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Kaon decays: motivation QFTHEP-2011 Relatively easy to get kaon beams Possibility to do precise measurements V.A.Duk, INR RAS Check SM predictions Search for NP 3 experimenttheory Low uncertainties in calculations within Standard Model (SM) New Physics (NP) contributions
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Search for heavy neutrino in K‾→ µ‾ ν γ decay at ISTRA+ setup
Viacheslav Duk, INR RAS
ISTRA+ collaboration
ISTRA+
IHEP U-70 (Protvino, Russia)
Plan
• LSND/KARMEN/MiniBooNE anomaly and heavy sterile neutrino νh
• Search for νh in kaon decays• ISTRA+ setup• Event selection for K‾→ µ‾ ν γ • Signal extraction• Limits for |Uµh|2
• Conclusions
QFTHEP-2011 2V.A.Duk, INR RAS
Kaon decays: motivation
QFTHEP-2011
Relatively easy to get kaon beamsPossibility to do precise measurements
V.A.Duk, INR RAS
Check SM predictionsSearch for NP
3
experiment theory
Low uncertainties in calculations within Standard Model (SM)New Physics (NP) contributions
Motivation for this work
Paper by S.N.Gninenko (INR RAS)Resolution of puzzles of LSND, KARMEN and
MiniBooNE experiments Phys.Rev.D83:015015,2011. arXiv: 1009.5536
QFTHEP-2011 4V.A.Duk, INR RAS
Neutrino oscillations: LSND
QFTHEP-2011 5V.A.Duk, INR RAS
Neutrino oscillations: KARMEN
QFTHEP-2011 6V.A.Duk, INR RAS
Neutrino oscillations: MiniBooNE, neutrino mode
QFTHEP-2011 7V.A.Duk, INR RAS
Neutrino oscillations: MiniBooNE, anineutrino mode
QFTHEP-2011 8V.A.Duk, INR RAS
Above 475 MeV:Event excess475-1250 MeV: 20.9±14.0475-3000 MeV: 24.7±18.0
Below 475 MeV:Event excess200-475 MeV: 18.5±14.3
LSND/KARMEN/MiniBooNE anomalies: summary
QFTHEP-2011 9V.A.Duk, INR RAS
Possible explanation of experimental results (S.Gninenko, INR RAS)
QFTHEP-2011 10V.A.Duk, INR RAS
Origin of excess
Possible explanation (S.N.Gninenko)
New weakly interacting particle νh:• Produced in NC• Mixing with νμ ( must be in CC, e.g. kaon
decays) or separate vertex (may be in NC only)• Decays radiatively via μtr
QFTHEP-2011 11V.A.Duk, INR RAS
Properties of a new particle νh
• m > 40 MeV: no event excess in KARMEN (threshold effect)
• m < 80 MeV: νh production in LSND suppressed by phase space factor for m > 80MeV
• τ(νh) > 10-11 sec: from LEP constraints: BR(Z→ννh) x BR(νh → ν γ) < 2.7 x 10-5
• τ(νh) < 10-9 sec: νh‘s decay within MiniBooNE detector volume
• 10-3 < |Uμh|2 < 10-2 : from event excess in MiniBooNE experiment
QFTHEP-2011 12V.A.Duk, INR RAS
New weakly interacting particle νh
QFTHEP-2011
Decays mostly as νh →νγ
40 MeV < m (νh) < 80 MeV 10-3 < |Uμh|2 < 10-2
10-11 sec < τ(νh) < 10-9 sec
13V.A.Duk, INR RAS
νh : limits from pion and kaon decays
QFTHEP-2011 14V.A.Duk, INR RAS
Muon energy in 2-body kaon decay
Search for νh in kaon decays
QFTHEP-2011
K→μνh : peak in Eμ (cms) background from K→μνμ insensitive to low masses of νh because of resolution
K→μνh , νh →ν γ: peak in Eμ (cms) signature the same as for K→ µ ν γ no background from K→μνμ
sensitive to low masses of νh
secondary decay vertex
Suitable for ISTRA+
Muon energy in 2-body kaon decay
15V.A.Duk, INR RAS
ISTRA+ collaboration
QFTHEP-2011
Institute for High Energy Physics, Protvino (IHEP) Institute for Nuclear Research, Moscow (INR) Joint Institute for Nuclear Research, Dubna (JINR)
ISTRA+
16V.A.Duk, INR RAS
ISTRA+ setup
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 godoscopeQFTHEP-2011
T0=S1 . S2 . S3 . S4 . C0 . C1 . C2 . S5 (prescaled by a factor of ~10)
T1=T0 . (∑SP1 > MIP)
17V.A.Duk, INR RAS
ISTRA+ setup: beam part
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 godoscopeQFTHEP-2011
T0=S1 . S2 . S3 . S4 . C0 . C1 . C2 . S5 (prescaled by a factor of ~10)
T1=T0 . (∑SP1 > MIP)
18V.A.Duk, INR RAS
ISTRA+ setup: decay volume
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 godoscopeQFTHEP-2011
T0=S1 . S2 . S3 . S4 . C0 . C1 . C2 . S5 (prescaled by a factor of ~10)
T1=T0 . (∑SP1 > MIP)
vacuum
He
19V.A.Duk, INR RAS
ISTRA+ setup: magnetic spectrometer
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 godoscopeQFTHEP-2011
T0=S1 . S2 . S3 . S4 . C0 . C1 . C2 . S5 (prescaled by a factor of ~10)
T1=T0 . (∑SP1 > MIP)
20V.A.Duk, INR RAS
ISTRA+ setup: ECAL, HCAL
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 godoscopeQFTHEP-2011
T0=S1 . S2 . S3 . S4 . C0 . C1 . C2 . S5 (prescaled by a factor of ~10)
T1=T0 . (∑SP1 > MIP)
21V.A.Duk, INR RAS
K→µνh (νh→νγ) event reconstruction: primary and secondary vertex for signal
QFTHEP-2011
K
K
μ
μ
νμ
ν
γ
γνh
A
A
B
B
Pγ calculated using A, B
Pγ calculated using A, B:additional energy smearing
Eνh ~ 240 MeV , mνh ~ 40–80 MeV
smearing not crucial
22V.A.Duk, INR RAS
K→µνh (νh→νγ): primary and secondary vertices
QFTHEP-2011
Zνh - ZK
(Zνh – ZK)/(ZECAL – ZK)
τ=10-11 sec τ=10-10 sec
τ=10-9 sec
τ=10-9 sec
τ=10-10 secτ=10-11 sec
dz, cm dz, cm dz, cm
23V.A.Duk, INR RAS
K→µνh (νh→νγ): Eγ smearing
QFTHEP-2011
τ=10-11 sec τ=10-10 sec τ=10-9 sec
dE, GeV dE, GeV dE, GeV
dE = Etrue - Emeasured
24V.A.Duk, INR RAS
K→µνh (νh→νγ): kinematics in kaon rest frame
QFTHEP-2011
νh ν
γ
μ
Eνh ~ 240 MeV , mνh ~ 40–80 MeV Eγ > 50 MeV
kaon decay vertex
Pγ: kaon rest frameP*γ: νh rest frame θ – (γ-νh) angle
cos θμγ ~ (-1)
peak sharper for smaller mh
25V.A.Duk, INR RAS
*
general caseassumed isotropic
*
K→µνh (νh→νγ) event selection: K→µνγ signature• Track requirements (one primary track, one secondary track,
cuts on track quality)• Veto requirements (no signals above threshold)• Vertex requirements (400 < z < 1600 cm, cut on vertex fit
probability)• Particle ID : Photon: isolated shower in ECAL Muon: 1) MIP in ECAL 2) ADC sum in HCAL < 200 3) relative energy deposition in last 3 layers of HCAL > 0.05
QFTHEP-2011 26V.A.Duk, INR RAS
K→µνγ : decay rate and kinematical variables
QFTHEP-2011
Kinematical variables:x=2*Eγ(cms)/Mk y=2*Eµ(cms)/Mk
3 main terms: IB – dominant SD±, INT± - most interesting (→ Fv , FA)
x
y
IBDalits-plot
27V.A.Duk, INR RAS
K→µνh (νh→νγ): background rejection and signal observation• Main background:• K→ µ ν γ (Kµ2γ)• 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: peaks in y and cos θμγ where θμγ is the angle between pµ and pγ in kaon rest frame. θμγ peaks at (-1) for signalBackground rejection procedure: scanning over (y, x) Dalits-plot and looking for a peak in cos θμγ
QFTHEP-2011 28V.A.Duk, INR RAS
K→µνh (νh→νγ): (y, x) Dalits plot
QFTHEP-2011
Kµ2γ (MC)
Kµ3 (MC)Kπ2 (MC) X
XX
Y
signal (MC)X
Y
29V.A.Duk, INR RAS
data
X
X
Y
Y Y
main background: Kπ2
K→µνh (νh→νγ): signal extraction
• (y, x) dalits-plot is divided into stripes with Δx=0.05 width (x-stripes)
• cut on y is put in each x-stripe: 1 < y < 1.2• Simultaneous fit of y and cos θμγ is done in x-stripes
QFTHEP-2011
X
y
signal (MC)
7 x-stripes selected for further analysisin the following region:1 < y < 1.20.2 < x < 0.55
30V.A.Duk, INR RAS
Possible signature for νh in x-stripes; |Uµh|2=0.01, m=60 MeV, τ=10-10 sec
QFTHEP-2011
Stripe 1: 0.2 < x < 0.25
Stripe 4: 0.35 < x < 0.4
Stripe 7: 0.5 < x < 0.55
cos θµγ
cos θµγ
cos θµγ
Y
Y
Y
31V.A.Duk, INR RAS
magenta: signalgreen: K→µνγblue: Kμ3red: Kπ2
peak sharper for large x
Possible signature for different masses of νh ; |Uµh|2=0.01 , τ=10-10 sec
QFTHEP-2011
m=80 MeV m=60 MeV m=40 MeV
cos θµγ cos θµγ cos θµγ
32V.A.Duk, INR RAS
peak sharper for small mh
Possible signature for different lifetimes of νh ; |Uµh|2=0.01 , m=60 MeV
QFTHEP-2011
τ=10-9 sec τ=10-10 sec τ=10-11 sec
cos θµγ cos θµγ cos θµγ
33V.A.Duk, INR RAS
peak sharper for large τh
Signal efficiency
QFTHEP-2011
mh τ(lab) because of Lorentz boost
low efficiency for small mh
2 effects
mh E(cms)
cut on y (y>1) kills signal
34V.A.Duk, INR RAS
τ=10-9 sec
τ=10-11 sec
τ=10-10 sec
mνh, MeV
mνh, MeV
mνh, MeV
K→µνh (νh→νγ): simultaneous fit in x-stripes
QFTHEP-2011
fitting cos θμγ and y simultaneously is more reliable
Signal and background shapes taken from MC
magenta – signal, green – Kμ2γ, blue – Kμ3, red – Kπ2
0.4 < x < 0.45
0.3 < x < 0.35
35V.A.Duk, INR RAS
Y cos θµγ
Y cos θµγ
|Uµh|2 calculation
• BR(νh) measured from
BR(νh)/BR(Kμ2γ)• BR(Kμ2) taken from PDG• BR(Kμ2γ) taken from theory• f(mh) contains chirality flip
and phase space factors
QFTHEP-2011
blue (chirality flip): 1+(mh/mμ)2
red (total): f(mh , mμ)
f(mh , mµ)
f = 1.1 – 1.5
mνh, GeV
36V.A.Duk, INR RAS
|Uµh|2 calculation
• |Uµh|2 is calculated for each x-stripe
• Nexp(νh)/ Nmc(νh) obtained from simultaneous fit
• Values |Uµh|2 for x-stripes are averaged
• Upper limit is set for averaged |Uµh|2
QFTHEP-2011 37V.A.Duk, INR RAS
Averaging |Uµh|2
QFTHEP-2011
|Uµh|2 = (6.6 ± 3.9)*10-6
m=50 MeV, τ=10-10 sec
X
|Uµh|2
38V.A.Duk, INR RAS
|Uµh|2
X
1σ interval
|Uµh|2 for τ=10-9 , 10-10 and 10-11 sec
QFTHEP-2011 39V.A.Duk, INR RAS
|Uµh|2|Uµh|2|Uµh|2
mνh, MeVmνh, MeV mνh, MeV
τ=10-9 τ=10-10 τ=10-11
effect does not exceed 2σ
Main sources of systematics
• Fit (shape) systematics• bin size in cos histogram• x-stripe width (bin size in the final fit)• Cut on x (number of x-stripes in the final fit)• Cut on y in x-stripes (study in progress)
QFTHEP-2011 40V.A.Duk, INR RAS
Main sources of systematics
• Fit (shape) systematics• bin size in cos histogram• x-stripe width (bin size in the final fit)• Cut on x (number of x-stripes in the final fit)• Cut on y in x-stripes (study in progress)
QFTHEP-2011 41V.A.Duk, INR RAS
Fit (shape) systematics
• MC shape is not perfect• Errors of simultaneous fit scaled to χ2=1• New |Uµh|2 has larger error • Additional error is treated as shape systematics• Dominant source
QFTHEP-2011 42V.A.Duk, INR RAS
m = 80 MeV τ = 10-10 sec
x
|Uµh|2
|Uµh|2 = (0.9 ± 0.5)*10-5 |Uµh|2 = (0.7 ± 0.8)*10-5
|Uµh|2
x
Main sources of systematics
• Fit (shape) systematics• bin size in cos histogram• x-stripe width (bin size in the final fit)• Cut on x (number of x-stripes in the final fit)• Cut on y in x-stripes (study in progress)
QFTHEP-2011 43V.A.Duk, INR RAS
Bin size in simultaneous (cos histogram) and final (x-stripe width) fits
• Varying bin size in cos histogram: results are compatible
• Varying x-stripe width: results are compatible• No systematics found
QFTHEP-2011 44V.A.Duk, INR RAS
Main sources of systematics
• Fit (shape) systematics• bin size in cos histogram• x-stripe width (bin size in the final fit)• Cut on x (number of x-stripes in the final fit)• Cut on y in x-stripes (study in progress)
QFTHEP-2011 45V.A.Duk, INR RAS
Systematics of a cut on x
• Varying number of stripes in the final fit• Fitting dependency of |Uµh|2 on x• slope multiplied by stripe width gives error
estimation• εsyst < 0.2 εstat
QFTHEP-2011 46V.A.Duk, INR RAS
x-stripe number
|Uµh|2
Setting UL on |Uµh|2
QFTHEP-2011 47V.A.Duk, INR RAS
upper line – total errorbottom line – statistical error only
τ=10-11 τ=10-10
τ=10-9
UL (95% C.L.) UL (95% C.L.) UL (95% C.L.)
mνh, MeV mνh, MeV mνh, MeV
Comparison with Gninenko’s prediction
QFTHEP-2011
blue stripe: predictions from LSND, KARMEN. MiniBoonE
Black line: ISTRA+ upper limit @ 95% C.L.
48V.A.Duk, INR RAS
mνh, MeVmνh, MeV mνh, MeV
|Uµh|2 |Uµh|2|Uµh|2
Preliminary results• |Uµh|2 < (4-6) x 10-5 (95% CL) for τ=10-9 sec• |Uµh|2 < (1-2) x 10-5 (95% CL) for τ=10-10 sec• |Uµh|2 < (1.5-2) x 10-5 (95% CL) for τ=10-11 sec
• More detailed scan of (m, τ) and study of systematics is in progress
QFTHEP-2011 49V.A.Duk, INR RAS
conclusions Heavy sterile neutrino νh is proposed for LSND/KARMEN/MiniBoone anomaly
explanation:
40 MeV < m(νh) < 80 MeV, 10-11 sec < τ(νh) < 10-9 sec, 10-3 < |Uμh|2 < 10-2
νh can be effectively searched for in kaon decay K→µνh (νh→νγ)
First preliminary limits on |Uµh|2 are obtained from K‾→ µ‾ ν γ decay at ISTRA+ setup:
|Uµh|2 < (4-6) x 10-5 (95% CL) for τ=10-9 sec |Uµh|2 < (1-2) x 10-5 (95% CL) for τ=10-10 sec |Uµh|2 < (1.5-2) x 10-5 (95% CL) for τ=10-11 sec
more detailed study is in progress
QFTHEP-2011 50V.A.Duk, INR RAS
QFTHEP-2011 51V.A.Duk, INR RAS
THANK YOU!
Back-up slides
QFTHEP-2011 52V.A.Duk, INR RAS
LSND: oscillation interpretation
QFTHEP-2011 53V.A.Duk, INR RAS
Neutrinos in LSND and KARMEN
QFTHEP-2011 54V.A.Duk, INR RAS
Full list of cuts
QFTHEP-2011 55V.A.Duk, INR RAS
General formula for decay rate
QFTHEP-2011 56V.A.Duk, INR RAS
Taken from: D.Gorbunov, M.Shaposhnikov. JHEP 0710:015,2007
(х, cosθμγ) correlations
QFTHEP-2011
τ=10-9 sec
τ=10-9 sec
τ=10-11 sec
τ=10-11 sec
m=40MeV m=40MeV
m=80MeV m=80MeV
Kπ2Kμ3 cos θ ~ 1/Eγ for large νh mass (similar to π0)
х
х
х
х
х
х
cosθμγ
cosθμγcosθμγ
cosθμγcosθμγ
cosθμγ
57V.A.Duk, INR RAS