Study of K→ µ ν γ decayatViacheslav Duk, INR Moscow
For ISTRA+ collaboration

Outline• K→ µ ν γ decay• ISTRA+ experiment• Event selection• Spectrum tuning• Background rejection• Signal extraction• Spectrum fitting• Results• Conclusions
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V.Duk, INR RAS, Moscow KAON09

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K→ µ ν γ decay: introduction• Motivation• Differential decay rate
• FV and FA theoretical predictions• Experiments

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K→ µ ν γ decay: motivation
photon emitted fromthe vertex (SD or DE)

Probing electroweak
structure of kaon

νμW-K-10.06.2009μγ

Testing predictionsof ChPT, LFQM, …

V.Duk, INR RAS, Moscow KAON09

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K→µνγ theory: differential decay rate

3 main terms:
IB – dominant
SD±, INT± - mostinteresting (→ Fv , FA)
Kinematicalvariables:
x=2*Eγ(cm)/Mk
y=2*Eµ(cm)/Mk

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K→µνγ theory: formfactors
ChPT O(p4)

ChPT O(p6)

LFQM• FV + FA = 0.137• FV - FA = 0.055• FV + FA = 0.116• FV - FA = 0.048• FV + FA =0.142• FV - FA = 0.070

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K→µνγ : main experimental results
experimentcollaboration

year

cuts

results

Barmin et al

1988

Pμ < 231.5 MeV/c

BR(IB)

Demidov et al

1990

Pμ < 231.5 MeV/c

BR(IB)

Akiba et al

E104 (KEK)1985

214.5 < Pμ < 231.5 BR(IB)MeV/cAdler et al

E787 (BNL)

2000

Pμ > 218.4 MeV/c
Eγ > 90 MeV|FV + FA|,BR(SD+)

Formfactors:
E787(BNL) Phys.Rev.Lett.85(2000)2256|FV+FA|=0.165 ± 0.013; -0.04<FV-FA<0.24(K→µνγ)E865(BNL) Phys.Rev.Lett.89(2002)061803(K→eνe+e- , K→µνe+e- )FV+FA=0.147 ± 0.026; FV-FA=0.077 ± 0.028
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ISTRA+ setup

T0=S1 . S2 . S3 . S4 . C0 . C1 . C2 . S5(prescaled by a factor of ~10)

T1=T0 . (∑SP1 > MIP)

C1-C4 – thresh. cherenkov counters; S1-S5 – scintillation counters; PC1-PC3 –proportional chambers; SP2 – veto calorimeter; SP1 – lead-glass calorimeter; DC – driftchambers; DT-drift tubes; MH – matrix scintilation godoscope
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V.Duk, INR RAS, Moscow KAON09

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ISTRA+: from π → e ν γ to K→ µ ν γ
1990Study of π→ e ν γ decay: measuring FV , γ=FV/FA , FT

200320072009> 200910.06.2009

Study of K→ µ ν γ decay: measuring FV - FA
ISTRA+OKA (see talk by Viсtor Kurshetsov)
V.Duk, INR RAS, Moscow KAON09

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Event selection: strategy• Track requirements• Photon requirements• Vertex requirements• Particle ID

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Event selection: track requirements• Exactly one beam track in each projection• Exactly one secondary track in each projection• Secondary track is negatively charged• track quality > 10-2 for each projection of beam track• track quality > 0.1 for each projection of secondary track• Angle between beam andsecondary track > 2mrad
cut(suppression of undecayed particles)

θKµ10.06.2009

V.Duk, INR RAS, Moscow KAON09

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Event selection: photon requirements• No photons in SP2 guard calorimeter• No photons in GS

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Event selection: vertex requirements• -3 < x < 3 cm
• -2 < y < 6 cm
• 400 < z < 1600 cm(decay volume: 300-1200cm, SP2 guardcalorimeter: z=1650cm)• Vertex fit probability > 0.01
cut

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V.Duk, INR RAS, Moscow KAON09

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Event selection: particle ID• Photon: shower in ECAL
not associated with any track• Muon:1) ADC sum in HCAL < 2002) relative energy deposition inlast 3 layers of HCAL > 0.05

10.06.2009

V.Duk, INR RAS, Moscow KAON09

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Spectrum tuning: strategy• Trigger efficiency for photon• Muon momentum kinematical calibration• Photon energy kinematical calibration

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V.Duk, INR RAS, Moscow KAON09

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Trigger efficiency ε for photon
Data structure:
T0 trigger: ~10%
T1=T0 . (∑ECAL > MIP) : ~90%
Trigger efficiency:
ε = T0*T1 / T0

Data with T1 areweighted by 1/εEnergy deposition in ECAL, GeV

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V.Duk, INR RAS, Moscow KAON09

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Kinematical calibration• General idea: use of 2-body kinematics• Pμ tuning: peaks in Kμ2 and Kπ2 mustcorrespond to table values• Eγ tuning: a peak in Eπ0 for Kπ2 selection mustcorrespond to table value

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V.Duk, INR RAS, Moscow KAON09

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Background rejection• Main backgrounds• Primary cuts
• Kinematical variables and signal observation

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V.Duk, INR RAS, Moscow KAON09

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Background rejection• 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

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V.Duk, INR RAS, Moscow KAON09

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Background rejection: primary cuts
• Missing momentum in ECAL plane: central holeregion is dominated by Kπ2 and excluded• Y-distance between muon and photon in ECAL plane:-20 < dy < 50 cm
y, cm

x, cm

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V.Duk, INR RAS, Moscow KAON09

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Background rejection: kinematical variables• Signal observation:M(µ ν γ)=√(Pµ+Pν+Pγ)2 wherepν=pK-pµ-pγ ; Eν=|pν|M(µνγ) peaks at MK=0.494 GeV for signal
Background rejection procedure: scanningover (x,y) Dalits-plot and looking for a peak in M(µνγ)

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V.Duk, INR RAS, Moscow KAON09

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Background rejection: Dalits-plot plot signalxxyxyx

Our strategy:Focusing on INT- regiony10.06.2009

yV.Duk, INR RAS, Moscow KAON09

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Background rejection: (x,y) Dalits plot
X

X

Signal (MC)Y

X

Kµ3 (MC)Kπ2 (MC)Y

Y

Previous experiments: looking for signal near y kinematical border
ISTRA+: looking for signal near Eν kinematical border

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Signal extraction: strategy• X-stripes and distribution over y in x-stripes• Cut on y in x-stripes• M(µ ν γ) in xy-stripes

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V.Duk, INR RAS, Moscow KAON09

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Signal extraction: X-stripes,distribution over y, cut on y
• (x,y) dalits-plot is divided into stripes with
δx=0.05 width (x-stripes)• A cut on y is put in each stripe (xy-stripe)• Ratio R=S/√(S+B) (S – number of INT- events,
B – IB+background) is used for putting cut on ywithin a particular stripe• Maximum of R corresponds to minimal error

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V.Duk, INR RAS, Moscow KAON09

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Signal extraction: X-stripes,distribution over y, cut on y
Y in x-stripe

Ratio R in x-stripe

Ry
Limits for R calculation
10.06.2009yPutting upper cut on y

V.Duk, INR RAS, Moscow KAON09

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Signal extraction: fitting M(µ ν γ) in xy-stripes~44000 events extractedX

fitting M(µ ν γ) inxy-stripe

Signal andbackgroundshapes takenfrom MC

xy-stripe

x-stripe

YM(µ ν γ), GeV
10.06.2009

V.Duk, INR RAS, Moscow KAON0927Spectrum fitting
Nmeasured / NIB

 N(IB) is taken from MC Negative sign of INT- clearlyseen ~2% effect of INT-

Preliminary result:fitting function:
p1*[ (f(IB) - p2*f(INT-, FV-FA=1) ]/f(IB)FV - FA=0.12±0.03±0.03

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FV-FA: comparison with theory
FV - FA=0.12±0.03(stat)±0.03(syst)

ChPT O(p4)

ChPT O(p6)

LFQM

FV - FA = 0.055

FV - FA = 0.048

FV - FA = 0.070

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V.Duk, INR RAS, Moscow KAON0929

ISTRA+ kinematical region:
complementary with previous experimentsX

E787(BNL)
E787(BNL)ISTRA+ISTRA+

KEK
E246
KEKY

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V.Duk, INR RAS, Moscow KAON0930

ISTRA+ result:complementary with previous experiments
experimentcollaboration

year

cuts

results

Barmin et al

1988

Pμ < 231.5 MeV/c

BR(IB)

Demidov et al

1990

Pμ < 231.5 MeV/c

BR(IB)

Akiba et al

E104 (KEK)1985

214.5 < Pμ < 231.5
MeV/c

BR(IB)

Adler et al

E787 (BNL)

2000

Pμ > 218.4 MeV/c
Eγ > 90 MeV|FV + FA|2009

Eγ < 148 MeV(x<0.6)

FV – FA

Akimenko et al ISTRA+~15 times larger
statistics

E787: 2800 events
ISTRA+: 44000 events
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V.Duk, INR RAS, Moscow KAON0931

conclusion• The K→ µ ν γ decay is observed at ISTRA+
setup in a new kinematical region• The event number observed is 44K (the largeststatistics in the world)• First measurement of INT- term gives
FV-FA=0.12±0.03(stat)±0.03(syst)• The sign of INT- is negative• The results are preliminary
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V.Duk, INR RAS, Moscow KAON0932

To KAON09 organizers and participants

THANK YOU!!!

10.06.2009

V.Duk, INR RAS, Moscow KAON09

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