Gluonic excitations in theCharmonium region
Hirschegg’07Dynamic and structure of hadrons
January 16th, 2007
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Felipe J. Llanes-EstradaUniv. Complutense Madrid
q, g (s, mq)
... (Mh, fh, li ...)
Confinement
Hadron structure is filtered
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Can peep through with 1) Hard probes 2) Flavor symmetries3) JPC exotica 4) Detailed branchings
Heavy quarkonium above threshold, p-distribution of open flavor decays
qq qqg qqqq gg ggg
qq X - - qqg - X - -qqqq - - X
gg - X - ggg - X
Fock space expansion
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Collaborators: S. Cotanch, E. Swanson, A. Szczepaniak,I. General, Ping Wang, P. Bicudo
- - X qq
X - ggg
- X - gg
X - -qqqq
- - X - qqg
ggg ggqqqq qqg qq
Exotic channel JPC=1- +
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Trigonometricor hyperbolic Bogoliubov rotation generates a quasiparticle mass gap
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Model Hamiltonian:
Take V as a classicalCornell potential betweencharge densities
Treat physicalgluon exchangein perturbation theory
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Tamm-Dancoff approximation
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IR Behavior of a connected, fully amputated Yang-Mills Green’s function
in Landau gaugewith 2n ghost and m gluon legs
Alkofer, Fischer, Llanes-Estrada, PLB05
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SpectrumIn quarksector
Llanes-Estrada,Szczepaniak,Swanson, Cotanch, PRC04 11
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 4+q states
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(4260)(4320)
Resonances above open charm threshold
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r(cc)
Gamow resonances?
DD
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p-wave
SESAMECollaborationG. Bali et alprd2005
“String breaking” in lattice computations
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Distinguish the wavefunctionsFranck-Condon principle (1925)
Molecular transitionsbetween two adiabaticlevels: nuclei are notaffected by the fastelectronic jump.
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Consider relative momentum distribution ofDD subsystem in DD final state
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The hybrid p distribution has no shoulders
To test the idea with a sharper signal:Belle run at the Y(5S)Look at the momentum distributionof BB in the BB final state.
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Search for a new vector state inY (to have a supernumerary matchingthe 4260) between the 4S and 5S. (W.S. Hou)
1 3
2 4
q
q
q
s1 s3
L13
s2
s4
L24
L12-34
sd q
sd q
jd q
jd q
S
J
P = (-1)L13+L24 +L12-34
C = (-1) S +L12-34 24
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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M (4 light q´s) = 1565 1450 MeVM (2 light 2 s) = 1950 1800 MeVM (4 s q´s) = 2260 2150 MeV
Badalyan (1987; Dafne 1991 LNF-91/017 (R)) Jaffe (1977)
JPC = 1states (Mulders, Aerts, de Swart)1500,1660,1830,1860,1940,2000,2070,2140,2210... P-wave exotica 1 from 1700
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Wang, General,Cotanch,FLEupcoming
1)Molecules are lighter(in agreement withIsgur and Weinstein)2)About every othernew state has a match3)1-+ in the 1.3-1.4GeVballpark (hybrids wellabove 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
p1+p2+p3+p4=0 (center of mom.)
Choose any 3 mesons
(p1xp2).p3
Area of faces
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((p1xp2).p3)2
Observable: off-planes:
(|p1xp2| |p2xp3| |p1xp3| |p1xp4| |p2xp4| |p3xp4|)1/2
1)Dimensionless2)Permutation invariant (1,2,3,4) in the cm frame
=
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Internal distribution of off-planes
For a hybrid For a 4q
# counts
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=0.59
(1,2,3) cube
Maximum: 0.707
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To distinguish charmonium fromcscs tetraquark
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Counting rules for inclusive productionin e-e+ collider
x= E/Ebeam
cc: (1-x)ccg: (1-x)3
1xJ.Gunion PLB79
Limit of thecross sectionas x 1
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e-e+ J/(4260) r = 2mc/Ebeam
Counting rules for exclusivedouble charmonium production
Bodwin, Lee and Braaten prl2003
Fixed angle production when r 0
d/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).)
YLm<s1 m1 s2 m2 | S mS>
0++
L=0 1++
2++
0
L=1 2
3 37
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 model’s largest weakness.39
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 OZIO(150) MeV Bicudo, Abreu stringO(400) MeV Cotanch, Williams VMD
Our new evaluation: Bicudo, Cotanch, Ll-E, Robertson 2006
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Motivation: new BES state f0(1810)
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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J/
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(600,1370,1500,1710,1790)
Should have been visible in at DM2
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But DM2 could not have seen it in 49
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 legendof the flavor-blind glueball decays
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Fock Space Expansion:
| qq > + | qqqq > + | gg > + | qqg > + | qqqqqq > . . .
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)
= 0 (color factor)
repulsive attractive
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qq qqg qqqq gg ggg
qq 1 - - qqg 1 - -qqqq 1 - gg 1 - ggg 1
Large Nc limit
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Collaborator: J. R. Pelaez
Gluonic excitations in theCharmonium region
Hirschegg’07Dynamic and structure of hadrons
January 16th, 2007
57
Felipe J. Llanes-EstradaUniv. Complutense Madrid