Charmonium spectroscopy above thresholds 11 th International Workshop

Charmonium spectroscopy above thresholds 11 th International Workshop on Meson Production, Properties and Interaction KRAKÓW, POLAND 10 - 15 June 2010 A. Valcarce University of Salamanca (Spain) T. Fernández-Caramés (U. Salamanca), J. Vijande (U. Valencia) 2/14/2022 Charmonium spectroscopy. . . 1

Motivation: New charmonium (open charm) mesons Below the DD threshold charmonium spectroscopy is a good example of the simple color Fermi-Breit structure of the heavy hadron spectra. Above this threshold new experimental data indicate a more complicated situation. Charmonium 3872 X (3872), X (3940), Y (3940), Z (3940), Y(4140), . . . DD Open charm cc mass spectrum Ds. J*(2317), Ds. J(2460), D 0*(2308), Ds. J(2632), Ds. J*(2700), . . . =0 R. L. Jaffe, Phys. Rev. D 15, 267 (1977) ccnn 2/14/2022 Charmonium spectroscopy. . . 2

Z+(4430) Y(4260) d X, Y, Z(3940) X(3872) uld se e th n ew Co c , t o n If 2/14/2022 e r r b ld u o y the e m e -m n o s e D*D 1|S Ds. Ds|S(0++) sb on s e m e ed ply n ou fou a qu ta s k ? tes ole r a l cu s? *|S(1++) e DD t sta DD|S(0++) m s b Charmonium spectroscopy. . . 3

MULTIQUARK states , although stationary in a potential or bag, do not in general correspond to stable hadrons or even resonances. Far from it, most, perharps even all, fall apart into valence mesons and baryons without leaving more than a ripple on the meson-meson or meson-baryon scattering amplitude. If the multiquark state is unsually light or sequestered from the scattering channel, it may be prominent. If not, it is just a silly way of enumerating the states of the continuum. c + –c cncn –n + ccnn –n D 2/14/2022 n –c –n –c n –– cncn — D D c c w J/ c – n n + c c –n c D –– ccnn Charmonium spectroscopy. . . –n –n 4

Solving the Schrödinger equation: HH or VM 1 ccnn 1 3 1 2 3 2 1, 2 c 4 3, 4 n Pauli principle must be imposed. 2/14/2022 cncn 3 1 2 3 2 1, 2 c 4 3, 4 n C-parity is a good symmetry. Charmonium spectroscopy. . . 5

Interacting potentials -Confinement: Linear potential BCN -One-gluon exchange: Standard Fermi-Breit potential Parameters determined on meson spectroscopy -Confinement: Linear screened potential CQC -One-gluon exchange: Standard Fermi-Breit potential Scale dependent as - Boson exchanges: Chiral symmetry breaking Not active for heavy quarks Parameters determined on the NN interaction and meson/baryon spectroscopy 2/14/2022 Charmonium spectroscopy. . . 6

cncn. CQC model 4 q Energy Theoretical threshold 4500 4400 4300 E (Me. V) J. Vijande et al. , Phys. Rev. D 79, 074010 (2009) 4600 4200 4100 4000 3900 3800 0+ (28) 1+ (24) 2+ (30) 0(21) 1(21) 2(21) 0+ (28) 1+ (24) I=0 2/14/2022 2+ (30) 0(21) 1(21) 2(21) I=1 Charmonium spectroscopy. . . 7

J. Vijande et al. , Phys. Rev. D 76, 094022 (2007) cncn (I=0). BCN model ü . r o ct he t n i s te a a p m No co ( d ? un o b y l p e de st ) t c e 4 q s. Energy n n Theoretical threshold c c r a l u o b a t s e t a t s c e l o m t u a h W 2/14/2022 Charmonium spectroscopy. . . 8

Molecular vs. compact states ← Unbound state (ΔE >0, ΔR → ∞, a single physical channel) ← Molecular state (ΔE 0, ΔR finite ~1– 2, a dominant single physical channel) ← Compact state (ΔE <0, ΔR <1, several different physical channels) 2/14/2022 Charmonium spectroscopy. . . 9

1 ccnn 3 y x 2 z 1, 2 c 2/14/2022 4 3, 4 n Charmonium spectroscopy. . . 10

Solving the Lippmann-Schwinger equation for the two meson system (I) (II) 2/14/2022 Charmonium spectroscopy. . . 11

Coupled channels [(cn)(nc)] JPC (I) (S, L) [(c c) (nn)] DD 0+ + (0) (0, 0) c - 1+ (+) (0) (1, 0), (1, 2) J/ - 1+ (–) (1, 0), (1, 2) J/ - 0+ + (0) (0, 0), (2, 2) c - 1+ – (0) (1, 0), (1, 2) c - 1– – (0) (0, 1), (2, 3) J/ - 1– + (0) (1, 1), (1, 3) c - 2+ + (0) (2, 0), (2, 2) J/ - 2– – (0) (1, 1), (2, 1), (1, 3), (2, 3) c - 0– + (1) (0, 0), (2, 2) J/ - 1+ – (1) (1, 0), (1, 2) J/ - 2+ + (1) (2, 0), (2, 2) J/ - DD* (I) D*D* 2/14/2022 Charmonium spectroscopy. . . (II) 12

where for practical purposes we have used the convention 2/14/2022 Charmonium spectroscopy. . . 13

Interacting potentials -Confinement: Linear potential BCN -One-gluon exchange: Standard Fermi-Breit potential Parameters determined on meson spectroscopy -Confinement: Linear screened potential CQC -One-gluon exchange: Standard Fermi-Breit potential Scale dependent as - Boson exchanges: Chiral symmetry breaking Not active for heavy quarks Parameters determined on the NN interaction and meson/baryon spectroscopy 2/14/2022 Charmonium spectroscopy. . . 14

2/14/2022 Strange twobaryon systems Charmonium spectroscopy. . . A. Valcarce et al. , Eur. Phy. J. A 37, 217 (2008) H. Garcilazo et al. , Phys. Rev. C 76, 034001 (2007) A. Valcarce et al. , Rep. Prog. Phys. 68, 965 (2005) Non-strange twobaryon systems Heavy baryons 15

T. Fernández-Caramés et al. , Phys. Rev. Lett. 103, 222001 (2009) JPC(I)=1++(0) DD* – J/ X(3872) No charge JP=1+ partners and I=1, of coupled the X(3872) to J/ [ diquark-antidiquark Repulsive ] 2/14/2022 Charmonium spectroscopy. . . 16

D D – c D* D* – J/ 2/14/2022 Charmonium spectroscopy. . . 17

Attractive channels for the two D(Ds)-meson systems R. Mizuk et al. , Phys. Rev. D 78, 072004 (2008) System DD JPC(I) 0++(0) DD* 1++(0) D* D* 0++(0) D* D* 2++(1) ! ! PRL 67, 556 (1991) N. A. Törnqvist. PV and VV two-meson systems are the most natural candidates to be bound, in spite of the different working framework. Y(3940) T. Branz et al. PRD 80, 054019 (2009). D*D* JPC(I)=0++ (0)[2++(0)]. Effective lagrangians. [Y(3940) J/ ]> 1 Me. V. Y(4140) T. Branz et al. PRD 80, 054019 (2009). D*s JPC(I)=0++ (0)[2++(0)]. Effective lagrangians. [Y(4140) J/ ]> 1 Me. V. R. M. Albuquerque et al. PLB 678, 186 (2009). D*s JPC(I)=0++ (0). QCD sum rules. G. -J. Ding. EPJC 64, 297 (2009). D*s JPC(I)=0++ (0). One-boson exchange model. Y(3940), Z(3940), X(4160) R. Molina et al. PRD 80, 114013 (2009). D*D* D*s JPC(I)=0++ (0), 2++(0). Dynamically generated resonances. 2/14/2022 Charmonium spectroscopy. . . 18

Summary • Hidden flavor components (unquenching the quark model) offer a possible explanation of the new experimental data in heavy meson spectroscopy. • Deeply-bound (compact) four-quark states with non-exotic quantum numbers are hard to justify [while “many-body (medium)” effects do not enter the game]. • Slightly bound (meson-meson molecules) four-quark states seem to be present in the heavy meson spectra. • PV: 1++ (0) are the candidate quantum numbers to lodge meson-meson molecules for systems made of non-identical mesons [X(3872)]. • PP: 0++ (0) would the only candidate to lodge a broad meson-meson molecule for systems made of identical pseudoscalar mesons. • VV: 0++ (0) and 2++ (0, 1) should show meson-meson molecules for systems made of identical vector mesons [Y(3940), Y(4140)]. 2/14/2022 Charmonium spectroscopy. . . 19