Test of Lepton Flavor
Universality with Ke2
decay at KLOE

Barbara Sciascia, LNF INFN
for the KLOE collaboration2009 Kaon International Conference
Tsukuba, Japan − 10nd June 2009

Measurement of RK=Γ(Ke2)/Γ(Kµ2)
Introduction: RK in and beyond SM.
Measurement of RK=ΓΓ(Ke2(γγ))/Γ
Γ(Kµµ2(γγ)) at KLOE.
- Based on 2.2 fb−1 of data collected ate+e− collider DaΦne.
- BR(φφ→ K+K−) ∼ 0.49, yielding 3×109
K+K− pairs, ∼50,000 Ke2 decays in FV- Signal selection; analysis basic principle- Background rejection- Ke2 event counting; with systematics- Reconstruction efficiencies- Results on RK.
Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba2

NP potential of RK = Γ(K±e2)/Γ
Γ(K±µ2)• SM prediction with 0.04% precision, benefits of cancellation of hadronic
uncertainties (no fK): RK=2.477(1)×10−5 [Cirigliano Rosell arXiv:0707:4464].
• Helicity suppression can boost NP [Masiero-Paradisi-Petronzio PRD74(2006)011701].
uLsReRH+ντ42mm
LFVSM31 26KτRK ≈ RK 1 + 4 2 ∆ R tan β  m H meRLFVKK → eν∑Γ (K → eν ) + Γ (K → eν τ )=≈Γ (K → µν µ )
K→µν
∑
iiii

SMe

SM

LFV from loop generates
an effective eH+ντ couplingeH +ν τ →g2 mτ 31 2
∆ R tan β2 MW

LFV can give O(1%) deviation from SM (∆∆R31∼5×10-4, tanββ ∼40, mH ∼ 500 GeV )• Exp. accuracy on RK (before KLOE and NA62 results) at 5% level.
• New measurements of RK can be very interesting, if error at 1% level or better.
Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba

3Entering the precision realm for RK
Main actors (experiments) in the challenge to push down precision on RK:
NA48/2: preliminary result with 2003 data: RK=2.416(43)stat(24)syst10−5,
from ∼4000 Ke2 candidates (2% accuracy)
NA48/2: preliminary result with 2004 data: RK=2.455(45)stat(41)syst10−5,
from ∼4000 Ke2 candidates from special minimum bias run (3% accuracy)
KLOE: preliminary result with 2001-2005 data: RK=2.55(5)stat(5)syst10−5,from ∼8000 Ke2 candidates (3% accuracy), perspectives to reach 1% error
after analysis completion.
NA62 (ex NA48): collected ~150,000 Ke2 events in dedicated 2007 run,aims to breaking the 1% precision wall, possibly reaching <∼0.5%
Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba4

Ke2(γ): signal definition
SM prediction is defined to be inclusiveof IB (ignoring DE contributions).

IBDE

From theory (ChPT) expect DE ∼ IBfor Ke2, but experimental knowledge ispoor: δDE/DE∼∼15%IB+DEIB• Define as “signal” events with Eγ<10 MeV.
• Evaluating IB spectrum (O(αα)+resummation of leading logs)
obtain a 0.0625(5) correction for the IB tail.
• Under 10 MeV, the DE contribution is expected to be negligible.
Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba

5Charged kaon at KLOE
φ decay at rest provides pure kaon
beams of know momentumpK ∼ 100 MeV
λ ∼ 90 cm (56% of K± decay in DC).
Kaon momentum measured (event byevent) with 1 MeV resolution in DC.
Constraints from φ 2-body decay.
Particle ID with kinematics and ToF.
Tagging provides unbiased control
samples for efficiency measurement.

4m

Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba

6Analysis basic principles

1) Select kinks in DC (∼ fiducial volume)- K track from IP- secondary with plep>180 MeV
for decays occurring in the FV;
the reconstruction efficiency is ∼51%.

2) No tag required on the opposite“hemisphere” (as we usually do!)→ gain ×4 of statistics

Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba

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Analysis basic principles
MCKµµ2Kππ23) Exploit tracking of K andsecondary: assuming mν=0 get M2lep:
M2lep = (EK −pmiss)2 − p2lep.
Ke2 (Eγ<10MeV)
Around M2lep=0 we get S/B ∼ 10-3,
mainly due to tails on the momentum
resolution of Kµµ2 events.

Ke2 (Eγ>10MeV)

M2lep (MeV2)
Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba

8Background rejection (track quality)
Background composition: Kµµ2 events with badpK, plep, or decay vertex position reconstruction• require good quality vertex
and secondary track (χχ2cut);• reduce Kµ2 tails cutting on theerror on M2lep expected fromtrack parameters;• quality cuts for K: thekinematic of φ →K+K− 2-bodydecay allows redundant pK
determinartion.

Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba

9Background rejection (track quality)• after cuts, we accept∼35% of decays in the FV

MC Kµ2• most of Ke2 events lost
have bad resolution• S/B ∼ 1/20, not enough!
• require the lepton track to
be extrapolable to thecalorimeter surface and tobe associated to an energy
release (cluster).

MC Ke2

before cuts
after cuts

M2lep (MeV2)
Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba

10Background rejection (PID)
1) Particle ID exploits EMC
granularity (energy deposits into
5 layers in depth):

200 MeV
electronthe energy distribution and theposition along the shower axis of
all cells associated to the cluster
allow for e/µµ PID (define 11descriptive variables).
2) Add E/p and ToF.
3) Combine all information in aneural network (NN).

200 MeVmuon
4.4 cmTest Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba

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Background rejection (PID)• Use a pure sample ofKLe3 to correct cell
response in MC.

data KLe3MC KLe3• KLe3 anf Kµµ2 for
NN training.

NNout
Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba

12Background rejection (PID)
Select a region with good S/B ratio in the M2lep – NNout plane
NNout10510.8

Data
Ke2

NNout

Data

104

0.6
0.4

Kµµ20.2103

0-10000

M2lep(MeV2)

102-0.2010000

M2lep(MeV2)

after selection: ε∼30% (∼15,000 Ke2)

S/B ∼ 5

Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba

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Ke2 event counting
Two-dimensional binned likelihood fit in the M2lep–NNout planein the region −4000<M2lep<6100 and 0.86<NNout<1.02
Ke2+ fit; M2lep proj for NNout>0.96
ev/700 MeV2NNout

χ2= 113/112

datafit
Kµµ2
Ke2 (Eγγ>10MeV)

M2lep (MeV2)M2lep (MeV2)

We count 7060 (102) Ke2+ 6750 (101) Ke2−− (σσSTAT=1%, 0.85% from Ke2)
Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba

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Ke2 event counting
Two-dimensional binned likelihood fit in the M2lep–NNout planein the region −4000<M2lep<6100 and 0.86<NNout<1.02
Ke2+ fit; M2lep proj for NNout<0.96
ev/700 MeV2NNout

χ2= 113/112

datafit
Kµµ2
Ke2 (Eγγ>10MeV)

M2lep (MeV2)
M2lep (MeV2)

We count 7060 (102) Ke2+ 6750 (101) Ke2−− (σσSTAT=1%, 0.85% from Ke2)
Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba

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Ke2 event counting: systematics
Repeat fit with different values of max(M2lep) and min(NNout):vary significantly (×20) bkg contamination + lever arm.
ev/700 MeV2NNout

χ2= 50/48
Ke2+ fitM2lep (MeV2)
M2lep (MeV2)

minimal bkg with:−4000 < M2lep < 4650 and 0.94 < NNout < 1.02

Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba

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Ke2 event counting: systematics
Repeat fit with different values of max(M2lep) and min(NNout):vary significantly (×20) bkg contamination + lever arm.
NNout

ev/700 MeV2

χ2= 168/192

Ke2+ fitM2lep (MeV2)
M2lep (MeV2)

maximum bkg with:−4000 < M2lep < 7500 and 0.78 < NNout < 1.02

Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba

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Ke2 event counting: systematics
min(NNout)

minbkg

RK pulls

We change by a factor of 20 theamount of bkg falling in the fit
region by moving- min(NNout)- max(M2lep).
Signal counts change by 15%.

From the pulls of the RK
measurements we evaluated a
0.3% systematic error.

maxbkgmax(M2lep) (MeV2)

Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba

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Ke2 fit: radiative corrections• Analysis inclusive of photons in the final state. In our fi region we expect:
Ke2 (Eγ>10MeV)
Ke2(Eγ<10MeV)∼10%• Repeat fit by varying Ke2 (Eγ>10 MeV)
by 15% (DE uncertainty) get 0.5% error.

We performed a dedicated study of theKe2γγ differential decay rate (see Moulsontalk):- Eγ spectrum measured for the first time
- confirm DE content of our MC, evaluatedwith ChPT O(p4), within ∼4% accuracy- obtain 0.2% systematic error on Ke2IB

MC spectra
PID>0.98

Kµµ2

Ke2 (Eγ<10MeV)

Ke2 (Eγ>10MeV)

M2lep (MeV2)

Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba

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Reconstruction efficiencies
The ratio of Ke2 to Kµµ2 efficiencies is evaluated with MCand corrected using data control samples1) kink reconstruction (tracking): K+e3 and K+µ2 data control
samples selected using the tagging and additional criteria based on EMC
information only (next slide)2) cluster efficiency (e, µ): KL control samples, selected withtagging and kinematic criteria based on DC information only3) trigger: exploit the OR combination of EMC and DC triggers(almost uncorrelated); downscaled samples are used to measureefficiencies for cosmic-ray and machine background vetoes
We obtain: ε(Ke2)/εε(Kµµ2) = 0.946±0.007

Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba

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Control samples for tracking efficiencies
Just an example: selection of K+e3 control sample to measure
tracking efficiency for electrons0) Tagging decay (Kµµ2 or Kππ2);1) Tagging decay (Kµµ2 or Kππ2): reconstructionof the opposite charge kaon flight path;
2) Using a ToF technique a π0→γγ decay vertex
is reconstructed along the K decay path;
3) Require an electron cluster: pe estimatedfrom a kinematic fit with constraints on E/p,ToF, cluster position, and Emiss− Pmiss.
Evaluate the K + electron kink reconstruction efficiency
Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba

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Control samples for tracking efficiencies

pe(fit)−pe(reco) (MeV)

pµ(fit)−pµ(reco) (MeV)• For electron tracks obtaina resolution σ∼19 MeV• With a similar method, getσ∼7 MeV for muon tracks

Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba

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Systematics and checks
Cross-check on efficiencies: use same algorithms to measure Rl3 = Γ(Ke3)/Γ(Kµµ3)
Rl3 = 1.507 ± 0.005 for K+
Rl3 = 1.510 ± 0.006 for K−

SM expectation (FlaviaNet)
Rl3 = 1.506 ± 0 .003

Summary of systematics:
K+ control samples
downscaled events
fit stability
measurement on data
KL control samples

TrackingTrigger
syst on Ke2 counts
Ke2γγ DE component
Clustering for e, µ

0.6%
0.4%
0.3%
0.2%
0.2%

Total Syst

0.8%
(0.6% from statistics of control samples)

Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba

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RK: KLOE result
RK = (2.493 ± 0.025 ± 0.019)×10−5
Total error:
1.3% = 1.0%stat + 0.8%syst
0.9% from 14k Ke2 dominated+ bkg subtraction by statistics• The result does not depend
upon the kaon charge:
K+: 2.496(37) vs K−: 2.490(38)(uncorrelated errors only)• Agrees with SM prediction

Clark, 1972

PDG 2008:
RK = (2.45±±0.11)×10−5
4.5% accuracy
New world average:
RK = (2.468±±0.025)×10−5
1% accuracy
RKSM = 2.477(1) ×10−5

Heard, 1975

PDG2008

Heintze, 1976
NA48/2 (2003)
NA48/2 (2004)
KLOESM(×105)
Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba24

RK : sensitivity to new physics
Sensitivity shown as 95% CL excluded regions in the tanββ−MH plane, fordifferent values of the LFV effective coupling, ∆13 = 10−3, 5 × 10 −4, 10−4

KLOE

Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba

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Conclusions• Using 2.2 fb−1 of data acquired atthe φ peak, KLOE measured:
RK = (2.493 ±0.025stat ±0.019syst)×10−5• This results confirms the SM
prediction within the 1.3% accuracy• The error is dominated by thecounting and the control samples
statistics.
• Can contribute to set constraints
on the parameter space of MSSM
with LFV.

Additionalinformation

Kµ2 : sensitivity to new physics
Scalar currents, e.g. due to Higgs exchange, affect K→ µν width
Vus (K µ 2 ) Vud (0 + → 0 + )Rl 23 =
×Vus (K l 3 )Vud (π µ 2 )m K2 +  m π2 +  tan 2 β= 1 − 2 1 − 2 m H +  m K +  1 − ε 0 tan β[Hou, Isidori-Paradisi]

Rl23 =1 in SM
we find

Rl23 = 1.008 ± 0.008
limited by lattice uncertainty on f+(0) and fK/fπ

From direct searches (LEP), MH+> 80 GeV, tanβ > 2
Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba

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Kµ2 event counting

M2lep (MeV2)

M2lep (MeV2)

Fit to M2lept distribution: 300 million Kµµ2 events per charge
Background under the peak <0.1%, from MC
Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba

29Tracking efficiency

pµ(fit)−pµ(MC) (MeV)

pµ(fit)−pµ(reco) (MeV)

Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba

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NN details
1) E/P;2) 1st momentum of the distribution of the longitudinal energy path deposition(cluster centroid depth) evaluated at cell level;3) the 3td momentum of the longitudinal energy path deposistion (skewness);4,5) asymmetry of energy lost in first two innermost (outermost) planes;
6) RMS of energy plane distribution;7) energy lost in the 1st plane;8) number of the plane with larges energy deposition;9) largest energy deposition in a single plane;10) slope of the E_int(x) energy distribution;11) curvature of the E_int(x) energy distribution;12) de/dx i.e. value of E_int(x)/x|x<15 cm
Additional separation using ToF information: difference δT of the time measured in
the EMC with that expected from the DC measurements in electron mass hypothesis
has been included in the final version of the NN: 12-25-20-1 becomes 13-25-20-1
Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba

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NN input distributions: some example
Cluster
centroid
depth

Asymmetryof energy lostin first two
innermostplanes

Data and MC
dE/dx

EINT(x) slope

Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba

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Distributions for Ke2γ decay

For Ke2γγ generator, the IB component is described with χPT atO(e2p2) including resummation of leading logaritms, while DEcomponent is described with χPT at O(e2p4).
Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba

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Ke2γ process
Dalitz densitydΓ (K → eνγ )= ρ IB (x, y ) + ρ SD (x, y ) + ρ INT (x, y )dxdy
helicity
suppressednegligible

x = 2E γ M K y = 2E e M K
Eγ, Ee in the K rest frame

Structure Dependent
2

GF2 Vus α 522
ρ SD (x, y ) =M
f+ff
x,y+f−ff SD− (x, y )
()
()
()
K
VASD +VA
64 π 2(fV , fA : effective vectorand axial couplings)

SD+ = V+A : γ polarization +SD− = V−A : γ polarization −Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba

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Ke2γ: theory predictions

SDfrom Phys. Rev. D77 (2008) 014004

1) ChPT at O(p4):fV ≈ 0.0945
fA ≈ 0.0425
no dependence on photon energy

Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba

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Bijnens, Ecker, Gasser 93IB2) ChPT at O(p6):fV ≈ 0.082(1+ λ (1-x))
fA ≈ 0.034
V linear x dependence ( λ ≈0.4)
Ametller, Bijnens, Bramon, Cornet 93
Geng, Ho, Wu 04
Chen, Geng, Lih 08

3) LFQM:
non trivial x dependence
fV = fA = 0 at x=0

x = 2E γ M K

Chen, Geng, Lih 08

Dalitz plots for SD+ and SD−pe (MeV)pe (MeV)

SD+

ν

SD−e+

γelectron peaks at 250 MeV,e-γ antiparallelEγ (MeV)νe+Eγ (MeV)γelectron peaks at 100 MeV: very bad,since Ke3 endpoint is 230 MeV

Test Lepton Flavor Violation with Ke2 at KLOE – B. Sciascia – Kaon09, Tsukuba

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