Rare Kaon Decays
Giuseppina Anzivino
University of Perugia and INFN
on behalf of the
NA48/2 and KLOE Collaborations
Heavy Quarks & Leptons 08
Melbourne, 5-9 June 2008
Overview
Mainly
Precision tests of ChPT in rare Kaon decays
In this talk:
recent results from NA48/2 and KLOE
not covered………
 semileptonic decays (Vus related) (talk by P. Massarotti)
 leptonic decays and LFV (talk by T. Spadaro)
 future of very rare kaon decays (talk by M. Moulson)
 results from KTeV
6-6-2008
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Outline
 NA48/2 recent results in charged Kaon decays
 K±→ p±e+e- BR and Form Factors (preliminary)
 K±→ p±gg
BR and kinematics (preliminary)
 K±→ p±e+e-g Branching Ratio (final)
 KLOE recent results in neutral Kaon decays
 KS→ gg
Branching Ratio (final)
 KS→ e+eDirect Search, Upper Limit (final)
 KS→ p+p-e+e- Branching Ratio (preliminary)
 KL→ peng
Branching Ratio (final)
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Experiments
CERN
NA48/2
NA48/2
SPS
LHC
LNF
KLOE
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NA48/2 @ CERN


+
–
K p e e
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Theoretical framework
K  pg*  pl+ldpee/dz ~ P(z)∙|W(z)|2
 suppressed FCNC processes
 one-photon exchange
 useful test for ChPT
z=(Mee/MK)2, P(z) phase space factor
Form-factor models:
(1) polynomial: W(z) = GFMK2∙f0∙(1+z)
(2) ChPT O(p6): W(z) = GFMK2∙(a++b+z) + Wpp(z)
(3) Dubna ChPT: W(z) = W(Ma, M , z)
(2) D’Ambrosio et al. JHEP 8 (1998) 4
(3) Dubnickova et al. hep-ph/0611175
(f0,) or (a+,b+) or (Ma,Mρ) determine a model-dependent BR
Parameters of models and BR in full kinematical range
Model-independent BR (z > 0.08) in visible kinematical range
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Data Samples
Kaon flux (2003+2004)  K=1.701011
K±→p±e+e-
K±→p±p0D
7146 events (Mee>140 MeV) (BG 0.6%)
12.23 x 106 events (BG 0.15%)
 The BR is measured normalizing to Kpp0D pe+e–g
→ particle ID efficiencies cancel at first order
 common selection criteria for signal and normalization channel
→ 3 track vertex, electron (pion) ID with E/p > 0.95 (< 0.85)
 Kpp0D BG suppressed using a kinematical cut Mee>140 MeV
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Fit results (preliminary)
polynomial: W(z) = GFMK2∙f0∙(1+z)
ChPT O(p6): W(z) = GFMK2∙(a++b+z) + Wpp(z)
Dubna ChPT:W(z) = W(Ma, Mρ, z)
(1)
 = 2.350.18
f0 = 0.5320.016
ρ(, f0) = –0.963
(2)
a+ = –0.5790.016
b+ = –0.7980.067
ρ(a+, b+) = –0.913
Analysis cut:
Available
set
unable 2 to
z>0.08,data
or Mee
>140MeV/c
distinguish among models
(3)
Model-Independent BR computed
by integrating d/dz
BRMI (z>0.08) = (2.26±0.08)10–7
6-6-2008
Ma = (0.9650.033) GeV
Mρ = (0.7110.013) GeV
ρ(Ma, Mρ) = 0.998
BR1 = (3.02  0.04stat)  10–7
BR2 = (3.11  0.04stat)  10–7
BR3 = (3.15  0.04stat)  10–7
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Results – BR in full kinematic range
Including the uncertainty due to the model dependence
BR=(3.080.04stat0.04syst0.08ext 0.07model)10–7=(3.080.12)10–7
NA48/2
‘75
6-6-2008
‘92
‘99
‘08
New “naïve” WA
BR(10-7)
First measurement of CPV parameter
(correlated K+/K– uncertainties excluded)
(Kpee) = (BR+–BR–)/(BR++BR–)
= (–2.1  1.5stat  0.3syst)%
Measurement
BR107
Bloch et al., PL 56 (1975) B201
2.700.50
Alliegro et al., PRL 68 (1992) 278
2.750.26
Appel et al. [E865], PRL 83 (1999) 4482
2.940.15
NA48/2 preliminary (2008)
3.080.12
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Results – FF slope 

NA48/2
 NA48/2 measurement of 
good precision
compatible with earlier results
 Contradiction of the data to VMD
‘92
‘99
‘00
further confirmed
‘08
VMD models [PRD60 (1999) 053007]
 NA48/2 values of (f0, a+, b+)
in agreement with BNL E865
Measurement
Process
Result
Alliegro et al., PRL 68 (1992) 278
K+p+e+e–
1.310.48
Appel et al. [E865], PRL 83 (1999) 4482
K+p+e+e–
2.140.20
Ma et al. [E865], PRL 84 (2000) 2580
K+p++–
2.45+1.30–0.95
NA48/2 preliminary (2008)
Kpe+e–
2.350.18
6-6-2008
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NA48/2 @CERN
Kpgg
Kpgg* pge+e–
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Theoretical framework
relevant only at low mgg
O(p4)
A(z)  loop diagrams contribution
C(z)  Wess-Zumino-Witten functional (10%)
B=D=0
[G. Ecker, A. Pich and E. de Rafael, Nucl., Phys. B303 (1988), 665]
O(p6)
unitarity corrections effects can increase the BR by 30-40 %
[G. D’Ambrosio and J. Portoles, Nucl., Phys. B386 (1996), 403]
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BR dependence on ĉ
 Both decay spectrum and rate strongly depend on the single ĉ parameter
 The Mgg spectrum has a pronounced cusp-like behaviour at 2p threshold.
WDM
O(p4)
FM
[G. D’Ambrosio and J. Portoles, Nucl., Phys. B386 (1996), 403]
The spectrum dependence will be used to extract the ĉ value
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±
K →p ±gg data sample and result
1164 events in 40% of the full data
~40 times larger wrt to world sample
3.3% BG mainly from ppg(IB)
The only previous measurement (E787),
based on 31 events (5 BG events)
BR=(1.100.32)∙10–6 ; ĉ=1.8±0.6
BR(O(p6),ĉ=2)=(1.070.04sta0.08sys)∙10–6
 MC O(p6) and ĉ=2 comparison data shape follows ChPT prediction
 Model independent measurement and extraction of ĉ is ongoing
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K ±→p ±e+e-g - first observation
never observed before!!
120 candidate events (6.1% BG)
Model-independent BR (Mgee> 260
MeV/c2)
Shape analysis [using ChPT O(p6) model,
F. Gabbiani, PRD59 (1999) 094022]:
BR(p±e+e−g)=(1.19±0.12stat±0.04sys)∙10−8
ĉ=0.90±0.45
[final result published, PLB659 (2008) 493]
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KLOE @ LNF
Mesurement of
BR(KS  gg)
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Motivations
 Important probe of ChPT
 Decay amplitude evaluated at leading order, O(p4)
D’Ambrosio and Espriu, Phys.Lett.B 175(1986) 237
BR(KS  gg) = 2.1 x 10-6
Kambor and Holstein, Phys.Rew.D 49(1994) 2346
 No full O(p6) calculation exists
 Experimental value of the BR changed along the years,
improving in precision
 Most recent measurement by NA48/1
BR(KS  gg) = (2.78±0.06±0.04) x 10-6
 Differs from ChPT O(p4) by 30%
possible large O(p6) contribution
In NA48, the KLgg background is a relevant component of the fit
In KLOE, the background from KL is reduced to zero (tagging)
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Analysis strategy
Full statistics (1.9 fb-1)
700 x 106 KS events after KL-crash tag
FCN/Ndof = 1.2
Main background  KS  2p0
with 2 photons lost in the beam-pipe
and/or colliding into QCAL
veto these photons using
a cut on arrival time
T = |TQCAL - RQCAL/c| < 5 ns
Background reduction to 70 %
••
--
DATA
MC all
cos *
Signal
Background
count signal events by fitting
Mgg and cos q*gg in the KS cms
Nsig = 711 ± 35
(4.9% stat. error)
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Result
BR(KS → gg) = (2.26 ± 0.12stat ± 0.06sys)∙10−6
now published
[JHEP05 (2008) 05]
NA31
There is a 3s discrepancy between
KLOE and NA48 results
cPT
NA48/00
NA48/03
O(p4) O(p6)
KLOE
The NA48 measurement implies
the existence of a sizeable O(p6)
counterterm in ChPT
The KLOE result makes this
contribution practically negligible
6-6-2008
NA48 Coll., Phys. Lett. B551 (2003) 7
NA48 Coll., Phys. Lett. B493 (2000) 29
NA31 Coll., Phys. Lett. B351 (1995) 579
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KLOE @ LNF
Direct Search for
KS  e+e-
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Search for FCNC in KS → e+eExotic mediators could produce
tree level FCNC processes
 Precise SM prediction, using ChPT, O(p4):
BR(KSe+e-)=1.6 x 10-15 [Ecker and Pich, Nucl. Phys. B366, 189, 1991]
 Most precise measurement by CPLEAR
BR(KS  e+e-) < 1.4 x 10-7 (90% C.L.)
In KLOE  direct search of this decay using a pure KS beam
After preselection: 1.1 Mevts in Data sample
Signal identification using a χ2 variable based on
time of particles, E/p and cluster position
Background rejection by kinematic cuts
Signal box defined in the plane χ2 vs Minv (e+e- hypotesis)
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Result
NO events found in the signal box
Upper Limit evaluated normalizing to the number of KS→p+p- events
BR(KS→e+e-) < 9.3 x 10-9 (90% C.L.)
Previous result improved by more than one order of magnitude
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CP test in KS → p+p-e+e Amplitude dominated by CP even IB
component (needed to predict the
CP violation in KL  ppee)
 CP test through measurement of angular
asymmetry between pp and ee planes
 Fit the distribution of (Emiss-Pmiss)ppee
 Normalize to the number of KSp+p-
ppee
pp (Eg<10 MeV)
ppg bp
ppg dc+p0p0+semil.
K+K-
c2=117.6/92
Prob~4%
 Data sample (900 pb-1)
 N (ppee) = 974 ± 53
  = 0.02359 ±0.00031
BR=(4.48 ± 0.24stat ± 0.15syst)×10-5
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KL → peng
Largely dominated by IB, negligible DE
Interference IB-DE small (1%)
→ test of ChPT O(p6)
A 2-dimensional fit in (Eg*,qg*)
allow to measure both R and <X>
Fit results
NA48 Coll., Phys.Lett. B605 (2005) 247
KTeV Coll., Phys. Rew. D71 (2005) 012001
6-6-2008
Adding ChPT
constraint
R = (924 ± 23 ± 16) x 10-5
<X> = -2.3 ± 1.3 ± 1.4
R = (944 ± 14) x 10-5
<X> = -2.8 ± 1.8
Giuseppina Anzivino@HQ&L08
arXiv:0710.3993
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Conclusions
The NA48/2 and KLOE experiments have produced important
experimental inputs to the Chiral Perturbation Theory,
the effective theory of strong interaction at low energy
Presented at this conference the most recent results from
NA48/2
charged kaon sector
Precise study of the Kpe+e– decay (preliminary)
Precise study of the Kpgg decay (preliminary)
First observation of the Kpge+e– decay (final)
KLOE
neutral kaon sector
Measurement of KSgg decay (final)
Upper limit for KS e+e- (final)
Measurement of KSp+p+e+e- decay (preliminary)
Measurement of KLpeng decay (final)
Still a lot to come ……stay tuned!
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SPARES
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Preliminary results
BRMI=
2.26  0.03stat
2.35  0.15stat
=
(1) f0 = 0.532  0.012stat
BR1=
3.02  0.04stat
a+ = –0.579  0.012stat
(2) b+ = –0.798  0.053stat
BR2=
3.11  0.04stat
Ma = 0.965  0.028stat
(3) Mρ = 0.711  0.010stat
BR3=
3.15  0.04stat










0.03syst
0.09syst
0.008syst
0.04syst
0.008syst
0.037syst
0.04syst
0.018syst
0.007syst
0.04syst
 0.06ext
 0.007ext
 0.08ext
 0.007ext
 0.017ext
 0.08ext
 0.002ext
 0.002ext
 0.08ext
= (2.26  0.08) 10-7 z>0.08
=
2.35  0.18
= 0.532  0.016
= (3.02  0.10) 10-7
= –0.579  0.016
= –0.798  0.067
=
(3.11  0.10) 10-7
= 0.965  0.033 [GeV/c]
=
0.711  0.013 [GeV/c]
=
(3.15  0.10) 10-7
Including uncertainty due to the model dependence, (full z range)
BR=(3.080.04stat0.04syst0.08ext 0.07model)10–7=(3.080.12)10–7
CPV parameter (first measurement! correlated K+/K– uncertainties excluded):
(K±pee) = (BR+–BR–) / (BR++BR–) = (–2.1±1.5stat±0.3syst)%
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Corrections/uncertainties
Parameter Electron
Beam
Radiative
ID
simulation corrections
BRmi107
0.02
0.01
Background
to Kpe+e–
Trigger
inefficiency
Fitting Externa
procedure (PDG)
0.01
–0.010.01
–0.010.01
0
0.06
–0.040.04
–0.030.03
0.03
0
0.003
0.007
0.02
0.08
Model (1): linear form-factor

0.01
0.04
0.05
f0
0.001
0.006
0.004
BR1107
0.02
0.02
0.01
+0.0020.002 +0.0010.001
–0.010.01
–0.010.01
Model (2): ChPT form-factor [D’Ambrosio, Ecker, Isidori, Portoles, hep-ph/9808289]
a+
0.001
0.005
0.004
–0.0010.001 –0.0020.002
0.004
0.007
b+
0.009
0.015
0.022
+0.0170.017 +0.0150.015
0.010
0.017
BR2107
0.02
0.02
0.01
0.02
0.08
–0.010.01
–0.010.01
Model (3): Dubna ChPT [Dubnickova et al., hep-ph/0611175]
Ma/GeV
0.004
0.009
0.009
+0.0080.008 +0.0060.006
0.006
0.002
Mρ/GeV
0.002
0.003
0.004
+0.0030.003 +0.0030.003
0.002
0.002
BR3107
0.02
0.02
0.01
0.02
0.08
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–0.010.01
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–0.010.01
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KS tagging
Two searches of rare KS decays :
1.6 fb-1 of collisions data analyzed for KSgg
1.3 fb-1 of collisions data analyzed for KSe+eBoth analyses use a clean KS beam from
KL-crash tagging based on KL interactions on EMC
KL-CRASH
b0.22
KL-crash ( ~ 30%)
This algorithm searches KL interacting
directly on EMC.
KL-crash calorimetric clusters are
selected using cuts on energy and b*.
KS angular resolution: ~ 1°
KS momentum resolution: ~ 2 MeV
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Two-Loop QCD Corrections to the Heavy-to

atlas