Mesoni Diquark-antidiquark: una nuova spettroscopia? Work in Progress con F. Piccinini, A. Polosa,...

Mesoni Diquark-antidiquark: una nuova spettroscopia?Work in Progress con F. Piccinini, A. Polosa, V. Riquer

Luciano MAIANI, Univ. di Roma1. Italia; INFN, Roma. Italia

Roma. 26/11/04 L.MAIANI. Scalar Mesons & 4-quarks 2

Mesoni tetraquark

• Un’ idea popolare negli anni ‘70• QCD incoraggia a pensare che siano possibili • In particolare i mesoni a(980), f(980) ne hanno l’ aspetto• Cruciale l’ esistenza di partner leggeri: e • Alternativa: “molecole” K-Kbar, legate da 1- exchange,

come i nuclei• Esp. recenti, a FNAL(E791) e Frascati, hanno “rivisto” il e

riaperto il problema• …e ci sono stati con charm (hidden/open) che non

sono/sembrano q-qbar: X(3872), X(3940), (Belle, Babar nei decad. di B+), X(2632) (SELEX)…


Sommario

• Attrazione e repulsione in QCD• Strutture a “stringa”: il modello del “barionio” (Rossi &

Veneziano, 1977)• I mesoni scalari leggeri (hep-ph/0407017, PRL to appear)• Decadimenti in mesone-mesone• Tetraquark con c-cbar:

– forze ~ spin indipendenti, molti piu’ stati– Allineamento alle masse dei quark, breaking di isospin

• Tetraquark in onda S e X(3872): lo spettro associato.• La particella di SELEX , X(2632), possibile spettro• Conclusioni


M=

Study of the Decay with the KLOE DetectorThe KLOE CollaborationarXiv:hep-ex/0204013 Apr 2002

Sigma parameters from E791


Attractive & repulsive channels in QCD

)]1(C)1(C)R(C[2

g

]TT)TT([2

gTTg

)2()2()2(

2

2

2

1

2

R

2

21

2

R21

2

−−=

=><−><−>+<=>⋅<∝

1 2

R

R

{qq = octet = +1/3 repulsionsinglet = -8/3 attraction

{qq = “3bar” = -4/3 attraction“6 “ = +2/3 repulsion

]2/3)1J(J)][R(C[gTTg eff)2(2

R2211

2 −+−∝>⋅<−∝

Spin-spin interaction

{qqandqq31=><>< spin 1= +1/2 repulsion

spin 0= -3/2 attraction

Interaction of two colored objects:

Baryons in the octet:=([ud] J=0 s); 0 =({ud}J=1s) is lighter than


Diquark: [qq] in color = 3bar, spin=0, SU3 flavour = 3bar makes a simple unit to form color singlets (Jaffe..more recently Jaffe&Wilcezck, Karliner & Lipkin for penta-quark)

[qq]

baryon (e.g. ), Y-shape[qbar qbar] scalar meson,

Diquark needs to combine with other colored objects

meson-meson molecules also suggested.But: do “residual” forces bind?

a new topology (Rossi&Veneziano) more related to B-B bar: if you stretch the string, [qq][qbar qbar] B Bbar pair


s-channel: qqq baryons (no exotics!!)

t-channel: q qbar mesons

B

M

The color junction

Duality in Meson-Baryon scattering


s-channel: [qq][qbar qbar] (Baryonium)

What about Baryon-Antibaryon scattering ?

B

B

Color junctions

[qq][qbar qbar] mesons are dual to q qbar mesons in B-Bbar scattering. The relation to B-Bar persists in decays!!

t-channel: q qbar mesons


]qc][cq[and]qq][cq[

Recent evidence for at low energy (E791, then KLOE) led us to reconsider the case of sub-GeV scalar mesons. Many previous investigations (Joffe, Close&Tornqvist, Schecter and coll...).We propose:

all scalars below 1 GeV are diquark-antidiquark bound states (1 nonet), the q-qbar scalar nonet (L=1, S=1, J=0) has to be above.

Results:•Low energy states show inverted mass spectrum, consistent with “perfect mixing”;•Strong decays are reasonably accounted for;•Decays S still to be studied;•Relations with ealier proposal by Rossi&Veneziano suggests connection to Baryon-Antibaryon, rather than Meson-meson states (or molecule)•A rich new spectroscopy is predicted in charm and beauty: X(3872), X(2632)…

•Heavy quark intcs: spin independent: new spin states? A work in progress

The present work


Quantum numbers and mass formula

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

βα

α=m = diquark masses


4 parameters, 4 masses+1 mixing, one overall relation:

-Almost “ideal mixing”-Linear mass formula gives very similar results-With Linear m.f., parameters related to diquark masses: α=480 MeV, β = 250 MeV -Note: αβ=230 MeV vs ms=150 MeV.

+


Strong Decays

m

n

l

k

ikn

jlm

j

i1MM)S(AL εε=

No derivative coupling!


A=2.6 GeV1.



The full SU(3) effective lagrangian...

has three couplings:


Diquark-antidiquark decays

2M

1M

S

S

1M

2M

Decay proceed via B- Bbar virtual states! Should we try the same for S

= switch amplitude a

= amplitude b


Quark rearrang.

M1

M2


c should be small: with c=0 we get (a)=30 MeV vs 6013MeV

Maybe f comes from “one-loop”:

or perhaps (!!) →→ BBf (Baryonium picture, see later)

Still too low.

Overall we get quite a consistent picture, reconciles with a and f widths, reinforces [qq][qbar qbar] assignement


Tetraquark con c-cbar (Work in progress)

• L’ interazione spin-spin tra quark pesanti e’ O(1/M)– Se diquark S=0 si legano, anche S=1– Tutti gli stati (0+1)x(0+1)= 0(x2)+1(x3)+2(x1)

• Self-energia: bilancio tra due effetti– Annichilazione: u ubar <-> d dbar, etc.: da’ una matrice con tutti 1– Autovettori :autostati di SU(N)– Massa dei quark: gli autovettori sono gli stati con tipo definito di quark

(es. mixing)– Alla scala del charmonio dovrebbe vincere la massa dei quark

(R&V,MPPR)– Gli autovettori sono [cu][cbar ubar], [cd][lcbar dbar],. e non I=1,0

• Belle osserva: X -> J+, J+ con simili B.R.!!!! Un nuovo fenomeno


Stati:[cu]S=0,1 [cbar ubar]S=0,1

input

Prediz.


Stati:[cu]S=0,1 [sbar ubar]S=0,1

input

Prediz.

DsJ(2317) 0+?

DsJ(2457) 1+?



Interferenza !


Conclusions

• A convincing picture of light scalars as [qq][qbar qbar]states:– Masses– Ideal mixing– Decays reasonably described (exact SU3!) but for OZI violating (??)– Annihilation amplitudes are small: – Note: m(f-a)~10MeV, m(up-down) ~5MeV: are f/a I-spin

eigenstates?

• New phenomena– States [cq][cbar qbar] and [cq][cbar qbar] should be very visible– I-spin breaking expected maximal in certain decays– SELEX particle: is it the first case? – X(3872) a good candidate, X(3940) predicted

WERE ARE THE EXOTIC STATES??? !

Study of decays in KLOE very important

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Mesoni Diquark-antidiquark: una nuova spettroscopia? Work in Progress con F. Piccinini, A. Polosa,...

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