qq qqg qqqq gg ggg

qq X - - qqg - X - -qqqq - - X

gg - X - ggg - X

Fock space expansionThe shell-model of hadron physics

-6

Collaborators: S. Cotanch, E. Swanson, A. Szczepaniak,I. General, Ping Wang, P. Bicudo

Fock Space Expansion:

| qq > + | qqqq > + | gg > + | qqg > + | qqqqqq > . . .

Whatever is not forbidden is mandatory: “This state is an (X) state”

misleading when strong mixing.

-5

Convergence: trigonometricor hyperbolic Bogoliubov rotation generates a quasiparticle mass gap.

-4

qq qqg qqqq gg ggg

qq 1 - - qqg 1 - -qqqq 1 - gg 1 - ggg 1

Large Nc limit

-3

Collaborators: J. R. Pelaez and Guillermo Rios

- - X qq

X - ggg

- X - gg

X - -qqqq

- - X - qqg

ggg ggqqqq qqg qq

Exotic channel JPC=1- +

-2

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

The Franck-Condon principleand exotic hadrons

SCADRON70SCAlar haDRON

February 17th, 2008

0

Felipe J. Llanes-EstradaUniv. Complutense Madrid

Outline

• The Franck-Condon principle

• The Sturm-Liouville nodes and quarkonium (conventional vs. hybrid)

• Tetraquarks and off-planes correlator

• Testing meson decay mechanisms

1

Edward U. Condon James Franck

Some old timers...

2

Distinguish the wavefunctionsFranck-Condon principle (1925)

Molecular transitionsbetween two adiabaticlevels: nuclei are notaffected by the fastelectronic jump.

3

It neatly explains the phenomenon offluorescence in molecular physics

(See book by Herzbachor even Wikipedia)

4

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.

5

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

6

7

(4660)

(4320)(4260)

Llanes-Estrada, Cotanch PLB504:15-20, 2001

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

8

Resonances above open charm threshold

9FJLEPRD72031503

2006

10 (Measured in the nuclear shell model)

11

Consider relative momentum distribution ofDD subsystem in DD final state

12

13

14

The hybrid p distribution has no shoulders

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.

15

b b

BB

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

In the cm frame of a hybrid, momenta and stresses lie instantaneously in a plane

17

However, for a tetraquark there is off-plane stress

18

Consider pure four-body (rare strong) decays

p1+p2+p3+p4=0 (center of mom.)

Choose any 3 mesons

(p1xp2).p3

Area of faces

19

((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

=

20

Internal distribution of off-planes

For a hybrid

# counts

21

For a 4q

?

=0.59

(1,2,3) cube

Maximum: 0.707

22

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

23

24

0

100

200

300

400

500

600

0-0.035

0.14 0.245 0.35 0.455

Off-planes

Z

DD

Outline

• The Franck-Condon principle

• The Sturm-Liouville nodes and quarkonium (conventional vs. hybrid)

• Tetraquarks and off-planes correlator

• Testing meson decay mechanisms

25

Relative wavefunctionof the pair?

Old question of the quark model 26

A gluon has JP 1-

Howeverquark model claimsare that 3P0 fits best

So a quark-antiquarkshould naturally beemitted as a 3S1 pair

27

Hermes: sea quarks are unpolarized

But we don’t know yet the s-s

28

Test mechanism with Franck-Condon

B-meson undergoessemileptonic decay(about 10% branch)

b-quark

29

DKK(B below

DDD threshold)

c-quark

u-quark DD(About1% ofabove)

B ll+DKK+Xud (Large branching fraction theoretically less clean)B ll+DD+Xud (10-5 but more reliable)

30

Application of the Franck-Condon principle:the momentum distribution of DD givesthe distribution of cc created inside B meson(and other hadrons)

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

The Franck-Condon principleand exotic hadrons

SCADRON70SCAlar haDRON

February 17th, 2008

32

Felipe J. Llanes-EstradaUniv. Complutense Madrid