1. Analysis of KSe decays
Outline
Motivations of the measurement
Analysis scheme
Ks tag
Signal selection
Efficiency estimates
Systematic sources
Uncertainty in efficiency determinations
Uncertainty in the knowledge of signal and background shapes
Where we stand (What has been understood and done)
What remains
Tommaso Spadaro
INFN LNF

2. Motivations I – study of CPT violation
1) Measure charge asimmetry to test CPT invariance:
CPT
p-e+nHWK0 = a + b
p+e-nHWK0 = a*- b*
p+e-nHWK0 = c + d
p-e+nHWK0 = c*- d*
DS=DQ
eS = eK + dK
eL = eK - dK
DSDQ
A 
G(p-e+n) - G (p+e-n)
G(p-e+n) + G (p+e-n)
AS = 2(Re eK + Re dK + Re b/a - Re d*/a)
AL = 2(Re eK - Re dK + Re b/a + Re d*/a)
CPT dec.
CPT mixing CP
DSDQ e CPT
SM: AS = AL
KTEV ’02: AL = (3.322   0.047)10-3
NA48 ’03 AL = (3.317   0.072)10-3
(preliminary: hep-ex )
AS: no existing measurement

3. Motivations II – DS=DQ rule violation
2) Measure BR(KSpen) to test of the validity of the DS=DQ rule:
x = A(DSDQ )/A(DS=DQ )
x+ = (x + x)/2  c*/a
x = A(DSDQ )/A(DS=DQ )
110-3
BRS(pen)/tS
1 + 4Re x+=
BRL(pen)/tL
710-3
810-3
SM: DSDQ transitions not allowed at tree level: |x| ~ GFmp2~10-7
CPLEAR ’98 Re x+ = (-1.8  4.1  4.5)10-3

4. Motivations III – extraction of Vus
3) Measure BR(KSpen) to extract Vus and test unitarity of 1st row of CKM matrix:
|Vud|2 + |Vus|2 + |Vub|2 = 1
dVud / |Vud|0.05%, |Vub| negligible
For Ke3 modes:
K+e3
K0e3
K+m3
K0m3
E865
|Vus| f+ (0)
K0p-
exp th
|Vus| =  exp  th
Comments:
Old data (Chiang ’72) or PDG fit values: inclusiveness for Ke3g?
New E865 measurement: agrees better with current values of Vud
SM: From unitarity and |Vud|: |Vus|=0.22690.0021

5. Analysis scheme – Ks beam
Simoultaneous KSKL production in a pure JPC = 1-- state: identification of a KS,L signals the presence of a KL,S (KL,S tag)
KL “crash”
= 0.22 (TOF)
KS  p-e+n
KS tag through identification of KL interactions in EmC through a TOF technique:
Neutral cluster in barrel, E>100MeV, 0.17<b<0.28
Efficiency ~ 30% (50% of KL’s decay before entering calorimeter)
F  KSKL is a two-body decay, tagged KS beam has definite momentum:
KS angular resolution: ~ 1° (0.3 in f)
KS momentum resolution: ~ 2 MeV

6. Analysis scheme – Signal selection
1) Two opposite charged tracks coming from IP, entering calorimeter,
invariant mass at the vertex below KSp+p- peak:
Mpp < Mcut
TOF rejection of KSp+p- background: both tracks connected to EmC clusters, calculate dt(M) = Tcl – L/cb(M)
2) Test of pp mass hypothesis:
|dt(Mp)1 - dt(Mp)2| > Tppcut
3) Test of ep, pe mass hypotheses: define
ddtpe = dt(Me)2 - dt(Me)1 ddtep = dt(Me)1 - dt(Me)2
e-p+
|ddtpe| < Tpecut1 and ddtpe > Tepcut2 OR
|ddtep| < Tpecut1 and ddtep > Tepcut2
e+p-
Data
MC pen

7. Analysis scheme – Counting signal events
Use KS momentum from tag and PID from TOF, to test presence of neutrino:
Emiss = ES - p1,2 + Me - p2,1 + Mp  2
Pmiss = |PS - p1- p2|
2001 data: L=170 pb-1
p-e+n
c2/d.o.f = 1.5
N(p-e+n) = 3854  92
p+e-n
c2/d.o.f = 1.1
N(p-e+n) = 3863  88
Data
 MC
Emiss – pmiss
MeV
MeV
Residual background due to KS  pp, with p  m before entering the tracking volume
Fit data distribution to a linear combination of signal and background MC histograms
Background MC histogram smeared with a gaussian, s = 2MeV

8. Efficiency estimates = To get BR:
1) normalize signal counts to KS  p+p- counts in the same data set
2) correct for selection efficiencies =
N(pen)
N(pp)
BR(KSpen)
BR(KSp+p-)
NSL
eL(crash clust)
epen(2 trks IP  EmC)
epp(2 trks IP  EmC)
epen(TCA T0 Trig)
epp(T0 Trig)
e(TOF)
Rtag
Rcosm
Two methods to extract most of signal efficiencies:
Selection relies on properties of p EmC clusters, better to estimate efficiencies from data:
1) extract single-particle probabilities from control samples;
parametrize as a function of the relevant kinematic variables;
weight MC by the ratio of data and MC efficiencies
2) directly measure efficiency in a sample of KL  pen prompt decays, selected in evts with KSp+p-
Signal efficiency 20% given the tag

9. Preliminary results from analysis* of year 2001 data
BR(p-e+n) = (3.46  0.09  0.06)10-4
Branching fractions by charge:
BR(p+e-n) = (3.33  0.08  0.05)10-4
Charge-independent analysis:
BR(pen) = (6.81  0.12  0.10)  10-4 6 7
810-4
CMD-2 ’99
KL PDG average
KLOE ’02
KLOE ’03 prelim. *
Test of the DS=DQ rule:
Re x+ = (3.3  5.2  3.5)10-3
CPLEAR ‘98
KLOE ’03 prelim.

10. Preliminary results from analysis* of year 2001 data
Charge asymmetry:
AS = (19  17  6)  10-3
N(p-e+n)/e+ - N(p+e-n)/e- AS =
N(p-e+n) /e+ + N(p+e-n)/e-
KLOE KS
K+e3
K0e3
K+m3
K0m3
|Vus| f+ (0)
K0p-
Extraction of |Vus|:
E865 *
Preliminary KS  pen (analysis of 170 pb-1) consistent with previous measurements

11. Uncertainty in efficiency determinations
Systematic error from:
1) statistics of data and MC control samples
2) comparison between results from the two methods
Analysis of data taken in year 2001, L170 pb-1
+??% due to radiative
correction

12. Uncertainty in knowledge of signal and background shapes
Not reliability of MC in reproducing background Emiss - Pmiss distribution
MC bkg normalized to data in the range:
Emiss- Pmiss(20-40) MeV
Evts/MeV
p-e+n
p+e-n
Data Y2001
– MC bkg
Data Y2001
– MC bkg
Emiss - pmiss (MeV)
Dependence of the number of estimated counts on the higher limit of the fit range is the dominant source of systematic uncertainty
Also a sizeable charge dependence of the background distribution...

13. Uncertainty in knowledge of shapes: TOF refinement
Tried to correct MC for ratio of efficiencies data/MC, tracking, TCA, T0, Trigger, but it does not help much
Different behavior of p+ and p- in EmC comparing data and MC:
different paths inside the calorimeter (dlong)
different dependence of the time delay (Tcl - Texp) at fixed path
Ks decay vertex
Cluster centroid
dlong
EmC DC
Paritcle track
Data - p+ on barrel, P=200 MeV
Tcl-Texp (ns)
Linear parametrization:
Tcl-Texp = a + b dlong
Fit separately in data and MC distinguishing:
particle type: p+, p- , m+ , m- , e+ , e-
dlong (cm)
impact position: barrel, endcap
momentum: 10 MeV slices

14. Uncertainty in knowledge of shapes: TOF parametrization
In the end, get a parametrization with O(100ps) accuracy, merely using average values of the fitted parameters
Data p+
MC p+
Tcl-Texp (ns)
dlong (cm)
dlong (cm)

15. Uncertainty in knowledge of shapes: inclusion of radiation
Radiative modes: simulation at O(a), IR finite, without any cutoff in energy
BR(KS  ppg; Eg > 50 MeV)
BR(KL  peng; Eg > 30 MeV,qeg > 20)
 0.26%
 0.9%
BR(KS  pp(g))
BR(KL  pen(g))
KS  ppg
KL  peng
~0.26%
~3%

16. New estimate of the number of signal events – p-e+n
Inclusion of events with one g in the final state and refinement of TOF estimates better significantly data/MC agreement for both signal and background

17. New estimate of the number of signal events – p+e-n
Inclusion of events with one g in the final state and refinement of TOF estimates better significantly data/MC agreement for both signal and background

18. New estimate of the number of signal events – pen
Inclusion of events with one g in the final state and refinement of TOF estimates better significantly data/MC agreement for both signal and background

19. New estimate of the number of signal events
Improvement in fit stability as upper limit of fit range varies:

20. New estimate of the number of signal events
The distance DPCA between tracks at PCA to IP discriminates background events with a p decaying to m before entering the tracking volume
The fit correlation can be lowered cutting on DPCA, thus reducing the error on the signal counts

21. what has been understood...
Conclusions – job done
what has been understood...
Necessary to include correct treatment of radiation:
1) At this level of statistical accuracy, radiation of photons is able to modify the signal shape
2) Radiation affects tracks acceptance for the signal at the 1% level (last-minute estimate), and for the normalizing sample at the few per-mil level (estimate included in published result for G(KSpp(g))/G(KS  p0p0))
Necessary to calculate TOF including the contribution of time delay inside the EmC:
1) Main dependence of background spectra on details of pions simulation in EmC (dlong) is removed, better agreement of data and MC bkg spectra
2) Selection efficiency for background almost independent on charge
...and done...
A selection in which TOF cuts have been loosened has been run on the entire data set, both for data and MC
Result: total relative error on signal counts now at 1%, fit robust
The 5 cut values (including DPCA) in the analysis have been varied independently in order to choose the optimal set

22. Conclusions – road map ...and what still remains
Having chosen the optimal cut values:
1) Run over the control samples to estimate again the efficiencies both at single-particle level (efficiency estimate method 1)
and at the whole-event level (efficiency estimate method 2)
2) Use the output to weight MC (efficiency estimate method 1)
3) Evaluate track acceptance both for signal and normalizing sample (efficiency estimate method 1)
Check result stability along the data set, etc
Explicitly try to identify events with a tagged photon in the final state

23. Spare slides

24. Vus from Kl3 decays |Vus|f+(0) K+e3 K0e3 K+m3 K0m3
KLOE KS
KLOE KL
K+e3
K0e3
K+m3
K0m3
|Vus|f+(0)
Measurements for the extraction of Vus
Canale
BR(%)
103 l+
103 l0
K+e3
4.870.06
27.81.9
K0e3
38.790.27
29.11.8
K+m3
3.270.06
3.31.0
49
K0m3
27.180.25
3.30.5
276
tL = (5.17  0.04) · 10-8 s
tS = (  ) · s
t = (  ) · 10-8 s
Preliminary KLOE results seem to confirm previous existing measurements of K0e3, K0m3
K+e3 will soon arrive…
At KLOE:
All BR’s will be measured at O(0.1%)
Significatively improve on l+, l0, tL
|Vus| =  exp  th
For Ke3 channel
exp th
f+ (0)=  0.008th
K0p-
1.2%  0.2%  0.3% K+e3
0.7%  0.8%  0.3% K0e3