Exotic charmed fourquark mesons molecules versus compact states

Exotic charmed four-quark mesons: molecules versus compact states A. Valcarce University of Salamanca (Spain) J. Vijande (U. Valencia) Beijing, October 23 rd, 2010 Exotic charmed four-quark states 1

Motivation: New open-charm and charmonium mesons 2800 Ds. J mesons Ds. J (2317) 2600 Ds 1 (2458) D* K E (Me. V) Open-charm mesons * 2400 D 0 K 2200 2000 1800 0– 1– 0+ 1+ 2+ Ok! J. V. , A. V. et al, Phys. Rev. D 73, 034002 (2006) Beijing, October 23 rd, 2010 Exotic charmed four-quark states 2

X (3872), X (3940), Y (3940), Z (3940), Y(4140), . . . More complicated (See J. Vijande talk on Thursday) Charmonium 3872 DD Simple color Fermi-Breit quark-antiquark scheme cc mass spectrum =0 R. L. Jaffe, Phys. Rev. D 15, 267 (1977) ccnn Beijing, October 23 rd, 2010 Exotic charmed four-quark states 3

Further evidences: light baryons The effect of the admixture of hidden flavor components in the baryon sector has also been studied. With a 30% of 5 q components a larger decay width of the Roper resonance has been obtained. 10% of 5 q components improves the agreement of the quark model predictions for the octet and decuplet baryon magnetic moments. The admixture is for positive parity states and it is postulated. D. Riska et al. , Nucl. Phys. A 791, 406 -421 (2007) From the spectroscopic point of view one would expect the effect of 5 q components being much more important for low energy negative parity states (5 q S wave) S. Takeuchi et al. , Phys. Rev. C 76, 035204 (2007) L(1405) [1/2–], QM 1500 Me. V (L(1520) [3/2–]) L= |3 q [(0 s)20 p]> + |5 q[(0 s)5]> OGE =0; QCM Sp–NK–L ud No resonance found , 0 A resonance is found T. -S. H. Lee et al. , Phys. Rev. C 61, 065203(2000) E. Oset et al. , Phys. Rev. Lett. 95, 052301(2005) Beijing, October 23 rd, 2010 Exotic charmed four-quark states 4

Solving the Schrödinger equation: VM and HH 1 ccnn Hyperspherical Harmonics Method 3 1 2 3 –– L=0 S=1 I=0 ccnn J. V. , A. V. et al. , Phys. Rev. D 79, 074010 (2009) 4 2 1, 2 c 3, 4 n HH VM E RMS 3860. 6 0. 367 3861. 4 0. 363 Variational Method J. V. , A. V. , Symmetry 1, 155 (2009) Pauli principle must be imposed. Beijing, October 23 rd, 2010 Exotic charmed four-quark states 5

1 ccnn 3 1 2 3 2 1, 2 c 4 3, 4 n Physical channels J. Vijande, A. V. , Phys. Rev. C 80, 035204 (2009) Beijing, October 23 rd, 2010 Exotic charmed four-quark states 6

4600 4 q Energy M 1 M 2 threshold 4500 4400 4300 E (Me. V) J. V. , A. V. , N. Barnea, Phys. Rev. D 79, 074010 (2009) cncn. CQC model 4200 4100 4000 3900 3800 0+ (2 8) 1+ (24) 2+ (30) 0 - (21) 1 - (21) 2 - (21) 0+ (28) 1+ (24) I=0 Beijing, October 23 rd, 2010 Exotic charmed four-quark states 2+ (30) 0 - (21) 1 - (21) 2 - (21) I=1 7

1 ccnn 3 y x 2 z 1, 2 c 4 3, 4 n Unbound Beijing, October 23 rd, 2010 Exotic charmed four-quark states 8

Molecular states: Probability of physical channels vs. binding energy We multiply the interaction between the light quarks by a fudge factor. This modifies the 4 q energy but not the threshold Beijing, October 23 rd, 2010 1 3 y x Exotic charmed four-quark states ccnn 2 z 4 1, 2 c 3, 4 n 9

ü No compact states in the ccnn sector (J. Vijande) üOne compact state in the ccnn sector (JP=1+) I. Which is the difference? c + –c cncn –n D ccnn c –n c w J/ c n + n –c –n –c n –– cncn II. Is that—all? NO! D –n + D Beijing, October 23 rd, 2010 c c –n c D –– ccnn Exotic charmed four-quark states –n –n 10

Beyond the naive quark model o Diquark hypothesis: The idea is to restrict the Hilbert Space selecting those components that may favor the binding of the system. A diquark is an S-wave bound state of two quarks, antisymmetric in color (3), isospin (0) and spin (0). I. For some quantum numbers this implies discarding a priori more than 90% of the basis vectors. II. Numerically, these vectors account for less than 3% of the total probability. Application to four-quark states can be found in several papers by Maiani, F. Piccinini, and A. D. Polosa and also by D. Ebert, R. N. Faustov, and V. O. Galkin. o Many-body interactions: Three- or four-body interactions not factorizable into a sum of two-body terms could be playing a role. Beijing, October 23 rd, 2010 Exotic charmed four-quark states 11

Many-body forces in nuclear physics AV 18 (2 B) CDBonn/TM (3 B) 2 H 3 H 4 He Beijing, October 23 rd, 2010 Exotic charmed four-quark states 12

Many-body forces in the hadron spectra a x y x x a V 2 B x a x x a ( ) rr 3 = - å l j li rij 16 i < j =- a ö 3æ 8 4 ç - (r 12 + r 34 )- (r 13 + r 24 + r 14 + r 23 ) 16 è 3 3 ø 1 1 1 3+ 2 » (a + a ) + ( 2 a + 2 a ) » a = 2. 21 a 2 4 2 2 ( ) VMB = LMIN = 4 x + y » a 2 3 + 2 » 5. 46 a Beijing, October 23 rd, 2010 Exotic charmed four-quark states 13

Beyond two-body interactions J. V. , A. V. , J. M. Richard, Phys. Rev. D 76, 114013 (2007) Beijing, October 23 rd, 2010 Exotic charmed four-quark states 14

Candidates for observation (QQnn). üCharm Sector: ccnn 1: JP=1+: CQC: ΔE= – 76, ΔR= 0. 81. Compact. Weak decay I=0 BCN: ΔE= – 7, ΔR~1 – 2. Molecular. γ decay Electromagnetic: E 4 q > M(D)+M(D) üBottom Sector: bbnn P=1+: CQC: Δ = – 214, Δ = 0. 74. Compact. Weak decay 1: Jmodes. • Decay E R I=0 BCN: ΔE= – 144, ΔR= 0. 76. Compact. Weak decay 2: JP=0+: CQC: ΔEWeak: = – 149, ΔR= 0. 76. Compact. γ decay E 4 q < M(D)+M(D) I=0 BCN: ΔE= – 52, ΔR= 0. 76. Compact. γ decay 3: JP=3 – : CQC: ΔE= – 140, ΔR= 0. 73. Compact. γ decay I=1 BCN: ΔE= – 119, ΔR= 0. 73. Compact. γ decay 4: JP=1 – : CQC: ΔE= – 11, ΔR ~1 – 2. Molecular. Weak decay I=0 Beijing, October 23 rd, 2010 Exotic charmed four-quark states 15

Summary • There is an increasing interest in hadron spectroscopy due to the advent of a large number of experimental data in several cases of difficult explanation. • These data provide with the best laboratory for studying QCD in the socalled strong limit. We have the methods, so we can learn about the dynamics. • Hidden flavor components (unquenching the quark model) offer a possible explanation of the new experimental data and old problems in the meson and baryon spectra. • Experimentalists: Exotic charmed four-quark systems may exist if our understanding of the dynamics does not hide some information. I hope you can answer this question to help in the advance of hadron spectroscopy. • Theorists: We have seen many different approaches to the new charmonium states, it would be great to have predictions for the exotic charmed meson states to be tested in the near future. Beijing, October 23 rd, 2010 Exotic charmed four-quark states 16