Recent development of the Constituent Quark Model including quarkantiquark effects and confinement'

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

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Is it a degrees of freedom problem?
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Key degrees of freedom----gtqq pair
QMs problems ----gt degrees of freedom
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There are two possibilitiesphenom
enological parametrizations
microscopic explicit constituent
description
(we have chosen this one)One
needs to find a qqbar creation mechanism 1) QCD
inspired2) without the problem of double
counting
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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 countinganswer ?
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-the OZI hierarchy is preserved
-near immunity of the long range
potentialit is necessary a to sum over very
large towers of intermediate statesto 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.
Isgurs last lessonflux-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

• 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 ??

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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.
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problems for the baryons----gt - big towers of
states authomatically generated by means of
powerful group theoretical methods- problems
linked with permutational symmetry(many different
diagrams)-gt solved with powerful group
theoretical methods
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hqq 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.
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Pair creation model applied to the strangeness
content of the proton, or Os ?S, Rs2,?s
In a flux-tube-breaking model, when a
chromoelectric flux tube breaks, a q and q are
created on the flux tube ends.
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Closure limit
Closure limit -----gt
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.
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The closure-limit and the symmetries give strong
constraints
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?u 1.00 ?uexp0.82(5) ?uLQCD 0.79(11)
?uNRM 4/3 ?uRQM 1.01 ?d -0.43
?dexp-0.44(5) ?dLQCD -0.42(11) ?uNRM
-1/3 ?uRQM -0.251 ?s-0.06
?sexp-0.10(5) ?sLQCD -0.12(11) ?uNRM
0 ?uRQM 0

calculated in the 3P0 limit, as a
check
Preliminary results
In the closure limit ?u ?d ?s 4-10
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Outlook of some of the new possible
applications

• - Lz
• - ????
• - ltr2gt
• - Sum rules (Gottfried, etc. )
• - Transition form factors etc.
• - Spin structure functions
• - and many others

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Thank you for your attention!!!
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Confinement hadron spectroscopy
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Preliminary Results
HERMES Collaboration, hep-ex/0609039