i=1 heavy-light tetraquarks and the Υ(ms) → Υ(ns)ππ puzzle francisco fernández instituto de...
DESCRIPTION
Outline ► Motivations ► the model ► D sJ mesons ► The Υ(mS) → Υ(nS)ππ puzzleTRANSCRIPT
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
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