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

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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 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