Phi meson physics Marianna Testa University of Roma La Sapienza & INFN for the KLOE collaboration “e + e - Collisions from Phi to Psi”, Novosibirsk 27 February-2 March 2006

2  High signal for the decay in KK, at the edge of the kinematically allowed region,  decay suppressed  Zweig rule  discovery  First seen in bubble chamber experiments at Brookhaven in 1962 in the reactions K - + p   + K+K K - + p   + K + +K - Mass  1020 MeV,  <<20 MeV Quantum numbers J PC = 1 --

3 W (MeV)  (e + e -  K S K L )  b    KSKLKS    KSKLKS    at e + e - collider Absolute BR can be determined using  (  f) and  e + e - ) (only) at a  factory SND  (e + e -  K S K L ) PRD 63, (2001) m  =  0.05 MeV  = 4.21  0.04 MeV Using  f /  tot from SND & CMD-2 with f = K + K -, KK,      , ,     e + e - ) from KLOE

4  factories Luminosity (pb -1 ) Total2482 VEPP 2M ( ) E beam : MeV scan step:  s = (1 –10 )MeV 1 bunch beam current mA L peak  3  cm -2 s -1 Circumference 18 m Time collisiont 60 ns 2 experiments CMD-2 & SND  40 pb -1 /detector DAFNE E beam :510 MeV 2 separate rings for e + e - to minimize beam- beam L peak  1.3  cm -2 s -1 up to 120 bunches 20 mA per bunch Crossing angle at 12.5 mrad KLOE experiment  2.4 fb -1

5 A  factory is a collider e + e - running at  s = M     b  (1020)   a 0 (980) f 0 (980)   '     KK    BR 83% BR 15% BR 1.3%   KAON physics V us, kaon form factors from semileptonic K S,L,K  decays Rare K S,L decays (K s        ) CPT test with semileptonic K s, K L charge asymmetries Non Kaon Physics radiative  decays (scalars, pseudoscalars + photon) hadronic cross section Physics at a  -factory

6  The KK pairs in the final state have the same  quantum numbers, i.e. are produced in a pure J PC = 1 – – state  K S (K  )K L (K  ) The  decay at rest provides monochromatic and pure beam of kaons Kaon production at the  resonance  1.5  10 9 K ± pairs/fb -1, 1.  10 9 K S K L pairs/fb -1

7 Kaon at a  Factory:  Tagging: observation of K S,L signals presence of K L,S precision measurement of absolute BR’s Kinematical closure of the events Pure beam of tagged K S mesons Interference measurementes in the K system Kaon physics at a  factory Kaon at fixed target experiments Higher rate production Higher energy particles

8 where t 1 (t 2 ) is the time of one (the other) kaon decay into f 1 (f 2 ) final state and : f i =          l              etc characteristic interference term at a  -factory entire set of K parameters from interferometry Kaon interferometry

9 Kaon interferometry (II) Integrating in (t 1 +t 2 ) we get the time difference (  t=t 1 -t 2 ) distribution (1-dim plot): From these distributions for various final states f i one can measure the following quantities: Phases (difference of) from the interference term only at a  factory

10 KLOE preliminary Fit with PDG values for  S,  L :  m = (5.34  0.34) × 10  ħ s  PDG ’04: (5.301  0.016) × 10  ħ s  Fix  m to PDG ’04 value, obtain: No simultaneous events: same final state/ antisymmetric initial state Peak position sensitive to  m Coherent K L regeneration on beam pipe |t 1  t 2 |/  S  S,L =     S,L = 0.13  0.16  0.15 cf. Bertlmann ’99 (CPLEAR): Data: 7366 evts –Fit:  2 /dof = 15.1/22 I(  t)  e  L   e  S   2(1  S,L ) e  S  L  cos(  m  t) K L(S)      at t 2 K S(L)     at t 1  13 K S K L interference and QM coherence

11 K physics K S “beam”: UL on BR(K S        ) BR(K S   e ) and charge asymmetry K L “beam”: main K L BR’s and K L lifetime form factors  K from K L   Re(  /  ’) Charged kaons: BR’s for semileptonic and 2-body decays, K  lifetime V us CP, CPT tests

12 At at  factory all experimental inputs are aviable : Branching ratios, lifetimes and form factors.  (K 0   e )  |V us | 2 |f + i (0) | 2 I i ( +,, 0,  ) S ew where i runs over the four modes K ,0 (e3), K ,0 (  3) f + i (0) form factor, I( ) phase space integral, S ew short distance correction (1.0232) Extract |V us | from  (K   (  ))/  (    (  )) ratio. Dominated by the theoretical uncertainity on the f K /f  evaluation. At af factory all experimental inputs aviable : Branching ratios, lifetimes, and form factors. V us at a  factory V us = ± KLOE preliminary Extract |V us | from  (K   (  ))/  (    (  ))  |V us | 2 /|V ud | 2 f K 2 /f  2. Extract |V us | From Kl3 decays: Can test if  = 0 at few : from super-allowed 0 +  0 + Fermi transitions, n  -decays: 2|V ud |  V ud = from semileptonic kaon decays (PDG 2004 fit): 2|V us |  V us = |V ud | 2 + |V us | 2 + |V ub | 2 ~ |V ud | 2 + |V us | 2  1 –  Most precise test of unitarity possible at present comes from 1 st row:

13 V us : K L branching ratios, life time, slopes Lesser of p miss -E miss in  or  hyp (MeV) Data 7% of sample  e    KLOE mmts at 0.5% BR(K L → π e ν ( γ )) =   BR(K L → πμν ( γ )) =   BR(K L → 3 π 0 ) =   BR(K L → π + π − π 0 ( γ ))=    L =  0.23 ns  ’  10  3  ’’  10  3 KTeV ISTRA+ KLOE NA48 1  contours For K e3 Form factors slopes: f  (t) = f  (0) [1   t] or f  (0) [1   ’ t  ½  ’’ t 2 ] see talk “Neutral Kaons at KLOE”...

14 K  0  0 K  0 K nucl.int. K  e3 K   3 V us : Charged kaon decays    e  P  * (MeV) Particle momentum in K rest frame Nev/MeV MC BR(K +   + (  )) =  stat.  syst PLB632,76-80(2006). KLOE preliminary BR(K  e3) =  stat BR(K   3 ) =  stat systematic error evaluation to be completed V us = ± see Versaci’s talk

15 V us at a  factory V us V us =  from K L e3, K L  3, K  e3, K   3,K s e3 V ud =  CKM 2005 Proceedings V us /V ud =  from K   2 Quad form-factor param. λ′+  λ′′+  λ0  (KTeV + ISTRA) Marciano hep-ph/ K L lifetime from KLOE:  L = 50.84(23) ns Fitting the 5 |V us f + (0)| KLOE determinations:  2 /dof=1.7/4 Quad form-factor param. (KLOE+KTeV + ISTRA+NA48) f + (0)=0.961(8) Leutwyler & Roos unitarity

16  S,L =     BR(Ks   e ) = (7.2 ±1.4)  _ _ MKMK MKMK  2×10    8×10   M K /M Planck = 4×10  20 ) A limit on BR(K S  3  0 ) at 10  7 level translates into a 2.5-fold improvement on the accuracy of Im , i.e.  (M K0  M K0 )  (M K0  M K0 ) CPT & CP test : K S physics 11 KLOE BR(K S   e ) = (7.09  0.08 stat  0.05 syst ) × 10  4 A S = (  2  9 stat  5 syst ) × 10  3 A L = (3.322   0.047) × Re(x) =1/4 (  (K S   e )/  (K L   e ) -1 )= ( .6  3.1 stat  1.8 syst ) 10  K S  3  0 is purely CP violating If CPT conserved,  S =  L |  ’ 000 | SM prediction: BR(K S  3  0 ) = 1.9 × 10  9 BR(K S  3  0 ) < 1.4×10  5 (first limit, SND) BR(K S  3  0 ) < 1.2×10  7 (KLOE) K S   e Sensitivity to CPT violating effects through charge asymmetry A S Test of the  S =  Q rule, V us determination CMD2’99 first observation P-Eloss-Eclu (MeV) CMD2 first observation PLB456,90 (1999)  Data — MC fit  signal    bad   bad  other  E miss (  e)  cP miss (MeV)  100  150

17 CP : BR K L     KLOE Preliminary result BR(K L      )= (1.963   0.017)  standard deviations discrepancy wrt PDG04 = (2.090  0.025)  agreement with KTeV PDG2004 KTeV KLOE BR(K L      )  Using BR(K L   ) and  L from KLOE and  S from PDG04  | = (2.216  0.013)  |  | PDG04 = (2.284  0.014)   agreement with prediction from Unitarity Triangle

18  ’ physics BR(   ) = (1.295 ±0.025)  BR(   ’  ) = (6.2 ± 0.7)  At a  factory: 4  10 7  /fb -1, 4.  10 5  ’/fb -1 lower bkg with respect to pp reactions tagging:  ’ antiparallel to monoenergetic photon (360 MeV for , 60 MeV for  ’)  ’ simultaneously collected   (’) /  tot  100 with respect to hadronic production  →  →        KLOE

19     biggest contribution p 6 in  PT KLOE preliminary: BR(  →    ) = ( 8.4 ± 2.7 stat ± 1.4 syst ) × agrees with Op 6 calcolutions    dominated by vector meson  ’   sensitive to box anomaly   ’ quark structure (gluonium content)    ll,lll (‘) l (‘) (Dalitz decays) e.m. form factors C,P,CP,  pt test:  physics M 4  (MeV) KLOE    l + l -,lll (‘) l (‘) (dalitz & double dalitz decays) e.m. form factors CMD-2 BR(  e+e - ) =(7.10 ± 0.64 ± 0.46)  BR(  e + e -     ) = ( – )  (CP violating in flavour conserving process) SND BR(  e + e - )= (5.15 ± 0.62 ± 0.39)    C violating KLOE BR(  3 .6  10  90% CL

20  e + e -,     a 4 process BR( 10 -8, ) helicity suppressed, sensitive to new interactions Lepton flavour violation   e +  -,  LF BR(PDG04 < )   (  ’)   Isospin violation lowest order of  PT: C,P,CP,  pt test:  physics (II) KLOE preliminary X  (T + -T - ), Y  T 0 Q = 22.8  0.4 [B.Martemyanov,V.Sopov, PRD 71 (2005) ] violation of the Dashen theorem (Q Dash. = 24.2 if (m 2  + -m 2  0 ) em = (m 2 K+ -m 2 K0 ) em ) CMD-2: BR < C.L. KLOE: BR < C.L.        C,CP violating see next talk

21 Scalar mesons Radiative decays:   f 0 (980)    a 0 (980)    f 0 (600)  a 0 (980 ) I=0I=1/2I=1 f 0 (980) f 0 (600) “  ” K* 0 (800) “  ”  (1020) Mass (MeV/c 2 ) not easily interpreted as qq meson ( 3 P 0 nonet) other interpretations: qqqq states (Jaffe ’77), KK molecules (Weinstein-Isgur ’90) Extract  to scalar “coupling” Since   |ss>  (    ”scalar”)  s-quark content  4-quark vs. 2-quark states confirm of f 0 (600) Both BR  S  and scalar mass spectra are sensitive to their nature [Achasov, Ivanchenko 1989]

22 First observation ’99 CMD-2 of       KLOE: evidence of f 0 in charge asymmetry S g  KK g SKK g SPP P KK KK P S V  g V S  g S pp P e+e+ e-e- f 0 more coupled to kaons than to pions      (      ): Looking for f 0          First observation’98 SND of   f 0  0  0  M(  ) MeV SND PLB485,349 (2000) (2  10 7  KLOE: clear evidence of  f 0        see next talk) f 0 (980) region M(  ) (MeV ) data  MC: ISR+FSR  MC: ISR+FSR+ f 0 (KL) M(  ) MeV

23  →     Looking for a 0 (980)→  π 0 KLOE PLB536,209 (2002) 16 pb –1 ’ BR(    ) = (8.5  0.5 stat  0.6 syst )  10 –5 Statistics x 20 First observation of  a 0    by SND PLB 438,441 CMD-2 PLB462,380 (1999) BR(    ) = (0.90  0.24 stat  0.10 syst )  10 –4 first observation

24 Future of  factory? Dafne short term upgrade L up to ~ 5  cm -2 s -1, L int  20fb -1 High lumnosity is necessary to access Search/measurement of forbidden/rare decays : sensitiv to short distance dynamiocs (rare K dec, g-2 CPT test) (complementry to LHC) Precision measuremente of fundamental SM parameters (CKM abgles, quark mass) Deeper undersanding of QCD in the non perturbative regime KS decays sensitivity to CPT test Neutral kaon Interferometry X pt studies Program complementary to LHC Proposal to upgrade the collider capable to delived 50 fb-1 in 2/3 years Present L in of KLOE now L peak = 1.3  cm -2 s -1 new machine L > 8  cm -2 s -1 L int > 50fb -1 LNF proposals see Venanzoni’s talk

25 Prospectives for K S physics K S   0  0  0 CP,CPT < < 5  seen K S  e CPT,  S=  Q (7.09  0.10)   0.2   0.1  A s CPT (1.5  11)   2   1  K S   +  -  0  pt (3  1)   0.4   0.3  K S  e + e - < 1.4  < 2  < 9  K S   0 e + e - K L (6  3)  seen  2  K S   pt (2.78  0.07)   0.03   0.02  Assuming present efficiencies or   5-10% fb -1 measurement L int = fb -1 CPT and  S=  Q violating parameters down to the per mill level Competitive on rare dacays, interesting for  pt mostly

26 Kaon interferometry: main observables measured quantity parametersmode

27 ModeParameterBest measurement or PDG-04 fit KLOE-2 L=100 fb -1          mm ±  10 9  s -1 ± 0.02 STAT  10 9  s -1          Re  ’  (1.67 ± 0.26)  ± 0.2 STAT           Im  ’  ± ± STAT       e ALAL (3322± 58 ± 47 )  ± 18 STAT   e    e Re(   )(0.29 ± 0.27)  ± 0.2 STAT   e    e Im(   )(0.24 ± 0.50)  ± 20 STAT  Prospectives for Interferometry

28 Several models can be tested (only) at a  factory Simple decoherence model:  0 QM Decoherence related to Quantum gravity and CPT violation, J. Ellis et al (1984) Test of Quantum Mechanics and CPT at a  factory Novel type of CPT violation for correlated KK states, J. Bernabeu et al. (2004)

29    int. lum. (fb -1 ) present KLOE KLOE + VDET -- CPLEAR results -- Planck’s scale region Decoherence related to Quantum gravity and CPT: 

30 Novel type of CPT for correlated KK states:  present KLOE KLOE + VDET -- Planck’s scale region int. lum. (fb -1 )  Re  (similar for Im  )

31 (1 + i tan  SW )(Re  iIm  f A*(K S  f) A(K L  f) SS 1 CPCPT Test of CPT trough Bell Steinberger relation At present f =  contributes with the bigger error to Im  sensitivity    only at a  factory: pure K S beams gives access low BR, access to K S K L interference term CPT: Bell-Steinberger

32     R( 8.0 ± 2.7 ) × 10  with  =4.63%3000 evts  study of  spectrum  ’   l + l -,lll (‘) l (‘) (Dalitz & double dalitz decays) with high statistics       e + e - test of CP violation beyond SM  ’      sensitive to   expcted events Prospectives for  & scalars -1 With 20 fb-1  f 0 , f   K + K - (KK) ( expected BR ~ 10 -6(-8) ) well measured (10 5 K + K - and 10 3 KK), direct measure of the g fKK coupling Large samaple of   9x10 8 and  ’  4x10 6 Intersting channels

33 Physics with fb -1 Kaon physics : General fb -1 CPT and  S=  Q violating parameters down to the per mill level competitive on super rare dacys, interesting for  pt mostly Re(x+) Contribution of BR(K S   e ( ) similar to ohers fb-1 3  measurement Bell Steinberger Relation Interference in the  (  ) channle bring to total error Im  to present of down to 10 -6, equivalent to K 0 K 0 mass relative difference below K S   0 l + l - pollution to K L   0 l + l - via K S K L fb sensitivity to theory request 15% accuracy K S   0  0  fb -1 5  few events obervable K S   +  -  fb -1 precision 15% K S  fb -1 5 error d (l0) 10-3 d(l0’) l0-4 check of the SU(3) breaking in f+(0)

fb-1 Kaon physics: CPT and  S=  Q violating parameters down to the per mill level Competitive on super rare dacays, interesting for  pt mostly (direct CPV) K L,S interferometry (CPT)  physics Dalitz decays   e + e - ,     , e + e - e + e-,     e + e - decays (BR’s ) C,P,CP,LF test via  , ,   e -,e +  , Significant improvement on UL    study of the shape on  mass, sensitive to test of VDM and a0  e + e -, exp BR 6   a 4 process BR( 10 -8, ) helicity suppressed, sensitive to new interactions  UL (< )     expe BR 4  () BR( )10-6 Physics program vs luminosity

fb-1 CPT unprecedentetest level of precision via 1) rare K L &K S interferences 2) rare direc CPV violation in K+ asym and rare KL 10 3 fb-1 sensitivity ot K L   (&KL pee, KL+ SM level f factory no bkg from neutral baryons, kaons 4 mom know) region of high discovery potential for non standards source of CPV via new tests of CKM mech in then kaon system

36  20 fb -1 6  10 8  mesons produced Dalitz and double Dalitz decays   e + e - ,     , e + e - e + e-,     e + e - decays (BR’s ) easily fb-1 C,P,CP,LF violating decays  , ,   e -,e +  , Signifacant improvement on UL Statistics benefit on other decays     study of the shape on  mass, sensitive to test of VDM and a0  e + e -, exp BR 6   UL (< ) (but bkg from ee ee(g))     expe BR 4  BR( )10-6

f KKG well measured 10 4 K+k+ and 103 K0K)

38 Sensitivity to CPT violating effects through charge asymmetry A S Test of the  S =  Q rule,  (K S   e )/  (K L   e ) = Re(x ) FISRT OBSERVATION CMD-2 BR(Ks   e ) = (7.2 ±1.4)  KLOE BR(K S   e ) = (7.09  0.08 stat  0.05 syst ) × 10  4 CPT: K S semileptonic decays  Data — MC fit  signal    bad   bad  other  E miss (  e)  cP miss (MeV)  100  150 A S = (  2  9 stat  5 syst ) × 10  3 A L = (3322  58  47) × Re(x) = ( .6  3.1 stat  1.8 syst ) 10  KLOE

39 Physics with 100 fb -1 A S sensitivity probe the K0 K0 mass difference to level (if CPT is violated only in the mass matrix) K S   0 l + l - pollution to K L   0 l + l - via K S K L mixing error at 10% level theory request 15% accuracy

40 Conclusions A f favcotry provides the ideal place to perform almosto without competitors KS physics Quantum interferencem studies h/h physics High luminosity to access rare KS decays sensitivity to CPT test Neutral kaon Interferometry X pt studies Program complementary to LHC

41 Spare slides

42  ll) Leptonic width  ll) SND, PRL 86, 1698 (2001) from e + e -   +  - B(   l + l - ) = sqrt(B(   e + e - ) B(    +  - ))= (2.89 ± 0.10 ± 0.06)  KLOE, PLB 608, 199 (2005) using e + e -  e + e - and e + e -   +  -  (   l + l - ) = (1.320 ± ± 0.015) keV

43 Measure using K L        tagged by K S  π + π - events KLOE  L =  0.17  0.25 ns Average with result from K L BR’s:  L =  0.23 ns cfr Vosburgh ’72,:  L =  0.44 ns × 10 2 Events/0.3 ns L/  c (ns) ns cm 0.37 L P K = 110 MeV Excellent lever arm for lifetime measurement K L lifetime

44 Parameterization: t = (p K  p  ) 2 /m 2   For K e3 :f  (t) = f  (0) [1   t] or f  (0) [1   ’ t  ½  ’’ t 2 ] KLOE preliminary Linear fit:  = (28.6 ± 0.5 ± 0.8)  10  3 Quadratic fit:  ’  = (25.5 ± 1.5 ± 1.9)  10  3  ’  ’  = (1.4 ± 0.7 ± 0.7)  10  3  (  ’,  ’’  ) =  0.95  ’  10  3  ’’  10  3 KTeV ISTRA+ KLOE NA48 1  contours K Le3 form-factor slopes

45 CMD2 collaboration PLB605, 26 (2005) BR(   ) = (1.373± ± 0.085)  BR(     ) = (1.258± ± 0.077)  SND collaboration PRD 63, (2001) ??BR(   e + e - ) = (2.93± 0.02 ± 0.14 ±0.02)  BR(      ) = (47.6± 0.3 ± 1.6 ± 0.3 )  BR(   K S K L ) = (35.1± 0.2 ± 1.2 ± 0.3 )  BR(   +  -  0 ) = (15.9± 0.2 ± 0.7 ± 0.4 )  ??BR(   ) = (1.33± 0.03 ± 0.05 ± 0.01 )  m  = ( ± 0.02 ± 0.04) MeV    (  ±  ±  )  MeV

46  s (MeV) First observation in f hpg by SND (PLB 438,441) 395 pb -1 at  peak + 10 pb -1 1)  →  (39.43%) 5  final state 2.2  10 4 events 2)  →π + π - π 0 (22.6%) π + π  4180 events Fit the two spectra simultaneously →→  →  →→ Kaon LoopNo Structure M  π (MeV) →→  →  Nature of the scalar a 0 : a 0 (980)→  π 0 KLOE 2000 data (2 107 f) PLB485,349 (2000)

47 First observation SND of   0  0  1998 Br(f f0g)= (3.42± 0.30 ± 0.36)10 -4 M(pp) MEV      Looking for f 0     Kaon-loop fit: 1. VDM part still not perfect (see residuals); 2. Scalar part ok BUT f 0 (600) is needed [p(  2 ) ~  30% !]; 3. f 0 (980) parameters agree with      analysis again R > 1 (g fKK > g f  - ). Residuals vs. DP position Data- fit comparison (on projections) KLOE preliminary

48 CP Test in flavour conserving processes SM predictions small  signature of New Physics beyond SM J PC = 0 -+       e  e  CP  asymmetry between  and ee planes (as KL) CMD –        P,CP (large background in hadron production)  4   P,CP 4 (background free) C Test not extensively studied in em and strong interactions     C    e+e-,      +  -, if  *  SM: via  BR

49 K S physics  Ks        Test of  pt K S   R  changed along the years Measurement of Na48 (   (relevant bkg from K L  ) differs for  PT O(p4) by 30%, useful to fix O(p6) counterterm

50 Sensitivity to CPT violating effects through charge asymmetry A S Test of the  S =  Q rule,  (K S   e )/  (K L   e ) = Re(x ) FISRT OBSERVATION CMD-2 BR(Ks   e ) = (7.2 ±1.4)  KLOE BR(K S   e ) = (7.09  0.08 stat  0.05 syst ) × 10  4 CPT: K S semileptonic decays  Data — MC fit  signal    bad   bad  other  E miss (  e)  cP miss (MeV)  100  150 A S = (  2  9 stat  5 syst ) × 10  3 A L = (3322  58  47) × Re(x) = ( .6  3.1 stat  1.8 syst ) 10  KLOE

51

52 First observation CMD-2 of       PLB462,371(1999) KLOE: evidence of f0 in charge asymmetry data  MC: ISR+FSR  MC: ISR+FSR+ f 0 (KL) M(  ) MeV S g  KK g SKK g SPP P KK KK P S V  g V S  g S pp P e+e+ e-e- f 0 more coupled to kaons than to pions      : Looking for f 0     M(  ) MeV f 0 (980) region M(  ) (MeV )

53 First observation SND in   0  0  PLB 440,442 (1998) SND BR(        )= (1.14  0.10  0.12)10 -4 M(pp) MEV      Looking for f 0     CMD  2 PLB463,380 (1999) BR(        )=(0.92  0.08  0.06)10 -4 SND PLB485,349 (2000) (2  10 7  BR(        )= (1.221   0.061)  KLOE PLB537,21 (2002) (5  10 7  ) BR(        )=(1.09  0.03 stat .05 syst )10  4 Fit to the M  spectrum, contribution from:   f 0     “ strong ” negative f 0  interference negligible contrib. from              M  (MeV) KLOE 17 pb  1 ’00 data N ev = 2438  61

54 First observation in   by SND PLB 438,441 CMD-2 PLB462,380 (1999) BR(    ) = (0.90  0.24 stat  0.10 syst )  10 –4  →     Looking for a 0 (980)→  π 0 KLOE PLB536,209 (2002) 16 pb –1 ’00 data BR(    ) = (8.5  0.5 stat  0.6 syst )  10 –5 New data (statistics x 20) first observation

55 Zweig rule: decay  KK prefered dispite of the phase sapce, because consttitunent qurks have to survive f = ss

56  f 0 (980)                 K + K -  [ 2m(K)~m(f 0 )~m(  ) ]  expected BR ~  K 0 K 0  ““ ~   a 0 (980)         K + K -   expected BR ~  K 0 K 0   expected BR ~ 10 -8