Discovery of charged bottomonium-like Z b states at Belle Antje Peters 1 Christoph Rosenbaum 2 1 Goethe-Universität Frankfurt am Main 2 Justus-Liebig-Universität Giessen HGS-HIRe Lecture Week on Hadron physics at the Belle and BES experiments May 2015
Overview 1 Motivation 2 Four-quark systems 3 Lattice QCD approach Lattice QCD and Hadron Spectroscopy Tetraquark structure 4 Experimental approach Experimental setup Event selection Amplitude analysis 5 Summary & Outlook Antje Peters & Christoph Rosenbaum Discovery of Z b 2 / 19
Motivation Motivation: Discovery of Z b states at Belle Resonances found at Belle in 2008 Decay to bottonium contains bottom quarks Isospin 1 no bottonium At least 4 constituents: bbdu Antje Peters & Christoph Rosenbaum Discovery of Z b 3 / 19
Four-quark systems Four-quark systems hadronic matter made up of color-neutral states common examples: mesons (e.g. pion, kaon) and baryons (e.g. proton, neutron) also allowed: pentaquarks and four-quark states e.g.z b Antje Peters & Christoph Rosenbaum Discovery of Z b 4 / 19
Lattice QCD approach Lattice QCD approach Antje Peters & Christoph Rosenbaum Discovery of Z b 5 / 19
Lattice QCD approach Lattice QCD and Hadron Spectroscopy Quantum chromodynamics (QCD) QCD: theory to describe quarks and forces between them ( S = d 4 x ψ ( ) (f ) γ µ ( µ ia µ ) + m (f )) ψ (f ) + 1 2g 2 Tr (F µνf µν ) f F µν = µ A ν ν A µ i [A µ, A ν ] no analytical solution for low energy observables no pertubative approach on the potential numerical solution (lattice QCD) Antje Peters & Christoph Rosenbaum Discovery of Z b 6 / 19
Lattice QCD approach Hadron spectroscopy I Lattice QCD and Hadron Spectroscopy application of suitable operator O(t) on the vacuum Ω O(t) contains quantum numbers of the hadronic system (spin, parity,...) obtain correlation function in time for each separation r of the static quarks via C(t, r) = Ω O (t)o(0) Ω = 1 ( ) Dψ (f ) D ψ (f ) DA µ O (t)o(0)e S[ψ(f ), ψ (f ),A µ] Z on the lattice: f DψD ψda µ = x µ ( ) dψ(x µ )d ψ(x µ )du(x µ ) Antje Peters & Christoph Rosenbaum Discovery of Z b 7 / 19
1 0.9 0.8 0.7 0.6 0.5 quark separation: r=1a 0 2 4 6 8 10 t/a 1 0.9 0.8 0.7 0.6 0.5 quark separation: r=2a 0 2 4 6 8 10 t/a 1 0.9 0.8 0.7 0.6 0.5 quark separation: r=3a 0 2 4 6 8 10 t/a Lattice QCD approach Hadron spectroscopy II Lattice QCD and Hadron Spectroscopy for large t one finds the effective mass m of the hadronic state described by O(t): lim Ω t O (t)o(0) Ω exp( V (r)t) (1) get a value of the potential for each quark separation and obtain the complete potential: m effective m effective m effective r=1a r=2a r=3a and so on... resulting potential 0.8 0.75 V 0.7 0.65 0 2 4 6 8 10 Antje Peters & Christoph Rosenbaum Discovery of Z b 8 / 19 r/a
Lattice QCD approach Composition of the operator Lattice QCD and Hadron Spectroscopy Study of BB systems use two static quarks and two quarks of finite mass: QQ qq, q {u, d, s, c} static quarks: no spin, no contribution to orbital angular momentum and isospin here: QQ qq with QQ = bb, e.g. in Zb (10610) and Z b (10650) Antje Peters & Christoph Rosenbaum Discovery of Z b 9 / 19
Lattice QCD approach Tetraquark structure The structure of a BB tetraquark experimentally observed Z b states have mass close to mass of BB and B B states preliminary assumption: mesonic molecule structure ( ) ( ) Γ AB ΓCD Qa C (x)q (1)a A (x) q (2)b B (y)qb D(y) other possibility: diquark-antidiquark ( Q d (x)ɛ dec q e (y) ) ( Qa (x)ɛ abc q b (y) ) Antje Peters & Christoph Rosenbaum Discovery of Z b 10 / 19
Experimental approach Experimental approach Antje Peters & Christoph Rosenbaum Discovery of Z b 11 / 19
Experimental approach Experimental motivation Experimental setup Observation by Belle observation of anomalously high rates for the e + e Υ(nS)π + π (n = 1, 2, 3) and e + e h b (mp)π + π (m = 1,2) transitions measured in the vicinity of the Υ(10860) peak measured partial decay widths Γ[Υ(10860) Υ(nS)π + π ] 0.5 MeV are about two orders of magnitude larger than the typical widths for the dipion transitions amongst Υ(nS) states with n 4 conclusion: exotic mechanism contributing to the Υ(10860) decays? Data sample three body process e + e Υ(nS)π + π integrated luminosity of 121.4 fb 1 collected at the peak of the Υ(10860) resonance (s = 10.865 GeV/c 2 ) with the Belle detector at the KEKB asymmetric-energy e + e collider Antje Peters & Christoph Rosenbaum Discovery of Z b 12 / 19
Detector Experimental approach Experimental setup Belle Detector large-solid-angle magnetic spectrometer 4-layer silicon vertex detector (SVD) 50-layer central drift chamber (CDC) aerogel threshold Cherenkov counters (ACC) time-of-flight scintillation counters (TOF) electromagnetic calorimeter (ECL) superconducting solenoid coil iron flux-return (KLM) e + e Υ(nS)π + π µ + µ π + π charged hadron identification provided by de/dx measurements in the CDC, ACC and TOF (information combined to form likelihood ratios) muons identified based on their penetration range and transverse scattering in the KLM Antje Peters & Christoph Rosenbaum Discovery of Z b 13 / 19
Event selection Experimental approach Event selection candidate events are identified via the measured invariant mass of the µ + µ combination and the recoil mass, M miss (π + π ), associated with the π + π system, defined by M miss (π + π ) = (E c.m. Eππ) 2 pππ 2 Cuts exclusively reconstructed events: Mmiss (π + π ) M(µ + µ ) < 0.2GeV /c 2 Candidate Υ(5S) Υ(nS)π + π events: Mmiss (π + π ) m Υ(nS) < 0.05GeV /c 2 Sideband regions: 0.05GeV /c 2 < Mmiss (π + π ) m Υ(nS) < 0.10GeV /c 2 background due to photon conversion: M miss (π + π ) > 0.20/0.14/0.10GeV /c 2 (Υ(1S),Υ(2S),Υ(3S)) Antje Peters & Christoph Rosenbaum Discovery of Z b 14 / 19
Amplitude analysis I Experimental approach Amplitude analysis Dalitz amplitude analysis performed by means of unbinned maximum likelihood fits to two-dimensionals M 2 [Υ(nS)π + ] vs. M 2 [Υ(nS)] π Dalitz distributions Two horizontal bands evident in Υ(2S)π system: 112 GeV 2 /c 4 and 113.3 GeV 2 /c 4 One-dimensional invariant mass projection two peaks observed in the Υ(2S)π system near 10.61 GeV/c 2 and 10.56 GeV/c 2 Z b (10610) and Z b (10650) Antje Peters & Christoph Rosenbaum Discovery of Z b 15 / 19
Amplitude analysis II Experimental approach Amplitude analysis parametrization of the Υ(5S) Υ(nS)π + π three-body decay amplitude: M = A Z1 + A Z2 + A f0 + A f2 + A nr A Z1 and A Z2 : contributions from Z b (10610) and Z b (10650) A f0 and A f2 : possible contributions in the π + π channel from the f 0(980) and f 2(1270) tensor states A nr : non-resonant amplitude nominal model adopts J P = 1 + of the observed Z b state logarithmic likelihood function L L = 2 log(f sig S(s 1, s 2 ) + (1 f sig )B(s 1, s 2 )) Events S(s 1, s 2): density of signal events M(s 1, s 2) 2 convolved with the detector resolution function B(s 1, s 2): constant combinatorial background f sig : fraction of signal events in data sample Antje Peters & Christoph Rosenbaum Discovery of Z b 16 / 19
Results Experimental approach Amplitude analysis Systematic uncertainties uncertainties in the parameterization of the decay amplitude variation of the reconstruction effieciency over the Dalitz plot uncertainties in the c.m. energy Antje Peters & Christoph Rosenbaum Discovery of Z b 17 / 19
Summary & Outlook Summary & Outlook Possible exotic contribution of Υ decay Which structure? Diquark-antidiquark or mesonic molecule? Bottonium and isospin puzzle solved? Antje Peters & Christoph Rosenbaum Discovery of Z b 18 / 19
References I. Adachi [Belle Collaboration], arxiv:1105.4583 [hep-ex]. S. Ohkoda, Y. Yamaguchi, S. Yasui and A. Hosaka, Phys. Rev. D 86 (2012) 117502 [arxiv:1210.3170 [hep-ph]]. A. Garmash et al. [Belle Collaboration], Phys. Rev. D 91 (2015) 7, 072003 [arxiv:1403.0992 [hep-ex]]. A. Ali, C. Hambrock and W. Wang, Phys. Rev. D 85 (2012) 054011 [arxiv:1110.1333 [hep-ph]].