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ITEP Winter School, 13-20 Feb 2010 New charmonium resonances Roman Mizuk, ITEP Outline Potential Models Traditional charmonium states New charmonium resonances X(3872) 1- - states from ISR 3940 family Z± Bottomonium Charmonium – meson containing cc quarks Family of excited states: c , J/ , cJ , hc , (2S) , … “Hydrogen atom” of QCD System Ground triplet state Name Mass, MeV G, MeV (v/c)2 POSITRONIUM e+e- Ortho- 1 5 10-15 ~0.0001 QUARKONIUM uu,dd r 800 150 ~1.0 ss f 1000 4 ~0.8 cc 3100 0.09 ~0.25 bb 9500 0.05 ~0.08 Basic properties of most states simple picture of non-relativistic cc pair. non-relativistic relativistic Quantum Mechanics Quantum Field Theory two-body problem Number of particles is not conserved multi-body problem Hydrogen atom non-relativistic Srödinger equation relativistic Dirac equation 2 Ze 2 n En n r 2m bispinor i eA n 0 Ze r A A0 Z 2 R1 En 2 n R1 13.6eV Ze 2 n i n 0 En r Precise description of hydrogen atom. EXCEPT FOR LAMB SHIFT. Field Theoretical description of bound state eAmplitude: p + +… + Analytic continuation into complex energy plane. Im E Re E poles bound states mp+me Hydrogen atom (2) Solutions of Dirac equation correspond to sum + + +… charge, distorts Coulomb potential + … = running too small effect to reproduce Lamb shift +… reproduces Lamb shift No way to account for in Dirac equation. not a single particle! ~ = v/c Non-potential effects are small if electron is slow in the time scale when additional degrees of freedom are present in the system. Potential Model of Charmonium + + +… Not justified: + …= + … constituent quark, heavier by 300MeV V (r ) s (r ) r r QCD motivated potential Assume that charm quark is heavy enough to neglect non-potential effects. (M(2S) – MJ/ ) / QCD = 590 MeV / 200 MeV is not small. Open question: why Potential Models work reasonably well for charmonium? Charmonium Potentials V (r ) s (r ) one-gluon exchange, asymptotic freedom r r “Cornel model” confining potential, “chromoelectric tube” There are other parameterizations, respecting or not respecting QCD asymptotics. After parameters of potential are fit to data, the potentials become very similar. 0.1<R<1fm c J/ c2 (2S) Charmonium levels without spin 2s 1p 2s 1d 1p Coulomb 1s 1s 2s QCD 1s 1p Harmonic oscillator Relativistic Corrections fine structure of states spin-singlet triplet splitting not commute with Assign Lorentz structure to potentials L̂ short distance u uv vV q vector Breit-Fermi expansion to order v2/c2 2 v confining u u v v Vs q 2 scalar Charmonium Levels M, GeV building blocks 4.50 (4415) 4.25 (4160) (4040) c2(2S) 4.00 (3770) 3.75 c(2S) (2S) hc 3.50 c2 c1 c0 spectroscopic notation conserved QN n(2S+1)LJ JPC S=0 L=0 1S 0 0– + c , c(2S) S=1 L=0 3S 1 1– – J/ , (2S) , (4040) , (4415) S=0 L=1 1P 1 1+ – hc S=1 L=1 3P 1 3P 2 3P 3 0+ + 1+ + 2+ + c0 c1 c2 , c2 (2S) S=1 L=2 3D 1 1– – (3770), (4160) 3.25 J/ 3.00 2.75 c 0– + 1– – P = (–1)L+1 C = (–1)L+S S = s1 + s2 = { 0, 1 } J=S+L n – radial quantum number 1+ – (0,1,2)+ + JPC (3770) = 13D1 + 0.2 23S1 “S - D mixing” Predictions of Potential Models State Experim M, GeV Predictions of Potential Models Potential models reproduce also annihilation widths J/, (2S)→ℓ+ℓc, cJ → and radiative transitions btw. charmonia. JPC Hadronic mass in Lattice QCD Calculate 2-point Green function G(t,0) = 0O (t)O(0)+0, creating hadron at time 0 and destroying at time t. For this Average over all possible configurations of fields generated on lattice and weighted with exp(iS). → exp(–S) Operator O has required quantum numbers: JPC, flavor content and is projected on zero momentum. Expect: G(t,0) = A1exp(im1t) + A2exp(im2t) + A3exp(im3t) + ... → A1exp(–m1t) + A2exp(–m2t) + A3exp(–m3t) + ... Multi exponential t-dependence of Green function complicates identification of excited states. Minkovsky → pseudo-Euclidian space. from first principles Charmonium in Lattice QCD Potential for static charm quarks. Shape is similar to that of phenomenological models. quenched approximation Predictions for charmonia up to the 1st radial excitation exist. Still a lot of room for improvement. QCD Sum Rules Green function is calculated analytically. Restricted to small interval of t, contributions from ground and higher states more difficult to resolve. Application restricted to lowest states only. Summary on Potential Models – Only model relation to underlying fundamental theory of QCD. difficult to assign uncertainties to results + Using 3-4 parameters can describe a lot of data. right choice of variables? good predictive power o In many cases the only available theoretical approach. higher resonances Shape of potential in agreement with Lattice QCD estimations, and with perturbative QCD calculations (at small distances). success of phenomenology Useful framework for refining our understanding of QCD and guidance towards progress in quarkonium physics. Observation of J/ BNL AGS SLAC SPEAR e+e- annihilation Mark I first 4 detector extracted 28 GeV p-beam Be target p + Be → e+e- + X , nb , nb e e hadrons Richter et al. ee , nb Ting et al. M( e+e- ) Width of t J/ is very narrow, JPC=1– –. ee ee E c.m.s. “Heavy but very narrow !” November 1974 revolution. Every possible explanation was suggested. Observation of charm quark. Quarks generally recognized as fundamental particles. Charm quark was predicted by GIM mechanism to cancel divergence in kaon box diagram. Observation of (2S) two weeks after observation of J/ SLAC SPEAR Mark I Event Display (2S) → J/ +J/ → e+e- (2S) is very narrow, JPC=1– –. Observation of cJ c – DASP, DESY (1976) – Crystall Ball, SLAC (1980) c – DASP (1977) c(2S) – CBall (1980) Crystal Ball: sphere with 900 NaI crystals e e hadrons 2 R N e c q e e e e 4 2 3s First results on R above DD threshold – SPEAR (1975). 4 peaks above 3.7 GeV : Why J/ is so narrow? G, MeV 0.093 ± 0.002 0.327 ± 0.011 27 ± 4 2S J/ c ~s3 ‾ c ‾ c c0 27 ± 1 85 ± 12 (3770) (4040) C-parity 1/3 2/3 c c 11 ± 1 c g ‾ c g e,,q e,,q̄ For J/ strong decays are suppressed so much that EM decays are competitive. DD* D*D* DD at threshold Charmonium level scheme after 1980 10 states were observed: • 6 ’s directly produced in e+e– annihilation. • 3 P-levels are well seen in (2S) radiative transitions. • The ground state c was observed in radiative decays of J/ and (2S). Charmonium level scheme before 2002 Superconducting Coil (1.5T) Instrumented Flux Return (IFR) [Iron interleaved with RPCs]. Silicon Vertex Tracker (SVT) e+ (3 GeV) e– (9 GeV) Drift Chamber [40 stereo lyrs](DCH) B-factories e+e– → Y(4S) BaBar Belle E = 10.6 GeV L ~ 2*1034/cm2/s 530 + 1000 fb-1 CsI(Tl) Calorimeter (EMC) [6580 crystals]. Cherenkov Detector (DIRC) [144 quartz bars, 11000 PMTs] e+e– → сharmonium CLEO-c BES-II E = 3.0 - 4.8 GeV L ~ 1033/cm2/s pp¯ collider CDF D0 E ~ 1.8 TeV Aerogel Cherenkov cnt. n=1.015~1.030 SC solenoid 1.5T 3.5 GeV e+ CsI(Tl) 16X0 TOF counter 8 GeV e– Tracking + dE/dx small cell + He/C2H5 Si vtx. det. 3 lyr. DSSD m / KL detection 14/15 lyr. RPC+Fe Charmonium production at B factories in B decays γγ fusion Any quantum numbers can be produced, to be determined from angular analysis. double charmonium production initial state radiation JPC = JPC = 0± +, 2± + 1– – Only JPC = 0± + observed so far. Reconstruction of B decays • In (4S) decays B are produced almost at rest. • ∆E = Ei - ECM/2 Signal peaks at 0. • Mbc = { (ECM/2)2 - (Pi)2}1/2 Signal peaks at B mass (5.28GeV). B0J/ KS ∆E, GeV Mbc, GeV Observation of c(2S) B (KSK) K M = 2654 6 8 MeV/c2 G < 55 MeV Belle (2002) in B decays and in double charmonium production. Confirmed by BaBar and CLEO-c in two-photon production, and by BaBar in double charmonium production. c(2S) M = 2630 12 MeV/c2 e+e– J/ X Good agreement with potential models for mass, width and 2-photon width. Width: 6±12 (CLEO) and 17± 8 MeV (BaBar) average Γ = (14 ± 7) MeV Observation of hc (2S) → 0 hc → 0 c hc M(hc) = (3524.4 ± 0.6 ± 0.4) MeV G < 1 MeV Potential model expectations: M(hc) = centre of gravity of χc states = 1/9 * [(2*2+1) * M(χc2) + (2*1+1) * M(χc1) + (2*0+1) * M(χc0) ] = 3525.3 ± 0.3 MeV 5.5 c2(2S) in interactions 395fb-1 e+ 2005, BELLE M = 3931 4 2 MeV/c2 G = 20 8 3 MeV e– γ γ e+ χс2’ D D e– Поляризация consistent with J=2 J=0 disfavored 2/dof=23.4/9 2009, BaBar Width and 2-photon width are in good agreement with models, mass is 50 MeV lower. Charmonium Levels 2010 Mass (MeV) (2S+1)L J Y (4415) (4160) (4040) ’c2 X ’c ′ c J/ New: X c2 c1 Y 3 identified charmonia. (3770) DD – mass – decay pattern – quantum numbers that do not fit expectations. h c0 hcc (Potential Models) JPC ~10 states with ?? New charmonium(like) states states contain cc About 10 charmonium(like) states do not fit expectations. Have Potential Models finally failed? yes, but coupled channel effect was taken into account Exotics? u c c tetraquark c u compact diquarkdiantiquark state c hybrid g state with excited qluonic degree of freedom π c c u u c c– π π molecule two loosely bound D mesons hadrocharmonium charmonium embedded into light hadron X(3872) CP X(3872) B→Xsγ 487 336 Belle citation count 480 Phys.Rev.Lett.91 262001, (2003) 7th anniversary! Swanson, CharmEx09 PRL91,262001 (2003) X(3872) was observed by Belle in B+ → K+ X(3872) → J/ψ π+ π- 2S X(3872) Confirmed by CDF, D0 and BaBar. Recent signals of X(3872) → J/ψ π+ πpp collisions PRL103,152001(2009) arXiv:0809.1224 PRD 77,111101 (2008) direct production only 16% from B PRL93,162002(2004) Mass & Width M = 3871.52 0.20 MeV, Γ = 1.3 0.6 MeV Close to D*0D0 threshold: m = – 0.42 0.39 MeV [ – 0.92, 0.08 ] MeV at 90% C.L. Branching Fractions Br(B+ X K+) Br(X J/ + -) (8.10 0.92 0.66) 10-6 = (8.4 1.5 0.7) 10-6 Absolute Br? missing mass technique PRL96,052002(2006) K reconstruct only B Xcc mX2=(pB+ – pK+)2 (4S) B- (4S) 4-momentum from beam energy Br(B+ X K+) < 3.210–4 at 90%C.L. Br(X J/ + -) > 2.5% K+ momentum in B+ c.m.s. Radiative Decays & J/ hep-ex/0505037 PRL102,132001(2009) J/ J/ X(3872) → J/ + - 0 subthreshold production of +-0 2S Decay modes Br relative to J/+- J/ 0.15 0.05 J/ 0.33 0.12 2S 1.1 0.4 J/ 1.0 0.5 CX(3872) = + X(3872) → J/+CX(3872) = + C+- = – (|+1,-1 – |-1,+1) ( r ) 1. Isospin (+-) = 1 2. L(+-) = 1 IJPC of r0 isospin M (+-) PRL96,102002(2006) hep-ex/0505038 L=0 L=1 M (+-) is well described by r0→+- (CDF: + small interfering →+- ). X(3872) → J/ +- X(3872) → J/ r0 Spin & Parity PRL98,132002(2007) Angular analyses by Belle and CDF excluded JP = 0++, 0+-, 0-+, 1-+ ,1+-, 1--, 2++, 2-- , 2+-, 3--, 3+- 2-+ 1++ 1-0++ JPC = 1++ or 2–+ 2–+ is disfavored by 1. Br(X → (2S) γ) / Br(X → J/ γ) ~ 3 2. Observation of D*0D0 decay multipole suppression centrifugal barrier at the threshold JP = 1++ are favorite quantum numbers for X(3872). 2–+ not excluded. X(3872) → D*0D0 B K arXiv:0810.0358 D0D*0 D*→Dγ PRD77,011102(2008) 4.9σ B+& B0 D0D*0K D*→D0π0 605 fb-1 347fb-1 Flatte vs BW similar result: 8.8σ ~2 Shifted X(3872) mass in D*D final state influence of nearby D*D threshold. X(3872) Experimental Summary JPC = 1++ (2–+ not excluded) M = 3871.52 0.20 MeV , Γ = 1.3 0.6 MeV Close to D*0D0 threshold: m = – 0.42 0.39 MeV. Decay modes Br relative to J/ r0 J/ r0 1 J/ 1.0 0.5 J/ 0.17 0.05 (2S) 1.1 0.4 D*0D0 ~10 Br(X(3872) J/ r0) > 2.5% (90% C.L.) Is there cc assignment for X(3872)? JPC = 1++ c1′ ~100 MeV lighter than expected 1++ 2-+ 3872 Br( c1′ → J/ ) Br( c1′ → J/ +-) expect 30 measure 0.170.05 JPC = 2–+ η c2 Expected to decay into light hadrons rather than into isospin violating mode. X(3872) is not conventional charmonium. Tetraquark? PRD71,014028(2005) Maiani, Polosa, Riquer, Piccini; Ebert, Faustov, Galkin; … [cq][cq] [cu][cu] [cd][cd] [cu][cd] Predictions: 1. Charged partners of X(3872). 2. Two neutral states ∆M = 8 3 MeV, one populate B+ decay, the other B0. Charged partner of X(3872)? PRD71,031501,2005 B0 B- No evidence for X–(3872) J/ –0 X(3872)– M(J/π–π0) X(3872)– M(J/π–π0) excludes isovector hypothesis X(3872) Production in B0 vs. B+ B0→XK0s arXiv:0809.1224 605 fb-1 5.9 M(J/) No evidence for neutral partner of X(3872) in B0 decays. Two overlapping peaks in J/ +- mode? PRL103,152001(2009) No evidence for two peaks m < 3.2 MeV at 90% C.L. Tetraquarks are not supported by any experimental evidence for existence of X(3872) charged or neutral partners. D*0D0 molecule? Swanson, Close, Page; Voloshin; Kalashnikova, Nefediev; Braaten; Simonov, Danilkin ... MX = 3871.52 0.20 MeV (MD*0 + MD0) = 3871.94 0.33 MeV m = – 0.42 0.39 MeV Weakly bound S-wave D*0D0 system a few fm Predict different line shapes for J/+- and D*0D0 modes: Bound state J/+- Virtual state D0D00 D*0D0 J/+- D0D00 D0D*0 molecule Br(X(3872) J/ ) ~1 Br(X(3872) J/ r) Br(X(3872) ) ~3 Br(X(3872) J/ ) Large isospin violation due to 8 MeV difference between D*+D- and D*0D0 thresholds. Similar ratio is expected for c1 decays c1 admixture? Large production rate in B decays and in pp c1 ? Bound or virtual? c1 admixture? Analysis of data Kalashnikova, Nefediev arXiv:0907.4901 State c1 admixture Belle data bound ~ 30% BaBar data virtual ~0 ~2 experimental difference reverses conclusion Present statistics are insufficient to constrain theory? There are other similar analyses which differ in the fit functions: Braaten, Stapleton Zhang, Meng, Zheng arXiv: 0907.3167 0901.1553 theorists here should agree on the proper form & then experimenters should use it in a proper unbinned fit Coupled Channels Effect Corrections to energy levels. If cc-DD coupling is strong enough – DD molecule. B → X(3872) K arXiv:0809.1224 605 fb-1 X(3872) sideband non-resonant Kπ Mass(Kπ) Br(B0 →X(K+π–)non_res) Br(X→J/ψπ+π–) = (8.1±2.0+1.1–1.4) 10–6 Br(B0 →XK*0) Br(X→J/ψπ+π–) < 3.4 10–6 at 90% C.L. Br(BJ/ K*0) Br(BJ/ KNR) ~4 DD* molecular models for the X(3872) attribute its production & decays charmonium to an admixture of c1′ in the wave fcn. But BKX(3872) is very different from BK charmonium. KX3872 K′ Kc1 Belle arXiv 0809.0124 Belle arXiv 0809.0124 Belle PRD 74 072004 M(K) M(K) KJ/ Kc M(K) Belle F.Fang Thesis BaBar PRD 71 032005 M(K) M(K) Conclusions Potential models have model relation to QCD by describe a lot of data. Finally potential models failed to describe charmonium? X(3872) – heavy, very narrow! at D*D threshold. Isospin violating decay is not suppressed. Favorite interpretation is D*0D0 molecule. Open question: (1) bound or virtual, (2) admixture of conventional charmonium. probably only next generation experiments will answer this Theoretical analysis of coupled channel effects. description of X(3872) within potential models? More interesting charmonium-like states to come next lecture.