NA48/2 Rare Decay Page
Overview
This page intends to collect the status, the most current plots, and
the recent presentations and publications of ongoing rare decay
analyses. All quoted numbers can be shown at conferences.
It can only be kept uptodate with the active help of the people who do the analyses.
Therefore, please send your plots/talks/papers
and comments/suggestions to Rainer Wanke!
K^{±} decays:
Looking for K^{0}_{L}, K^{0}_{S}, or Hyperon decays from NA48 and NA48/1?
Here you find them!
K^{±} → π^{+} π^{−} e^{±} ν (K^{±}_{e4})
Measurement of ππ scattering lengths and relative form factors (2003+2004 data):
People involved in the analysis:
Brigitte BlochDevaux
Formerly: Spasimir Balev, Massimilano Fiorini, Gerard Marel, Lucia Masetti, Bernard Peyaud
Status of the analysis:
(6.11.2010)
In the whole 2003/2004 data set about
1.310 × 10^{6} events with a background of
about 0.95% were selected.
The form factors relative to f_{s} were measured to
f_{s}'/f_{s}  =  0.152 ± 0.007_{stat} ± 0.005_{syst}, 
f_{s}''/f_{s}  =  − 0.073 ± 0.007_{stat} ± 0.006_{syst}, 
f_{e}/f_{s}  =  0.068 ± 0.006_{stat} ± 0.007_{syst}, 
f_{p}/f_{s}  =  − 0.048 ± 0.003_{stat} ± 0.004_{syst}, 
g_{p}/f_{s}  =  0.868 ± 0.010_{stat} ± 0.010_{syst}, 
g_{p}'/f_{s}  =  0.089 ± 0.017_{stat} ± 0.013_{syst}, 
h_{p}/f_{s}  =  − 0.398 ± 0.015_{stat} ± 0.008_{syst}. 
All other form factors (including f_{e}', f_{e}'')
were set to 0 in the fit.
The Swave ππ scattering lengths a_{0}^{0}
and a_{0}^{2} were measured from a fit to the
phase difference δ_{0}−δ_{1} as
function of m_{ππ}.
The result depends on the assumptions used in the fit:
The paper has been published in
EPJ C 70 (2010) 635.
Written documents and talks:
Blessed plots:
(by Brigitte BlochDevaux, 3.6.2009)

Plots of the CabibboMaksymowicz variables:
s_{π},
s_{e},
m_{ππ},
m_{ev},
cos θ_{π},
cos θ_{e},
φ (K^{±},
K^{+} and
K^{−})

m_{ππ} dependence of the form factors
f_{s},
f_{e} (2003 data),
f_{p},
g_{p},
h_{p}.

m_{ππ} dependence of δ from the twoparameter fit
with isospin corrections,
with and without isospin corrections.

Effect of isospin corrections on δ.

Comparison of 2003 and 2004 Ke4 results in a_{0}a_{2} plane:
NA48 Ke4 2003 + 2004.

Comparison of Ke4 & Cusp & DIRAC results in a_{0}a_{2} plane:
All uncertainties
(stat. errors only,
stat. + syst. errors only)

Comparison of Ke4 & Cusp & DIRAC results in (a_{0}−a_{2})a_{2}
plane:
All uncertainties
(stat. errors only,
stat. + syst. errors only)

Comparison of all a_{0} results
(the yellow band is the ChPT prediction).
Analysis on the 2003 data only (now included in the 2003/2004 measurement!):
Status of the analysis:
(12.3.2008)
In the whole 2003 data about 677 500 events were found with
a background of less than 0.5%.
The form factors were measured to
f_{s}'/f_{s}  =  0.172 ± 0.009_{stat} ± 0.006_{syst}, 
f_{s}''/f_{s}  =  − 0.090 ± 0.009_{stat} ± 0.007_{syst}, 
f_{e}/f_{s}  =  0.081 ± 0.008_{stat} ± 0.009_{syst}, 
f_{p}/f_{s}  =  − 0.048 ± 0.004_{stat} ± 0.004_{syst}, 
g_{p}/f_{s}  =  0.873 ± 0.013_{stat} ± 0.012_{syst}, 
g_{p}'/f_{s}  =  0.081 ± 0.022_{stat} ± 0.015_{syst}, 
h_{p}/f_{s}  =  − 0.411 ± 0.019_{stat} ± 0.008_{syst}. 
All other form factors (including f_{e}', f_{e}'')
were set to 0 in the fit.
The Swave π π scattering lengths a_{0}^{0}
and a_{0}^{2} are measured from a fit to the phase
difference δ_{0} − δ_{1} as
function of m(ππ).
The result depends on the assumptions used in the fit:
The paper has been published (EPJ C54 (2008) 411).
Written documents and talks:
 Ke4 paper on total 2003 data set: EPJ C54 (2008) 411, CERNPHEP/200735.
 Talk Brigitte Bloch, KAON07, Frascati, May 2007.
 Talk Brigitte Bloch, Weekly Meeting, May 10, 2007.
 Talk Brigitte Bloch, QCD06, Montpellier, July 2006.
 Talk Lucia Masetti/Brigitte Bloch, Weekly Meeting, June 22, 2006 (contains the blessed results).
Blessed plots:
(by Brigitte BlochDevaux, 26.6.2008)
 Decay topology (Figure 1).
 z vertex (in cm) (Figure 2a).
 Minimum radial track distance (in cm) (Figure 2b).
 Kaon momentum (in GeV/c) (Figure 2c).
 Ke4 acceptance (Figure 3).
 φ for different m(ππ) bins (Figure 4).
 Plots of the CabibboMaksymowicz variables (Figure 5, units are GeV/c^{2} for m(ππ), m(ev)):
m(ππ),
m(ev),
cos(θ_π),
cos(θ_e),
φ (K+),
φ (K).
The background is enlarged by a factor 10! This has to be indicated when showing these plots in public.
 Plots of the CabibboMaksymowicz variables without enlarged background (units are (GeV/c^{2})^{2} for s(π), s(e)):
s(π), s(e),
m(ππ), m(eν),
cos(π), cos(e),
φ (K±, K+ and K−).
 Form factors and phase shift (Figure 6, all units are GeV/c^{2}):
fs as function of m(ππ),
fs as function of m(ev),
fp as function of m(ππ),
gp as function of m(ππ),
hp as function of m(ππ),
δ as function of m(ππ),
 m(ππ) dependence of δ, all experiments (no isospin corrections, Figure 7).
 Figure 7 with fits superimposed:
 fit of all experiments at center of the universal band without isospin corrections.
 same, but including predictions for a_{0}^{0} = 0.20 and 0.25 in the universal band.
 no fit, only universal band predictions for a_{0}^{0} = 0.22 and 0.26.
 Comparison of results in a0a2 plane (Figure 8).
 Comparison of a0 results (Figure 9).
 Old plots (SS123 only, by Brigitte BlochDevaux and Lucia Masetti):
 Kaon invariant mass (assuming pK = 60 GeV/c along z) in
linear and logarithmic scale.
 Kaon momentum (using Saclay ν reconstruction) in linear and logarithmic scale.
(K+ only: lin, log;
K− only: lin, log)
 Ratio z(data) / z(MC).
 Plots of the CabibboMaksymowicz variables:
s(π) (lin, log),
s(e) (lin, log),
cos(π)(lin, log),
cos(e) (lin, log),
φ (lin, log,
K+ lin, K+ log,
K lin, K log).
 Invariant ππ and eν masses:
m(ππ) (lin, log),
m(eν) (lin, log),
 m(ππ) dependence of the form factors fs,
fp,
gp,
hp.
 m(ππ) dependence of the phase δ.
 Correlation between fs' and fs'' with comparison between K^{±}e4 and K^{00}e4.
 Sketch of the decay and the CM variables.
K^{+} → π^{0} π^{0} e^{+} ν (K^{00}_{e4})
People involved in the analysis:
Brigitte BlochDevaux
Formerly: Marco Gersabeck
Status of the analysis: (22.6.2006)
In super samples 13 of the 2003 data 9642 events are found with a background of about 2.9%,
in the 2004 data 28025 events with a background of about 2.1%
Using the 2003 data only and K3π as normalization channel, the branching fraction was measured to
Br(K^{00}e4) = (2.587 ±
0.026_{stat} ± 0.019_{syst} ± 0.029_{norm}) × 10^{−5}.
The form factors are measured from 2003+2004 data to
f_{s}'/f_{s} = 0.129 ± 0.036_{stat} ± 0.020_{syst},
f_{s}''/f_{s} = −0.040 ± 0.034_{stat} ± 0.020_{syst}
with a correlation coefficient of ρ = −0.94.
All other form factors (i.e. f_{e}, f_{e}', etc.) were set to 0 in the fit.
The results have been blessed on the Weekly Meeting, June 22, 2006, to be shown as preliminary
on conferences.
Written documents and talks:
Blessed plots: (by Marco Gersabeck, 30.6.2006)
K^{+} → π^{+} π^{−} μ^{+} ν (K^{±}_{μ4})
People involved in the analysis:
Andrey Belkin.
Formerly: Ludovic Houchu.
Status of the analysis:
(17.8.2009)
The analysis was finished (as diploma thesis), but not published.
Written documents and talks:
Blessed plots:
None.
K^{+} → π^{0} π^{0} μ^{+} ν (K^{00}_{μ4})
People involved in the analysis:
Anna Korotkova
Status of the analysis:
(9.10.2014)
The analysis is ongoing.
Written documents and talks:
Blessed plots:
None.
K^{+} → π^{+} e^{+} e^{−}
People involved in the analysis:
Evgueni Goudzovski, Eva Gersabeck
Formerly: KhaiVinh Vi.
Status of the analysis:
(8.7.2009)
The analysis uses the whole NA48/2 data set and selects 7253
events with a background of 1.0%. From this,
the modelindependent branching fraction was determined to
Br(K+ → π+ e+ e−, z > 0.08) = (2.28 ± 0.03_{stat} ± 0.04_{syst} ± 0.06_{ext}) × 10^{7}.
The total branching ratio was obtained as
Br(K+ → π+ e+ e−) = (3.11 ± 0.04_{stat} ± 0.05_{syst} ± 0.08_{ext} ± 0.07_{model}) × 10^{−7},
where the last uncertainty reflects the differences between the
theoretical models in the invisible region z < 0.08.
The form factors were determined for a number of different models:

Linear form factor slope δ:
δ = 2.32 ± 0.15_{stat} ± 0.09_{syst},
f_{0} = 0.531 ± 0.012_{stat} ± 0.008_{syst} ± 0.007_{ext}
with a correlation of ρ = −0.96.

ChPT (D'Ambrosio et al, JHEP 9808 (1998) 004):
a_{+} = −0.578 ± 0.012_{stat} ± 0.008_{syst} ± 0.007_{ext},
b_{+} = −0.779 ± 0.053_{stat} ± 0.036_{syst} ± 0.017_{ext},
with a correlation of ρ = −0.91.

ChPT parametrization from Friot et al.
("largeN_{c} QCD", Friot et al, PLB 595 (2004) 301):
w = 0.057 ± 0.005_{stat} ± 0.004_{syst} ± 0.001_{ext},
β = 3.45 ± 0.24_{stat} ± 0.17_{syst} ± 0.05_{ext},
with a correlation of ρ = +0.999.

ChPT parametrization from Dubna ("Mesonic ChPT",
Dubnickova et al, Phys.Part.Nucl.Lett. 5 (2008) 76):
M_{a} = 974 ± 30_{stat} ± 19_{syst} ± 2_{ext} MeV/c^{2},
M_{ρ} = 716 ± 11_{stat} ± 7_{syst} ± 2_{ext} MeV/c^{2},
with a correlation of ρ = +0.998.
Finally, the CPviolating asymmetry between K^{+} and
K^{} was measured to
(BR^{+} − BR^{−})/(BR^{+} + BR^{−}) = −0.021 ± 0.015_{stat} ± 0.006_{syst}.
This is the final result. It is published in PLB 677 (2009) 246.
Written documents and talks:
Blessed plots:
(by Evgueni Goudzovski, 23.4.2009)

π^{+} e^{+} e^{−} invariant mass (color, b/w)
 e^{+} e^{−} invariant mass: normal and samesign, normal − 2 × samesign
 Data z distribution (color, b/w)
 Data/MC for cos θ_{πe} (color, b/w)
 Fit to the z distribution (color, b/w)
 Form factor W(z)^{2} (color, b/w)
 Acceptance as function of z (color, b/w)
 Trigger efficiency as function of z (color, b/w)
 π^{+} π^{0}_{D} invariant mass (normalization) (color, b/w)
 Error ellipses for the different parameter sets: linear FF,
ChPT, Friot et al., Dubnickova et al.
K^{+} → π^{+} μ^{+} μ^{}
People involved in the analysis:
Evgueni Goudzovski
Formerly: Teresa Fonseca Martin, Venelin Kozhuharov.
Status of the analysis: (23.01.2011)
The analysis uses the whole NA48/2 data set and selects 3120 events including a background
of (3.3±0.7)%. From this, the branching fraction was determined to
Br(K+ → π+ μ+ μ−) = (9.62 ± 0.21_{stat} ± 0.11_{syst} ± 0.07_{ext}) × 10^{−8}.
Form factor measurement:

Assuming a linear form factor slope δ, the parameters were determined to
δ = 3.11 ± 0.57,
f_{0} = 0.470 ± 0.040.

Using ChPT for the form factors (D'Ambrosio et al, JHEP 9808 (1998) 004), the results are
a_{+} = −0.575 ± 0.039,
b_{+} = −0.813 ± 0.145.

Using the ChPT parametrization from Friot et al.
("largeN_c QCD", Friot et al, PLB 595 (2004) 301), we obtain
w = 0.064 ± 0.014,
beta = 3.77 ± 0.62.

Using the ChPT parametrization from Dubna
("Mesonic ChPT", Dubnickova et al, Phys.Part.Nucl.Lett. 5 (2008) 76),
the results are
M_{a} = 993 ± 85 MeV/c^{2},
M_{ρ} = 721 ± 28 MeV/c^{2}.
Because of the statistics, the systematic and external
uncertainties on the form factors are negligible.
Finally, the CPviolating asymmetry between K+ and K− has been measured to
(BR^{+} − BR^{−})/(BR^{+} + BR^{−}) = 0.011 ± 0.023
and the forwardbackward asymmetry between kaon and opposite
sign muon to
A_{FB} = (N^{cos θ(K,μ)>0} − N^{cos θ(K,μ)<0})/(N^{cos θ(K,μ)>0} + N^{cos θ(K,μ)<0}) = −0.024 ± 0.018
This is the final result. It is published in PLB 697 (2011) 107.
Written documents and talks:
Blessed plots: (by Evgueni Goudzovski, 1.11.2009)
 π+ μ+ μ− invariant mass: linear scale (color, b/w);
log scale (color, b/w);
same sign muons(color, b/w).
 z distribution: color, b/w.
 form factor fit: color, b/w.
 fit results: polynomial fit,
ChPT,
ChPT + large N_c QCD,
"Meson" ChPT.
 cos θ(K,μ): color, b/w.
 K → 3π normalization: color, b/w.
K^{+} → π^{+} π^{0} γ
People involved in the analysis:
Silvia Goy Lopez, Mauro Raggi, Don Cundy.
Status of the analysis: (14.8.2010)
In the total 2003/04 data sample about 600k events have been selected, with very small backgrounds,
From the fit to extract
the fractions of Direct Emission (DE) and the interference (INT) between Direct Emission
and Inner Bremsstrahlung (IB) we obtain for the range 0 < T < 80 MeV is
frac(DE) = (3.32 ± 0.15_{stat} ± 0.14_{syst})%,
frac(INT) = (−2.35 ± 0.35_{stat} ± 0.39_{syst})%.
The correlation coefficient between DE and INT is ρ = −0.92.
From this, the normalised electric and magnetic amplitudes are determined to
X^{E} = (−24 ± 6) GeV^{−4},
X^{M} = (254 ± 9) GeV^{−4}.
In addition, the CP violating asymmetry between K^{+} and K^{}
was determined to be less than 1.5 × 10^{−3}
The paper has been published as EPJ C 68 (2010) 75.
Written documents and talks:
Blessed plots: (by Mauro Raggi and Silvia Goy Lopez, 14.8.2010)
K^{+} → π^{+} π^{0} e^{+} e^{−}
People involved in the analysis:
Milena Misheva, Mauro Raggi
Formerly: Yvonne Kohl
Status of the analysis: (09.10.2014)
In the total 2003 data sample about 1916 candidates have been observed
including an estimated background of 56 events,
which is the first observation of this decay channel.
From these events the branching fraction is determined to
Br(K^{+} → π^{+} π^{0} e^{+} e^{−}) = (4.06 ± 0.10_{stat} ± 0.06_{syst} ± 0.13_{ext}) × 10^{−6}.
The result was blessed to be shown as preliminary on conferences on the analysis meeting of Oct 9, 2014.
Written documents and talks:
Blessed plots: (by Mauro Raggi, 12.12.2014)
K^{+} → π^{+} γ γ
People involved in the analysis:
Simone Bifani, Cristina Morales.
Status of the analysis: (19.2.2008)
In super samples 13 of the 2003 data 1164 events are found with a background of about 3.3% (mostly from K+ → π+ π0 γ).
Using ChPT with ĉ = 2 and O(p^{6}) corrections, the branching fraction was determined to
Br(K^{+} → π^{+} γ γ) = (1.07 ± 0.04_{stat} ± 0.08_{syst}) × 10^{−6}.
This result has been blessed at the weekly meeting Feb 15, 2008, to be shown as preliminary on
conferences.
Written documents and talks:
Blessed plots: (by Simone Bifani, 20.2.2008)
K^{+} → π^{+} γ e^{+} e^{−}
People involved in the analysis:
Carsten Handel, Rainer Wanke.
Status of the analysis: (7.1.2008)
In all 2003+2004 data we observe 120 signal candidate events with 7.3 ± 1.7 estimated background events.
The measurement of the modelindependent branching fraction gives
Br(K^{+} → π^{+} γ e^{+} e^{−}, m(eeγ) > 260 MeV)
= (1.19 ± 0.12_{stat} ± 0.04_{syst}) × 10^{−8}.
Using the calculation of F.Gabbiani (PRD 59 (1999) 094022), the value of the free O(p^{}) parameter
ĉ was determined to ĉ = 0.90 ± 0.45.
The paper has been published as PLB 659 (2008) 493 and as CERN preprint CERNPHEP/2007033 and hepex/0711.4313.
Written documents and talks:
Blessed plots: (by Carsten Handel, 29.11.2007)
K^{+} → π^{+} π^{0} γ γ
People involved in the analysis:
Natalia Molokanova.
Status of the analysis: (1.7.2006)
The analysis is ongoing.
Written documents and talks:
 Talk Natasha Molokanova, NA48 Blessing Meeting, Apr 26, 2006
(pdf, ppt)
Blessed plots:
Last modified: Thu Oct 16 05:51:12 CEST 2014
Rainer Wanke