Fulvio Piccinini. INFN, Sezione di Pavia

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1 Tetraquarks and XY Z states Fulvio Piccinini INFN, Sezione di Pavia INTERNATIONAL SCHOOL OF NUCLEAR PHYSICS 37th Course Probing Hadron Structure with Lepton and Hadron Beams Erice, Sicily, 16-4 September 015 based on work with A. Esposito, A. Guerrieri, L. Maiani, A. Pilloni, A.D. Polosa and V. Riquer F. Piccinini (INFN) XY Z Erice, Italy, 0/09/015 1 / 31

2 Introduction Charmonium as a c c bound state: the hydrogen atom of meson spectroscopy spectrum and transitions predicted by potential models ψ(4415) main ingredients color Coulomb term linear scalar confining term spin dependent terms relativistic corrections M [GeV] S ψ(4040) ψ (3686) η c (3638) J/ ψ(3097) η c (979) P χ (3556) χ 1 (3511) χ 0 (3415) D ψ(4159) ψ(3770) F G DD Barnes, Godfrey and Swanson, hep-ph/ F. Piccinini (INFN) XY Z Erice, Italy, 0/09/015 / 31

3 003 and the opening of XY Z spectroscopy BELLE Events/0.0 GeV M(π + π - l + l - ) - M(l + l - ) (GeV) M(π + π - l + l - ) - M(l + l - ) (GeV) Candidates/ 5 MeV/c 3000 CDF II J/ψπ + π - Mass (GeV/c ) Candidates / MeV/c 800 DØ ψ(s) Candidates / MeV/c X(387) M µ + - µ (GeV/c ) M µ - M µ + - (GeV/c ) + µ - π + π - µ 0 J/ψ Phys.Rev.Lett. 91 (003) 6001, most cited paper of Belle Collaboration F. Piccinini (INFN) XY Z Erice, Italy, 0/09/015 3 / 31

4 c c spectrum 1 years after X(387) discovery Y(4660) A. Esposito, A. Guerrieri, F.P., A. Pilloni, A. Polosa, IJMPA30 (014) 04n05, Mass (MeV) 4500 ψ(4415) Y(4360) X(4350) Y(490) Y(460) Y(40) DD1 X(4160) Ds D s ψ(4160) Y(4140) Y(4008) 1 D DsD D s 4000 η χ c(3s) c1(p) D ψ(4040) Y(3915) DsDs X(3940) ψ(3770) DD h χ c(p) X(387) c(p) η c(s) 1 1 D DD ψ(s) 3500 h c χ χ c c1 χ c0 Mass (MeV) Z(4430) Z c(400) Z c(400) Z c(3900) Z (450) Z 1(4050) DD1 Ds D s DsD s D D DsDs DD 3000 η c J/ψ DD J PC ?? J P 1 +?? All c c states below open c threshold identified All J P C = 1 c c states filled New neutral and charged particles above threshold Some may be charmonia, others not (exotica, X, Y, Z), in particular the charged ones (the neutral ones have quantum numbers compatible with charmonia) F. Piccinini (INFN) XY Z Erice, Italy, 0/09/015 4 / 31

5 XY Z: naming scheme convention X: neutral states which decay in S-wave, with P = + Y : neutral states seen in e + e annihilations, with J P C = 1 Z: charged states, with P = + for S-wave decay to J/ψπ ± for complete experimental information and more detailed discussions on molecular approaches see the talks by T. Iijima Y. Guo Y. Dong U. Uwer F. Piccinini (INFN) XY Z Erice, Italy, 0/09/015 5 / 31

6 Few recent clue measurements: LHCb confirmed BELLE on Z(4430) and measured J P = 1 + B 0 K + Z K + ψ(s)π (LHCb) PRL11 (014) 00 M = MeV, Γ = MeV, J P = 1 + B 0 K ψ(s)π ± Belle PRL0 (008) 14001; PRD80 (009) 0314, PRD88 (013) M = MeV, Γ = MeV ) Candidates / ( 0. GeV LHCb Z Im A 0. LHCb [GeV m ψ'π ] Z Re A valence structure c cu d required = true tetraquark π phase shift with energy crossing the mass = true resonance mass not close to a meson pair threshold F. Piccinini (INFN) XY Z Erice, Italy, 0/09/015 6 / 31

7 Y (460) radiative decay to X(387) Events / 3 MeV/c M(π + π J/ψ) (GeV/c ) BESIII: e + e Y (460) X(387)γ Data Total fit Background With B[X(387) π + π J/ψ] = 5% J/ψ) (pb) π + σ B (γx(387) γπ B[Y (460) γx(387)] B(Y (460) π + π J/ψ) = 0.1 M. Ablikim et al., Phys. Rev. Lett. 11 (014) data Y(460) Phase Space Linear E cm (GeV) Strong indication that Y (460) and X(387) share a similar structure F. Piccinini (INFN) XY Z Erice, Italy, 0/09/015 7 / 31

8 main th. phenomenological models for exotica c 3 c c 3 c 3 c 1 c 1c 3 c 3 c 3 c 1 c q q 8 c overall picture still not clear 8 c F. Piccinini (INFN) XY Z Erice, Italy, 0/09/015 8 / 31

9 Idea of light diquarks From QCD Breit interaction A. De Rujula, H. Georgi, S.L. Glashow, PRD1, (1975) 147 H eff i j λ i λ j σ i σ j = 4P F P S 1 + P C 1 3 P1 X are C, F, S exchange operator with eigenvalue ( ) + 1 for states (anti)symmetric under exchange Flavor Spin Color E 3(A) 1(A) 3(A) 8 3(A) 3(S) 6(S) 4/3 6(S) 3(S) 3(A) 8/3 6(S) 1(A) 6(S) 4 R.L. Jaffe, hep-ph/ Diquarks [qq ] can be the basic building blocks of new hadrons F. Piccinini (INFN) XY Z Erice, Italy, 0/09/015 9 / 31

10 Diquarks applied to the light scalar meson sector D. Black, A.H. Fariborz, F. Sannino, J. Schechter, PRD (1999) from L. Maiani lectures in Erice 014 a diquark based model for light scalar mesons developed in L. Maiani, F.P., A.D. Polosa, V. Riquer, PRL93 (004) 100 G. t Hooft, G. Isidori, L. Maiani, A.D. Polosa, V. Riquer, PLB66 (008) 44 F. Piccinini (INFN) XY Z Erice, Italy, 0/09/015 / 31

11 Heavy diquarks as building blocks L. Maiani, F.P., A.D. Polosa, V. Riquer, PRD 71 (005) A natural extension of the diquark model is the inclusion of diquarks involving one heavy constituent ([cq][ c q ]), assuming [cq] is binding For [cq][ c q] the near spin independence of heavy quark interactions (exact in the limit m c ) implies the presence of both spin zero and spin one diquarks. As a consequence, a reach spectrum is implied, with states with J = 0, 1, and both natural and unnatural J P C (C = ( 1) L+Sq q+sc c ) mass spectrum calculated in terms of constituent diquark masses spin-spin interactions F. Piccinini (INFN) XY Z Erice, Italy, 0/09/ / 31

12 Evolution of the tetraquark model The absence of charged partners of the X(387) made many people skeptical on the original model however B(B + K + X) B(X ρ 0 J/ψ) = (8.4 ± 1.5 ± 0.7) 6 (BaBaR) = (8.6 ± 0.8 ± 0.5) 6 (Belle) B( B 0 K X + ) B(X + ρ + J/ψ) < (BaBar), < 4. 6 (Belle), B(B + K 0 X + ) B(X + ρ + J/ψ) < 6 (BaBar) < (Belle) after discovering new charged states, there is now renewed interest in the tetraquark model e.g. S. Brodsky, R. Lebed et al. 014, 015 studying the tetraquark in large-n QCD, S. Weinberg showed 1 that the Coleman theorem (tetraquark correlators reduce to disconnected propagators) does not apply if the connected tetraquark correlator develops a pole that the decay amplitude 1 N S. Weinberg, PRL 1 (013) F. Piccinini (INFN) XY Z Erice, Italy, 0/09/015 1 / 31

13 Diquark-antidiquark / tetraquark model L. Maiani, F.P., A.D. Polosa, V. Riquer, PRD 71 (005) in the original version a democratic hypothesis was made on spin-spin interactions H = i m i + i<j κ ij S i S j From conventional S-wave mesons and baryons H κ q q S q S q with the accumulated data it has been necessary to revisit the model, w.r.t. the hierarchy within the spin interactions F. Piccinini (INFN) XY Z Erice, Italy, 0/09/ / 31

14 From type-i to type-ii diquark-antidiquark model L. Maiani, F.P., A.D. Polosa, V. Riquer, PRD 89 (014) 1140 new ansatz: only spin-spin coupling inside the diquark is leading H κ qc (S q S c + S q S c ) J P C cq c q c c q q Resonance Assig. Decays , 0 1/ 0, 0 + 3/ 1, 1 0 X 0 ( 3770 MeV) η c, J/ψ + light mesons , 1 0 3/ 0, 0 1/ 1, 1 0 X 0 ( 4000 MeV) ηc, J/ψ + light mesons / ( 1, 0 + 0, 1 ) 1, 1 1 X 1 = X(387) J/ψ + ρ/ω, DD 1 + 1/ ( 1, 0 0, 1 ) 1/ ( 1, 0 0, 1 ) Z = Z(3900) J/ψ + π, h c/η c + π/ρ 1 + 1, 1 1 1/ ( 1, 0 + 0, 1 ) Z = Z(400) J/ψ + π, h c/η c + π/ρ ++ 1, 1 1, 1 X ( 4000 MeV) J/ψ + light mesons with a value of the coupling κ qc = 67 MeV (cfr. MeV of type I) M(X 1 ) M(Z) M(Z ) M(Z) κ qc = 134 MeV M(X ) M(X 0 ) 4000 MeV M(X 0 ) 3770 MeV F. Piccinini (INFN) XY Z Erice, Italy, 0/09/ / 31

15 Type-II diquark-antidiquark model (cnt d) in this scheme Z(4430) is the first radial excitation of Z(3900) note that M(Z(4430)) M(Z(3900)) = 593 MeV M(ψ(S)) M(J/ψ) = 589 MeV both Z(3900) and Z(400) have s c c = 1, 0 = Z(400) πh c ( 1 P 1 ) F. Piccinini (INFN) XY Z Erice, Italy, 0/09/ / 31

16 Y states: tetraquarks with L = 1 H κ (S q S c + S q S c ) A S L + 1 B L State P (S c c = 1) : P (S c c = 0) Assignment Radiative Decay Y 1 3:1 Y (4008) γ + X 0 Y 1:0 Y (460) γ + X Y 3 1:3 Y (490)/Y (40) Y 4 1:0 Y (4630) γ + X 0 γ + X Y (4360): radial excitation of Y (4008); Y (4660): radial excitation of Y (460), since both decay to ψ(s) Y (460) and X(387) have the same spin structure = the observed radiative decay Y (460) γx(387) is an E1 transition ( L = 1 and S = 0) as in radiative decays of χ states F. Piccinini (INFN) XY Z Erice, Italy, 0/09/ / 31

17 some predictions on radiative decays type-ii tetraquark model seems to capture several features making also additional predictions Y 4 = Y (4630) γ + X (J P C = ++ ) = γ + X(3940),?? Y 3 = Y (490/40) γ + X 0 (J P C = 0 ++ ) = γ + X(3916),?? Y = Y (460) γ + X 1 (J P C = 1 ++ ) = γ + X(387), seen Y 1 = Y (4008) γ + X 0 (J P C = 0 ++ ) = γ + X(3770??),?? F. Piccinini (INFN) XY Z Erice, Italy, 0/09/ / 31

18 molecules vs. compact tetraquarks: where are we? brief summary of the present situation molecular model is the most economic one but no firm predictions to be tested on the contrary, for tetraquarks models two many predictions Z(4430), with J P = 1 +, challenges the molecular interpretation closest threshold D (0) D 1 (40) would imply negative parity J. Rosner, PRD76 (007) other molecular hypothesis would require unlikely excited components D D(1S, S) or P -wave D D1 T. Barnes, F.E. Close and E.S. Swanson, Phys.Rev. D91 (015) 1, on the other hand tetraquark models predict charged states, not necessarily close to thresholds L. Maiani, F.P., A.D. Polosa, V. Riquer, Phys.Rev. D71 (005) many new data still required to clarify the picture on the theory side: point out whether there are distinctive signatures able to distinguish between different models F. Piccinini (INFN) XY Z Erice, Italy, 0/09/ / 31

19 X(387), the oldest and still debated one M(X(387)) = ± 0.17 MeV Γ X < 1. MeV J P C = 1 ++ LHCb 014 M M(X(387)) (M D 0 + M D 0) = 3 ± 19 kev Tomaradze et al. 015 production production through B decays at e + e and p p/pp colliders decay J/ψρ J/ψπ + π J/ψω J/ψπ + π π 0 D 0 D 0 D 0 D 0 π 0 (large isospin violation) D 0 D 0 D 0 γ J/ψγ, ψ γ BR(ψ γ) BR(J/ψγ)) =.46 ± 0.64 ± 0.9 (LHCb) M < 0 = molecular interpretation natural isospin violation explained with the distance of D + D and D 0 D0 thresholds of 8 MeV c R = = R fm µ( M) F. Piccinini (INFN) XY Z Erice, Italy, 0/09/ / 31

20 X(387) and the production cross section issue Candidates / 5 MeV < p < 50 GeV T y < 1. Candidates / 3.15 MeV CMS s = 7 TeV -1 L = 4.8 fb data total fit background signal m(j/ψ π + π - ) [GeV] Events / MeV/c LHCb s = 7 TeV m(j/ψ π + π ) [GeV] large production cross section M(J/ψ π π) [MeV/c ] detected at large p T prompt production dominant over B decay ( features at odds with a loosely bound molecule F. Piccinini (INFN) XY Z Erice, Italy, 0/09/015 0 / 31

21 Prompt X(387) production: upper theoretical bounds Bignamini, Grinstein, F.P., Polosa, Sabelli: Phys. Rev. Lett. 3, 16001, 009 hypothesis: X(387) as an S-wave bound state of two D mesons σ(p p X(387)) d 3 k X D D (k) D D (k) p p d 3 k D D (k) p p σ(p p X(387)) max prompt R k is the rest-frame relative 3-momentum between the D and D D D (k) p p can be computed with MC simulations result: measured prompt cross section upper estimate by more than orders of magnitude unless integration over k extended up to 400 MeV this could be made possible by FSI Artoisenet and Braaten, PRD81 (0) actually the large hadronic activity (mainly π) close to D and D could prevent the effectiveness of FSI (Bignamini et al., PLB684 (0) 8) but the same π could give an alternative contribution F. Piccinini (INFN) XY Z Erice, Italy, 0/09/015 1 / 31

22 Possible mechanism alternative to FSI A. Esposito, F.P., A. Pilloni and A.D. Polosa, J.Mod.Phys. 4 (013) 1569 A.L. Guerrieri, F.P., A. Pilloni and A.D. Polosa, PRD90 (014) 3, π D 0 X(387) candidate large k0 t = tπ t = td D 0 D 0 reduced k0 D 0 π π π D formation π formation π Expanding hadronization sphere (a) P lane π D rescattering (b) F. Piccinini (INFN) XY Z Erice, Italy, 0/09/015 / 31

23 results additional pions close to D 0( ) in momentum space can interact elastically and change the rel. momentum between D 0 and D 0 given the initial asymmetric distribution in k rel there could be a feed-down process from larger relative momenta to lower ones and bring D pairs from positive to negative energies (bound state) 30 0 σ (nb) k 0 (GeV) there is a contribution but not enough additional ways to check the molecular hypothesis? F. Piccinini (INFN) XY Z Erice, Italy, 0/09/015 3 / 31

24 T Antideuterium - X(387) A.L. Guerrieri, F.P., A. Pilloni, A.D. Polosa, PRD90 (014) 3, deuterium is the known hadronic molecule, would be analog of X(387) antideuterium production is measured at ALICE (in particular pp) we could study the relation indicated by data between antideuterium and X(387) production unfortunately, up to now, they are measured in two completely different p regimes. We can only have a qualitative idea through MC, referring to the coalescence model dσ/dp (nb/gev) Events p (GeV) T p (GeV) T F. Piccinini (INFN) XY Z Erice, Italy, 0/09/015 4 / 31

25 Alice measured 3 He and 3 ΛHe in Pb-Pb@.76 TeV -1 x B.R. (GeV/c) dy T N/dp d Λ H 3 He + π 3 H 3 He + π + Λ 3 Λ H 3 H Λ Pb-Pb ALICE 0-% =.76 TeV s NN p (GeV/c) T ALICE, arxiv: ) (GeV/c) T N/(dydp ) d T 1/(πp 1/N ev Data/Fit ALICE, Pb Pb, s NN =.76 TeV d 0 0% 3 He 0 0% Comb. fit p (GeV/c) T p (GeV/c) T ALICE, arxiv: can we use this information to give an estimate of the cross section in p p collisions?... yes, under certain hypothesis = F. Piccinini (INFN) XY Z Erice, Italy, 0/09/015 5 / 31

26 3 He and 3 ΛHe from Pb-Pb to p-p collisions A. Esposito, A. Guerrieri, L. Maiani, F.P., A. Pilloni, A.D. Polosa, V. Riquer, arxiv: Approximations no medium effects on the production of light nuclei, i.e. each Pb-Pb collision is an independent product of N coll collisions (N coll function of the centrality class through a Glauber MC calculation) TeV can be rescaled to s = 7TeV through the ratio of total inelastic pp cross sections no coalescence/recombination effects in Pb-Pb collisions, which usually favor the production of many-body hadrons in medium w.r.t. vacuum ( dσ 3Λ H) dp pp = = = y B( 3 He π) 1 L pp ( ) d N( 3 He π) dp dy pp y B( 3 He π) σ inel ( ) pp d N( 3 He π) N evt dp dy pp y B( 3 He π) σ inel ( ) pp 1 d N( 3 He π). N coll N evt dp dy Pb-Pb F. Piccinini (INFN) XY Z Erice, Italy, 0/09/015 6 / 31

27 3 He and 3 ΛHe from Pb-Pb to p-p collisions (nb/gev) 1 (rescaled from Pb-Pb) (nb/gev) 1 (rescaled from Pb-Pb) /dp d σ pp -1 - (rescaled from Pb-Pb ) /dp d σ pp -1 - (rescaled from Pb-Pb ) -3 R AA = 1-3 R AA = R AA = p (GeV) = 5-5 R AA p (GeV) neglecting possible medium effects, the production cross sections for 3 Λ H and 3 He at pp collisions are several order of magnitudes smaller thatn the X(387) production cross section medium effects are expected to further decrease the cross section a conclusive statement should come from direct measurements at pp collisions F. Piccinini (INFN) XY Z Erice, Italy, 0/09/015 7 / 31

28 A check with future precision measurements by considering the scattering amplitude f(dd DD ), assuming it proceeds through a pole f(dd X DD ) in the soft limit, A. Polosa arxiv: [hep-ph] f g E + T in NRQM the amplitude for the scattering of two slow particles interacting through an attractive potential with superficial discrete level E has the universal form f E i T E + T = E = g4 5 µ 51π MD 4 M D 4 with g the coupling XDD future measurements of M, Γ X, BR(X DD ) at LHC and BELLEII, crucial to test the molecular hypothesis F. Piccinini (INFN) XY Z Erice, Italy, 0/09/015 8 / 31

29 Z c ( ) η c ρ: a channel able to discriminate between molecule and tetraquark ρ j q ρ j q ρ j q according to tetraquark models according to molecular model A. Esposito, A. Guerrieri and A. Pilloni, arxiv: [hep-ph] Kinematics only Dynamics included type I type II type I type II BR(Zc ηcρ) 554 1/ /.1 BR(Zc J/ψπ) BR (Z c ) ηcρ BR(Z c hcπ) Z i P D D D D D D l l q l l q l l q ηc Z i ηc Z i ηc P q P P q P P q D P l D P l D P l ρ j ρ j q q D D D D l l q l l q Z i ηc Z i ηc P P q P P q D P l D P l BR(Z c η c ρ) BR(Z c J/ψπ) BR(Z c η c ρ) BR(Z c h c π) F. Piccinini (INFN) XY Z Erice, Italy, 0/09/015 9 / 31

30 To be improved: threshold distances for charged Z Z + b (6) Υ(nS)π+ (n = 1,, 3) M Z = 607. ±.0 MeV, Γ Z = 18.4 ±.4 MeV M B + M B = ± 0.43 MeV M 3 ± MeV Z + b (650) h B(nP )π + (n = 1, ) M Z = 65. ± 1.5 MeV, Γ Z = 11.5 ±. MeV M B + M B = ± 0.6 MeV M ± MeV Z c (3900) J/ψπ + M Z = ± 6.1 (MeV), Γ Z = 46 ± MeV (in J/ψπ ± ); M Z = ± 4.5 (MeV), Γ Z = 4.8 ± 1 MeV(in D D ) M D 0 + M D + = ± 0.18 MeV; M D ± + M D 0 = ± 0.1 MeV M 4/8 ± 5 MeV Z c(400) h c (1P )π + M Z (h c π) = 40.9 ± 1.8 MeV, Γ Z = 7.9 ± 3.8 MeV; M D + + M D 0 = ± 0.0 M 6 ± MeV Z c(405) D D M Z (D D ) = ± 4.5 MeV, Γ Z = 4.5 ± 9.5 MeV M Z > 0 (even if higher experimental precision needed) F. Piccinini (INFN) XY Z Erice, Italy, 0/09/ / 31

31 Ab initio approach with LQCD What we name as exotic is actually contained within the QCD Lagrangian In principle, every bound structure should come out from a first principle calculation, as in LQCD recently first attempts to investigate tetraquarks with heavy quarks on the lattice. see e.g. S. Prelovsek at CHARM015 arxiv: A. Guerrieri, M. Papinutto, A. Pilloni, A.D. Polosa, N. Tantalo, arxiv: not yet firm conclusions because of several difficulties, e.g. difficult the separation of the diquark-antidiquark contribution from the meson-meson one lattices with dimensions of few fm s not suited for the simulation of extended objects such as the X(387) extrapolation from few hundreds MeV to the physical point can be critical Work in progress by several groups F. Piccinini (INFN) XY Z Erice, Italy, 0/09/ / 31