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Meson-meson molecules and compact four-quark states

The 5-th International Conference on Quarks and Nuclear Physics Beijing , September 21－26, 2009. Meson-meson molecules and compact four-quark states. A. Valcarce University of Salamanca (Spain) J. Vijande , N. Barnea, J.-M. Richard. 3872. Charmonium. cncn. ccnn. DD.

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Meson-meson molecules and compact four-quark states

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

  2. 3872 Charmonium cncn ccnn DD meson-meson molecules, compact four-quark states cc mass spectrum 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 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 ...

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

  4. 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 Meson-meson molecules ...

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

  6. 3 1 3 1 2 4 2 1,2  c 3,4  n ccnn Meson-meson molecules ...

  7. 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, ΔRfinite ~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. Meson-meson molecules ...

  8. Confinement: Linear potential • One-gluon exchange: Standard Fermi-Breit potential BCN Parameters determined on meson spectroscopy Interacting potentials • 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 Meson-meson molecules ...

  9. cncn (I=0). CQC Model 4q Energy Theoretical threshold Meson-meson molecules ...

  10. cncn (I=0). BCN Model 4q Energy Theoretical threshold Meson-meson molecules ...

  11. Theorerical Thresholds 5! cncn (I=0). BCN Model Experimental threshold Meson-meson molecules ...

  12. cncn. CQC Model 4q Energy Theoretical threshold Meson-meson molecules ...

  13. 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). Thresholds Uncoupled threshold ≥ Coupled threshold Meson-meson molecules ...

  14. cncn. CQC Model 4q Energy Uncoupled threshold Coupled threshold Meson-meson molecules ...

  15. 3 ccnn 1 y x z 4 2 1,2  c 3,4  n Meson-meson molecules ...

  16. 3 ccnn 1 y x z 4 2 1,2  c 3,4  n Meson-meson molecules ...

  17. 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 Meson-meson molecules ...

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

  19. 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? Meson-meson molecules ...

  20. n – – – + c c c c – – – – – – – n n n n n n n c n w J/ – – c cncn — + D n D – – ccnn c c c + c D D Meson-meson molecules ...

  21. 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? Meson-meson molecules ...

  22. 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. Meson-meson molecules ...

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

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

  25. 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. Meson-meson molecules ...

  26. Beyond two-body interactions Meson-meson molecules ...

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

  28. Electromagnetic: E4q > M(D)+M(D) • Decay modes. Weak: E4q < M(D)+M(D) Candidates for observation (QQnn). • Charm Sector: ccnn • 1: JP=1+: CQC: ΔE= –76,ΔR= 0.81. Compact. Weakdecay • I=0 BCN: ΔE= –7,ΔR~1 –2. Molecular. γ decay • Bottom Sector: bbnn • 1: JP=1+: CQC: ΔE= –214,ΔR= 0.74. Compact. Weakdecay • I=0 BCN: ΔE= –144,ΔR= 0.76. Compact. Weakdecay • 2: JP=0+: CQC: ΔE= –149,ΔR= 0.76. Compact. γ decay • I=0BCN: ΔE= –52,ΔR= 0.76. Compact. γ decay • 3: JP=3 – : CQC: ΔE= –140,ΔR= 0.73. Compact. γ decay • I=1BCN: ΔE= –119,ΔR= 0.73. Compact. γ decay • 4: JP=1 – : CQC: ΔE= –11,ΔR~1 –2. Molecular. Weakdecay • I=0 Meson-meson molecules ...

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