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(4260) To what extent a charmonium?
International workshop on heavy quarkonium
June 27th, 2006
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Felipe J. Llanes-EstradaUniv. Complutense Madrid
Model Hamiltonian:
Take V as a classicalCornell potential betweencharge densities
Treat physicalgluon exchangein perturbation theory
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Trigonometricor hyperbolic Bogoliubov rotation generates a quasiparticle mass gap
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Tamm-Dancoff approximation
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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
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 9
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Here comes the surprise from Babar
(4260): new vector state from Babar
Clearly contains cc and is a vector11
With the 4s assignment the c,b spectra lock
Figurecourtesy of J. Rosner
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Not apparentIn R!!
Look at the worldupside-down
No one can miss the (4260) now
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Interference fit:Calculate DD, DsDs productionForm factors including (4040) and/not (4260) (+)(4160), (4440) (-)
Theoretical inspiration? Godfrey and Isgur
D
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Of course, a lot of it should proceed by intermediate D*(Cornell prd81)
Interference fit increased ee widthsBetter agreement with theory!
ee(4040) up to 1.5 keV from 0.75keV (1.7-1.9 keV theory)
ee(4260) Theory: 1keV (being 4S) would give a (probably unnoticed) bump in RAt the level of 0.5 keV, wiped out byInterference 17
The Cornellcoupled channelapproach
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SESAMECollaborationG. Bali et alprd2005
“String breaking” in lattice computations
1) Softer potential (levels closer together)2) Does not support resonances above threshold19
Test 0:When R is remeasured, try interference fit(allow three free phases for [4160,4260,4440] )
Very likely, larger lepton widths
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J/ width seems too large for the 4SNo good theory: resort to analogy
[Y(4S) Y(1S)]= 1.8(4)keVBabar hep-ex/060431
[Y(2S) Y(1S)]= 7 keV[(2S) (1S)]= 90 keVWe would expect:[(4S) (1S)]= 20-25 keV
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Total width ((4260))=88(25) MeV
ee B(J/) =5.5(10)(8) eV
Taking the max. acceptable with interference
1keV
((4260) J/) = 485 keV
A factor of 20 off !!22
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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A usual misquoteIn theory papers:f0 J/ not in Babar
nor Cleo
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Test 1: to distinguish charmonium fromcscs tetraquark
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FLEprd05
Distinguishing conventional from hybridCharmonium is more subtle
Test 2: Counting rules for inclusive production
in 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
Test 3: counting rules for exclusivedouble charmonium production
Bodwin, Lee and Braaten prl2003
Fixed angle production when r 0 d/dx constant for cc 1/r2 for ccg
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Test 4: 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)Test 5: Look at the momentum distributionof BB in the BB final state.
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Test 6: search for a new vector state inY (to have a supernumerary matchingthe 4260) between the 4S and 5S. (W.S. Hou)
Conclusions
• New state should be named (4260)
• Interference fits in R will lead to increased lepton widths and could hide the 4s state
• J/ has no credible explanation
• DsDs spectrum to distinguish 4q from 2q
• Counting rules apply to disentangle qq,qqg
• Locate nodes of the wavefunction by examining final state momentum distribution.
A conventional state (4s) could be feeding a part of the signal at 4260 MeV
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(4260) To what extent a charmonium?
International workshop on heavy quarkonium
June 27th, 2006
38
Felipe J. Llanes-EstradaUniv. Complutense Madrid