Upload
leroy-mcdonald
View
34
Download
4
Tags:
Embed Size (px)
DESCRIPTION
Fock space expansion The shell-model of hadron physics. Collaborators: S. Cotanch, E. Swanson, A. Szczepaniak, I. General, Ping Wang, P. Bicudo. -6. Fock Space Expansion :. | qq > + | qqqq > + | gg > + | qqg > + | qqqqqq >. Whatever is not forbidden is mandatory: - PowerPoint PPT Presentation
Citation preview
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