I=1 heavy-light tetraquarks and the Υ(mS)→Υ(nS)ππ

puzzleFrancisco Fernández

Instituto de Física Fundamental y Matemáticas

University of Salamanca

Multiquark structures in heavy-light meson systems

Meson structure is a few-body problem

Outline

► Motivations► the model►DsJ mesons► The Υ(mS)→Υ(nS)ππ puzzle

Motivations

Why four quarks configuration?

qqqq

csJπ=0+,1+

L=0

L=1P( s )=-1

−

→

→P(qq)=+1−

−

the model

Constituent Quark ModelGeneralization to heavy flavours of the original SU(2)F model developed in J. Phys. G19 2013 (1993)

Basic ingredients•Chiral symmetry is spontaneously broken at some momentum scale provinding a constituent quark mass M(q2) for the ligth quarks

• As a consecuence light constituent quarks exchange Goldstone bosons

•Both light and heavy quarks interacts besides by gluon exchange

•Finally both type of quarks are confined by a two body linear potential screened at large distancies due to pair creation

Details can be found in J. of Phys. G: Nucl. Part Phys. 31 1-26

Constituent Quark Model• N-N interaction

– F. Fernández, A. Valcarce, U. Straub, A. Faessler. J. Phys. G19, 2013 (1993)– A. Valcarce, A. Faessler, F. Fernández. Physics Letters B345, 367 (1995)– D.R. Entem, F. Fernández, A. Valcarce. Phys. Rev. C62 034002 (2000)– B. Juliá-Diaz, J. Haidenbauer, A. Valcarce, and F. Fernández. Physical

Review C 65, 034001, (2002)

• Baryon spectrum– H. Garcilazo, A. Valcarce, F. Fernández. Phys. Rev. C 64, 058201, (2001)– H. Garcilazo, A. Valcarce, F. Fernández. Phys. Rev. C 63, 035207 (2001)

• Meson spectrum.– L.A. Blanco, F. Fernández, A. Valcarce. Phys. Rev. C59, 428 (1999)– J. Vijande, F. Fernández, A. Valcarce. J. Phys. G31, (2005)

http://web.usal.es/~gfn/menu_i.htm

Deuteron

NN phase shifts

Triton

qq system

The QCD OGE diagram with point-like quarks gives

0

20

1Contact term 4

ijr r

ijij

err r

0 0̂nn

ijij

r r

1Typical size

reduced mass

02 2

020

lns

4 0 8 0 1 2 0 1 6 0 2 0 0

Q (G e V )

0.05

0.1

0.15

0.2

0.25

0.3

s

Constituent Quark Model

T ij ij OGE ij CON ijV r V r V r V r

Ligth quarks

Solve the Schrödinger equationin the two- and four-body systems

Nonrelativistic approximation

0.542

0.127

ns

s Z

m

M

Heavy quarks

T ij OGE ij CON ijV r V r V r

Meson spectra (I)

0

2 0 0

4 0 0

6 0 0

8 0 0

1 0 0 0

1 2 0 0

1 4 0 0

1 6 0 0

1 8 0 0

2 0 0 0

E (M

eV)

0 -+ 2 -+ (1 --) 3 -- b 1(1 + -) a 2(2 + +) a 1(1 + +)

Light I=1

40 0

60 0

80 0

1 0 0 0

1 2 0 0

1 4 0 0

1 6 0 0

1 8 0 0

2 0 0 0

E (M

eV)

h 1 f 2 f 1

Meson spectra (II)

Light I=0

4 0 0

6 0 0

8 0 0

1 0 0 0

1 2 0 0

1 4 0 0

1 6 0 0

1 8 0 0

2 0 0 0

E (M

eV)

0 - 1 - 1 + 2 + 2 - 3 -

Meson spectra (III)

Kaons

Meson spectra (IV)

2 8 0 0

3 0 0 0

3 2 0 0

3 4 0 0

3 6 0 0

3 8 0 0

4 0 0 0

4 2 0 0

4 4 0 0

4 6 0 0E

(MeV

)

c0 -+ J /(1 --) c(0 + + ) c(1 + +) c(2 + + ) h c(1 + -) (2 --)

Charmonium

Meson spectra (VI)

92 0 0

94 0 0

96 0 0

98 0 0

1 0 0 0 0

1 0 2 0 0

1 0 4 0 0

1 0 6 0 0

1 0 8 0 0

11 0 0 0

11 2 0 0

E (M

eV)

b(0 -+ ) (1 --) b 0(0 + + ) b 1(1 + +) b 2(2 + + ) (2 --)

Bottomonium

qqqq system

Numerical techniques

4q

3q1q

2qx y

z

The two-body problem is solved using the Numerov algorithm. The four-body problem (two particles and two antiparticles) is solved by

means of a variational method.

Three main difficulties:• Non-trivial color structure.

• Symmetry properties in the radial wave function (Pauli Principle)• Two- and four-body mixing.

2q

1qr +

3 3 3 8 8 101Baryon

6 6 8 276

13 8 10

3 6 8 103 3 3 3

3 3 1 8

Tetraquark

3 3 81Meson

•Non-trivial color structure.

Four-Body formalism

1 2!

We expand the radial wave function in terms of generalized gaussians with

-Well defined permutation properties (SS, AA, AS, SA).- L= 0 (relative angular momenta li 0)- Positive parity

•Symmetry properties in the radial wave function (Pauli Principle)

Four-Body configurations.

1 2| 0 | |B qq qqqq

q

q

q

q

q

q s

s

q

q

s

s

qC

• Two- and four-body mixing

nncnncD

nscnscD

nscnscD

J

SJ

SJ

33*

22

11*

)2308(

)2460(

)2317(

0 1

0 0,

0 0qq

qqqq

H wH H

H w

0 1H H H

DsJ mesons

DSJ*(2317)

BaBar: PRL 90, 242001 (2003)

•Narrow peak in DS0. JP=0+ I=0 favored.

•Width consistent with the detector resolution, less than 10 MeV.

•Mass near 2317 MeV, 40 MeV below DK threshold.

DSJ (2460)

•Narrow peak in D*S0,

and also observed in DS. JP=1+ favored.

•Width consistent with the detector resolution, less than 8 MeV.

•Mass close to 2460 MeV, below D*K threshold.

CLEO: PRD 68, 032002 (2003)

18 0 0

20 0 0

22 0 0

24 0 0

26 0 0

28 0 0

E (M

eV)

0 - 1 - 1 + 2 +0 +

qq qqqq

1 8 0 0

2 0 0 0

2 2 0 0

2 4 0 0

2 6 0 0

2 8 0 0

E (M

eV)

0 - 1 - 1 + 2 +0 +

qq only

Open charm sector

←

The Υ(mS)→Υ(nS)ππ

puzzle

Most of the tetraquark resonances are coupled to pairs

qq

Isolate resonances ?

qbqb qcqc They exist?

I=1 Heavy light tetraquarks

qbqb 10,06 GeV.

qcqc 3,66 GeV.

Υ(mS)→Υ(nS)ππ

X(qbqb) →

Υ(1S) 9,460 GeV.Υ(2S) 10,023 GeVΥ(3S) 10,335 GeV.Υ(4S) 10,580 GeV.

→

Υ(2S) →Υ(1S)ππ Υ(3S) →Υ(1S)ππ

Υ(3S) →Υ(2S)ππ

Guo et al NPA 761 269mX=10.08 GeV.

qbqb 10,06 GeV.

←

SUMMARY• We have analyzed the meson spectra using two- and four-quark states within a model which has also been applied to the NN interaction and the hadron phenomenology.

• We have observed that to describe the open-charmed heavy-light meson sector (D and DS) it is necessary to go beyond the conventional quark-antiquark models including other components, as for instance four quark components.

•We have shown that they are several indication of isolated I=1 tetraquark resonances

J. Vijande, A. Valcarce University of Salamanca

End

H. Vogel FPCP 2006 44

Dipion Transitions in cc_

CLEO-c Y(4260) → JBaBar X(3872) → JCLEO-c (3770) → JBES (3682) → J

(3682) (3770)

X(3872)

Y(4260)

compare with

hep-ex/0602034PRD 71 (2005) 071103PRL 96(2006) 082004hep-ex/9909038

3,659 0,140 3,800qqcc →

Most of the mesons fits nicely in a pattern where they have quantum numbers of quark-antiquark bound states.

However this simple and succesfull picture is difficult to apply to the Jπ=0+ scalar meson sector. Apparently scalar are different

Motivations

6 0 0

7 0 0

8 0 0

9 0 0

1 0 0 0

11 0 0

1 2 0 0

E (M

eV)

ss

u s u s

u dd u u u /d d

J= 1 -

K *

0

1 0 0

2 0 0

3 0 0

4 0 0

5 0 0

6 0 0

7 0 0

8 0 0

9 0 0

1 0 0 0

1 1 0 0

E (M

eV)

u s u s

u dd u u u /d d

J= 0 -'

K

u u /d d /ss

u u /d d /ss

4 0 0

5 0 0

6 0 0

7 0 0

8 0 0

9 0 0

1 0 0 0

11 0 0

1 2 0 0

E (M

eV)

ss

u su s

u dd u

u u /d d

J= 0 +

a

f

u u /d d