1. Protvino-Moscow, Russia
Recent Results
on Charged Kaon Decays
from
ISTRA+
EXPERIMENT
Viacheslav Duk
INR RAS
ICHEP 2006
INR/IHEP
Protvino-Moscow, Russia

2. Talk outline 1. ISTRA+ experimental setup
2. Recent results on radiative decays:
2.1 K­ → µ- ν γ
2.2 K- → µ- ν π0 γ
2.3 K- → e- ν π0 γ
3. K- → e- ν π0 (γ)
4. Conclusions

3. ISTRA+ experimental setup (U-70, Protvino) for studying rare kaon decays
C1-C4 – thresh. cherenkov counters; S1-S5 – scintillation counters; PC1-PC3 – proportional chambers; SP2 – veto calorimeter; SP1 – lead-glass calorimeter; DC – drift chambers; DT-drift tubes; MH – matrix scintilation godoscope

4. K→ µ ν γ : Theory Differential decay rate : 3 main terms:
IB – dominant
SD±, INT± - most interesting (→ Fv, FA)
Kinematical variables:
x=2*Eγ(cm)/Mk y=2*Eµ(cm)/Mk

5. K→ µ ν γ : background suppression
Main background:
K→ µ ν π0 (Kµ3)
with 1 gamma lost (from π0→γγ)
K→ π π0 (Kπ2)
with 1 gamma lost (from π0→γγ) and π misidentification
Signal observation:
M(µ ν γ)=√(Pµ+Pν+Pγ)2 where
pν=pk-pµ-pγ ; Eν=|pν|
M(µ ν γ) peaks at for signal
Background rejection procedure:scanning
over Dalits-plot and fitting M(µνγ) in each bin
Signal peak in (x,y) bin
M(µ ν γ)

6. K→ µ ν γ: Dalits-plot for signal, Kµ3 and Kπ2x x x
Kµ3 (MC)
Kπ2 (MC)
Signal (MC) y y y x
Experimental Dalits-plot after event selection and preliminary cuts
Real data
Signal peak in (x,y) bin
Selected bins (signal peak in M (µ ν γ) )
M(µ ν γ) y

7. 22472±465 events of K→ µ ν γ observed BR(K→ µ ν γ)/BR(Kµ3) is measured
K→ µ ν γ: BR measured
22472±465 events of K→ µ ν γ observed
BR(K→ µ ν γ)/BR(Kµ3) is measured
Supposing BR(Kµ3)=(3.27±0.06)x10-2 (PDG)
BR(K→µ ν γ)=[1.25±0.04(stat)±0.02(norm)]x10-3
Region: 30< Eγ <130MeV 150<Eµ<230MeV
Theory: BR(K→ µ ν γ)~1.28x10-3

8. K→ µ ν γ: comparison with other experiments
Main experiments:
KEK: Akiba et al, 1985
BNL: E787, 2000
ISTRA+: 2006 x
E787(BNL)
KEK
ISTRA+ y

9. K→ µ ν π0 γ : theory and experiment
µ--
µ--
Amplitudes and BR
(known at O(p4) )
ChPT tests
ξ=pγ(pμxpπ)mk3
Aξ=[N(ξ>0)-N(ξ<0)] / [N(ξ>0)+N(ξ<0)]
SM: Aξ~1.14x10-4
SM extensions: Aξ ≤2.6x10-4
New Physics
Previous experiments
Not observed
BR < 6.1x10-5

10. K→ µ ν π0 γ : background and kinematical regions
Main background:
K→ µ ν π0 (Kµ3)
K→ π π0 (Kπ2)
K→ π π0 π0 (Kπ3)
with 1 gamma lost (from π0→γγ) or accidental gamma
Signal observation:
M(μνπ0γ)=√(Pµ+Pν+Pπ0+Pγ)2 where
pν=pk-pµ-pγ ; Eν=|pν| ; M(μνπ0γ) peaks at for signal
2 kinematical regions:
I: 5 < Eγ < 30 MeV small background
II: 30 < Eγ < 60 MeV large background

11. K→ µ ν π0 γ : 1-st kinematical region 5 < Eγ < 30 MeV
Signal observation in M(μνπ0γ)
Non-π0 background: estimated from side bands in m(γγ)
384 ± 41 events in M(μνπ0γ)
BR(K→ µ ν π0 γ)/BR(Kµ3) is measured
Using PDG value for BR(Kµ3)
K→ π π0 π0
K→ μ ν π0
BR=(8.82±0.94(stat)±0.86(syst))x10-5
Theory: 6.86x10-5
T-odd asymmetry: Aξ=-0.03±0.13
SM extensions: Aξ~2x10-4

12. K→ µ ν π0 γ : 2-nd kinematical region 30<Eγ<60 MeV
Strong background from
K→ π π0, K→ π π0 π0
additional cut
0.1<p*(π–)<0.185 GeV/c
153±39 events in M(μνπ0γ)
BR(K→ µ ν π0 γ)/BR(Kµ3) is measured
Using PDG value for BR(Kµ3)
BR=(1.46±0.22(stat)±0.32(syst))x10-5
Theory: 1.53x10-5
Non-π0 background
K→ π π0 π0
K→ μ ν π0

13. K→ e ν π0 γ : theory and experiment
Amplitudes and BR
(known at O(p4) )
ChPT tests
ξ=pγ(pμxpπ)mk3
Aξ=[N(ξ>0)-N(ξ<0)] / [N(ξ>0)+N(ξ<0)]
SM: Aξ=-0.59x10-4
SM extensions: Aξ ≤0.8x10-4
New Physics
Previous experiments
~200 events

14. K→ e ν π0 γ : background suppression
Main background:
K→ π π0 π0, K→ π π0, K→ e (γ) ν π0, K→ π π0 γ , K→ e ν π0 π0
M2(π0 e γ)=(PK-Pπ0-Pe-Pγ)2; -0.01< M2(π0 e γ)<0.01
m2(π π0)=(PK-Pπ-Pπ0)2; 0.009< m2(π π0)< against K→ π π0
0.002< θeγ< against K→ e (γ) ν π0
m2(π π0)
M(π0 e γ)
θ(e γ) angle in
laboratory frame

15. K→ e ν π0 γ : resulting spectra
5378 events selected
(3852 – signal,1526 – background)
Histogram – data
after background subtraction
Points with errors - MC

16. K→ e ν π0 γ : results
R=BR(K→ e ν π0 γ, E*γ>10MeV)/BR(Ke3) is measured
Comparison with previous experiments:
additional cut 0.6<cosθeγ<0.9
R=(0.48±0.02(stat)±0.03(syst))x10-2
better accuracy and larger statistics
Comparison with theory:
additional cuts E*γ>30MeV; θ*eγ>20º
BR=(3.05±0.02)x10-4
Theory: 2.8x10-4 (tree level)
3.0x10-4 (O(p4) level)
T-odd asymmetry: Aξ=-0.015±0.021
SM: Aξ =-0.59x SM extensions: Aξ~0.8x10-4
Rexp, x10-2
Events
experiment
0.48±0.04
1382
ISTRA+
0.46±0.08 82
Barmin et al
0.56±0.04
192
ISTRA
0.76±0.28 13
Romano et al

17. K→ e ν π0 : theory and experiment
Decay width:
|Vus | , |Vud|2+|Vus|2+|Vub|2=1-δ
Previous experiments (PDG):
BR (Ke3)=(4.87±0.06)x δ=(3.2±1.4)x PDG 04
BR (Ke3)=(5.13±0.10)x δ=(0.3±1.6)x BNL E685

18. K→ e ν π0 : event selection and backgrounds
New approach to BR measurement:
1 charged track events are selected
E/p is used for e- identification
Ke3 is the dominant source for
events with 1 inclusive e- (<0.1% for other decay modes)
Normalisation on Kπ2 decay
Fitting E/p Ke3 event number
Fitting Pπ(cm) Kπ2 event number
Pπ(cm) – charged track momentum in c.m.s. assuming pion hypothesis
E/p
MC for Ke3 and backgrounds
Pπ(cm)
MC for Kπ2 and backgrounds

19. K→ e ν π0 : results N(Ke3)=(2.1781±0.0024)x106
N(Kπ2)=(10.426±0.0056)x106
BR(Ke3)/BR(Kπ2) is measured;
using PDG value for BR(Kpi2)
E/p
Pπ(cm)
Experimental data – final fit
BR(Ke3)=[5.170±0.011(stat)±0.034(norm) ±0.045(syst)]x10-2
E/p
Good agreement
with BNL E685;
smaller errors
|Vus f+(0)|=0.2197±0.0012(BR)±0.0011(IKe)
|Vus|=0.2286±0.0016(BR)±0.0020(f+(0))
δ=(-4.7±15.4)x10-4

20. Recent ISTRA+ Results Conclusions
BR=(1.25±0.05)x10-3 (Theory: BR=1.28x10-3)
Region: 30 < Eγ < 130 MeV, 150 < Eμ < 230 MeV (~22500 events)
K– → µ- ν γ :
First observation (~800 events)
BR=(8.82±1.27)x10-5 (Theory: BR=6.86x10-5)
Region 1: 5 < Eγ < 30 MeV
BR=(1.46±0.39)x10-5 (Theory: BR=1.53x10-5)
Region 2: 30 < Eγ < 60 MeV
T-odd asymmetry Aξ=-0.03±0.013
K– → µ- ν π0 γ :
BR=(3.05±0.02)x10-4 (Theory: BR=3x10-4)
Region: Eγ > 30 MeV, θeγ > 20o ( ~3850 events)
T-odd asymmetry Aξ=-0.015±0.021
K– → e- ν π0 γ :
BR=[5.170.011(stat)0.034(norm) 0.045(syst)]× (PDG: BR=(4.87±0.06)x10-2)
|Vus|=0.2286±0.0026
K– → e– ν π0 (γ) :

21. Acknowledgments ISTRA+ work is supported by:
RFBR grants N (IHEP) and N (INR)
Russian Science Support Foundation (INR)