ds (2317) and d (2308) as candidates for tetraquarks?€¦ · string), 4-body (“flip-flop”)...
TRANSCRIPT
V. Dmitrasinovic, Nagoya, Dec. 08
Ds+(2317) and D*(2308) as
candidates for tetraquarks?
ヴェリコ ドミトラシノビッチ
Veljko DmitrašinovićLaboratory of Physics (010),Vinča Institute of NuclearSciences, Belgrade, Serbia
“New Hadrons with Various Flavors” Workshop Nagoya , 6-7 December 2008
V. Dmitrasinovic, Nagoya, Dec. 08
• Introduction: scalar D mesons• ‘t Hooft interaction in the
constituent quark model (CQM) Ann.Phys.321, 355 (06)
• Charm tetraquark spectrum in CQM: D+(2308) - Ds
+(2317) Mass PuzzlePRD70,096011 (04); PRL94,162002 (05); MPLA21, 533 (06)
• Summary and Outlook
Outline:
V. Dmitrasinovic, Nagoya, Dec. 08
Charmed strange mesons• Predicted spectrum in
potential models (pre-2006) :
• Two (?) old strange scalar (JP = 0+) states: Ds
**+(2317) (BaBar) and Ds
**+(2632) (SELEX, unconfirmed!?);
• New X(2690) (BaBar) state, equivalent to newDs1
**+(2700) (Belle) JP = 1- state?
• Too light ! Too many?!
317)
DsJ*(2317)
DsJ(2460)
Ds
Ds*
Ds1(2536)
Ds2(2573)
consistent with models
not consistent
to be found
V. Dmitrasinovic, Nagoya, Dec. 08
Charmed nonstrange mesons• Spectrum predicted in
potential models:• Scalar (0+) nonstrange state:
D+(2308) (Belle), equivalent toD+(2405) (FOCUS) ? (2- σapart, see [I. Bigi and Orsay group, hep-ph/0512270]
• Strange (2317) and nonstrange(2308) states degenerate!?!
• The 2308 is too light. If 2405 is a different state, then too many and too heavy!
V. Dmitrasinovic, Nagoya, Dec. 08
Two approaches to tetraquarks
• Colorless: “hadronic molecules”/ “mesonia” in quasi-“bootstrap” models based on Bethe-Salpeter eqn (v. Beveren & Rupp, Valencia group, Kolomeitsev & Lutz, Sassen & Krewald)
• Colorful: constituent quarks, need a model of confinement (2-body (“F.F”), 3-body (Y-string), 4-body (“flip-flop”) forces)
V. Dmitrasinovic, Nagoya, Dec. 08
“True” tetraquarks • Check if D+(2308), Ds
+(2317) = (q2q*2) might be “true tetraquarks”?
• Colour quark force dependence important:Multiquarks related to multiple colour singlets (expected since 1976)
• “F.F”/“Coulomb gauge” Lorentz vector two-body confinement model leads to a q2q*2 in the colourstate
341233
V. Dmitrasinovic, Nagoya, Dec. 08
The constituent quark model
• Schrödinger eqn for wave fns.• Must define the constituent-quark dynamics, • OGE + linear scalar two-body confinement, widely used
in quarkonium spectroscopy leads to unstable two-meson systems and unstable baryons!
• need vector two-body confinement, or must add as yet unknown three-quark forces (PRD67, 114007 (’03)) to the scalar two-body confinement to stabilize the nucleon & two meson states.
• Spin-dep. “hyperfine” forces, treated perturbatively. Calculate tetraquark mass!
V. Dmitrasinovic, Nagoya, Dec. 08
Example of a bound two-meson state due to two-body vector colour potential
• Tetraquarks bound for large enough q/q* mass ratio. [Ader, J.M. Richard and TaxilPRD25,2370(‘82)]
• Double-b heavy-light tetraquark mass as a function of separation.(D. Janc, 2004)
• The “hidden-colour”state (88) is confined.Saturation visible in the (11) two-meson state.
10500
10550
10600
10650
10700
10750
10800
10850
10900
10950
11000
0 0.5 1 1.5 2 2.5 3
s [fm]
M [M
eV]
all config.triplet config.singlet config.sextet config.octet config.
V. Dmitrasinovic, Nagoya, Dec. 08
SU(6) contents of single-charm tetraquarks
• Hyperfine interactionsdetermine the spin-flavoursplittings of mass spectra1) ‘t Hooft h.f. Interaction2) colour-spin h.f. interaction
• Scalar states are generally the lowest-lying tetraquarks
� w(w w )l , s t
6 120,84,
6 120,
V. Dmitrasinovic, Nagoya, Dec. 08
Hyperfine interactions in the CQM
• The “color-magnetic” CS (Fermi-Breit) interaction believed to be the main source of SU(6) multipletsplittings in CQM.
• CS HFI cannot solve the “UA(1) problem” in mesons (and lesser problems in baryons).
• The ‘t Hooft interaction solves the UA(1) problem, and improves baryon spectra.
• “Calibrate” HFI in mesons and baryons, then use it in multiquarks Ann.Phys.321, 355 (06)
V. Dmitrasinovic, Nagoya, Dec. 08
Instanton-induced ‘t Hooft interaction in QCD
• Instantons induce a new three-quark, flavour-dependent, contact interaction
• Closing one pair of “legs” leads to a two-quark HF interaction that depends on flavour and spin.
uL
dR
sR
� dL
sL
uR
NF=3
I
uL
dR
sR
dL
sL
uR
I
�
NF=3
I q2L
< qq3R 3L>
I
q1R
q2L
q1L q1L
q2R
q1R
q2R
< qq3R 3L>
V. Dmitrasinovic, Nagoya, Dec. 08��� ������ �� ����� ���� ������ ���� ��
��� ��������� ������� � ���������
��� � ������������� ��� ��� � ���� ��� � ���
����� �
���
���
�� � ���
� ���
� ���� ��� ���� �������� �!" #������ �� �� ��
��� ����� � ����#$
��� %� &���� ���� ������ ���� ���� �� ��� �� ���
��� � ���������
���� � ��������
����
�����
��� � ����
� ��� � ������ � ���
����� �
���
��'
���
�����
�� � �� ( ����������
��
� � ���
�
V. Dmitrasinovic, Nagoya, Dec. 08
Light mesons with ‘t Hooft interaction
• Vector and pseudoscalars• Only p.s. mesons affected
by ‘t Hooft HFI• Vector mesons still ideally
mixed (contrary to Glozman-Riska int.)
• Correct ordering of states: U(1) problem solved even in non-relativistic approx.
• Only the pion (still) too heavy (non-relativistic).Ann.Phys.321, 355 (06)
0.25
0.5
mas
s(G
eV)
SU(3)K = 0
�c > 0
�����
����
Expt
�� ��
S.break.
����
1.0
0.75 ����
�
� � ���
K > 0
�� ���
�������
�����
�����
� � ���
�
�c = 0 �c = 0
K > 0
V. Dmitrasinovic, Nagoya, Dec. 08
Single-charm tetraquark SU(3) classification
• Tetraquark SU(3) C.G. series: two3*-, 6-, 15*-plets. V.D. PRD70,096011 (2004)
• The two 3*-plets and the “inner” triplet in the 15*-plet may mix!
�
�
�
�
���
Y YY
I3
→
3 3 3 3 3 6 15A S× × = + + +
V. Dmitrasinovic, Nagoya, Dec. 08
Single-charm tetraquark masseswith ‘t Hooft h.f. interaction
• Flavour dependence of ‘t Hooft interaction breaks degeneracy.
• SU(3) symmetry breaking s-u/d quark mass difference adds to the splitting.PRD70,096011 (2004)
2.25
2.75
mas
s(G
eV)
6
K = 0 K > 0
D+K
DS+h
Expt
DS+p
2.50
3.00
S3
15
A3
m ms u,d¹
D (2632)S
D (2317)S
V. Dmitrasinovic, Nagoya, Dec. 08
and mixings with ‘tHooft HFI• CG series predicts three Ds and
four D mesons• The lowest mass Ds and D in the
antisymmetric 3*-plet• Symmetric 3*-plet mixes with the
15*-plet• This mixing splits the two Ds states
into a “light” and a “heavy” one. • Antisymmetric 3*-plet D mixes with
the 6-plet and allows the small deviation of D from Ds mass to be calculated
mas
s(G
eV)
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
2.2
2.4
2.6
2.8
3
3.2
3.4
D+K
DS+h
D (2632)S
D (2317)S
A( )GeV
153 −S 63 −A
V. Dmitrasinovic, Nagoya, Dec. 08
D+(2308) - Ds+(2317) Mass Puzzle I
• All members of the antisymmetric 3*-plet and 6-plet are degenerate irrespective of their strangeness!PRL94,162002 (2005)
• Hidden strangeness in flavour w.f.
3
3
1 ( ( ) ( ) )21 ( ( ) ( ) )2
n A
s A
D c s u s s u d d u u d
D c u u s s u d d s s d
= − − −
= − − −
V. Dmitrasinovic, Nagoya, Dec. 08
D+(2308) - Ds+(2317) Mass Puzzle II
• Explains the near degeneracy of D+(2308) and Ds
+(2317). PRL94,162002 (2005)
• This mass pattern is due to the SU(3) flavour wave function permutation antisymmetry.
• Such multiplets exist only in multiquarks: the first and the simplest are found in tetraquarks!
• Similar to a0(1450) – K0*(1430) near-degeneracy in
light scalars.• Can calculate the mass difference based on the mixings
of multiplets
V. Dmitrasinovic, Nagoya, Dec. 08
Summary and outlook• One antitriplet: [Ds
+(2317) (BaBar), D+(2308)(Belle)] mightbe tetraquarks lowered in mass by the ‘t Hooft interaction.
• Small strange-nonstrange meson mass difference Ds+(2317) -
D+(2308) could be a “smoking gun” evidence of tetraquarkstructure!
• Another antitriplet: [D+(2405) (FOCUS), Ds+(2632)
(SELEX), or Ds+(2690) (BaBar)] might be a mixture of cq
bar and tetraquark• The Ds
+(2632) partial decays indicate unusual flavourmultiplet (15-plet) (Zhu et al) that exists only in tetraquarks.
• Models predict many exotic tetraquarks. Experimental search is made more difficult by their large (“fall-apart”) widths!
• Many theoretical uncertainties
V. Dmitrasinovic, Nagoya, Dec. 08
Exotic tetraquark mass predictions with ‘tHooft HFI
2317 2317 - - - -2724 2724 2724 2724 - -2632 2561 2520 2520 2657 23833437 3224 - - - -
3A
+sJD +
JD
6
3S
0*JsD ++
sJD +ssJD ++
JD
15
•Many exotic states, most of them within exptl reach of Belle and BaBar
•Model independent searches for exotica at present accelerators suggested by Cheng&Hou, PLB566, 193 (‘03). Two exp. search so far (CDF, BaBar).
V. Dmitrasinovic, Nagoya, Dec. 08
2. Color-spin HFI in QCD
• Color-magnetic HFI from Fermi-Breitcontact in OGE.
• Its spin-dependence splits the vector and pseudoscalar mesons
V. Dmitrasinovic, Nagoya, Dec. 08
Color-spin HFI in tetraquarks
• Terasaki assumes CS HFI; that leads to an isosinglet, and an isotriplet Ds
+(2317)! predicts degenerate iso-partners.
• ‘t Hooft HFI also leads to isotriplets, and many other exotics, but at higher masses.
• Model independent searches for exotica at present accelerators suggested by Cheng&Hou, PLB566, 193 (‘03). Only one exp. search so far (CDF).
V. Dmitrasinovic, Nagoya, Dec. 08
mixing with CS HFI• Predict three D_s mesons: two “light” and a “heavy” one
• Lowest mass D is the ideal mixture of the antisymmetric3*-plet and the 6-plet. Lowest Ds is pure 3*-plet.
• Symmetric 3*-plet Ds,D mix with the 15*-plet ideally
• Mixing splits the two states into a heavy (hidden strangeness) and a light one
153 −S
V. Dmitrasinovic, Nagoya, Dec. 08
Single-charm tetraquark masses with colour-spin h.f. interaction
• CS HFI implies no flavourdependent splitting among multiplets
• Many degenerate iso-partners due to ideal mixing!
• Two states at 2320 MeV: the iso-singlet Ds
+(2317),and iso-triplet Ds
++(2317)! • Isotriplet expected to be as
wide as the D+(2308): G = 250-350 MeV
C = 0 C 0�
m ms u,d�
(2690)
(3-15)+(2600)
(2490)
(2560)
(2350)
(2460)
(3-15)-
(2230)
(2360)
(3-6)-
(3-6)+
(2320)(2320)
(2270)
V. Dmitrasinovic, Nagoya, Dec. 08
Exotic tetraquark mass predictionswith CS HFI
2320 2360 - - - -2320 2230 2250 2320 - -2460 2350 2500 2460 2550 23502690 2600 - - - -
3A
+sJD +
JD
6
3S
0*JsD ++
sJD +ssJD ++
JD
15
•Many exotic states, most of them within exptl reach of Belle and BaBar
•Model independent searches for exotica at present accelerators suggested by Cheng&Hou, PLB566, 193 (‘03). Two exp. searches so far (CDF, BaBar).
V. Dmitrasinovic, Nagoya, Dec. 08
Searches for isotriplet DsJ mesons
• CDF has conducted a search for isopartnersof Ds
+(2317) (M. Shapiro) eConfC030603:MAR06,2003
• without success: no visible structure in the isotriplet spectra (lower figures)
]2
Cand. [GeV/c-π+Mass of D
2 2.2 2.4 2.6 2.8 3 3.2
Num
ber
of E
ntrie
s / 1
0 M
eV
0
2000
4000
6000
8000
10000
12000
-π+D
+π+D
)22.0 MeV/c± (PDG=2458.9 *02D
0π-01D 0π-*0
2D
Candidates2*0 300 D±9100
2 1.0(stat) MeV/c±Mass: 2464.2
2 2.2(stat) MeV/c±2278.1
2 4.3(stat) MeV/c±2323.4
CDF Run II Preliminary-1 ~80 pb
]2
Cand. [GeV/c-πs+Mass of D
2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3
Num
ber
of E
ntrie
s / 1
0 M
eV0
50
100
150
200
250
300
-πs+D
+πs+D
CDF Run II Preliminary-1 ~80 pb) > 350 MeV/cπ(tp
V. Dmitrasinovic, Nagoya, Dec. 08
DsJ’s - Overtly Exotic ?• BaBar conducted two
searches for isopartners of Ds
+(2317) so far (2004 and 2006, A. Palani)
• No clear signs of exotic charge states !
• These exotics should be very wide (G = 250-350 MeV) due to “fall-apart”nature of the decay, however.
Ds+π-
Ds+π+
DsJ(2460) ?DsJ(2317) ?
232 fb-1 hep-ex/0604030
V. Dmitrasinovic, Nagoya, Dec. 08
Decays as tetraquark signature?
• Two kinds of decays measured so far (still incomplete): hadronicand EM.
• Ds+(2317) is very narrow due isospin conservation: main hadronic
decay (Ds+(1969) π0) violates isospin.
• Other predicted tetraquarks should be wider due to their being above the allowed decay thresholds.
• Ds+(2632) partial decays indicate unusual flavour multiplet (15-
plet?) that exists only in tetraquarks.Liu et al.PRD70, 094009,2004
• decays in agreement with tetraquark assumption. • Most EM decays of Ds
+(2317) consistent with cs content, however.ssB D D⎯⎯→ +
V. Dmitrasinovic, Nagoya, Dec. 08
Outlook: theoretical uncertainties in multiquark calculations
• Colour confining dynamics• Hyperfine interactions• Relativity• Chiral symmetry• Dynamical pair production
V. Dmitrasinovic, Nagoya, Dec. 08
Colour in Multiquarks
• Color interactions must confine quarks. • Confinement must not act between quarks in two separate
color singlets (“color saturation”), except perhaps for the v.d.Waals force.
• There are multiple color singlets and the interactions mix them. Color singlet eigenstates are mixtures that depend on the spatial separation.
• All color singlets ought to be stable, as all of them may be admixed. All color eigenstates ought to be observable: new (“hidden color”) hadrons.
V. Dmitrasinovic, Nagoya, Dec. 08
Modelling Confinement• Two-body interaction
• with the “saturating” colour factor has been used.
• “Saturation” of color forces = no confining forces between colour singlets (modulo v.d.Waals force)
• Lorentz vector confining int.: all c. singlets stable.• Lorentz scalar confining int.: some c. singlets unstable!
)()()(41)(
8,..,1ijjiij
a
aj
aiij rvFFrvrV ⋅≡= ∑
=
λλ
)( ji FF ⋅
V. Dmitrasinovic, Nagoya, Dec. 08
Tetraquark colour states• Color quark interactions mix the
two colour singlets• One state turns into two mesons at
asymptotic distances; another is a confined hidden-colour (hc) tetraquark state.
• Diagonal states are orthogonal: h.c. state cannot decay into two mesons.
• No physical process in the NRCQM can turn one c. eigenstateinto another. Need annihilation processes (relativity).
341234122413
341234122413
66cos33sin88
66sin33cos11
θθ
θθ
+−=
+=
0 1 2 3 4 5
0
10
20
30
40
50
Colour singlet mixing angle in tetraquarks
V. Dmitrasinovic, Nagoya, Dec. 08
• A “saturating” three-body force has been introduced, V.D. PLB499,136 (2001)
• Two scenarios: (a) Allow all color states, demand that color 8, 10 be heavy; (b) Forbid all non-singlets
• Scenario (a) demands 3-, 4-,5-body forces etc.; (b) allows only dominant 2-body and a weak 3-body.
• PRD 67, 114007 (03).
( )3
2 2 23 0 0
1, , exp[ ( ) / ]8
b
a b cabcb i j k i j k i j k
V V V
V r r r d U r r r aλ λ λ
→ +
= − + +r r r
18
abc a b ci j kd λ λ λ
Three-body force: stability and saturation
V. Dmitrasinovic, Nagoya, Dec. 08
Three-quark colour force in tetraquarks
• Saturation: mixes states in the asymptotic basis, but changes only thehidden-colour stateenergy
• Does not mix states in the Pauli basis, but changes theirenergies. Unstable.PRD 67, 114007 (03).
12 341 1
12 341 1 12 348 8
12 348 8
13 243 3
13 243 3
13 246 6
13 246 6
5 2 /18−
5 2 /18−
5 /(9 3)
5 /(9 3)
5 2 /(18 3)−
5 2 /(18 3)−
0
0
0
5 2 /(9 3)−
5 2 /(9 3)−
5 /(18 3)−
5 /(18 3)−
5 /18−
5 / 9
5 /18
18
abc a b ci j kd λ λ λ
V. Dmitrasinovic, Nagoya, Dec. 08
3850
3875
3900
3925
3950
3975
4000
0 1 2 3 4 5 6
s [fm]
E [M
eV] Uo = 0
Uo = -20MeV (a.=3fm)Uo = -40MeV (a.=3fm)
Effects of three-quark colour force on double-charm tetraquarks (D. Janc)