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qq qqg qqqq gg ggg
qq X - - qqg - X - -qqqq - - X
gg - X - ggg - X
Fock space expansionThe shell-model of hadron physics
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Collaborators: S. Cotanch, E. Swanson, A. Szczepaniak,I. General, Ping Wang, P. Bicudo
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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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Convergence: trigonometricor hyperbolic Bogoliubov rotation generates a quasiparticle mass gap.
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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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Collaborators: J. R. Pelaez and Guillermo Rios
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- - X qq
X - ggg
- X - gg
X - -qqqq
- - X - qqg
ggg ggqqqq qqg qq
Exotic channel JPC=1- +
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q, g (s, mq)
... (Mh, fh, li ...)
Confinement
Hadron structure is filtered -1
Can peep through with 1) Hard probes 2) Flavor symmetries3) JPC exotica 4) Detailed branchings5) Counting rules in production
Momentum distribution of decay products
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The Franck-Condon principleand exotic hadrons
SCADRON70SCAlar haDRON
February 17th, 2008
0
Felipe J. Llanes-EstradaUniv. Complutense Madrid
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Outline
• The Franck-Condon principle
• The Sturm-Liouville nodes and quarkonium (conventional vs. hybrid)
• Tetraquarks and off-planes correlator
• Testing meson decay mechanisms
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Edward U. Condon James Franck
Some old timers...
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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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It neatly explains the phenomenon offluorescence in molecular physics
(See book by Herzbachor even Wikipedia)
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What about it in hadron physics?
Heavy quarks: nucleiGluons, pions... : electrons
Conjecture (obvious in the heavy quark limit)
When a hadron decays, the relative momentumdistributions of the hadron products containing
a heavy quark, coincide with the initial momentumdistributions ot those quarks in the parent hadron.
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Outline
• The Franck-Condon principle
• The Sturm-Liouville nodes and quarkonium (conventional vs. hybrid)
• Tetraquarks and off-planes correlator
• Testing meson decay mechanisms
General, Cotanch, Llanes-Estrada, EPJC51:347-358,2007
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7
(4660)
(4320)(4260)
Llanes-Estrada, Cotanch PLB504:15-20, 2001
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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 4+q states
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Resonances above open charm threshold
9FJLEPRD72031503
2006
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10 (Measured in the nuclear shell model)
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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
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To test the principle with a sharper signal:Belle run at the Y(5S)
Look at the relative momentum distributionof BB in the BB final state.
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b b
BB
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Outline
• The Franck-Condon principle
• The Sturm-Liouville nodes and quarkonium (conventional vs. hybrid)
• Tetraquarks and off-planes correlator
• Testing meson decay mechanisms
General et al, PLB653:216-223,2007 16
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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 frame3)Vanishes for 2,3-body intrinsic wavefunctions
=
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Internal distribution of off-planes
For a hybrid
# counts
21
For a 4q
?
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=0.59
(1,2,3) cube
Maximum: 0.707
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For the Coulomb-gauge model with meson-meson type clusters, can compute correlator
Example: Belle’s record pion Z(4430) ’
ud + udg + ccud + ...
Has been suggested to be a D1 D* molecule
RGM (Ribeiro, Bicudo)attractive
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0
100
200
300
400
500
600
0-0.035
0.14 0.245 0.35 0.455
Off-planes
Z
DD
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Outline
• The Franck-Condon principle
• The Sturm-Liouville nodes and quarkonium (conventional vs. hybrid)
• Tetraquarks and off-planes correlator
• Testing meson decay mechanisms
25
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Relative wavefunctionof the pair?
Old question of the quark model 26
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A gluon has JP 1-
Howeverquark model claimsare that 3P0 fits best
So a quark-antiquarkshould naturally beemitted as a 3S1 pair
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Hermes: sea quarks are unpolarized
But we don’t know yet the s-s
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Test mechanism with Franck-Condon
B-meson undergoessemileptonic decay(about 10% branch)
b-quark
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DKK(B below
DDD threshold)
c-quark
u-quark DD(About1% ofabove)
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B ll+DKK+Xud (Large branching fraction theoretically less clean)B ll+DD+Xud (10-5 but more reliable)
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Application of the Franck-Condon principle:the momentum distribution of DD givesthe distribution of cc created inside B meson(and other hadrons)
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Conclusions
• The Franck-Condon principle could provide the intelectual framework to decide on intrinsic wf based on decay output in model independent way
• Testable on Y(5S) to BB• (4260) to DD hybrid or
charmonium?• Z(4430) and others, how much 4-quark?• Semileptonic or not, semiinclusive B to
DD, direct test of 3P0 pair creation mechanism 31
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The Franck-Condon principleand exotic hadrons
SCADRON70SCAlar haDRON
February 17th, 2008
32
Felipe J. Llanes-EstradaUniv. Complutense Madrid