Theoretical study of e+e- PP' and the new resonance X(2175)

M. NapsucialeUniversidad 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.

Outline

● Outline of the calculation for e+e- PP'.➢ PP' vertex function in RPT.➢ involved scales.➢ physics● Results.● X(2175) as a three body resonance.● Conclusions.

e+

e-

P=

P'=

s2GeV

mPP'≈m f , ma

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 thePP’ 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.

Examplevertex 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 ( )?

GeVs 2fmm

Physics

= 0,KK

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 .GeVs 2

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, 114009 (2001)

Unitarized meson-meson scalar amplitudes *

● Von 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) 438-456J.A. Oller, E. Oset, J.R. Pelaez Phys Rev. D59, 074001 (1999)

KK

I=J=0

T = V + V G T

= +

V=V on∑i pi

2−mi2 L PT

2

Resonances are (universal) poles in the scattering amplitude

∣t KK 0 ∣2

++=

● 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:0710.4451e+e- K*K

K

K* I s =∣F I s ∣2 f s

K*K transition form factors from data

Isoscalar form factor

Data from BaBar :ArXiv:0710.4451)

Isovector form factor

All parameters have been fixed in advance

Finally (

Different final states: 0,KK

P

P'

PP '=K K≈ F K K0 F K∗K

0 tKK0 ' F K K

1 ' F K∗K1 tKK

1

PP '=≈ F K K0 F K∗K

0 t K0

PP '=≈ ' F K K1 ' F K∗K

1 t K K 1

t K0 ≝tK K

0 t K K0 ≝tK K K K

0

and contain the a0(980) polet K K1 ≝tK K K K

1

and

t K K 1

contain the f0(980) pole

Results: e+e-

mf0 peak

t≈ F K K0 F K∗K

0 tK 0

M.Napsuciale, E. Oset, K. Sasaki, C.A. Vaquera-Araujo PRD 074012 (2007)

Cross section

Accounts for most of the BaBar events except for the resonant ones at s=2175 MeV

Results: e+e- K K . Rescattering.+ -

t≈ F K K0 F K∗K

0 tKK0 ' F K K

1 ' F K∗K1 tKK

1

isoscalar

isovector

-Rescattering dominates close to the KK threshold (enhancement due to the f0 and a0 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

Results: e+e-

a0 peak

m

s

-Within the reach of BaBar.-Isovector companion of the X(2175) would be cleanly seen here.

t≈ ' F K K1 ' F K∗K

1 tK K 1

X(2175)

BES Coll. ArXiv:0712.1143BaBar Coll. Phys.Rev. D74, 091103(R)(2006); D76,012008 (2007)

X(2175)

e+e- mMeV

J/f0

X=65 23 17 MeV

MX=2175 10 MeV X=58 16

MeV

MX=2186 10 6 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.

)(3 13 ssS

gss

ssss

s s

Ding-Yan, PLB650, 390 2007

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

MX~2150(8) X~18 MeV

Total energy of the three body system Energy 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.

Remarks: Narrow resonance. component of the f0 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 mPP' . 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.

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:0710.4451)

K

K*

Problem: transition form factor

K

The only substraction constant needed is the one associated to GK

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)

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.