Sin ttulo de diapositiva

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Gluonic excitations in the Charmonium region
Hirschegg07 Dynamic and structure of
hadrons January 16th, 2007
Felipe J. Llanes-Estrada Univ. Complutense Madrid
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Hadron structure is filtered
Can peep through with 1) Hard probes 2) Flavor
symmetries 3) JPC exotica 4) Detailed
branchings
Heavy quarkonium above threshold, p-distribution
of open flavor decays
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Fock space expansion
Collaborators S. Cotanch, E. Swanson, A.
Szczepaniak, I. General, Ping Wang, P. Bicudo
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Exotic channel JPC1-
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Trigonometric or hyperbolic Bogoliubov rotation
generates a quasiparticle mass gap
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Model Hamiltonian
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Tamm-Dancoff approximation
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IR Behavior of a connected, fully amputated
Yang-Mills Greens function in Landau gauge with
2n ghost and m gluon legs
Alkofer, Fischer, Llanes-Estrada, PLB05
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Spectrum In quark sector
Llanes-Estrada,Szczepaniak,Swanson,
Cotanch, PRC04
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Glueish mesons in the 4-5 GeV region
1) High-pitch glueballs 2) Oddballs 3) Hybrid
mesons Confused with some conventional cc And
a multitude of 4q states
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y(4260) y(4320)
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Resonances above open charm threshold
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Gamow resonances?
DD
p-wave
r(cc)
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String breaking in lattice computations
SESAME Collaboration G. Bali et al prd2005
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Distinguish the wavefunctions Franck-Condon
principle (1925)
Molecular transitions between two
adiabatic levels nuclei are not affected by the
fast electronic jump.
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Consider relative momentum distribution of DD
subsystem in DDp final state
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The hybrid p distribution has no shoulders
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To test the idea with a sharper signal Belle run
at the Y(5S) Look at the momentum distribution of
BB in the BBp final state.
Search for a new vector state in Ypp (to have a
supernumerary matching the 4260) between the 4S
and 5S. (W.S. Hou)
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GROUND STATE S-waves only
0??????????????????? P-wave 1??? (0 1 2 3)??
(0 1 2) ????
(with various multiplicities) Rich spectrum
state inflation hopefully most are too broad.
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Badalyan (1987 Dafne 1991 LNF-91/017 (R))
Jaffe (1977)
M (4 light qs) 1565 1450 MeV M (2
light 2 s) 1950 1800 MeV M (4 s qs)
2260 2150 MeV
JPC 1?????states (Mulders, Aerts, de
Swart) 1500,1660,1830,1860,1940,2000,2070,2140, 22
10... P-wave exotica 1?? from 1700
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Wang, General, Cotanch,FLE upcoming 1)Molecules
are lighter (in agreement with Isgur and
Weinstein) 2)About every other new state has a
match 3)1- in the 1.3-1.4GeV ballpark (hybrids
well above 2GeV)
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In the cm frame of a hybrid, momenta and
stresses lie instantaneously in a plane
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However, for a tetraquark there is off-plane
stress
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Consider pure four-body (rare strong) decays
p1p2p3p40 (center of mom.)
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Observable off-planes
((p1xp2).p3)2
P
(p1xp2 p2xp3 p1xp3 p1xp4 p2xp4
p3xp4)1/2
1)Dimensionless 2)Permutation invariant (1,2,3,4)
in the cm frame
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Internal distribution of off-planes
counts
P
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P0.59
(1,2,3) cube
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To distinguish charmonium from cscs tetraquark
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Counting rules for inclusive production in e-e
collider
Limit of the cross section as x 1
x Ey(4260)/Ebeam
cc (1-x) ccg (1-x)3
J.Gunion PLB79
1
x
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Counting rules for exclusive double charmonium
production
Bodwin, Lee and Braaten prl2003
e-e J/y y(4260) r 2mc/Ebeam
Fixed angle production when r 0
ds/dx constant for cc
r2 for ccg
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Coulomb gauge BCS-TDA glueballs (A. Szczepaniak
et al. PRL 76, 2011 (1996), F. Llanes-Estrada et
al. NPA (2002).)
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GLUEBALLS
(Lattice spectrum from Morningstar and Peardon)
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Glueballs fall on Regge Trajectories
Interaction between color densities as
suggested by QCD in the Coulomb gauge (non
abelian gluon-gluon interaction) Slope of
Regge trajectories much smaller than for
quark mesons because color factor 3 instead of
4/3 In (L,S) notation model (0,0) 0??, (2,0)
2??, (4,0) 4 fall on Regge trajectory
parallel to pomeron. The 2?? (0,2) falls on
Pomeron Regge trajectory, within lattice error
bands. These are little sensitive to
spin-orbit coupling which is the models
largest weakness.
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F.J.L.E. et al. 2000
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Three body sector hybrids, oddballs
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Oddball Regge trajectories
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Glueball decay width Previous
estimates O(10-30) MeV Carlson et al
OZI O(150) MeV Bicudo, Abreu string O(400)
MeV Cotanch, Williams VMD Our new
evaluation Bicudo, Cotanch, Ll-E, Robertson
2006
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Motivation new BES state f0(1810)
(600,1370,1500,1710,1790)
J/? ??????
Angular analysis shows quant. numbers
0 Threshold cusp? No. Tail of the
f0(1710)? Adjust for phase space and still
off-threshold
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Should have been visible in ???at DM2
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But DM2 could not have seen it in ??
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Prefered decay modes open flavor

• For C charmonia this is an experimental fact
• For glueballs it is expected on the basis of
  string breaking
• For radiative J/y decays... as much as a glueball
  in the middle

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In the end, glueballs are not so broad... Many
dynamical effects dispell the legend of the
flavor-blind glueball decays
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Fock Space Expansion
qq gt qqqq gt gg gt qqg gt qqqqqq
gt . . .
Whatever is not forbidden, is
mandatory This state is an (X) state
misleading when strong mixing.
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Molecules with closed flavor mesons unlikely
(Explanation by E. Ribeiro 1980)
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Large Nc limit
Collaborator J. R. Pelaez
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Gluonic excitations in the Charmonium region
Hirschegg07 Dynamic and structure of
hadrons January 16th, 2007
Felipe J. Llanes-Estrada Univ. Complutense Madrid
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