flux tubes

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Hybrid Mesons in the Flux Tube Model
100
JLab, May 2003

• flux tubes
• hybrids
• checks
• IKP decay model

extensions
charge radii surface mixing spin dependence spin
dependence II vector decay model other
applications
comparison to lattice adiabatic small
oscillation
conclusions
Eric Swanson
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construct a ladder from the debris of nuclear
explosions to the beauty of Babylon
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Flux Tubes
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Isgur Paton, PRD31, 2910 (85)
strong coupling Hamiltonian lattice gauge theory
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string Hamiltonian
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Hybrids
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Aside
Giles and Tye, PRL37, 1175 (1976)
Coupled quarks to a relativistic 2d sheet... the
Quark Confining String Model.
The presence of vibrational levels gives ...
extra states in quantum mechanics. ... that are
absent in the charmonium model.
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GT also computed finite-mass corrections, and
spin-orbit splittings.
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Checks
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Comparison to the lattice
IP N1 state
IP ground state
Juge, Kuti, Morningstar
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Comparison to the lattice
IP N1 state, no Coulomb
IP ground state
Juge, Kuti, Morningstar
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strings and flux tubes
etc
a 0gt
?
a 0gt
?
a a 0gt
?
?
a a 0gt
?
?
a a 0gt
?
?


2
2-
1
1
1-
1-
1
1-
a 0gt
?
a 0gt
?
1
1-
0gt
Juge, Kuti, Morningstar
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strings and flux tubes
N4
N3
N2
N1
Juge, Kuti, Morningstar
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Adiabatic approximation (ground state meson)
Monte Carlo
adiabatic
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Adiabatic approximation (hybrid gap)
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IKP decay model
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Extensions
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A. Charge Radii
Isgur, PRD60,114016 (99)
Q
r
q
flux tube zero point motion induces
transverse oscillation in the quarks ? larger
charge radius
increased elastic form factor slope ? flux lost
to hybrid production
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A. Charge Radii
Isgur, PRD60,114016 (99)
Q
r
q
flux tube zero point motion induces
transverse oscillation in the quarks ? larger
charge radius
increased elastic form factor slope ? flux lost
to hybrid production
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B. Adiabatic Surface Mixing
Merlin Paton, J. Phys. G11, 439 (85)
adiabatic surface mixing is induced by terms
neglected by IP, eg
resulting mass shifts were quoted in IP
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C. Spin-Orbit Force
Merlin Paton, PRD35, 1668 (87)
obtain a small spin-orbit shift and conclude
that spin-orbit splittings are mostly due to
Thomas precession
find uug splittings of -140 (2-) -20
(2-) 20 (1-) 40 (0-)
140 (1-) 280 (0-)
0 (1) 0 (1--)
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D. Spin-Orbit Force, II
Szczepaniak ES, PRD55, 3987 (97)
map chromofields to phonon degrees of freedom
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spin-dependence in the confinement potential
Gromes
Eichten Feinberg
Ng, Pantaleone, Tye
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spin-dependence in the confinement potential
examine in Coulomb gauge via the
Foldy-Wouthuysen transformation
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spin-dependence in the confinement potential
perform Rayleigh-Schrödinger perturbation theory
basis
first order
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second order perturbation theory in H
1
zero
hyperfine tensor
V
V
1
2
evaluate matrix elements in the flux tube model
V sr V O(1/N)
1
2
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Szczepaniak ES, PRD56, 5692 (97)
E. Vector Decay Model
Page, Szczepaniak ES, PRD59, 014035 (99)
use the same mapping to obtain ? a.A ?
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Isgur Paton, PRD31, 2910 (85)
F. Other
glueballs (glue loops) baryons check Luescher
term and adiabatic surfaces apply to glueloops
in SU(2) apply to 21 U(1) improve
semiclassical fragmentation formalism examine
long range spin-spin and spin-orbit forces
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Conclusions

• the FTM provides a compelling picture of strong
  QCD dynamics
• it is a picture only!
• many extensions and applications, explored and
  unexplored, exist

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fin
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strings and flux tubes
Juge, Kuti, Morningstar
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strings and flux tubes
Lüscher Weisz
-p/24
-p/12
see talk by Juge
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strings and flux tubes
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strings and flux tubes
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strings and flux tubes
Ichie, Bornyakov, Schierholz, Streuer,
hep-lat/0212036
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strings and flux tubes
1/2 fm
Ichie, Bornyakov, Schierholz, Streuer,
hep-lat/0212036