1. B. Sciascia, INFN/Frascati for the KLOE collaboration
Vus measurement
at KLOE
B. Sciascia, INFN/Frascati
for the KLOE collaboration
DIF2006
28 February LNF

2. Unitarity test of CKM matrix – Vus
Most precise test of unitarity possible at present comes from 1st row:
|Vud|2 + |Vus|2 + |Vub|2 ~ |Vud|2 + |Vus|2  1 – D
Can test if D = 0 at level:
from super-allowed nuclear b-decays: 2|Vud|dVud =
from semileptonic kaon decays: |Vus|dVus =
Extract |Vus| from Kl3 decays. EM effects must be included:
G(K  pℓn(g)) 
|Vus f+K0p-(0) |2 I(lt) SEW(1 + dEM + dSU(2) )
d|Vus| dG
dI(lt)
df+K0p-(0)
Relative uncertainty:
=  
|Vus| G
I(lt)
f+K0p-(0)
Extract |Vus| from (K())/(()) ratio. Dominated by the theoretical uncertainity on the fK/f evaluation.
KLOE can measure all experimental inputs:
branching ratios, lifetimes, and form factors.

3. Outline - DAFNE and KLOE
- Measuring absolute Branching Ratios at a f-factory
- Vus related results on:
K short: BR(KSe3), KSe3 form factor, BR(KSm3)
K long: BR(KLℓ3), tL direct measurement and from BR=1, KLℓ3 form factors
Charged kaons: t, BR(Kℓ3), BR(K+m2)
- Vus from KLOE results
- Unitarity test

4. The DAFNE e+e collider
Collisions at c.m. energy around the f mass:
s ~ MeV
Angle between the beams at crossing:
acrs 12.5 mrad
Residual laboratory momentum of f:
pf ~ 13 MeV/c
Cross section for f peak:
sf ~ 3.1 mb
Grand total (2001/5):
L = 2.5 fb-1.
L peak=1.3×1032 cm-2s-1.
Results presented in this talk from 2001/2 data: L = 450 pb-1.
KLOE plots: end 2005

5. The KLOE detector Large cylindrical drift chamber
Lead/scintillating-fiber calorimeter.
Superconducting coil: 0.52 T field.
He/IsoC4H10 90/10 drift chamber
4m-, 3.75m-length, all-stereo
sp/p = 0.4 % (tracks with q > 45°)
sxhit = 150 mm (xy), 2 mm (z)
sxvertex ~1 mm
Lead-Scintillating fiber calorimeter
sE/E = 5.7% /E(GeV)
st = 54 ps /E(GeV)  50 ps
(relative time between clusters) PID capabilities
sL(gg) ~ 2 cm (p0 from KL  p+p-p0)

6. K physics at KLOE - tagging
KSKL (K+K-) produced from f are in a pure JPC = 1-- state:
f decay mode BR
K+K-
49.1%
KSKL
34.1% f
KS, K+
KL, K-
Observation of KS,L signals presence of KL,S ; K+, signals K ,+
Allow precise absolute branching ratio measurement, by means of a tag technique:
BR = (Nsig/Ntag)(1/esig),
This relies on the capability of selecting a tag kaon independently on the decay mode of the other.
In fact some dependency on signal mode exists:
BR = (Nsig/Ntag) (1/esig) (eTageTag(sig)).
Tag bias: carefully measured using MC and data control samples. K- m- K+ p+ g

7. Tagged KL and KS “beams”
KL tagged by KS  p+p- vertex at IP
Efficiency ~ 70% (mainly geometrical)
KL angular resolution: ~ 1°
KL momentum resolution: ~ 1 MeV
KS  p+p-
KL  2p0
KS tagged by KL interaction in EmC
Efficiency ~ 30% (largely geometrical)
KS angular resolution: ~ 1°
KS momentum resolution: ~ 1 MeV
KL “crash”
= 0.22 (TOF)
KS  p-e+n

8. Measurement of BR(KS  pen)
- Kinematic cuts to reject background from KS  pp
- e/p ID from TOF: identifies charge of final state
Determine number of signal counts by fitting Emiss(pe) - pmiss data distribution to a linear combination of MC spectra for signal and bkg (MC includes peng and ppg processes).
Event selection:
Normalize using KS  pp events in same data set.
Final result:
Accepted by PLB
BR(p-e+n) = (3.528  0.062)  10-4
BR(p+e-n) = (3.517  0.058)  10-4
BR(pen) = (7.046  0.091)  10-4
BR(pen) [KLOE ’02, 17 pb-1]:
(6.91  0.34  0.15)  10-4
l+ = ( 33.9  4.1 )  10-3

9. KS  pmn: first observation
• Measurement never done before
• More difficult than KSe3:
1) Lower BR: expect 410-4
2) Background events from
KS  pp, p  mn: same
PIDs of the signal
• Event counting from the fit to Emiss(pm) -Pmiss distribution:
 3% stat error
• Efficiency estimate from KLm3 early decays and from MC + data control samples.
 Data
KS  m-p+n + ppg + pp
-40
-20 20 40
Emiss(pm)-Pmiss (MeV)

10. Dominant KL branching ratios
Absolute BR measurements to 0.5-1%
from ’01-’02 data set (328 pb-1)
KL tagged by KS  p+p- :
13106 for the measurement
4106 used to evaluate efficiencies
BR’s to pen, pmn, and p+p-p0:
KL vertex reconstructed in DC
PID using decay kinematics
Fit with MC spectra including radiative processes and optimized EmC response to m/p/KL
BR to p0p0p0:
Photon vertex reconstructed by TOF using EmC (3 clusters)
Erec = 99%, background < 1%
(7% of the sample)
Lesser of pmiss-Emiss in pm or mp hyp.

11. Dominant KL BR’s and KL lifetime
Errors on absolute BR’s dominated by error on tL, via the geometrical efficiency (eFV)
eFV
BR(pen + pmn + p+p-p0 +3p0)KLOE
+ BR(p+p- + p0p0)PDG’04 = 
l(KL)
Using the constraint BR(KL) = 1 we get:
BR(KL e() ) =  stat  syst ~ 8105 events
BR(KL () ) =  stat  syst ~ 5105 events
BR(KL 3) =  stat  syst ~ 7105 events
BR(KL () ) =  stat  syst ~ 2105 events
BR, misura diretta: stat=stat + syst-stat dell’articolo; syst=syst+corr-syst dell’articolo
PLB608(2005) 199
Published
tL=  0.17  ns

12. Direct measurement of KL lifetime
× 102
Events/0.3 ns
Measure using KL  p0p0p0
Require  3 g’s
e(LK) ~ 99%, uniform in L
sL(gg) ~ 2.5 cm
Background ~ 1.3%
Use KL π+π-π0 to determine:
- EmC time scale
- Photon vertex efficiency
PK = 110 MeV
Excellent lever arm for lifetime measurement ns cm
0.37 lL
KLOE 400 pb-1:
107 KL  p0p0p0 evts
tL =  0.17  0.25 ns
Published
PLB626(2005) 15
L/bgc (ns)
Average with result from KL BR’s:
tL =  0.23 ns
Vosburg, ’72:
tL = ± 0.44 ns

13. KLe3 form factor slopes l+
Data divided into 14 periods
Good stability of results
Good agreement for e+p-, p-e+ l+
period
Needed for evaluation of phase-space integrals (extraction of Vus)
Fit of momentum transfer spectrum with different hypothesis on form factor f+(t)/ f+(0):
Linear: 1 + l+t
Quadratic: 1 + l+ t/mp+ + 1/2 l+ (t/mp+)2
Pole model: MV2/(MV2-t),
Taylor exp. with l+=(mp/MV)2, l+=2 l+2
o.5/1.6
328 pb-1, 2  106 Ke3 decays
t measured from p and KL momenta: st/mp2 0.3
Kinematic cuts + TOF PID to reduce background ( ~ 0.7% final contamination )
Separate measurement for each charge state (e+p-, p+e-) to check systematics

14. KLe3 form factor slopes: result
Linear fit: l+ c2/dof
e+p  /181
p+e  /181
All  /363
l+ = (28.6  0.5  0.4)  10-3
Quadratic fit: l+103 l+ c2/dof
e+p   /180
p+e   /180
All   /362
l+ = (25.5  1.5  1.0)  10-3
l+ = ( 1.4  0.7  0.4)  10-3
Correlation: r(l+, l+) = -0.95
Pole model: mV = 870(7) MeV
(*) ISTRA+ mp/mp0 correction
25.5 +/- 1.8, fractional error 7%
1.4+/-0.8 fractional error 57%
Integrale spazio delle fasi: Pole model (world av.): (11); Quadratico (world av.): (13)
Pole model (KTev): (14); Quadratico (KTeV) = (32)
Pole model (KLOE): (16); Quadratico (KLOE) = (29)
Phase space integral, Pole model versus Quadratic parameterization:
KLOE: 0.5 per mil difference
KTeV: 6 per mil difference.
Accepted by PLB

15. Measurement of the K lifetime
Two different methods to measure t allow cross checks on the systematic error.
Common to both methods:
Tag events with Km2 decay
Identify a kaon decay vertex in the fiducial volume
Tag(Km2)
1st method: obtain t from the K decay length
Measure the kaon decay length taking into account the energy loss: tK = i Li/(bigic)
Tracking efficiency and resolution measured on data by means of neutral vertex identification.
Fit of the tK distribution.
KLOE preliminary: t=  0.044Stat  0.065Syst ns
2nd method: obtain t from the K decay time
Use only Kp2 decays
Use tag information to estimate the T0 i.e. the fK+K time.
Measure the kaon decay time: tK = (tg – Rg/c –T0)gK, using the p0 clusters
Lorentz factor gK: slowly changing along the kaon path

16. K semileptonic decays
Tag using kaon 2 body decays.
4 independent samples: K+m2, K+p2, K-m2, and K-p2; allow to keep the systematic effects due to the tag selection under control.
Obtain number of signal events from a constrained likelihood fit of a m2 data distributions from ToF measurements.
Non semileptonic events are rejected using kinematical cuts; the residual background is about 1.5% of the selected Kl3 sample and has the mp2 signature.
Measure selection efficiency on MC and correct for Data/MC differences.
Ev/(14MeV)2
K nucl.int.
Kpp0p0
Kpp0 MC

17. Measurement of BR(Kℓ3)
Perform the BR measurement on each tag sample separately normalizing to tag counts in the same data set.
Averages carefully calculated taking correlations into account:
Ev/(14MeV)2
KLOE preliminary:
BR(Ke3) =
(5.047  0.019Stat  0.039Syst-Stat  0.004SysTag)×10-2
BR(Km3) =
(3.310  0.016Stat  0.045Syst-Stat  0.003SysTag)×10-2
MeV2
Fractional accuracy of 0.9% for Ke3, 1.4% for Km3.
c2/DoF for the 4 independent-tag measurements:
Ke3: 3.20/3, P(c2> cM2)  36%
Km3: 5.32/3, P(c2> cM2)  15%
The error is dominated by the error on Data/MC efficiency correction and the systematics due to the signal selection efficiency is under evaluation.
Ke3, Km3; BR(Ke3) = / ; BR(Km3) = / (Ricalcolati il 22 febbraio 2006 a partire dagli errori scritti nella trasp, ripresi dalla memo p. 57)
MeV2

18. Measurement of BR(K++())
Tag from K--.
2002 data set: 1/3 used for signal selection, 2/3 used as efficiency sample
Subtraction of p0 identified background.
Count events in (225,400) MeV window of the momentum distribution in K rest frame (p hypothesis)
Selection efficiency measured on data.
Radiated g acceptance measured on MC.
BR(K+  m+n(g)) =  stat.  syst.
Published
PLB632(2006) 76
(K())/(())  |Vus|2/|Vud|2fK2/f2
From lattice calculations: fK /f =1.198(3)(+165) (MILC Coll. PoS (LAT 2005) 025,2005)

19. Vus from KLOE results (BR’s and tL)
Slopes:
l+ = (30)
l+ = (3)
KLe3
KLm3
KSe3
Ke3
Km3 BR
0.4007(15)
0.2698(15)
7.046(91)×10-4
(46)
(40) t
50.84(23) ns
89.58(6) ps
12.384(24) ns
(Pole model: KLOE, KTeV, and NA48 average)
l0 = (95)
(KTeV and, Istra+ average)
dal Perl di Matt con i numeri di Paolo Franzini
from Vud and unitarity Vusf0 = / ; from Kl3 Vusf0 = / ; Vus = /
Vusxf+(0) with pole model, Tau_L KLOE = (48) i.e (5) Using as pole masses: Mv=876.7(5.1 )MeV, Mp=1182(38)MeV
c2/dof = 1.9/4
From unitarity
f+(0)=0.961(8), Leutwyler and Roos Z.Phys. C25, 91, 1984
Vud= (27), Marciano and Sirlin Phys.Rev.Lett ,2006
Vus×f+(0) = (22)

20. Vus and Unitarity <Vus×f+(0)>WORLD AV. = 0.2164(4) Vus f+(0)
tL = 50.99(20) ns, average KLOE-PDG
Including all new measurements for semileptonic kaon decays (KTeV, NA48, E865, and KLOE)
plot: F.Mescia courtesy
Questa e` quella buona! Average KLOE+KTeV+NA48+E865 Vus(Mescia) =0.2164(4)
<Vus×f+(0)>WORLD AV. = (4)
From unitarity
f+(0)=0.961(8), Leutwyler and Roos Z.Phys. C25, 91, 1984
Vud= (27), Marciano and Sirlin Phys.Rev.Lett ,2006
Vus×f+(0) = (22)

21. The Vus- Vud plane Inputs: Vus = 0.2254  0.0020
Kl3 KLOE, using f+(0)=0.961(8)
Vud = 
Marciano and Sirlin
Phys.Rev.Lett ,2006
Vus/Vud = 
Km2 KLOE
(K())/(())  |Vus|2/|Vud|2fK2/f2
Fit results, P(c2) = 0.66:
Vus = 
Fit result assuming unitarity, P(c2) = 0.23:
Vus = 
unitarity
Vud from Fermi super-allowed beta decays, valore di Vud=.97377(27) verificato in Marciano hep-ph/ , pubbl. Phys.Rev.Lett. 96:032002
Vus from: Kl3 e tauL KLOE NEW(24feb2006) Vus = (195)
Kl3 e tauL AVE NEW(24feb2006) Vus = (194)
Fit1 a due parametri: P(chi2) = 66%
Fit2 a un parametro+unitarieta`: P(chi2) = 23%

22. Vus at KLOE - Conclusions
“All” kaon semileptonic branching ratios measured with a fractional accuracy accuracy ranging from 0.4% to 1.4%;
the measurements are completely inclusive: Kℓ3(g).
First direct measurement of BR(KS  pmn) coming soon with a statistical accuracy of 3%.
Two independent measurements of tL: 0.5% fractional accuracy.
KLe3 form factors: pole model.
Significant contribution to the determination of Vus f+(0) to 0.2%
0.3% fractional accuracy on BR(Km2(g)) measurement
Independent determination of Vus at 0.7% level, dominated by theoretical uncertainy.
Preliminary result on K lifetime.
Perspectives with 2.5 fb-1 of collected data:
Fractional accuracy of < 1% on the BR for KS  pen and for Kℓ3
More and better measurements of form-factor slopes (Ke3 and Km3).
Measurement of BR(KS  pmn), accuracy < 2%

23. the “young” physicists of KLOE
Thank you, Paolo!
Photos: S. Chi and P. Valente courtesy
the “young” physicists of KLOE

24. Spares slides

25. KLe3 form factor slopes: result
Linear fit: l+10-3 c2/dof
e+p  /181
p+e  /181
All  /363
l+ = (28.6  0.5  0.4)  10-3
Quadratic fit: l+ l+10-3 c2/dof
e+p   /180
p+e   /180
All   /362
l+ = (25.5  1.5  1.0)  10-3
l+ = ( 1.4  0.7  0.4)  10-3
Correlation: r(l+, l+) = -0.95
Pole model: mV = 870(7) MeV
Pole model versus Quadratic parameterization: 0.5 per mil difference in phase space integral, Ie.
25.5 +/- 1.8, fractional error 7%
1.4+/-0.8 fractional error 57%
Integrale spazio delle fasi: Pole model (world av.): (11); Quadratico (world av.): (13)
Pole model (KTev): (14); Quadratico (KTeV) = (32)
Pole model (KLOE): (16); Quadratico (KLOE) = (29)
(*) ISTRA+ mp/mp0 correction

26. KS  pen: Signal extraction
Fit distributions of 5 variables in data with various MC sources
Close kinematics: Emiss(pe) - pmiss = 0
MC includes peng and ppg processes
dPCA = PCA1 – PCA2 eliminates p  m kinks and badly reconstructed tracks
Data
MC fit
pen
pp, p  m
ppg
pbadp
ppbad
other
-50 50
100
200
300
400
500
600
700
Emiss(pe) - pmiss (MeV)
-100
-150
Evts/MeV
dPCA (cm) -4 4 8 -8
100
200
300
400
500
Evts/0.2cm
PCA2
PCA1
Tagging methods, accuracy on tagged beam momentum
Beta of the klong cluster instead of crash

27. Comparing form factor models
f+(0) = 0.961(8) from Leutwyler and Roos
tL = 50.99(20) ns, average KLOE-PDG
Form factors: average KLOE, KTeV, Istra+, NA48
- Quadratic parameterization
l+ = 
l+ = 
l0 = 
- Pole model
l+ = 
MV =  5.1 MeV
l0 = 
MP = 1182  38 MeV
Vus f+(0)
plot: F.Mescia courtesy
Vus = / ; aggiungere frase su coerenza delle misure con il modello polare
Quadratic paramet.
Pole model

28. Vus at KLOE – summer 2005
Using:
f+(0) = 0.961(8) from Leutwyler and Roos
KL lifetime from KLOE: tL = 50.84(23) ns
All BR’s from KLOE:
KLe3
KLm3
KSe3
Ke3
Km3 BR
0.4007
0.2698
0.0505
0.0331
dBR
0.0018
0.0012
0.0004
0.0005
Usare plot nuovo di Federico Mescia
Fitting the 5 |Vusf+(0)| KLOE determinations: 2/dof=1.7/4
Using also KTeV inputs, Vusf+(0) becomes (4)