Quark can not observed individually (charge current within nucleon which couple to virtual photon)

"An infinitely strong the force field" that bind quarks inside of nucleon

"A string-like flux-tube" that "breaks" with the qq

ss produced From flux-tube ss produced From photon Color flux-tube model 3 P 0 state

L. Micu (1969) Introduction R. Carlitz/M. Kislinger (1970) Concept - qq vacuum pair creation A. Le Yaouanc (1972) Dynamics - Approximation as tunneling from harmonic OSC potential A. Casher/H. Neuberger/S. Nussinov (1979) A guide note - Description of color flow between quarks B. Anderson/G. Gustafson/G. Ingelman/T. Sjostrand (1983) LUND model - A successful phenomenology developing - Now they are well known authors of the high energy program PYTHIA

Color flux-tube - stretched between the outgoing quark and the remainder quarks from the hadronic target, breaks first at a space point located approximately ~1 fm behind the leading quark with the production of a qq followed by a second break ~1 fm or so behind the new leading quark and so on... Probability - Calculated by assuming the quarks are bound in a square-well potential with depth proportional to the C onstituent Q uark(CQ) mass - The CQ mass is an effective degree-of-freedom

A quark pair creation "The essence of many theories to describe a hadronic decays ! ”

Assumption : 3 P 0 state Reasons: - It is natural way because it is the simple wave function : + parity / no net L p l, the Q n of the vacuum - Matrix element is simple no exchange of L p l, and Q n - Pair creation takes place in the middle of a color field S. Capstick, C. Robert

A limited experimental info of angular momentum state: - A decay of  -mson proceed via two amplitudes (by d -wave and s -wave analyzed) Result : the s-wave dominated the d-wave by a factor of 4  consistent with a 3 P 0 wave function (not a 3 S 1 )  3 S 1 wave function : a single vector gluon field produced the qq - CLAS "exclusive K +  electroproduction" the first measurement of large transferred polarization from a polarized electron beam by assuming that qq was produced in a spin state s =0. P. Geiger, E. Swanson, PRD (1994) D. S. Carman et al., PRL (2003)

Measure ratios: K +  :  + n :  0 p K+K+  s s d ++ n 00 p d u u

s K+K+  ++ n 00 p s d d u u

 Apr. 04 ~ Jul. 26, 2003  E0 =5.499GeV (pol. e), LH2 target  Length = 5cm, Φ = 6mm  I B = 2250A  Trigger = EC in x EC tot x CC  Luminosity ~20 fb -1

Single meson electroproduction Unpol. cross-section w/ one-photon exchange approx.

Applying toolsApplying tools –Phase space correction –Background subtraction –Acceptance correction using same PYTHIA/JETSET (fitting and MC generator) –Same kinematic bin size & range –Misc. corrections/cuts Momentum correction Electron energy (Hall-A) Vertex correction and cut Fiducial volume cut, missing mass cut (3  )

Ambiguity All consistent hypotheses for PID, a single positive track might pass the K+, pi+,proton in  -momentum cuts if at high momentum. However, statistically, only the correct hypothesis will produce a peak signal. The alternate hypothesis simply forms a smooth background under the MMx. No double-counting

BEFORE AFTER Mx(ep  e’X) (GeV) SECTOR 1  e = 17 (deg)

fiducial cut … more chees…zZ…e pizza

ep  e’K + Xep  e’  + Xep  e’p X

“Elementary Particles”, William R. Frazer, Prentice-Hall (1966).

K+K+ n+n+ p0p0 A + B cos  + C cos2 

-Phenomenological conclusion from the observation  * couple to quark in proton 2.Significant  *-dependence 3.Constant term [~  U (K   :n   :p   )] ratio from  *- fit 4.K/  ratio falls off slowly as cos  * 5.K  /   ~ 0.17  0.01  0.02,   /   ~ 0.49  0.02  0.09

-Phenomenological conclusion from the observation  * couple to quark in proton 2.Significant  *-dependence 3.Constant term [~  U (K   :n   :p   )] ratio from  *- fit 4.K/  ratio falls off slowly as cos  * 5.K  /   ~ 0.17  0.01  0.02,   /   ~ 0.49  0.02  0.09

-Phenomenological conclusion from the observation  * couple to quark in proton 2.Significant  *-dependence 3.Constant term [~  U (K   :n   :p   )] ratio from  *- fit 4.K/  ratio falls off slowly as cos  * 5.K  /   ~ 0.17  0.01  0.02,   /   ~ 0.49  0.02  0.09

Questions/comments ? Thank you for your attention

Can the Lund model work in the limit of single qq -pair production ? –recent analysis of a Hall C  + (n) production experiment Kaskulov, Gallmeister, Mosel; arXiv: v4 [hep-ph] –model was developed to explain Rosenbluth separated exclusive electro-production of  + (n) a  L described well as t-channel exchange a  T described well as “quark-scattering followed by string-breaking” with Lund model parameters –model also works for un-separated data

Lund model: successful phenomenology for hadron production; e.g. in e + e - reactions –color flux-tube broken by qq production –production rate depends on constituent quark mass – uu : dd : ss ~ 1 : 1 : 0.2 Vector meson dominance: photon fluctuates into a virtual qq meson –production rate depends on quark charge – uu : dd : ss ~ 1: 0.25 : 0.25

Model-independent goal –Measure ratio of  + n :  0 p : K +  cross-sections –Proportional to uu : dd : ss rate Extend Kaskulov, Gallmeister, Mosel model –Extend to dd and ss production Analysis update –Identify final states –Decide on binning ( W, Q 2, cos ,  ) –Tune PYTHIA/JETSET (fitting and MC generator) –Calculate acceptance –Extracting the cross sections and ratio Study single quark-pair creation ! ! !Study single quark-pair creation ! ! ! Model-independent goal –Measure ratio of  + n :  0 p : K +  cross-sections –Proportional to uu : dd : ss rate Extend Kaskulov, Gallmeister, Mosel model –Extend to dd and ss production Analysis update –Identify final states –Decide on binning ( W, Q 2, cos ,  ) –Tune PYTHIA/JETSET (fitting and MC generator) –Calculate acceptance –Extracting the cross sections and ratio Study single quark-pair creation ! ! !Study single quark-pair creation ! ! !

No tools appliedNo tools applied –Absolute normalization (Luminosity) –Radiative correction –EC (E/p), nphe cut Applying toolsApplying tools –Phase space correction –Background subtraction –Acceptance correction using same PYTHIA/JETSET (fitting and MC generator) –Momentum correction –Electron energy (Hall-A) –Same kinematic bin size & range –Vertex correction and cut –Fiducial volume cut, missing mass cut (3  )

Simulation with PID of kaons (allow pion contamination) Simulation with PID of kaons with assigning fake pion mass

S/B is not improved significantly except statistics drop. Same conclusion from the polarization measurement (B. Raue, FIU)

* EC sampling fraction cut / CC number of photoelectron cut were NOT applied because ….

Experimental data from ep  e’p X MC simulation ( x scale factor) from ep  e’p  +  -

ep  e’K + Xep  e’  + Xep  e’p X Experimental data MC simulation (shadow histo.)

Required [1] minimum number of phi-bin (>8), [2] 4\sigma outlier cut

Q 2 - dependence