The X(4260) and X(4360) Mesons as a ρ DD Molecular State and States of ρ D*D* with J = 3

Transcription

1 The X(4260) and X(4360) Mesons as a ρ DD Molecular State and States of ρ D*D* with J = 3 Melahat Bayar Kocaeli University Collaborators: B. Durkaya, Xiu Lei Ren, E. Oset XVI International Conference on Hadron Spectroscopy, 15/09/2015

2 OVERVIEW Motivation and Introduction Formalism Results and Discussion Summary

3 MOTIVATION and INTRODUCTION Recently, the large number of new states found in the hadron experiments The properties of some of them are still not easy to explain within the quark model spectrum There are no compelling theoretical pictures that provide unquestionable description of what is seen in the experiments an The Quarkonium Working Group (QWG) concluded: there are still a lot of surprises and puzzles in the studies of heavy quarkonium The motivation of the this talk: understand the properties of the particles found in the hadron experiments ( structure ect...) search for new states of the hadron spectroscopy theoretically

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5 GG PC PC)=0++(??+ X(4140) I (J X(4140) I (J )=0 (??+))

6 GG PC PC)=0++(??+ X(4140) I (J X(4140) I (J )=0 (??+))

7 GG PC PC)=0++(??+ X(4140) I (J X(4140) I (J )=0 (??+))

8 GG PC PC)=???(1 ) X(4260) I (J X(4260) I (J )=? (1 )

9 GG PC PC)=???(1 ) X(4260) I (J X(4260) I (J )=? (1 )

10 GG PC PC)=???(1 ) X(4260) I (J X(4260) I (J )=? (1 )

11 GG PC PC)=???(1 ) X(4360) I (J X(4360) I (J )=? (1 )

12 GG PC PC)=???(1 ) X(4360) I (J X(4360) I (J )=? (1 )

13 MULTIBODY INTERACTION (the fixed center approximation to Faddeev equations) A cluster of two bound particles DD, (I=0), X(3700) and ρ D, (I=1/2), D1(2420) Third particle interacts with the cluster

14 FORMALISM OF THE TWO BODY SCATTERING AMPLITUDE to construct a unitary T matrix for extending chiral symmetry: the inverse amplitude method N/D method Bethe Salpeter (BS) equation Fig: Diagrammatic representation of the Bethe Salpeter equation

15 ρ D (vector pseudoscalars mesons) two body scattering : 15 plet 15 pletof ofpseudoscalars pseudoscalarsmesons mesonsfor forthe the SU SU(4): (4): 15 plet 15 pletof ofvector vectormesons mesonsfor forthe thesu SU(4): (4): SU (4) multiples (a) for the 16 plets of pseudoscalar mesons and (b) for the 16 plets of vector mesons

16 ρ D (vector pseudoscalars mesons) two body scattering : 15 plet 15 pletof ofpseudoscalars pseudoscalarsmesons mesonsfor forthe the SU SU(4): (4): The TheHadronic HadronicCurrents: Currents: 15 plet 15 pletof ofvector vectormesons mesonsfor forthe thesu SU(4): (4): The TheLagrangian: Lagrangian:

17 The potential: The scattering of a pseudoscalar with a vector meson: D. Gamermann and E. Oset Eur. Phys. J. A 33, (2007) Table. Pole positions for the model. The column Irrep shows the results in the SU(3) limit. The results in brackets for the Im s are obtained taking into account the finite width of the ρ and K* mesons. Table: Channel content in each sector for the pseudoscalar vector meson interaction

18 The interaction kernel for the scattering of pseudoscalars with vector mesons: the potentials, projected over s wave:

19 The Unitarized T matrix for ρ D aadiagonal diagonalmatrix matrixwith witheach eachelement: element: the vector pseudoscalar mesons loop function: the three momentum of the mesons in the center of mass frame:: the theconvolution convolutionof ofthe theloop loopfunction function::

20 The Unitarized T matrix for DD D. Gamermann, E. Oset, D. Strottman and M. J. Vicente Vacas, Phys. Rev. D 76, (2007) Bethe Salpeter equation for DD : The Lagrangian: the pseudoscalar pseudoscalar mesons loop function: The amplitudes in charge base: The amplitudes in isospin base:

21 FIXED CENTER FORMALISM FOR THE THREE BODY SYSTEM t1 t2 FIG. Diagrammatic representation of the fixed center approximation to Faddeev equations T1: all diagrams beginning with interaction in 1 meson. T2: all diagrams beginning with interaction in 2 meson.

22 For the normalization The S matrix for the single scattering: Using the low energy reduction S matrix for the double scattering: The full three body scattering:

23 For the normalization The S matrix for the single scattering: Using the low energy reduction S matrix for the double scattering: we get: The full three body scattering: The function G0 is the meson exchange propagator

24 The Function G0 the energy carried by particle 3 the rest energy of the three body system The TheForm Formfactor: factor:

25 The arguments of the three body amplitude T(s) and two body amplitudes tj(sj) s the total invariant mass of the three body system sj the invariant masses of the two body systems the binding energy among the three particles, proportionally to their masses: the thetotal totalenergy energyof ofthe thetwo twobody bodysystem: system: the binding energy of particle 2 (1)

26 The Isospin the cluster of X(3700),

27 The Isospin the cluster of X(3700),

28 RESULTS AND DISCUSSION B. Durkaya and M. Bayar, Phys. Rev. D 92, (2015) m~4320 m~4320,,γ~25 Γ~25 m mρ ρ+m +mdd+m +mdd=4535 =4535 m +m mx(3700) +mρ ~4475 ~4475 X(3700) ρ!!!!!!!!~160 ~160 below belowthe thex(3700) X(3700) and ρ meson threshold and ρ meson threshold X(4360) X(4360)? -? IIGG(J(JPCPC)=? )=?(1 (1--)) m~4361 m~4361,,γγ~74 ~74 X(4260) X(4260)? -? IIGG(J(JPCPC)=? )=?(1 (1--)) m~4251 m~4251,,γγ~120 ~120

29 m~4256 m~4256,,γ~25-30 Γ~25-30 m mρ ρ+m +mdd+m +mdd=4535 =4535 m +m md1(2420) +mdd~4290 ~4290 D1(2420)!!!!!!!!~40 ~40 below belowthe thedd1(2420) (2420) 1 and andddmeson mesonthreshold threshold X(4360) X(4360)? -? IIGG(J(JPCPC)=? )=?(1 (1--)) m~4361 m~4361,,γγ~74 ~74 X(4260) X(4260)? -? IIGG(J(JPCPC)=? )=?(1 (1--)) m~4251 m~4251,,γγ~120 ~120

30 m~4241 m~4241,,γ~20 Γ~20 m mρ ρ+m +mdd+m +mdd=4535 =4535 m +m md1(2420) +mdd~4290 ~4290 D1(2420)!!!!!!!!~60 ~60 below belowthe thedd1(2420) (2420) 1 and andddmeson mesonthreshold threshold!!!!could Couldbe be m~4248, ΓΓ~177 m~4248, ~177 P? P? I(J )=?(? ) I(J )=?(? )!!!!or orthe thex(4140) X(4140) m~4159,,γγ~20 m~4159 ~20 PC +?+ PC +?+ IGIG(J )=0 (? ) (J )=0 (? ) AANew New State State......

31 States of ρ D*D* with J = 3 M. Bayar, Xiu Lei Ren, E. Oset, Eur. Phys. J. A51 (2015) 5, 61 The ρd*d* system is new and has not been studied so far. the vector vector interaction is found to be very strong (J = 2) The The ρρd*d* D*D* three body three bodyscattering: scattering:

32 RESULTS (The ρd*d* three body amplitude with J = 3) The X(3915) ρ System m~4338 m~4338,,γγ~50 ~50 m mρρ+m +md*d*+m +md*d*=4792 =4792 m +m mx(3915) +mρρ~4693 ~4693 X(3915)!!!!!!!!~360 ~360 below belowthe thex(3915) X(3915) and andρρ meson mesonthreshold threshold The Thevector vector vector vectorinteraction interactionin inj=2 J=2isisindeed indeedvery verystrong. strong. m md*+m +mρ m md *=320 =320 D* ρ D22* extra extra40 40 binding binding

33 The D2*(2460) D* System with total isospin I=0 m~4000 m~4000,,γγ~250 ~250 m mρρ+m +md*d*+m +md*d*=4792 =4792 m +m mdd2*(2460) +mρρ~4471 ~4471 *(2460) 2!!!!!!!!~470 ~470 below belowthe thedd22*(2460) *(2460) and andd* D*meson mesonthreshold threshold the thed* D*with withaaρρwould wouldbe bebound boundby by ,, the thed* D*with withthe thed* D*by byabout about63 63 Why Why !!!!and andγγ !!!!ItItisisnot notclear clear

34 The D2*(2460) D* System with total isospin I=1 m~4195 m~4195,,γγ~60 ~60 m mρρ+m +md*d*+m +md*d*=4792 =4792 m +m mdd2*(2460) +mρρ~4471 ~4471 *(2460) 2!!!!!!!!~270 ~270 below belowthe thedd22*(2460) *(2460) and andd* D*meson mesonthreshold threshold

35 SUMMARY Chiral dynamics is a good tool to deal with hadron interaction. Its combination with nonperturbative unitary techniques allows to study the interaction of hadrons. Poles in amplitudes correspond to dynamically generated resonances. Many known resonances can be described in this way. The interaction of vector mesons with other mesons or baryons plays an important role in many hadronic reactions We investigate the three body systems of ρ DD by taking the fixed center approximation to Faddeev equations, and find A bound states around 4320 and 4256 associated to X(4260) Predict a new state: mass about 4241 X(4360) and

36 SUMMARY The ρd*d* three body amplitude with J = 3 ρ (D*D*) a clear and narrow peak around 4340 D* (D*ρ) more uncertain I = 0 state around 4000 I = 1 state around 4200 md* > mρ, the FCA is less reliable!!!! Our results should be taken as indicative

37 Thank you for your attention!