Interpretation of the X(3872) as a charmonium state plus an extra component due to the coupling to the meson- meson continuum

Transcription

1 Interpretation of the X(387) as a charmonium state plus an extra component due to the coupling to the meson- meson continuum E. Santopinto (INFN), J. Ferretti (INFN), G. Galatà (UNAM) PWA7 013 Ferretti, Galatà,E. S.,Phys. Rev. C 88, (013)

2 Unquenching the quark model for mesons Ferretti, Galatà,E. S., Vassallo,Phys. Rev. C 86, (01) Ferretti, Galatà,E. S.,Phys. Rev. C 88, (013) Ferretti, E. S: arxiv

3 The X(387) puzzle The nature of the recently discovered X(387) resonance has not been understood yet The quark structure of the X(387) resonance, observed for the first time by the Belle Collaboration and then confirmed by CDF, D0 and BABAR, still remains an open puzzle. We only know thanks to LHCb that it is 1 ++

4 The X(387) puzzle The nature of the recently discovered X(387) resonance has not been understood yet At the moment there are two possible interpretations for this meson. 1) A weakly- bound 1 ++ DD* molecule ) A cc state with 1 ++

5 X(387) as a ccbar state In this case, the resonance would correspond to a 1 1 D (J PC = - + ) state or to a 3 P 1 one [χ c1 (P), J PC = 1 ++ ] the relativized CQM predicts these states to be at energies of 3.84 and 3.95 GeV Moreover, from LHCb we know that the X(387) has 1 ++ quantum numbers

6 The CQM with loop corrections The calculation, accomplished in our work, is the first tentative to calculate the spectrum of charmonia within the UQM, including loop corrections, and makes it possible to perform a comparison to the already existing and to the future experimental data. the calculated masses of our mesons are the sum of a bare energy term, computed within the relativized QM by Godfrey and Isgur, and a self energy correction, computed within the unquenched quark model (UQM)

7 Self-energies (1) The Hamiltonian we consider, is the sum of an "ʺunperturbed"ʺ part H 0, acting only in the bare meson space, and of a second part, V, which can couple a meson state to a continuum made up of meson- meson intermediate states. The dispersive equation can be wriden as where the bare energy E a satisfies where is the self- energy

8 Self-energies () one has to take the contributions from various channels BC into account. A channel BC is a meson- meson intermediate state The matrix element Va,bc results from the coupling, due to the operator V, between the intermediate state BC and the unperturbed quark- antiquark wave function of the meson A one has to choose a precise form for the transition operator, V, responsible for the creation of qq pairs: our choice is that of the unquenched quark model (UQM)

9 ( UQM ) Unquenched quark model In the unquenched quark model the effects of qq sea pairs are introduced explicitly into the constituent quark model (QM) through a QCD- inspired 3P0 pair- creation mechanism. To leading order in pair creation, the meson wave function is given by where T represents the 3P0 quark- antiquark pair creation operator

10 3P0 pair-creation operator The 3P0 quark- antiquark pair- creation operator is Since the operator T creates a pair of constituent quarks with an effective size, the pair creation point has to be smeared out by a gaussian factor. The pair- creation strength γ 0 is a dimensionless constant, fided to the strong decay widths of a few cc states. γ 0 is substituded by a γ effective defined as γ 0 times m_u/m_i. The matrix elements of the pair- creation operator were derived in explicit form in the harmonic oscillator basis

11 Godfrey and Isgur relativized QM The relativized QM by Godfrey and Isgur is a potential model for qq meson spectroscopy. This model assumes a relativistic kinetic energy, a QCD- motivated running coupling constant, a flavor dependent potential smearing parameter, and replaces factors of quark mass with quark kinetic energy

12 Godfrey and Isgur relativized QM The Godfrey and Isgur Hamiltonian is

13 Strong decay widths The decay widths are calculated within the 3P0 model Impossibile visualizzare l'immagine. La memoria del computer potrebbe essere insufficiente per aprire l'immagine oppure l'immagine potrebbe essere danneggiata. Riavviare il computer e aprire di nuovo il file. Se viene visualizzata di nuovo la x rossa, potrebbe essere necessario eliminare l'immagine Impossibile e inserirla visualizzare di nuovo. l'immagine. La memoria del computer potrebbe essere insufficiente per aprire l'immagine oppure l'immagine potrebbe essere danneggiata. Riavviare il computer e aprire di nuovo il file. Se viene visualizzata di nuovo la x rossa, potrebbe essere necessario eliminare l'immagine e inserirla di nuovo. Impossibile visualizzare l'immagine. La memoria del computer potrebbe essere insufficiente per aprire l'immagine oppure l'immagine potrebbe essere danneggiata. Riavviare il computer e aprire di nuovo il file. Se viene visualizzata di nuovo la x rossa, potrebbe essere necessario eliminare l'immagine e inserirla di nuovo. we calculated the strong decay widths of 3S, P, 1D and D charmonium states above the DD threshold The introduction of quark form factors determines slightly different values for the model parameters than standard 3P0 models Another difference is the use of a effective strength, introduced to suppress diagrams where heavy qq pairs are created

14 Strong decay widths: results

15 Strong decay widths: results State DD DD D D D s D s D s D s D sd s Total Exp. η c (3 1 S 0 ) Ψ(4040)(3 3 S 1 ) ± 10 h c ( 1 P 1 ) χ c0 ( 3 P 0 ) χ c ( 3 P ) Ψ(3770)(1 3 D 1 ) ± 1.0 Ψ 3 (1 3 D 3 ) η c ( 1 D ) Ψ(4160)( 3 D 1 ) ± 8 Ψ ( 3 D ) Ψ 3 ( 3 D 3 ) TABLE III: Strong decay widths in heavy meson pairs(in MeV) for 3S, P,1D and D charmonium states. The values of the model parameters are given in Table II. The symbol in the table means that a certain decay is forbidden by selection rules or that the decay cannot take place because it is below threshold.

16 Self-energies calculations The relativized QM is used to compute the bare energies of the cc states we need in the self energy calculation. In our case, the quantities fided to the spectrum of charmonia are the physical masses and therefore the fiding procedure is an iterative one. Once the values of the bare energies are known, it is possible to calculate the self energies of 1S, S, 1P, P and 1D cc states

17 Self-energies calculations () If the bare energy of the meson A is over the threshold BC The imaginary part of the self- energy is related to the decay amplitude by

18 Self-energies: results State J PC D D DD D D D s Ds D s D s D s D s η c η c η c J/Ψ J/ΨJ/Ψ Σ(E a ) E a M a M exp. D D Ds D s η c (1 1 S 0 ) J/Ψ(1 3 S 1 ) η c ( 1 S 0 ) Ψ( 3 S 1 ) h c (1 1 P 1 ) χ c0 (1 3 P 0 ) χ c1 (1 3 P 1 ) χ c (1 3 P ) h c ( 1 P 1 ) χ c0 ( 3 P 0 ) χ c1 ( 3 P 1 ) χ c ( 3 P ) η c (1 1 D ) Ψ(3770)(1 3 D 1 ) Ψ (1 3 D ) Ψ 3 (1 3 D 3 )

19 Charmonium spectrum with SE corrections Ferretti, Galatà and Santopinto, PRC88, (013) M GeV 4.0 X J PC

20 X(387). Comparison with other works Ferretti, Galatà and Santopinto, PRC88, (013) Calculations of charmonium spectrum including continuum coupling effects (loop effects) χ c1 (P) mass [MeV] Reference 3908 Ferre9 et al Eichten et al. (004) 3990 Kalashnikova Eichten et al. (006) 3896 Pennington and Wilson References Ferretti, Galatà and Santopinto, PRC88, (013) Eichten et al., PRD69, (004) Kalashnikova, PRD7, (005) Eichten et al., PRD73, (006) Pennington and Wilson, PRD76, (007)

21 X(387). Charmonium interpretation Ferretti, Galatà and Santopinto, PRC88, (013) Ratio between X(387) J/Ψ ρ and X(387) J/Ψ ω decay modes and for the rate X(387) D 0 D 0 π 0 favor charmonium interpretation Meng and Chao, PRD75, (007) X(387)-> ψ(s) γ dominant with respect to X(387)-> J/ψ γ De Fazio B(B ± K ± B(B ± K ± X )B(X ψ(s)γ ) = (9.9 ±.9 ± 0.9) 10 6 X )B(X J /ψγ ) = (.8 ± 0.8 ± 0.) 10 6

22 X(387). Molecule interpretation Is the X(387) a meson-meson molecule? DD * The system can be found by π-exchange and forms a meson-meson molecule. Törnqvist, PRL67, 556 (1991) Prompt production incompatible with molecule interpretation Molecule of a few fm, with intrinsic fragility can be promptly produced?!? Bauer [CDF Collaboration], Int. J. Mod. Phys. A0, 3765 (005) Bignamini et al., PRL103, (009)

23 Bottomonium spectrum with SE corrections Ferretti and Santopinto, arxiv:

24 χ b (3P) system Ferretti and Santopinto, arxiv: χ b (3P) system discovered by ATLAS Collaboration Aad et al., PRL108, (01) M = ± (stat.) ± (syst.) GeV (mass barycenter for the χ b (3P) signal) Confirmed by D0 Collaboration Abazov et al., PRD86, (01) M = ± (stat.) ± (syst.) GeV (mass barycenter for the χ b (3P) signal) Further analysis is underway to determine whether this structure is due to the χ b (3P) system or some exotic bottom quark state BB,"BB * and"b * B * χ b (3P) states lie close to decay thresholds Continuum coupling effects are important?

25 χ b (3P) system. Mass barycenter Ferretti and Santopinto, arxiv: ATLAS Collaboration: M = ± (stat.) ± (syst.) GeV Aad et al., PRL108, (01) D0 Collaboration: M = ± (stat.) ± (syst.) GeV Abazov et al., PRD86, (01) Our work: M = GeV χ b0 (3P) χ b1 (3P) χ b (3P) χ b (3P) 10578

26 Continuum coupling (pair creation) effects Mass shifts because of pair creation effects (self energy terms) Already shown by several authors in baryon and meson sectors Törnqvist and Zenczykowski, PRD9, 139 (1984); Z. Phys. C30, 83 (1986); Horacsek et al., PRD3, 3001 (1985); Blask et al., Z. Phys. A36, 413 (1987); Brack and Bhaduri, PRD35, 3451 (1987); Silvestre-Brac and Gignoux, PRD43, 3699 (1991); Fujiwara, Prog. Theor. Phys. 89, 455 (199); 90, 105 (1993); Morel and Capstick, nucl-th/ Ono and Törnqvist, Z. Phys. C3, 59 (1984); Heikkila, Ono and Törnqvist, PRD9, 110 (1984); van Beveren and Rupp, PRL91, (003); Eichten, Lane and Quigg, PRD69, (004); Hwang and Kim, PLB601, 137 (004); Kalashnikova, PRD7, (005); Pennington and Wilson, PRD76, (007); Barnes and Swanson, PRC77, (008); Li and Chao, PRD79, (009); Danilkin and Simonov, PRL105, 1000 (010); Liu and Ding, EPJC7, 1981 (01). Importance of orbital angular momentum in proton spin Bijker and Santopinto, PRC80, (009); Santopinto and Bijker, Few Body Syst. 44, 95 (008). Flavor Asymmetry of the proton Santopinto and Bijker, PRC8, 060 (010). Strangeness content of the proton Bijker, Ferretti and Santopinto, PRC85, (01).

27 Why Unquenching the QM? It brings Widths Moreover the coupling with the continuum, brings shifts in hadron masses, that expecially near to thresholds can not be reabsorbed into the renomalization of the parameters. Is it possible to reformulate it in terms of S-matrix? (Swanson)

28 Charmonium spectrum with SE corrections. X(387) Ferretti, Galatà and Santopinto, PRC88, (013) M GeV 4.0 X J PC

29 Comparison with other calculations taking into account the continuum, open or nearby closed channels: χ c1 ( 3 P 1 ) s mass [MeV] Reference 3908 this paper [1] 3990 [3] [4] 3896 [7] Eicthen (004) Kalashnikova(005) Eicthen (006) Pennigton Wilson(007)

30 Open charm strong decays. Results Ferretti, Galatà and Santopinto, PRC88, (013) State DD DD D D D s D s D s D s D sd s Total Exp. η c (3 1 S 0 ) Ψ(4040)(3 3 S 1 ) ± 10 h c ( 1 P 1 ) χ c0 ( 3 P 0 ) χ c ( 3 P ) Ψ(3770)(1 3 D 1 ) ± 1.0 c c(1 3 D 3 ) c c( 1 D ) Ψ(4160)( 3 D 1 ) ± 8 c c( 3 D ) c c( 3 D 3 ) Charmonium strong decay widths in open charm mesons [MeV] Parameter Value Parameters of the 3 P 0 model: fitted to the strong decays γ α GeV r q fm GeV GeV 1.50 GeV m n m s m c

31 Unquenching the quark model for baryons R.Bijker,E..S.,PRC 80, (009), PRC 8, 060 (010); J. Ferrettii,Santopinto, Bijker, Phys. Rev. C 85, (01).

32 different CQMs for bayons Kin. Energy SU(6) inv SU(6) viol date Isgur-Karl non rel h.o. + shift OGE Capstick-Isgur rel string + coul-like OGE 1986 U(7) B.I.L. rel M^ vibr+l Guersey-R 1994 Hyp. O(6) non rel/rel hyp.coul+linear OGE 1995 Glozman Riska non rel/relplessas h.o./linear GBE 1996 Bonn rel linear 3-body instanton 001

33 Non strange spectrum Capstick & Isgur s Model Capstick and Isgur, Phys. Rev. D34, 809. U(7) Algebraic Model Bijker, Iachello, Leviatan, Ann. Phys. 36, 69 (1994). GB Model Glozman & Riska, Phys. Rept. 68, 63 (1996) Hypercentral CQM V(x) = - τ/x + α x Giannini, Santopinto, Vassallo, Eur. Phys. J.A1:447

34 Phys.Lett.. B 364,3 (1995),Eur. Phys. J.A1: N * D * D m ê mw s D s1 1-1 D1 3-3 Giannini, Santopinto, Vassallo, Eur. Phys. J.A1:447

35 N * D * m êmw

36 Nucleon resonces studied at Jlab and Jlab1 A 3/ D13(150) (10-3 GeV -1/ ) A 1/ D13(150) (10-3 GeV -1/ ) S 1/ D13(150) (10-3 GeV -1/ ) (a) Q (GeV ) Q (GeV ) hcqm PDG Maid07 Mok09 Azn09 FH 83 (b) hcqm PDG Maid07 Azn09 Mok09 FH (c) Q (GeV ) hcqm Maid07 Mok09 Azn09 Helicity amplitudes Systematic study of longitudinal and transverse helicity amplitudes in the ypercentral constituent quark model E. S.,.M. Giannini, Phys.Rev. C86 (01) 0650

37 E. S.,A. Vassallo, M. M. Giannini, and M. De Sanctis, Phys. Rev. C 8, (010)

38 Unquenched QM for baryons Bijker, Santopinto,Phys.Rev.C80:06510,009. The formalism to study the effects of the sea Bijker, ( Higher Santopinto,Phys.Rev.C80:06510,009. Fock components) preserves after renormalization, the good QM magnetic moment results. The good magnetic moment results of the CQM are preserved by the UQM, R. Bijker, E.S.,PRC88,06510(009) Genova 01 38

39 ( UQM ) Unquenched quark model In the unquenched quark model the effects of q- antiq sea pairs are introduced explicitly into the constituent quark model (QM) through a QCD- inspired 3P0 pair- creation mechanism. To leading order in pair creation, the baryon wave function is given by where T represents the 3P0 quark- antiquark pair creation operator

40 Flavor Asymmetry Gottfried sum rule UQM Santopinto, Bijker, PRC 8,060(R) (010)

41 Proton!Strange!Magne&c!Moment!and!Radius! moment!and!radius!ar compa&ble!with!zero. Μ s Μ N 0. UCQM 0.1 SAMPLE Global An Ferretti, Bijker,Santopinto, PRC 85,03504 (01)

42 Meson spectroscopy and hybrids We are intrested in exotic of the II kind!! Mesons with qu. n. not possible for qqbar only!

43 light Lowest exotic state 1-+

44 The Same sequence was found also by LQCD for heavy quarks : This sequence has been explained by the hamiltonian approach to QCD, P. Guo, A. P. Szczepaniak,G. Galata`, A. Vassallo, eppe Galatà, Andrea Vassallo and Elena E.Santopinto, Phys. Rev. D 78, d(008) in Phys.Rev.D77:056005,008.

45 Conclusions Our results for the self energies of charmonia show that the pair creation effects on the spectrum of heavy mesons are relatively small. In particular, for charmonium states they are of the order of 6% However, as in the heavy quark sector CQM'ʹs can predict the meson masses with a relatively high precision, even these corrections can become signi cant, such as in the case of the X(387) In fact, we were able to calculate its mass significantly beder than with usual CQM

46 N * D * m êmw

47 Unquenching the quark model for baryons R.Bijker,E..S.,PRC 80, (009), PRC 8, 060 (010);J. Ferrettii,Santopinto, Bijker Phys. Rev. C 85, (01).

48 Non strange spectrum Capstick & Isgur s Model Capstick and Isgur, Phys. Rev. D34, 809. U(7) Algebraic Model Bijker, Iachello, Leviatan, Ann. Phys. 36, 69 (1994). GB Model Glozman & Riska, Phys. Rept. 68, 63 (1996) Hypercentral CQM V(x) = - τ/x + α x Giannini, Santopinto, Vassallo, Eur. Phys. J.A1:447

49 s CQMs: Good description of the spectrum and magnetic moments Predictions of many quantities: strong couplins photocouplings helicity amplitudes elastic form factors structure functions Based on the effective degrees of freedom of 3 constituent quarks

50 Calculated values! Boosts to initial and final states Expansion of current to any order Conserved current G E p G M p G E n G M n De Sanctis, Giannini, Santopintoi, Vassallo Phys. Rev. C76, 0601 (007)

51 Further support Ratio between proton Nachtmann moments & CQ distribution n = Bloom-Gilman duality Inelastic proton scattering as elastic scattering on CQ (approximate) scaling function F(Q ) = 1/(1+ 1/6 r CQ Q ) square of CQ ff r CQ 0.-:0.4 fm Ricco,,et al., PR D67, (003)

52 With quark form factors De Sanctis, Giannini, Santopinto, Vassallo Phys. Rev. C76, 0601 (007)

53 De Sanctis, Giannini, Santopinto, Vassallo Phys. Rev. C76, 0601 (007)

54 E. Santopinto,A. Vassallo, M. M. Giannini, and M. De Sanctis, Phys. Rev. C 8, Milbrath et al. Gayou et al. Pospischil et al. Punjabi et al., Jones et al. Puckett et al. µ p G E p /GM p Q (GeV/c)

55 E. Santopinto,A. Vassallo, M. M. Giannini, and M. De Sanctis, Phys. Rev. C 8, M p / p Q F p /F1 p Milbrath et al. Gayou et al. Pospischil et al. Punjabi et al., Jones et al. Puckett et al Q (GeV/c)

56

57 Ratio µ p G Ep /G M p De Sanctis, Ferretti, Santopinto, Vassallo, Phys. Rev. C 84, (011) 57 Interacting Quark Diquark model, E. Santopinto, Phys. Rev. C 7, 001(R) (005)

58 A_1/( helicity amplitude ½) for the S11 A 1\ hcqm JPG 4, 753 (1998)

59 Is it a degrees of freedom problem? qq corrections? important in the outer region A 3\ qq corrections? D13 transition amplitu A 1\ U(7) PRC 54, 1935 (1996) hcqm JPG 4, 753 (1998)

60 Considering also CQMs for mesons, CQMs able to reproduce the overall trend of hundred of data but they show very similar deviations for observables such as photocouplings helicity amplitudes,

61 please note the medium Q behaviour is fairly well reproduced there is lack of strength at low Q (outer region) in the e.m. transitions emerging picture: quark core plus (meson or sea-quark) cloud Meson cloud Quark core

62 There are two possibilities: phenomenological parametrization microscopic explicit quark description

63 Problems 1) find a quark pair creation mechanism QCD inspired ) implementation of this mechanism at the quark level but in such a way to do not destroy the good CQMs results

64 Unquenching the quark model Geiger and Isgur D44, 799 (1991) 3P0 Pair-creation operator with 3P0 quantum number q anti q Note: sum over a complete set ( in flavor) of intermediate states necessary for preserving the OZI rule linear interaction is preserved after renormalization of the string constant

65 The good magnetic moment results of the CQM are preserved by the UCQM Bijker, Santopinto,Phys.Rev.C80:06510,009.

66 Flavor Asymmetry Gottfried sum rule

67 Proton Flavor asymmetry Santopinto, Bijker, PRC 8,060(R) (010)

68 Flavor asymmetry of the octect baryons in the UCQM Santopinto, Bijker, PRC 8,060(R) (010) Flavor asymmetry Nonperturbative QCD Pauli blocking (Field & Feynman, 1977) too small Pion dressing of the nucleon (Thomas et al., 1983) Meson cloud models

69 Flavor asymmetries of octect baryons Santopinto, Bijker, PRC 8,060(R) (010) Eichen Y.-J Zhang Alberg

70 3. Proton Spin Crisis 1980 s 1990 s 000 s Naive parton model 3 valence quarks QCD: contributions from sea quarks and gluons.. and orbital angular momentum HERMES, PRD 75, (007) COMPASS, PLB 647, 8 (007) Genova 01

71 Proton Spin Gluon contribution is small (sign undetermined) Unquenched quark model Ageev et al., PLB 633, 5 (006) Platchkov, NPA 790, 58 (007) More than half of the proton spin from the sea! Orbital angular momentum Suggested by Myhrer & Thomas, 008, but not explicitly calculated

72 4. Strangeness in the Proton The strange (anti)quarks come uniquely from the sea: there is no contamination from up or down valence quarks The strangeness distribution is a very sensitive probe of the nucleon s properties Flavor content of form factors New data from Parity Violating Electron Scattering experiments: SAMPLE, HAPPEX, PVA4 and G0 Collaborations There is no excellent beauty that hath not some strangeness in the proportion (Francis Bacon, ) Genova 01 7

73 Quark Form Factors Charge symmetry Quark form factors Kaplan & Manohar, NPB 310, 57 (1988) Musolf et al, Phys. Rep. 39, 1 (1994) Genova 01

74 Static Properties Genova 01 74

75 Strange Magnetic Moment Jacopo Ferretti, Ph.D. Thesis, 011 Bijker, Ferretti, Santopinto, Phys. Rev. C 85, (01) Genova 01 75

76 Strange Radius Jacopo Ferretti, Ph.D. Thesis, 011 Bijker, Ferretti, Santopinto, Phys. Rev. C 85, (01) Genova 01 76

77 Strange Proton Strange radius and magnetic moment of the proton Theory Lattice QCD Global analysis PVES Unquenched QM Jacopo Ferretti, Ph.D. Thesis, 011 Genova 01 Bijker, Ferretti, Santopinto, Phys. Rev. C 85, (01) 77