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Theoretical study of e+e- PP' and the new resonance X(2175) M. Napsuciale Universidad de Guanajuato E. Oset, K. Sasaki, C. A. Vaquera Araujo, S. Gómez Avila,, A. Martínez Torres, K. Kemchandani, L.S. Geng: Phys.Rev.D76:074012,2007; arXiv:0711.4147; arXiv:0801.3635.
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Outline ● Outline of the calculation for e+e- PP'. ➢ PP' vertex function in R PT. ➢ involved scales. ➢ physics ● Results. ● X(2175) as a three body resonance. ● Conclusions.
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e+ e- P= P'= Suitable for the study of scalar mesons How do we perform a reliable calculation?
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Similarities with decays Properly described by meson loops Difficulties: ● Highly virtual photon. ➢ probes higher multipoles in the KKbar system ( neutral kaon loops). ● Probable excitation of higher mass states (K*Kbar). Fortunately ● Experimental data for both neutral and charged kaon form factors available up to ● Calculation of the kaon form factor in UCHPT also available. ● Experimental data on the K*K transition form factor in the 2-3 GeV region.
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Leading order em contributions: single photon exchange Requires to calculate the PP ’ vertex function for high photon virtualities and dimeson mass close to the scalar poles. P P’ We proceed as follows: ● Calculate the PP’ vertex function for low photon virtualities and low dimeson mass (within the scope of RCHPT) ● Identify the relevant scales and the main physical effects in this context (form factors and meson-meson amplitudes). ● Use a characterization of these elements valid for high photon virtualities and high dimeson mass.
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Example vertex function in RCHPT G. Ecker, J. Gasser, A. Pich, E. de Rafael Nucl. Phys. B 31,311 (1989) Tree level contributions due to mixing are negligible. X
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Cancellation of off-shell contributions to meson-meson rescattering in RCHPT ● The “pinched” diagrams coming from the off-shell terms cancel the genuine diagrams d) e) and f). ● We are left with diagrams a) b) c) with on-shell meson-meson amplitudes.
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- Replace the so obtained lowest order terms of the kaon form factor by the full form factor ( data or unitarized). - Replace the lowest order KK (on-shell) amplitudes by the complete amplitude (we use the unitarized KK scattering amplitudes containing the scalar poles) Form factors (leading order terms). Meson-meson amplitudes to leading order (with on-shell interactions) + …… Finite calculation valid for low photon virtualities and low dipion invariant mass. How to extend these domains to high photon virtualities ( ) and high dipion mass ( )? Physics = Reliable calculation in spite of the huge energies involved Scales in the reaction: ● meson-meson scattering at the dipion invariant mass. ● KK vertex at the mass ● Kaon form factor at. Clear separation of the effects at the involved scales.
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Data from DM2 Coll. Z Phys C39,13 (1988) Unitarized kaon form factor Coupled channel Unitarization (p-wave meson meson amplitudes) Matching to : + ➢ Perturbative QCD at s infty ➢ One-loop CHPT at low energy Oller,Oset & Palomar PRD 63, 114009 (2001)
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Unitarized meson-meson scalar amplitudes * ● V on factorizes out of the loop integral. ● Algebraic equation: T=V/(1-GV). ● Coupled channel analysis required. Substraction constant Matching cutoff vs a( GeV)=-1 *J.A. Oller, E. Oset: Nucl.Phys.A 620 (1997) 438-456 J.A. Oller, E. Oset, J.R. Pelaez Phys Rev. D59, 074001 (1999) KK I=J=0 T = V + V G T =+ Resonances are (universal) poles in the scattering amplitude ++=
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● Yields the light vector meson contributions to the K*K transition form factor. Excitation of higher mass states Production of vector mesons and rescattering
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BaBar data: ArXiv:0710.4451 e+e- K*K K K*
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K*K transition form factors from data Isoscalar form factor Data from BaBar : ArXiv:0710.4451 ) Isovector form factor
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All parameters have been fixed in advance Finally (
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Different final states: P P' andcontain the a 0 (980) pole andcontain the f 0 (980) pole
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Results: e+e- f 0 peak M.Napsuciale, E. Oset, K. Sasaki, C.A. Vaquera-Araujo PRD 074012 (2007)
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Cross section Accounts for most of the BaBar events except for the resonant ones at
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Results: e+e- K K. Rescattering. + - isoscalar isovector -Rescattering dominates close to the KK threshold (enhancement due to the f 0 and a 0 lying slightly below threshold). -Sizeable contribution from tree level vector exchange for sqrt(s)>2.4 GeV. -Measurement within the reach of BaBar. -Would confirm X(2175) properties and test effects of the companion isovector resonance if it exists. -Entangled isoscalar and isovector effects. BaBar data for e+e- K+K-K+K- close to threshold S. Gomez-Avila, M. Napsuciale, E. Oset ArXiv:0711.4147
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Results: e+e- a 0 peak -Within the reach of BaBar. -Isovector companion of the X(2175) would be cleanly seen here.
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X(2175) BES Coll. ArXiv:0712.1143 BaBar Coll. Phys.Rev. D74, 091103(R)(2006); D76,012008 (2007) X(2175) e+e- m MeV J/ f 0 X =65 23 17 MeV M X =2175 10 MeV X =58 16 MeV M X =2186 10 6 MeV
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Quark model predictions 100 MeV above the expected value and too narrow to be a state Other possibilities: ● tetraquark : Break-up into f0 -> broad reasonance ● Hybrid meson ( ) Width generally larger than 100 MeV ● Three body resonance. Ding-Yan, PLB650, 390 2007 Z. G. Wang NPA791,106 (2007)
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Three body resonance? ● X(2175) f(980) ● f(980) is dynamically generated resonance in meson-meson scattering Large “meson-meson component in its wave function” ● The f(980) pole appears neatly in pure KK scattering ● M( KK component is dominant X(2175) is close to threshold _ _ _
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X(2175) as a three body resonance Solving the Faddeev equations for (KK) I=0 : Isoscalar channel M X ~2150(8) X ~18 MeV Total energy of the three body systemEnergy of the KK system A. Martínez, K. Khemchandani, L.S. Geng, M. Napsuciale, E. Oset: arXiv:0801.3635 No resonant structure in the isovector channel.
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Remarks: Narrow resonance. component of the f 0 missing. The sbar s state predicted around the same mass (m=2050 MeV, =378 MeV). Not seen in K*K. KK? It could be a more complex object with a large three body component
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Conclusions We present a reliable calculation of e+e- PP'. The starting point is the PP' vertex function in RCHPT for low photon virtuality and low dimeson invariant mass. There are effects at two different scales sqrt(s) and m PP'. The physics at these scales is given by form factors and on-shell meson-meson amplitudes. The range of validity of the RCHPT vertex functions is enlarged considering the full form factors and rescattering effects through the unitarized meson-meson amplitudes containing the scalar poles. Our calculation describes the events for of BaBar data except for the resonant ones close to the f0 threshold. The calculated cross section for the PP'=K+K-, is within the reach of BaBar. The signals of the isovector companion of the X(2175) could be seen here. A solution of the three body problem for KK in the isoscalar channel yields a sharp peak at 2150 + i 18 MeV. More work needed to fully understand this state but it has a large three body component.
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Thank you !
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There are tree level contributions… and rescattering Turn out to be negligible. Rescattering enhanced by the presence of the a0(980) and f0(90) poles in the unitarized KK->KK meson meson amplitudes. These poles lie slightly below the threshold for the production of the K+K- system in this reaction. e e +- +-
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Excitation of higher mass states Production of vector mesons and rescattering ● Production of K*K observed in e+e- annihilation( DM2 Coll. Z. Phys.C52 (1991), BaBar, ArXiv:0710.4451 ) K K* Problem: transition form factor K
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The only substraction constant needed is the one associated to G K
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Extracting the K*K transition form factor from data Data on at sqrt(s)=1400-2180 MeV : ● Dominated by production through ' and ' ● No signal for contributions of ' !! ● Small fraction of the charged channel ', ' ( DM2 Coll. Z. Phys.C52 (1991) ) ', ' More precise and copious data from BaBar : ArXiv:0710.4451 )
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Loop tensor Decomposed in terms of: ● Three point scalar functions (finite) ● Two point scalar functions 1 GeV GeV Technical issues: scales, divergent integrals and substraction constants.
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