Can the S(980) mesons be described as KK? introduction: the f 0 /a 0 (980) resonances structure: leading hypotheses test: radiative decays of phi(1020)

Can the S(980) mesons be described as KK?

• introduction: the f0/a0(980) resonances

• structure: leading hypotheses

• test: radiative decays of phi(1020)

• experiments and recent results

• evaluation: what have we learned?

• conclusions

Richard JonesUniversity of Connecticut

EMI2001, Osaka, Dec. 4-7 2001

Electromagnetic Interactions in Nuclei and Hadrons Symposium

Introduction: f0(980)

EMI2001, Osaka, Dec. 4-7 2001

primary decay s-wave

PDG: m0 = 980 10 MeV = 40 – 100 MeV

often seen through interferencewith background ()

also seen as large thresholdenhancement in K+ K

- s-wave

strong coupling to strange quarksobserved in J/ radiative decays

2

Introduction: a0(980)

EMI2001, Osaka, Dec. 4-7 2001

primary decay s-wave

PDG: m0 = 983 1 MeV = 50 – 100 MeV

seen through interference with

background in final state

observed as a peak in inclusivephotoproduction data

neutral a0 has strong coupling tostrange quarks (unexpected)

)( 0m )( 00m

Crystal Barrel

CERN Omega

)( 0m

3

EMI2001, Osaka, Dec. 4-7 2001

Structure: leading hypotheses4

1. Exotic (nsns) state explains near-degeneracy of two states narrow widths explained by OZI suppression explains strong couplings to strange quarks? where are the other members of the nonet?? few constraints

2. KK molecule (or non-exotic nsns state) inspired by nearness of states to 2K threshold narrow widths explained by large physical size of hadron explains strong couplings to strange quarks no missing states are required to exist

? few constraints

3. Dynamics of 2-pseudoscalar scattering coupled-channel fits to 2P scattering data exhibit dynamical poles in the

s-wave near 2K threshold that arise from kaon loops no resonances have to be included (in contrast to p-wave)? simple no physical picture (like a molecule) is correct

EMI2001, Osaka, Dec. 4-7 2001

5Test: radiative decays of Phi

Close, Isgur, Kumano (1993):

look at the decays

can discriminate between 3 models using

members of ordinary nonet

molecular kaon/antikaon state

members of exotic qqqq nonet

BR of order expected in the molecular model

a real prediction (no data on these channels existed in 1993)

)980(Sγ

019

5105

EMI2001, Osaka, Dec. 4-7 2001

6Experiment: results from VEPP-2M

e+e- collider (Novirsibirsk)

2 experiments:

SND CMD-2

2001:total of 90 M analyzed

)γfBR( 0

4105.0

3.13.05.3

EMI2001, Osaka, Dec. 4-7 2001

7continued: results from VEPP-2M

)γaBR( 0

41009.014.088.0

04.025.0r

EMI2001, Osaka, Dec. 4-7 2001

8Experiment: results from DA NE

e+e- collider (Frascatti)

KLOE detector

2001:total of 90 M recorded

50 M analyzed

700MeV)ππ(m

)γfBR( 0

4102.06.04.2

EMI2001, Osaka, Dec. 4-7 2001

9continued: results from DA NE

)γaBR( 0

41006.005.058.0

03.024.0r

EMI2001, Osaka, Dec. 4-7 2001

10Radphi at JLab: analysis in progress

0π

ω

η

Fixed-target (Jlab):

Radphi detector E GeV

status:40 M collected Y

expected:

ppγ

γa60~γf200~

0

0

Parameters of model canaccommodate a largerange in absolute B.R.s

Ratio r = 1 is a predictionof the molecule only forthe I=1/I=0 states; moregenerally r = tan2 mixing

Neutral a0/f0 mixing anglerecently measured incentral production gives

EMI2001, Osaka, Dec. 4-7 2001

11Evaluation: does the molecule survive?

Close, Kirk: cautious yes Achasov: molecule excluded

05.03.0tan2

B.R. of 10-4 is too largefor a molecular KK state.

EMI2001, Osaka, Dec. 4-7 2001

12Evaluation: a simple model

V r

V0

a

Simple non-relativistic model

V0 ~ 250 MeV

a = 1 fm

Eb = -8 MeV

(Born approximation)Apm

e'V

EMI2001, Osaka, Dec. 4-7 2001

13Can you stretch a molecule far enough?

Restore unitarity usingBreit Wigner propagator

constant m0, (n.r.a.)

transition strength thatappears above 2Kthreshold assumed100% absorbed to KKfinal state

EMI2001, Osaka, Dec. 4-7 2001

13Can you stretch a molecule far enough?

Try moving shifting andbroadening resonance

Restore unitarity usingBreit Wigner propagator

constant m0, (n.r.a.)

transition strength thatappears above 2Kthreshold assumed100% absorbed to KKfinal state

EMI2001, Osaka, Dec. 4-7 2001

13Can you stretch a molecule far enough?

Try forcing a dipolemoment very large

no

Restore unitarity usingBreit Wigner propagator

constant m0, (n.r.a.)

transition strength thatappears above 2Kthreshold assumed100% absorbed to KKfinal state

Try moving shifting andbroadening resonance

EMI2001, Osaka, Dec. 4-7 2001

14Evaluation: threshold dynamics

Oset et.al. (2000): Effective field theory

Uses only leading-order XPT interactions

Unitarization leads to expansion of T-1 instead of T

Coefficients set from fits to 2-pseudoscalar elastic scattering data

Dominant contributions come from imaginary part of K+K- loops

Some phases remain ambiguous

EMI2001, Osaka, Dec. 4-7 2001

14Evaluation: threshold dynamics

Oset et.al. (2000)

1. Surprising early results from SND/CMD-2 now supported bymore data, and independent confirmation from KLOE:

2. In the molecular picture, B.R. ratio of 0.3 measures neutrala0/f0 isospin mixing angle, in quantitative agreement withanalyses of data in central production.

BUTThe magnitude of these radiative decay widths is unnaturallylarge for the molecular picture – a major problem

3. A unitarized XPT analysis of 2-pseudoscalar scatteringobtains qualitative agreement; updated comparison is needed

4. New results from Radphi at Jefferson Lab are expected soon.

Conclusions

EMI2001, Osaka, Dec. 4-7 2001

15

40 101.08.0)γaBR(

40 103.05.2)γfBR(