Vus saga at KLOE

1
Vus measurement at KLOE
B. Sciascia, INFN/Frascati for the KLOE
collaboration HEP2005 21-27 July 2005 - Lisbon
2
Unitarity test of CKM matrix Vus

• Most precise test of unitarity possible at
  present comes from 1st row

Vud2 Vus2 Vub2 Vud2 Vus2 ? 1
D
Can test if D 0 at few 10-3 from super-allowed
0? 0 Fermi transitions, n b-decays 2VuddVud
0.0010 from semileptonic kaon decays (PDG 2002
fit)
2VusdVus 0.0011

• Extract Vus from Kl3 decays. EM effects must
  be included

G(K ? pln(g)) ?
I(lt) (1 DI(lt,a))
(1 dEM) dSU(2)
Vus fK0p-(0) 2
dVus
dG
dI(lt)
dfK0p-(0)
Relative uncertainty
0.5 ? 0.5 ?
G
Vus
I(lt)
fK0p-(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 BRs at a f-factory
• Charged kaon results
• Semileptonic decays.
• Lifetime.
• Km2 branching ratio.
• Neutral kaon results
• KL semileptonic decays.
• KL lifetime.
• KL form factors
• KS semileptonic decays
• Vus at KLOE

see M. Moulson talk Joint Session CP Violation
/ Rare Decays, Saturday 23, 11, Room 1
4
The DAFNE ee? collider

• Collisions at c.m. energy around the f mass
• ?s 1019.4 MeV
• Angle between the beams at crossing
• acrs? 12.5 mrad
• Residual laboratory momentum of f
• pf 13 MeV/c
• Cross section for f production _at_ peak
• sf 3.1 mb

• Results presented in this talk from 2001/2 data
  ?L 450 pb-1.
• New run in progress, 2004/5
• Lpeak 1.261032 cm-2s-1.
• Since 2001 1.7 fb-1
• Goal collect 2.5fb-1 grand total, Dec. 2005

Total
KLOE plots 27 june 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 gt 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 ? pp-p0)
6
K physics at KLOE - tagging
KSKL (KK-) produced from f are in a pure JPC
1-- state
f decay mode BR
KK- 49.1
KSKL 34.1
Observation of KS,L signals presence of KL,S
K,? signals K ?, Allows precision measurement
of absolute BRs Allows interference measurements
of KSKL system
lS 6 mm KS decays near IP in vacuum lL 3.4
m Appreciable acceptance for KL decays in the
DC ( 0.5lL) l? 0.9 m Appreciable acceptance
for K? decays in the DC ( 0.6l?)
Can efficiently tag kaons by identifying the
other charge kaon
7
Measuring absolute branching ratios

• KL crash
• 0.22 (TOF)

KS ? pp-
KS ? p-en
KL ? 2p0

• Tagging of KS, KL, and K? beams.
• The absolute branching ratio measurement
• BR (Nsig/Ntag)(1/esig),
• 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
  tag bias
• BR (Nsig/Ntag) (1/esig) aTB.
• Tag bias carefully measured using MC, and data
  control samples.

8
Charged kaon semileptonic decays
Measure the absolute Ke3 and Km3 branching ratios
via a Tag technique.
Analysis scheme

• Tag using kaon 2 body decays
• 4 independent samples Km2, Kp2, K-m2, and K-p2
• Keep the systematic effects due to the tag
  selection under control.
• On signal side, kinematic rejection of the Km2
  and Kp2 dominant backgrounds by cutting on pp.
• Obtain number of signal events from a constrained
  likelihood fit of data distributions.
• Measure selection efficiency on MC and correct
  for Data/MC differences.
• Perform the BR measurement on each tag sample
  separately normalizing to tag counts in the same
  data set.

N(Kl3) 1 1 ? (eTAG(i)
BR(i))
aCF
BR(Kl3)
NTAG (1-fNI) eFV eSELE eTAG(Kl3)

9
K?l3 - Tag selection

• Track from IP, momentum cut
• 70 MeV? pK ? 130 MeV
• Decay vertex in fiducial volume
• 40cm ? rVTX ? 150 cm
• daughter track extrapol. to EMC
• 2-body decays identified in kaon
• rest frame 3s cut around p? peak
• p?(mm) 236 MeV
• p?(mp) 205 MeV
• For Kp2 tags, require also p0 identification.
• To reduce the dependency of the tag selection on
  signal kaon decay mode, requires the tag to
  satisfy the trigger.
• 2001-2002 data set

Tag Km2 Kp2 K-m2 K-p2
NTAG 21 699 562 8 466 737 22 655 426 8 233 472
10
K?l3 - Signal selection

• 1-prong kaon decay vertex in the fiducial volume
  rVTX in (40,150) cm
• daughter track extrapol. to EMC
• Reject two-body decays
• p?(mp) ? 195 MeV
• p0 search 2 neutral clusters in EmC, with ToF
  matching the K decay vertex (d(dt)lt3st)
• Spectrum of charged daughter mass, m2lept, from
  TOF measurement

Ev/(14MeV)2
MC
tdecayK tlept -Llept /(bleptc) ?tg-Lg/c?

• Additional kinematical cuts to reject
  non-semileptonic decays.
• The residual background is about 1.5 of the
  selected K?l3 sample, and has the mp2 signature.

11
K?l3 Event counting

• Fit m2lept spectrum with a linear combination of
  Ke3 and Km3 shapes, and background contribution.
• Correct MC shapes for Data/MC differences on the
  calorimeter timing.
• The residual distribution show the same trend
  for all the tag samples. Possible residual
  different Data-MC resolution.
• c2 and fit correlation matrix for the Kp2 tag
  sample

Ev/(14MeV)2
cM2/DoF P(c2gtcM2) Ke3Km3 Ke3Bkg Km3Bkg
250/220 8 - 4.6 - 1.9 - 27

• Selected signal events in 2001/2002 data set

Tag Km2 Kp2 K-m2 K-p2
NKe3 62 781(321) 24 914(208) 66 657(334) 24 225(204)
NKm3 37 461(264) 14 827(170) 39 988(277) 14 608(168)
12
K?l3 - Results

• The error accounts for the data and Monte Carlo
  statistics used in the fit, the MC statistics for
  the efficiency estimation, the Data/MC efficiency
  corrections, and the systematics on the tag
  selection.
• The systematics due to the signal selection
  efficiency is under evaluation.
• c2/nDof for the 4 measurements
• Ke3 3.20/3, P(c2gt cM2) ? 36
• Km3 5.32/3, P(c2gt cM2) ? 15
• Averages carefully calculated taking
  correlations into account

BR(Ke3) 5.047 ? 0.046 ? Sys Sig
BR(Km3) 3.310 ? 0.040 ? Sys Sig
KLOE preliminary

• The error is dominated by the error on Data/MC
  efficiency correction.
• Fractional accuracy of 0.9 for Ke3, 1.2 for
  Km3.

13
Charged kaon lifetime - 1

• Vus experimental input.
• 0.2 fractional accuracy 0.1 for Vus.
• Affects the BR measurement via the geometrical
  acceptance.
• t? PDG entries discrepancies between in-flight
  and at-rest measurements discrepancies between
  different stoppers in at-rest measurements.
• New high statistics t? measurement almost
  complete at KLOE, now under the review of the
  collaboration.
• Two different methods to measure t?.
• Measuring K decay length
• Measuring K decay time
• Cross check on the systematic error.

14
Charged kaon lifetime - 2

• Common to both methods
• Tag events with Km2 decay
• Identify a kaon decay vertex in DC fiducial
  volume

• 1st method
• 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.
• 0.2 fractional error.

• 2nd method
• Use only Kp2 decays
• Use tag information to estimate the T0 i.e. the
  f?KK? time.
• Identify the clusters belonging to p0.
• Measure the kaon decay time
• tK (tg Rg/c T0)gK.
• gK average over the kaon path (0.5 fractional
  error on tK)

15
Vus from BR(K???(?))
Particle momentum in K rest frame
??

• Tag from K-??-? to reduce the tag bias, tag
  selection requires EMC trigger.
• 2002 data set 1/3 used for signal selection,
  2/3 used as efficiency sample
• Count events in (225,400) MeV pp window after
  the subtraction of p0 identified background.
• Selection efficiency measured on data.
• Radiated g acceptance measured on MC.

Nev/MeV
?e? ???
??
MC
P?(MeV)
BR(K ? mn(g)) 0.6366 ? 0.0009stat. ?
0.0015syst.

• Following Marciano hep-ph/0406324
• ?(K???(?))/?(????(?)) ? Vus2/Vud2fK2/f?2
• From lattice calculations fK /f? 1.2100.014
  (MILC Coll. hep-lat/0407028)
• Vud0.97400.0005 (superallowed ?-decays)

Vus 0.22230.0025 KLOE preliminary
16
Dominant KL branching ratios
Absolute BR measurements to 0.5-1 using KL beam
tagged by KS pp-

• 328 pb-1 01-02 data
• 13?106 tagged KLs for measurement (75)
• 25 used to evaluate efficiencies
• BRs to pen, pmn, and pp-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 lt 1

Data (7 of the sample)
KL ? pen
KL ? pmn
KL ? pp-p0
KL ? pp-
Lesser of pmiss-Emiss in pm or mp hyp. (MeV)
17
Dominant KL BRs and KL lifetime
BR(KL? ?e?(?) ) 0.4049 ? 0.0010stat ?
0.0031syst 8?105 events BR(KL? ???(?) )
0.2726 ? 0.0008stat ? 0.0022syst 5?105
events BR(KL? 3??) 0.2018 ? 0.0004stat ?
0.0026syst 7?105 events BR(KL? ??????(?) )
0.1276 ? 0.0006stat ? 0.0016syst 2?105 events
eFV
r(cm)
Errors on absolute BRs dominated by error on tL,
via the geometrical efficiency (eFV)
BR(pen pmn pp-p0 3p0)KLOE BR(pp-
p0p0)PDG04 1.0104 ? 0.0076
Using the constraint ?BR(KL) 1
tL 50.72 ? 0.17 ? 0.33 ns
BR(KL? ?e?(?) ) 0.4007 ? 0.0006 ?
0.0014(tag-trk) BR(KL? ???(?) ) 0.2698 ?
0.0006 ? 0.0014(tag-trk) BR(KL? 3??) 0.1997 ?
0.0005 ? 0.0019(tag- ?-counting) BR(KL? ??????(?)
) 0.1263 ? 0.0005 ? 0.0011(tag-trk)
18
Direct measurement of KL lifetime
102
Events/0.3 ns

• Measure using KL ? p0p0p0
• Require ? 3 gs
• e(LK) 99, uniform in L
• sL(gg) 2.5 cm
• Background 1.3
• Use KL ?pp-p0 to determine
• ? EmC time scale
• ? Photon vertex efficiency

PK 110 MeV Excellent lever arm for lifetime
measurement
6 - 24.8 ns 40-165 cm 0.37 lL
KLOE 400 pb-1 10M KL ? p0p0p0 evts tL 50.92 ?
0.17 ? 0.25 ns
L/bgc (ns)
Average with result from KL BRs tL 50.84 ?
0.23 ns
Vosburg, 72 tL 51.54 0.44 ns
19
Vus at KLOE

• Using
• f(0) 0.961(8) from Leutwyler and Roos
• KL lifetime from KLOE tL 50.84(23) ns
• All BRs from KLOE

KLe3 KLm3 KSe3 K?e3 K?m3
BR 0.4007 0.2698 0.00709 0.0505 0.0331
dBR 0.0018 0.0012 0.00009 0.0004 0.0005
Fitting the 5 Vusf(0) KLOE determinations
?2/dof1.7/4 Using also KTeV inputs, Vusf(0)
becomes 0.2172(4)
20
Vus and Unitarity
f(0) 0.961(8) from Leutwyler and Roos KL
lifetime from KLOE tL 50.84(23) ns plot
F.Mescia courtesy
21
Conclusions

• All experimental inputs to the Vusf(0) can be
  measured at KLOE
• KL physics
• Fractional accuracy of ?0.4 on the BR of
  semileptonic decays.
• Two independent measurements of tL 0.5
  accuracy
• Preliminary resulst on KLe3 form factors see
  M.Moulson talk
• K? physics
• Preliminary result on semileptonic BR.
  Fractional accuracy of ?1
• K lifetime analysis tK at the 0.2, under the
  review of the collaboration.
• Final BR(Km2) get Vus at 1 level, dominated by
  theoretical uncertainy.
• Perspectives with 2.5 fb-1 of collected data
• Fractional accuracy of lt 1 on the BR for KS ?
  pen and for K?l3
• Form factors of KL and K? semileptonic decays.
• First direct measurement of BR(KS ? pmn),
  accuracy lt 2

22
Spare slides
23
Tag selection - 2

• Calorimeter trigger (2 sectors over threshold
  ?50 MeV) satisfied by tag

• Tag Km2 ask for associated m-cluster on
  barrel with energy gt 90 MeV. m-cluster fires at
  least one sector.
• m-cluster fires two sectors (e?30)
• ask for additional fired trigger sectors to
  satisfy calorimeter trigger (e?45 for K, e?40
  for K-)

• Tag K?p2
• a) look for a p0 from vertex using the D(dt)
  technique and f? constraint.
• b) p0 clusters satisfy the Emc trigger (e?90)

• For each kaon charge, 21 different tag samples
  Km2mTrg, Kp2p0Trig, and Km2mNoTrg.
• 2 tag 2 charge 4 samples for the
  measurements
• 1 tag 2 charge 2 control samples

24
Background rejection-1
K??pp0, p??mn
K??p0e?n
K??p0l?n
K??pp0p0
K??p0m?n
K??pp0p0
P(MeV)
Emiss-Pmiss (MeV)

• K??p?p0 events are rejected evaluating the
  missing momentum at the decay vertex, and cutting
  on momentum of the secondary track in the Pmiss
  rest frame (Pgt90 MeV)

• K??p?p0p0 are rejected cutting on Emiss-Pmiss
  spectrum (lt90MeV) the p0 momentum is obtained by
  mean of a kinematic fit

25
Background rejection-2
K??p0e?n

• Use kaon ToF and Tag to estimate tK
• b L/ (c (tCLU - tK)).
• For incorrect TCA bgt1 may happen.
• Define Q p2 (c (tCLU - tK)/L)2.
• Events with an incorrect TCA are rejected
  cutting the unphysical velocities Qlt(33 MeV)2

K??pp0p0
26
Fit of m2 distribution Km2 tag

• The residuals for all the Tag samples show the
  same trend.
• Possible residual different Data-MC resolution.

Tag cM2/DoF Ke3Km3 Ke3Bkg Km3Bkg
Km2 256/222 -4.3 -1.6 -28
27
Fit of m2 distribution Kp2 tag
Tag cM2/DoF Ke3Km3 Ke3Bkg Km3Bkg
Kp2 250/220 -4.6 -1.9 -27
28
Fit of m2 distribution K-m2 tag
Tag cM2/DoF Ke3Km3 Ke3Bkg Km3Bkg
K-m2 332/222 -4.3 -2.1 -28
29
Fit of m2 distribution K-p2 tag
Tag cM2/DoF Ke3Km3 Ke3Bkg Km3Bkg
K-p2 236/219 -4.2 -1.7 -28
30
Absolute BR(Ke3(g)) measurement
Tag BR(Ke3) ? dBR
Tag Km2 4.991 ? 0.075
Tag Kp2 5.065 ? 0.094
Tag K-m2 5.066 ? 0.071
Tag K-p2 5.125 ? 0.091

• Uncorrelated errors between the 4 tag samples
  Nsig, tag bias, FilFo, CosmicVeto/T3, MC stat.
  used for efficiency evaluation, photon
  efficiency.
• Partially correlated error kink and TCA
  efficiency corrections of MC efficiency.
• c2/nDof 3.20/3 for the 4 measurements with
  uncorrelated errors, P(c2gt cM2) ? 36

31
Absolute BR(Km3(g)) measurements
Tag BR(Km3) ? dBR
Tag Km2 3.264 ? 0.067
Tag Kp2 3.272 ? 0.079
Tag K-m2 3.336 ? 0.064
Tag K-p2 3.398 ? 0.079

• c2/nDof 5.32/3 for the 4 measurements with
  uncorrelated errors, P(c2gt cM2) ? 15
• The number of signal events is evaluated in each
  sample separately, using the SAME FIT PROCEDURE.
  Systematic errors coming from the fit are common
  to all samples.
• Also the systematic coming from the selection
  efficiency is COMMON TO ALL SAMPLES.

32
Rm/e G(Km3)/G(Ke3)
Tag R ? dR
Km2 0.654 ? 0.012
Kp2 0.646 ? 0.014
K-m2 0.658 ? 0.011
K-p2 0.663 ? 0.014

• Rm/e (Nm3/Ne3) (ee3/em3) aTB
• aTB is the tag bias correction for the ratio
• The correlation between Ke3 and Km3 (about 4)
  coming from the fit has been taken into account
  in calculating dRm/e
• c2 1.55/3 for the 4 measurements with
  uncorrelated errors, P(c2gt cM2) 67

33
Details on BR errors
Source Sys Tag() Fit() MC stat() r() Sys Sig
K?e3 0.009 0.022 0.016 0.056 tbe
Ke3 0.004 0.022 0.015 0.054 tbe
Ke3 0.004 0.015 0.011 0.039 tbe

• Averages carefully calculated taking
  correlations into account.
• 5 contributions to the error
• the systematic due to the signal selection
  efficiency is under evaluation can move the
  central values.

Source Sys Tag() Fit() MC stat() r() Sys Sig
K?m3 0.006 0.020 0.013 0.065 tbe
Km3 0.003 0.020 0.013 0.061 tbe
Km3 0.003 0.014 0.009 0.045 tbe
BR(e3) () BR(m3) () Rme
K? 5.010(66) 3.266(57) 0.6517(11)
K 5.081(64) 3.352(55) 0.6597(11)
BR(Ke3) 5.047 ? 0.046 ? Sys Sig
BR(Km3) 3.310 ? 0.040 ? Sys Sig
Rm/e 0.656 ? 0.008 ? Sys Sig
34
Details on the Kmn(g) result
BR(K ? mn(g)) 0.6366 ? 0.0009stat. ?
0.0015syst.
35
Vus from BR(Kmn(g))
Following the method from Marciano hep-ph/0406324

fK /f? 1.2100.014 (MILC Coll. hep-lat/0407028)
Vud0.97400.0005 (superallowed ?-decays)
Vus0.22230.0025 KLOE preliminary
new unpublished Vud value will shrink the error
band
36
KL BRs comparison
KL ??e?
KL ????
KLOE NA48 KTeV PDG04
KLOE KTeV PDG04
KLOE NA48 KTeV PDG04
KL ?pp-?0
KLOE KTeV PDG04
KL ? 3?0
37
Ke3g and Km3g acceptance
K-m3g
K-e3g
Eg gt30 MeV, 2.110-2
Eg gt 30 MeV, 0.710-3

• The signal selection efficiency is sensitive to
  the presence of a photon in the final state. The
  simulation includes an IR-finite treatment (no
  energy cutoff) of radiation for all K decay.
• By neglecting the radiative BR(Ke3) changes of
  about 2.
• The Km2 sample is shown all samples show the
  same trend.