L-T Separated Kaon production Cross Sections from 5-11 GeV
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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