Recent development of the Constituent Quark Model including quark-antiquark effects and confinement. E. Santopinto and R. Bijker Dedicated to Nathan Isgur NSTAR2007, 5-8 september 2007

Many versions of CQMs have been developed (KI, CI, GBE, U(7), hCQM, etc.) non relativistic and relativistic: for all of them the main problem is the qq problem

s CQMs: Good description of the spectrum Predictions of many quantities: photocouplings helicity amplitudes elastic form factors structure functions Missing:degrees of freedom beyond CQ quark-antiquark pairs

Is it a degrees of freedom problem?

Key degrees of freedom---->qq pair QM’s problems ----> degrees of freedom

There are two possibilities: phenomenological parametrizations microscopic explicit constituent description ( we have chosen this one ) One needs to find a qqbar creation mechanism 1) QCD inspired 2) without the problem of double counting

Problems 1) find a quark pair creation mechanism QCD inspired 2) implementation of this mechanism in such a way to a) do not destroy the good QMs results b) in a systematic and consistent way c) powerful symmetry constraint prevent double counting answer ?

- the OZI hierarchy is preserved -near immunity of the long range potential it is necessary a to sum over very large towers of intermediate states to see that the spectrum was only weekly perturbed (after unquenching and renormalization) and no simple truncation of the set of meson loops can reproduce such results great shift only from non adiabatic effects, as the result of the coupling of a resonance to a very nearby threshold for decays into other two. the change in the linear potential due to pairs bubbling in the string can be reabsorbed in a new strength of the linear potential, i.e. in a new string tension,thus the net effect of mass shifts from pair creation is smaller then the naïve expectation of the order of  Isgur’s last lesson:flux-tube-breaking model for mesons In a flux tube model where quark pair creation occur with a 3P0 quantum number with the ‘geometry” of flux tube-breaking models, it has been shown ( Isgur et al.) that a “miraculous” set of cancellations between apparently uncorrelated sets of mesons occurs in such a way that

String-breaking model It encodes the CQs but they are dressed with the gluon field degrees via the flux tube, wherein the gluonic degrees of freedom are subsumed into flux tubes. qq can buble up in the flux tube, thus excitations of the flux tubes can be described. In a flux-tube-breaking model, when a chromoelectric flux tube breaks, a q and q are created on the flux tube ends.

problems for the baryons----> - big towers of states authomatically generated by means of powerful group theoretical methods - problems linked with permutational symmetry(many different diagrams)-> solved with powerful group theoretical methods

h qq pair creation operator, Y* and K* intermediate baryon and meson, q and l relative radial momentum and angular momentum of Y* and K*, S spins We shall sum over a complete set of intermediate states, rather than just a few-lying states. Not only does this has a significant impact on the numerical result, but it is necessary for consistency with the OZI-rule and success of the QMs in spectroscopy.

Pair creation model applied to the strangeness content of the proton, or O s =  S, R s 2,  s In a flux-tube-breaking model, when a chromoelectric flux tube breaks, a q and q are created on the flux tube ends.

Closure limit Good stringent test for the program but also it explains when it holds why the successes of the CQMs : the corrections due to qq-pairs are zero in the closure limit,while the sums over big towers of states are constrained by the closure limit in such a way that very different meson and baryon states compensate. Closure limit ----->

The closure-limit and the symmetries give strong constraints

 u =1.00  u exp =0.82(5)  u LQCD =0.79(11)  u NRM = 4/3  u RQM = 1.01  d =-0.43  d exp =-0.44(5)  d LQCD =-0.42(11)  u NRM = -1/3  u RQM =  s=-0.06  s exp =-0.10(5)  s LQCD =-0.12(11)  u NRM =0  u RQM =0 calculated in the 3P0 limit, as a check Preliminary results In the closure limit  u:  d:  s= 4:-1:0

Outlook of some of the new possible applications - L z -  - - Sum rules (Gottfried, etc. …) - Transition form factors etc. - Spin structure functions - and many others…

Thank you for your attention!!!

Confinement & hadron spectroscopy

Preliminary Results HERMES Collaboration, hep-ex/