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: ; arXiv:

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.

e+ e-  P=  P'=  Suitable for the study of scalar mesons How do we perform a reliable calculation?

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.

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.

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 

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.

- 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.

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, (2001)

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) J.A. Oller, E. Oset, J.R. Pelaez Phys Rev. D59, (1999) KK  I=J=0 T = V + V G T =+ Resonances are (universal) poles in the scattering amplitude ++=

● Yields the light vector meson contributions to the K*K transition form factor. Excitation of higher mass states Production of vector mesons and rescattering

BaBar data: ArXiv: e+e- K*K  K K*

K*K transition form factors from data Isoscalar form factor Data from BaBar : ArXiv: ) Isovector form factor

All parameters have been fixed in advance Finally ( 

Different final states:  P P'  andcontain the a 0 (980) pole andcontain the f 0 (980) pole

Results: e+e-  f 0 peak M.Napsuciale, E. Oset, K. Sasaki, C.A. Vaquera-Araujo PRD (2007)

Cross section Accounts for most of the BaBar events except for the resonant ones at

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:

Results: e+e-    a 0 peak -Within the reach of BaBar. -Isovector companion of the X(2175) would be cleanly seen here.

X(2175) BES Coll. ArXiv: BaBar Coll. Phys.Rev. D74, (R)(2006); D76, (2007) X(2175) e+e-  m   MeV  J/  f 0  X = MeV M X = MeV  X =58 16 MeV M X = MeV

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, Z. G. Wang NPA791,106 (2007)

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 _ _ _

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: No resonant structure in the isovector channel.

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

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 i 18 MeV. More work needed to fully understand this state but it has a large three body component.

Thank you !

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  +- +-

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: ) K K* Problem: transition form factor K

The only substraction constant needed is the one associated to G K

Extracting the K*K transition form factor from data Data on at sqrt(s)= 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: )

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.