model
Q2=0.4 GeV2
In the hard scattering limit, these terms are expected to scale:
σLT ~ Q-7
σTT ~Q-8
Additional information about the reaction mechanism may be obtained for free if one performs a full cross section separation
Q2=3.5 GeV2

26. Significance of multiple epsilon points
Additional epsilon settings require additional beam time
Resulting benefit in systematic uncertainty must be weighted against the increased statistical uncertainty