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Meson spectroscopy

Meson spectroscopy. Hybrid mesons and Multiquark states Samuel Hoekman Zorione Herrasti. Introduction. To understand the dynamics on quark scale one relies on lattice QCD and phenomological methods

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Meson spectroscopy

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  1. Meson spectroscopy Hybrid mesons and Multiquark states Samuel Hoekman Zorione Herrasti

  2. Introduction • To understand the dynamics on quark scale one relies on lattice QCD and phenomological methods • Last time glueball spectroscopy was discussed as a way to confirm QCD by searching for exotic JPC quantum numbers • Another way is using hybrid mesons, since hybrid mesons are richer in number (theoretically…) • One can also search for exotic flavors: multi quarks

  3. Overview • Hybrid meson (Zorione) • QCD (Zorione) • Flux Tube model (Zorione) • 3P0 pair creation • Phenomenological methods (Samuel) • Simulation • Monte Carlo Methods • Partial Wave Analysis • Conclusions (Samuel) • Multi quarks (Samuel) • MIT-bag model (Samuel) • BES-II experiment (Zorione) • Conclusions (Zorione)

  4. Mesons • Formed by a quark antiquark pair. • Quantum numbers. - Parity (-1)l+1 - Charge conjugation (-1)l+s

  5. Hybrid mesons • Quantum numbers for hybrid mesons • Quantum numbers that cannot be explained by the quark model. (JPC) • Formed by a pair plus one explicit gluon. • If kinematics and other conservation laws allow, the production cross section for hybrids, is expected to be the same as that for ordinary mesons. • Hybrid mesons and ordinary mesons with the same quantum numbers can mix freely. • Identification of hybrid mesons difficult unless they have exotic quantum numbers.

  6. Quantum chromodynamics (QCD) • Seems to be the correct theory of the strong interactions. • The spectrum of QCD is probably richer than that of the naive quark model. • If we remove the quarks from QCD, there should remain a nontrivial color SU(3) which must have its own spectrum of states. • Constituent quark, constituent gluon.( g) • Gluonic degrees of freedom condensed into collective string like flux tube.

  7. A QCD FLUX TUBE BETWEEN TWO QUARKS (sapac) A quark-antiquark pair, linked by a strong color field. The arrows point the direction of the color field. This system can have excitations with a vibration perpendicular to the axis.

  8. Theoretical foundation of the flux tube model • In the Hamiltonian formulation of QCD on a cubic spatial lattice, – Quark degrees of freedom “live” on the lattice sites – Gluonic degrees of freedom “live” on the links between this sites. HQCDlattice = Hglue + Hquark • We define QCD field operators (Ul), on this lattice, the points are linked with Gauge transformations. • We can define: pure gluon states, or quark gluon states. a

  9. The pure glue sector, the simplest states are “glue loops”. Energy: (2g2 /3a2)L g= coupling constant a=lattice spacing L=Length of the path The simplest quark containing state consits of a quark antiquark on the lattice joined by a path of flux links. Energy: mq+ mq +(2g2/3a2)L

  10. The Flux tube model • The quarks move adiabatically in an effective potential generated by the dynamics of the flux tube. • The flux tube can rotate along its axis, but the orbital angular momentum along the flux tube is 0. • The ground state, well approximated by a pair with a string in its quantum-mechanical ground state. (Quark model, low frequency limit) • Hybrid mesons: Excitations of the color flux tube.

  11. Hybrid mesons • There are two transverse polarization states of the string, clockwise (+) or anticlockwise (-) about the quark-antiquark axis. • We define an angular component momentum about the axis (Λ) – The dependence of the string wave function on the angle γ about the axis is eiγΛ • Λ= Σ (n m+ - n m- ) , nm+- mode occupation numbers • η p= (-1)L+Λ+1 • ηC= (-1)L+S+ΛΠm[(-1)m]n(m-) + n(m+)

  12. -Lowest hybrids with one m=1 phonon, leading to among other possibilities, the exotic quantum numbers: JPC= 0+-, 1-+, 2+- The complete set of quantum numbers to one phonon m=1: S=1, JPC= 2+-, 2-+, 1+-, 1-+, 0+-, 0-+ S=0, JPC= 1++, 1-- Prediction of mass for different flavor hybrid mesons

  13. EXAMPLE (1-+) L=1, S=1 J= 0, 1, 2 Λ= Σ (n m+ - n m- ) , η p= (-1)L+Λ+1 ηC= (-1)L+S+ΛΠm[(-1)m]n(m-) + n(m+) J=1 m=1 mode, nm+ =1, Λ=1 P= (-1)1+1+1= -1 C= (-1)1+1+1 (-1) = +1

  14. 3P0 quark pair creation • The hybrid meson (A) can decay into two B, C mesons. • In the breaking process there´s no introduction of extra angular momentum • The relative angular momentum during the breaking process has (S=1, L=1, J=0). A B + C B + C A

  15. The angular momentum Λ, has to be absorbed. • Cannot decay into a pair of ground state mesons, as ππ, πη, πρ... • The preferential decay modes, those with one excited meson: b1π, f1π...

  16. Isgur and Paton ’85 • Many decay channels are predicted from the FTM! 17

  17. “Practical” part of hybrids • Easiest to search for lower lying states • For instance states with JPC=1-+ • Crystal Barrel Collaboration experiment ‘98 • Resonant behavior of  P-wave @ 1.4 GeV • Experiment is ongoing @ BES-III • BESIII/GEANT4 sensitivity simulation • Monte Carlo simulation of J/0

  18. Reaction: J/0 Energy diagram for the reaction: Kinematics of the reaction: 19

  19. Simulation • Monte Carlo method • Define input domain, i.e. the decay channels • Generate the inputs using a prob. density • Compute a result • Generated input • 1(1400) ~ 14.57% • a0(980) ~ 4.38% • a1(1320) ~ 21.39% • a2(1700) ~ 41.64% • Background

  20. Criteria for 1-+ candidates • Require two ‘good’ tracks with zero net charge (i.e. being a -+-pair for sure)… • Within polar angle region • 5 cm within interaction region • …and at least four ‘good’ photons • Energy deposit > 50 MeV in the EM calorimeter • Angles correspond to kinematics 21

  21. Selection from data • Kinematic fit with criteria used as input Allow values to vary within uncertainty • Points with 2 < 15 were chosen • Constraint on the photons from 0 and  decay: 22

  22. Results • Use invariant mass for products: • The MCS shows three “resonances” 23

  23. Partial Wave Analysis • Today: simplified PWA of elastic scattering in terms of plane waves interacting with a centre and spins 0 • Plane waves in spherical harmonics 24

  24. Partial wave analysis • A result is the formula for the DCS: • How about the resonances? Take the partial wave amplitude and let’s see: 25

  25. Breit-Wigner fit • What follows is the Breit-Wigner formula for the cross section (here most general form): 26

  26. Results • Four fits appear for the different resonances: a2* a2 a0 1 27

  27. Results • The simulation was good, the angular distributions shows no irregularities 28

  28. Conclusions • The results from PWA correspond to the input values from MC • So with the setup at BES-III these resonances can be identified (if they exist)

  29. Multi quarks: confinement • A multiquark state is formed if there are more than four quarks confined in a so called MIT-bag • The Dirac eqn. gives with appropriate boundary conditions a zero normal quark flow • To conserve energy and momentum at the boundary, the external pressure is balanced by internal pressure 30

  30. Multiquarks: measurement • Above a threshold value, the multiquark decays into mesons & baryons • So, such a state has a broad width (makes experiments difficult) • However, a number of new structures were seen in J/ decays 31

  31. BES II Experiment • An anomalous enhancement near the mass threshold in the invariant mass-spectrum J/ψ γ • Theoretical interpretation of the pp mass threshold enhancement: pp bound state= baryonium • Baryonium interpretation of the mass enhancement requires a new resonance with a mass around 1.85 Gev/c2

  32. Observation of X(1835) in J/Ψγπ+π-η’ J/ψ γ Χ(1835) π+ γ η’ ρ π+π- π- π+π-η π+π- γγ

  33. π0 π0 η ω η η’ η’

  34. Selection of candidates • Reject events Mγγ < 0.22 GeV/c2 and 0.72 GeV/c2< Mγγ < 0.82 GeV/c2 • [Mγγ – mη] < 0.05 GeV/c2 • [Mπ+π-η – mη´] < 0.015 GeV/c2 • [Mπ+π- - mρ] < 0.2 GeV/c2 • [Mγπ+π- - mη´] < 0.025 Gev/c2

  35. Conclusion • To ensure that the peak near 1835 MeV/c2 is not due to background, extensive studies of potential background processes, using both data and MC have been made. • The main background channel J/ψ π0π-π+η´, and other background processes with multiphotons and /or kaons are reconstructed with data. • None of these background processes produce a peak around 1835 MeV/c2 in the π-π+η´ invariant-mass spectrum. Baryonium is a candidate for a 6 quark system.

  36. Summary There is a wide field within QCD theory describing exotic mesons Good tools to analyse meson spectroscopy are on the market Measured decay channels at BES-III can be identified pretty well There may be a 6 quark state which is a multi quark 37

  37. Bibliography • IHEP-Physics-Report-BES-III-2008-001-v1(chapters 9.4-9.5) • N.Isgur, R.Kokoski and J.Paton, Phys. Rev.Lett 54 (1985) 869 • N.Isgur and J.Paton, Phys.Rev. D31 (1985) 2910 • BES collaboration, M.Ablikim et al., Phys.Rev.Lett.95, 262001 (2005) • R. Jaffe, Phys. Rev. D17 (’78) 1444 • Any readable QM book • B. Muller, Gluon Quark Physics, Ch. 2

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