The 5-th International Conference on Quarks and Nuclear Physics Meson-meson molecules and compact four-quark states The 5-th International Conference on Quarks and Nuclear Physics Beijing , September 21－26, 2009 A. Valcarce University of Salamanca (Spain) J. Vijande, N. Barnea, J.-M. Richard. 25 February, 2019 Meson-meson molecules ...

Motivation: New open-charm and charmonium mesons Heavy meson spectroscopy is the best example of the color Fermi-Breit structure of the heavy hadron spectra The formerly comfortable world of heavy meson spectroscopy is being severely tested by new experiments 3872 DD cc mass spectrum Charmonium X (3872), X (3940),Y (3940), Z (3940), Y(4260),Y(4385), X(4664), Z (4430)+,... Open charm DsJ*(2317), DsJ(2460), D0*(2308), DsJ(2632), DsJ*(2700), DsJ(2860), ... meson-meson molecules, compact four-quark states ccnn cncn 25 February, 2019 Meson-meson molecules ...

Solving the Schrödinger equation: (I) HH 1 2 3 1 2 3 4 1,2  c 3,4  n ccnn 1 2 3 1 2 3 4 1,2  c 3,4  n cncn C-parity is a good symmetry. Pauli principle must be imposed. Radial part is expanded into HH functions, hyperangular part, (up to a Kmax value) and a sum of Laguerre functions, hyperradial part. 25 February, 2019 Meson-meson molecules ...

Solving the Schrödinger equation: (II) VM The radial part is expanded in terms of generalized gaussians: where a,b,c,d,e, and f are variational parameters Each generalized gaussian contains an infinite number of relative angular momentum l1, l2, and l3, but it has L=0 and positive parity (can be generalized, not trivial) – – L=0 S=1 I=0 ccnn HH VM E RMS 3860.6 0.367 3861.4 0.363 25 February, 2019 Meson-meson molecules ...

Bound states: Meson-meson molecules vs. Compact four-quark states Figures of merit. Physical channel: A vector of the Hilbert space whose quantum numbers allow to identify it with two physical mesons. 25 February, 2019 Meson-meson molecules ...

Meson-meson molecules ... 1 2 3 1 2 3 4 1,2  c 3,4  n ccnn 25 February, 2019 Meson-meson molecules ...

The four-quark zoo: what can we expect? Unbound state (threshold ): An state with ΔE >0, ΔR → ∞, and whose wave-function comes determined in terms of a single physical channel. Meson-meson molecule: An state with ΔE <0, ΔR finite ~1–2, and described dominantly in terms of a single physical channel. Compact four-quark state: An state with ΔE <0, ΔR <1, and whose wave function contains several different physical channels. 25 February, 2019 Meson-meson molecules ...

Interacting potentials Parameters determined on meson spectroscopy BCN Confinement: Linear potential One-gluon exchange: Standard Fermi-Breit potential Confinement: Linear screened potential One-gluon exchange: Standard Fermi-Breit potential Scale dependent as Boson exchanges: Chiral symmetry breaking Not active for heavy quarks CQC Parameters determined on the NN interaction and meson/baryon spectroscopy 25 February, 2019 Meson-meson molecules ...

Meson-meson molecules ... cncn (I=0). CQC Model 4q Energy Theoretical threshold 25 February, 2019 Meson-meson molecules ...

Meson-meson molecules ... cncn (I=0). BCN Model 4q Energy Theoretical threshold 25 February, 2019 Meson-meson molecules ...

cncn (I=0). BCN Model Experimental threshold Theorerical Thresholds 5! 25 February, 2019 Meson-meson molecules ...

Meson-meson molecules ... cncn. CQC Model 4q Energy Theoretical threshold 25 February, 2019 Meson-meson molecules ...

Thresholds Uncoupled two-meson threshold: Impose L, S, J, I, P, C (when defined) conservation, and the spin-statistic theorem (when identical particles are considered). Coupled two-meson threshold: Impose J, I, P, C (when defined) conservation, and the spin-statistic theorem (when identical particles are considered). Uncoupled threshold ≥ Coupled threshold 25 February, 2019 Meson-meson molecules ...

Meson-meson molecules ... cncn. CQC Model 4q Energy Uncoupled threshold Coupled threshold 25 February, 2019 Meson-meson molecules ...

Meson-meson molecules ... x z y 1 2 3 4 1,2  c 3,4  n ccnn 25 February, 2019 Meson-meson molecules ...

Meson-meson molecules ... x z y 1 2 3 4 1,2  c 3,4  n ccnn 25 February, 2019 Meson-meson molecules ...

Probability of physical channels vs. Binding energy We multiply the interaction between the light quarks by a fudge factor. This modifies the 4q energy but not the threshold 25 February, 2019 Meson-meson molecules ...

Behaviour of the radius ← Compact state (1+ CQC) ← Molecular state (1+ BCN) ← Unbound state (0+ CQC) 25 February, 2019 Meson-meson molecules ...

Meson-meson molecules ... No compact states in the ccnn sector. One bound state in the ccnn sector (and four/three bound states in the bbnn sector). which is the difference? 25 February, 2019 Meson-meson molecules ...

Meson-meson molecules ... – D — J/ w + c n – ccnn cncn c n – D + 25 February, 2019 Meson-meson molecules ...

Meson-meson molecules ... No compact states in the ccnn sector. One bound state in the ccnn sector (and four/three bound states in the bbnn sector). which is the difference? is that all? 25 February, 2019 Meson-meson molecules ...

Beyond the naive quark model 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. Many-body interactions: Three- or four-body interactions not factorizable into a sum of two-body terms could be playing a role. 25 February, 2019 Meson-meson molecules ...

Many-body forces in nuclear physics AV18 (2B) 2H 3H 4He CDBonn/TM (3B) 2H 3H 4He 25 February, 2019 Meson-meson molecules ...

Many-body forces in the hadron spectra ( ) a y x L V r MIN MB ij j i B 46 . 5 2 3 4 21 1 8 16 23 14 24 13 34 12 » + = ø ö ç è æ - å < l a a x x x a 25 February, 2019 Meson-meson molecules ...

Meson-meson molecules ... Summary There is an increasing interest in heavy 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 the predictions of QCD in what has been called the strong limit. There are enough data to learn about the glue holding quarks together inside the hadrons. Hidden flavor components, unquenching the quark model, seem to be necessary to tame the bewildering landscape of hadrons, but an amazing folklore is borning around. Compact four-quark states with non-exotic quantum numbers are hard to justify while “many-body (medium)” effects do not enter the game. Meson-meson molecules seem to be present in the meson spectra. Four-quark exotic systems should exist if our understanding of the dynamics does not hide some information. I hope experimentalists can answer this question to help in the advance of hadron spectroscopy. 25 February, 2019 Meson-meson molecules ...

Beyond two-body interactions 25 February, 2019 Meson-meson molecules ...

Subject for another talk X(3872) X,Y,Z(3940) Y(4260) Z+(4430) DD|S(0++) DD*|S(1++) DSDS|S(0++) DD1|S(1--) D*D1|S(1--) Subject for another talk Charmonium 25 February, 2019 Meson-meson molecules ...

Candidates for observation (QQnn). Decay modes. Electromagnetic: E4q > M(D)+M(D) Weak: E4q < M(D)+M(D) Charm 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 Bottom Sector: bbnn 1: JP=1+: CQC: ΔE= –214,ΔR= 0.74. Compact. Weak decay I=0 BCN: ΔE= –144,ΔR= 0.76. Compact. Weak decay 2: JP=0+: CQC: ΔE= –149,ΔR= 0.76. Compact. γ decay 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 25 February, 2019 Meson-meson molecules ...