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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,

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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

meson reaction dynamics
Meson Reaction Dynamics



  • 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


π, K, etc.





t-channel process

  • 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]

π, K, etc.




form factors and gpds
Form Factors and GPDs
  • Form factors and GPDs are essential to understand the structure of nucleons, which make up nucleons and mesons (q-q systems)


π, K, etc

  • 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, etc.


  • A comparison of pion and kaon production data may shed further light on the reaction mechanism, and intriguing 6 GeV pion results

Hard Scattering


  • 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
transverse contributions
Transverse Contributions

Hall C 6 GeV data (W=1.84 GeV)

  • In the resonance region at Q2=2.0 GeV2σT is not small
  • In pion production, σT is also much larger than predicted by the VGL/Regge model [PRL97:192001 (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




0.5<Q2<2.0 GeV2





High quality σL and σT data for both kaon and pion would provide important information for understanding the meson reaction mechanism

r l t kaon form factor prerequisite
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 σTabove 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

high q 2 q n scaling of l and t
High Q2: Q-n scaling of σL and σT

Hall C p+ production data at 6 GeV

  • The QCD scaling prediction is reasonably consistent with recent JLab π+σL data, BUTσT does not follow the scaling expectation
  • To access physics contained in GPDs, one is limited to the kinematic regime where hard-soft factorization applies

Q2=2.7-3.9 GeV2

Q2=1.4-2.2 GeV2

  • 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



T. Horn et al., Phys. Rev. C78, 058201 (2008)

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


Bonus: Fπ,K - a factorization puzzle?

T. Horn et al., Phys. Rev. Lett. 97 (2006) 192001.

T. Horn et al., arXiv:0707.1794 (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 FFmagnitude with kaon production would allow for better understanding of the onset of factorization

motivation summary
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°/Λratio)
    • Quasi model-independent comparison of pion and kaon data would allow a better understanding of the onset of factorization

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

Q2=3.0 GeV2 was optimized to be used for both t-channel and Q-n scaling tests


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)
separation in a multi dimensional phase space
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



Radial coordinate (-t),

Azimuthal coordinate (φ)

kaon pid
Kaon PID

Heavy Gas Cherenkov and 60 cm of empty space

  • 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


  • Four sets of aerogel would provide reliable K+/p separation over the full momentum range (2.6-7.1 GeV/c)
  • Alternate PID methods (such as RICH) are also possible

Kaon 12 GeV Kinematics

π/K Discrimination power

Heavy Gas Cerenkov

Momentum (GeV/c)

expected missing mass resolution
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





Simulation at Q2=2.0 GeV2 , W=3.0 and high ε

projections of r l t
Projections of R=σL/σT
  • 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
  • PR12-09-011 may indicate larger values of R, with associated smaller uncertainties
    • Reaching Q2=8 GeV2 may ultimately be possible

VGL/Regge calculation

Hall C parameterization


Fπ param

projected uncertainties for l and t
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


Precision data for W > 2.5 GeV


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

Projected Uncertainties for Q-n scaling



  • QCD scaling predicts σL~Q-6and σT~Q-8
  • Projected uncertainties use R from the Hall C parameterization



Fit: 1/Qn


Is onset of scaling different for kaon than pion?

Kaons and pions together provide quasi model-independent study

pr12 09 011 summary
PR12-09-011 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.


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

transverse contributions in pion production
Transverse Contributions in Pion production
  • 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, 192001 (2006)

bonus interference terms
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

significance of multiple epsilon points
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