C.Gatti LNF-INFN

center of mass system Tag efficiency independent of pion energy (linear in t) within few permil Measurement of the parameters of the form factors with...

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KLOE measurement of form factor slopes for →πlν ν decays KL→π C.Gatti LNF-INFN

Form factors: motivations I π ( p ) jµ K ( P ) = C K [( P + p ) µ f + (t ) + ( P − p) µ f − (t )] t = ( P − p ) 2 = M K2 + mπ2 − 2M K Eπ

t f − (t ) f 0 (t ) = f + (t ) + 2 2 mK − mπ ƒ0 and ƒ+ related to the transition amplitudes 0+ and 1-, respectively Pole expansion:

Power expansion:

C.Gatti

1 f + , 0 (t ) = f + (0) 1 − t / mV2 , S f + , 0 (t ) = f + (0) × (1 + λ+′ , 0

t t 1 ′ ′ + λ+ , 0 2 2 mπ 2 mπ

2

+ ...)

KAON’07-Frascati 21/5/2007

Form factors: motivations II δVus/Vus ∝ 0.5 δI / I

λ′+= λ′′+= 0 λ′+=0.029 λ′′+= 0 λ′+=0.025 λ′′+= 0.002

Ik0e(λ′ λ′+) – Ik0e(λ′ λ′+ , λ′′+) / Ik0e = 0.4% Ik0µµ(λ′ λ′+ , λ′′+) – Ik0µµ(λ′ λ′+ , λ′′+ , λ0) / Ik0µµ = 3%

K0e3

λ′+ and λ′′+ 95% correlated λ′0 and λ′′0 ~100% correlated

λ′+= λ′′+=λ λ0 = 0 λ′+=0.025 λ′′+= 0.002 λ0 = 0 λ′+=0.025 λ′′+= 0.002 λ0 = 0.016

% error on Vus׃(0)* Mode %err BR

τ



I

KLe3 0.25 0.09 0.19 0.10 0.09 KLµ3 0.31 0.10 0.18 0.15 0.17

K0µ µ3

* CKM’06

C.Gatti

KAON’07-Frascati 21/5/2007

ϕ→KSKL ϕ→ ϕ→ KSKL almost at rest (p(ϕ) ~13 MeV) We tag a KL looking for KS→π+π- decays KL momentum computed from 2 body kinematics (~1% resolution) We measure form factor parameters by measuring kinematical variables in kaon center of mass system Tag efficiency independent of pion energy (linear in t) within few permil

KS → π+π−

Measurement of the parameters of the form factors with L=330 pb-1 collected during 2001 and 2002 corresponding to ~2 million Ke3 and Kµ3 selected

C.Gatti

KAON’07-Frascati 21/5/2007

Ke3 Selection: DC 4 m dia., 3.5 m long 12,000 cells He + 10% iso-C4H10 B=5.2 kG σ(pT)/pT = 0.4 %

ππ

πππ

After kinematical cuts: bkg ~ 10 % (Kµ3) and ε ∼ 96% We must distinguish π from e to compute Eπ

πππ πeν

ππ

Emiss(ππ)2- pmiss2-Mπ02 (MeV2) C.Gatti

πeν

√Emiss(ππ)2+ pmiss2(MeV)

πµν

πeν |Emiss(πµ)- pmiss| (MeV) KAON’07-Frascati 21/5/2007

Ke3 Selection:TOF ∆t(e) + ∆t(π) (ns)

Kµ3

Pb scintillating-fibers L~4 m ~5000 pm tubes σ(E)/E=5.7%/√ √E(GeV) σ(t)=57 ps/ √E(GeV) ⊕100 ps Tracks are associated to clusters in EmC (TCA) We reject the background and perform Particle ID using TOF ε∼40% bkg ∼ 1% (Kµ3)

C.Gatti

Ke3 signal Ke3 opposite charge ∆t(e) - ∆t(π) (ns) KAON’07-Frascati 21/5/2007

Ke3 Selection:TOF TCA efficiency different for the two charge modes (different behavior of low-p π+ and π- in EmC). If not corrected different results for λ′+ (15%) for each charge. EmC time-response in MC simulation tuned with data control samples

C.Gatti

KAON’07-Frascati 21/5/2007

Ke3 Selection: Purity

Residual background ~1% δλ′+/ λ′+ ~ 10% if not corrected

NN

→e π µ

We cut on a variable calculated using a neural network (NN) Reducing the background by a factor 2, the variations of the measured slopes are well within statistical errors C.Gatti

Signal (A.U.)

E/p, cluster shape →

S/(S+B)

t/m2 KAON’07-Frascati 21/5/2007

Radiative corrections ‘bare’ ρ(t) Ke3γ MC t/m2 Inner bremsstrahlung affects mainly the low t region (3-5% effect) Final state radiation included in the simulation of kaon decays

C.Gatti

KAON’07-Frascati 21/5/2007

Fit

dN dt (i ) = N 0

20 j =1

A(i, j ) × ρ ( j; λ+′ , λ+′′) × ε ( j ) × FFSR ( j )

linear

quadratic t/m2

C.Gatti

t/m2

KAON’07-Frascati 21/5/2007

λ′+, λ′′+: Results λ+

From 2 million Ke3 events selected

Linear fit

π-e+ν π+e-ν Comb.

λ+×103

28.7±0.7 28.5±0.6 28.6±0.5

χ2/ndf

156/181 174/181 330/363 Data periods

Quadratic fit λ′+×103

λ′′+×103

π-e+ν π+e-ν Comb.

1.9±1.0 152/180 1.0±1.0 173/180 1.4±0.7 325/362

C.Gatti

24.6±2.1 26.4±2.1 25.5±1.5

χ2/ndf

P(χ2) ~ 90%

KAON’07-Frascati 21/5/2007

λ′+, λ′′+: Results λ′+=(25.5±1.5stat±1.0syst)×10-3 λ′′+=(1.4±0.7stat±0.4syst)×10-3 Correlation -0.95 Pole parametrization:

MV=(870±6stat±7syst) MeV P(χ2) ~ 92%

C.Gatti

Values only from Ke3 KAON’07-Frascati 21/5/2007

Emiss(µ π)- pmiss (MeV)

Emiss(µ π)- pmiss (MeV)

Kµ µ3 Selection

Emiss(πµ)- pmiss (MeV)

Emiss(πµ)- pmiss (MeV)

Kinematic preselection cutting on Emiss- pmiss Rejection of ππ, πππ, and πeν: similar cuts used for the Ke3 selection 4% contamination (Ke3) We don’t distinguish π from µ

C.Gatti

KAON’07-Frascati 21/5/2007

Kµ µ3 Selection

Ke3 background reduced by a combined cut on NN output and on TOF variable Final background ~2% π-µ separation by TOF difficult due to the small ∆m and at low energy (100 MeV) calorimetry doesn’t help much we fit the Eν spectrum (no need to distinguish π from µ)

C.Gatti

KAON’07-Frascati 21/5/2007

Kµ µ3: t vs Eν λ′+= λ′′+=λ λ0 = 0 λ′+=0.025 λ′′+= 0.002 λ0 = 0 λ′+=0.025 λ′′+= 0.002 λ0 = 0.016

— = (— - —)//—

Statistical errors on slopes are 2-3 times bigger using Eν and higher correlations The error on λ0 is only 30% bigger if the fit is performed combining Ke3 and Kµ3 C.Gatti KAON’07-Frascati 21/5/2007

λ0: Fit result 1.8 million selected events Combined fit Ke3 and Kµ3 +1.5%

λ0

1

λ′+

λ′′+

0

-0.95 1

0.31 -0.41 1

-1.5%

Pre

ry a n i il m

lt u s re

λ0=(15.6±1.8stat±1.9syst)×10-3

C.Gatti

Eν ν (MeV)

χ2/ndf =21/31 KAON’07-Frascati 21/5/2007

Comparison of experimental results (Ke3 and Kµ µ3) KTeV KLOE NA48 ISTRA+ λ′′+×103

λ′+×103

Each ellipse is from the average of Ke3 and Kµ µ3

λ′′+×103

λ′+×103

λ0×103

λ0×103

λ′+=(24.8±1.1)×10-3 λ′′+=(1.64±0.44)×10-3 λ0=(13.4±1.2)×10-3 P(χ χ2) ~ 10-6 S=1.4, 1.3, 1.9 C.Gatti

KAON’07-Frascati 21/5/2007

Conclusion With ~0.3 fb-1 KLOE has measured the form factor parameters with K0e3 and K0µ3 decays, with relative errors of 7%, 58%, and 17% for λ′+ λ′′+ and λ0 respectively. Experimental situation for λ0 comparing different experiments is not very clear. The overall fit has very low χ2 probability, the systematics must be kept under control. The first row of the CKM matrix offers the most precise test of unitarity. The ratio rµe , test of lepton universality, with kaons is now reaching the precision obtained with πl2 decays (0.5% vs 0.3%). KLOE still has to analyze 2 fb-1 of data. For instance, the relative error on λ0 can be reduced to 5-10%. Measurements on charged kaons form factors are underway.

C.Gatti

KAON’07-Frascati 21/5/2007