(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