1. 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)

2. Plan LSND/KARMEN/MiniBooNE anomaly and heavy sterile neutrino ν h Search for ν h in kaon decays ISTRA+ setup Event selection for K ‾ → µ ‾ ν γ Signal extraction Limits for |U µh | 2 Conclusions QFTHEP-20112V.A.Duk, INR RAS

3. 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

4. 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-20114V.A.Duk, INR RAS

5. Neutrino oscillations: LSND QFTHEP-20115V.A.Duk, INR RAS

6. Neutrino oscillations: KARMEN QFTHEP-20116V.A.Duk, INR RAS

7. Neutrino oscillations: MiniBooNE, neutrino mode QFTHEP-20117V.A.Duk, INR RAS

8. Neutrino oscillations: MiniBooNE, anineutrino mode QFTHEP-20118V.A.Duk, INR RAS Above 475 MeV: Event excess 475-1250 MeV: 20.9±14.0 475-3000 MeV: 24.7±18.0 Below 475 MeV: Event excess 200-475 MeV: 18.5±14.3

9. LSND/KARMEN/MiniBooNE anomalies: summary QFTHEP-20119V.A.Duk, INR RAS

10. Possible explanation of experimental results (S.Gninenko, INR RAS) QFTHEP-201110V.A.Duk, INR RAS Origin of excess

11. Possible explanation (S.N.Gninenko) New weakly interacting particle ν h : Produced in NC Mixing with ν μ ( must be in CC, e.g. kaon decays) or separate vertex (may be in NC only) Decays radiatively via μ tr QFTHEP-201111V.A.Duk, INR RAS

12. Properties of a new particle ν h m > 40 MeV: no event excess in KARMEN (threshold effect) m 80MeV τ(ν h ) > 10 -11 sec: from LEP constraints: BR(Z→νν h ) x BR(ν h → ν γ) < 2.7 x 10 -5 τ(ν h ) < 10 -9 sec: ν h ‘s decay within MiniBooNE detector volume 10 -3 < |U μh | 2 < 10 -2 : from event excess in MiniBooNE experiment QFTHEP-201112V.A.Duk, INR RAS

13. New weakly interacting particle ν h QFTHEP-2011 Decays mostly as ν h →νγ 40 MeV < m (ν h ) < 80 MeV 10 -3 < |U μh | 2 < 10 -2 10 -11 sec < τ(ν h ) < 10 -9 sec 13V.A.Duk, INR RAS

14. ν h : limits from pion and kaon decays QFTHEP-201114V.A.Duk, INR RAS Muon energy in 2-body kaon decay

15. Search for ν h in kaon decays QFTHEP-2011 K→μν h : peak in E μ (cms) background from K→μν μ insensitive to low masses of ν h because of resolution K→μν h, ν h →ν γ: peak in E μ (cms) signature the same as for K→ µ ν γ no background from K→μν μ sensitive to low masses of ν h secondary decay vertex Suitable for ISTRA+ Muon energy in 2-body kaon decay 15V.A.Duk, INR RAS

16. 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

17. 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 godoscope QFTHEP-2011 T 0 =S1. S2. S3. S4. C0. C1. C2. S5 (prescaled by a factor of ~10) T 1 =T 0. (∑SP1 > MIP) 17V.A.Duk, INR RAS

18. 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 godoscope QFTHEP-2011 T 0 =S1. S2. S3. S4. C0. C1. C2. S5 (prescaled by a factor of ~10) T 1 =T 0. (∑SP1 > MIP) 18V.A.Duk, INR RAS

19. 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 godoscope QFTHEP-2011 T 0 =S1. S2. S3. S4. C0. C1. C2. S5 (prescaled by a factor of ~10) T 1 =T 0. (∑SP1 > MIP) vacuum He 19V.A.Duk, INR RAS

20. 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 godoscope QFTHEP-2011 T 0 =S1. S2. S3. S4. C0. C1. C2. S5 (prescaled by a factor of ~10) T 1 =T 0. (∑SP1 > MIP) 20V.A.Duk, INR RAS

21. 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 godoscope QFTHEP-2011 T 0 =S1. S2. S3. S4. C0. C1. C2. S5 (prescaled by a factor of ~10) T 1 =T 0. (∑SP1 > MIP) 21V.A.Duk, INR RAS

22. K→µν h (ν h →νγ) event reconstruction: primary and secondary vertex for signal QFTHEP-2011 K K μ μ νμνμ ν γ γνhνh A A B B P γ calculated using A, B P γ calculated using A, B: additional energy smearing E νh ~ 240 MeV, m νh ~ 40–80 MeV smearing not crucial 22V.A.Duk, INR RAS

23. K→µν h (ν h →νγ): primary and secondary vertices QFTHEP-2011 Z νh - Z K (Z νh – Z K )/(Z ECAL – Z K ) τ =10 -11 sec τ =10 -10 sec τ =10 -9 sec τ =10 -10 sec τ =10 -11 sec dz, cm 23V.A.Duk, INR RAS

24. K→µν h (ν h →νγ): E γ smearing QFTHEP-2011 τ=10 -11 secτ=10 -10 secτ=10 -9 sec dE, GeV dE = E true - E measured 24V.A.Duk, INR RAS

25. K→µν h (ν h →νγ): kinematics in kaon rest frame QFTHEP-2011 νhνh ν γ μ E νh ~ 240 MeV, m νh ~ 40–80 MeV E γ > 50 MeV kaon decay vertex P γ : kaon rest frame P* γ : ν h rest frame θ – (γ-ν h ) angle cos θ μγ ~ (-1) peak sharper for smaller m h 25V.A.Duk, INR RAS * general case assumed isotropic *

26. K→µν h (ν h →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-201126V.A.Duk, INR RAS

27. K→µνγ : decay rate and kinematical variables QFTHEP-2011 Kinematical variables: x=2*E γ (cms)/M k y=2*E µ (cms)/M k 3 main terms: IB – dominant SD±, INT± - most interesting (→ F v, F A ) x y IB Dalits-plot 27V.A.Duk, INR RAS

28. K→µν h (ν h →νγ): background rejection and signal observation Main background: K→ µ ν γ (Kµ2γ) K→ µ ν π 0 (Kµ3) with 1 gamma lost (from π 0 →γγ) K→ π π 0 (Kπ2) with 1 gamma lost (from π 0 →γγ) and π misidentification Signal observation: peaks in y and cos θ μγ where θ μγ is the angle between p µ and p γ in kaon rest frame. θ μγ peaks at (-1) for signal Background rejection procedure: scanning over (y, x) Dalits-plot and looking for a peak in cos θ μγ QFTHEP-201128V.A.Duk, INR RAS

29. K→µν h (ν h →νγ): (y, x) Dalits plot QFTHEP-2011 Kµ2γ (MC) Kµ3 (MC) Kπ2 (MC) X X X Y signal (MC) X Y 29V.A.Duk, INR RAS data X X Y YY main background: Kπ2

30. K→µν h (ν h →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 θ μγ is done in x-stripes QFTHEP-2011 X y signal (MC) 7 x-stripes selected for further analysis in the following region: 1 < y < 1.2 0.2 < x < 0.55 30V.A.Duk, INR RAS

31. Possible signature for ν h in x-stripes; |U µh | 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 θ µγ Y Y Y 31V.A.Duk, INR RAS magenta: signal green: K→µνγ blue: Kμ3 red: Kπ2 peak sharper for large x

32. Possible signature for different masses of ν h ; |U µh | 2 =0.01, τ =10 -10 sec QFTHEP-2011 m=80 MeVm=60 MeV m=40 MeV cos θ µγ 32V.A.Duk, INR RAS peak sharper for small m h

33. Possible signature for different lifetimes of ν h ; |U µh | 2 =0.01, m=60 MeV QFTHEP-2011 τ =10 -9 sec τ =10 -10 sec τ =10 -11 sec cos θ µγ 33V.A.Duk, INR RAS peak sharper for large τ h

34. Signal efficiency QFTHEP-2011 m h τ(lab) because of Lorentz boost low efficiency for small m h 2 effects m h 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 m νh, MeV

35. K→µν h (ν h →νγ): simultaneous fit in x-stripes QFTHEP-2011 fitting cos θ μγ 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 θ µγ Y

36. |U µh | 2 calculation BR(ν h ) measured from BR(ν h )/BR(Kμ2γ) BR(Kμ2) taken from PDG BR(Kμ2γ) taken from theory f(m h ) contains chirality flip and phase space factors QFTHEP-2011 blue (chirality flip): 1+(m h /m μ ) 2 red (total): f(m h, m μ ) f(m h, m µ ) f = 1.1 – 1.5 m νh, GeV 36V.A.Duk, INR RAS

37. |U µh | 2 calculation |U µh | 2 is calculated for each x-stripe N exp (ν h )/ N mc (ν h ) obtained from simultaneous fit Values |U µh | 2 for x-stripes are averaged Upper limit is set for averaged |U µh | 2 QFTHEP-201137V.A.Duk, INR RAS

38. Averaging |U µh | 2 QFTHEP-2011 |U µh | 2 = (6.6 ± 3.9)*10 -6 m=50 MeV, τ =10 -10 sec X |U µh | 2 38V.A.Duk, INR RAS |U µh | 2 X 1σ interval

39. |U µh | 2 for τ=10 -9, 10 -10 and 10 -11 sec QFTHEP-201139V.A.Duk, INR RAS |U µh | 2 m νh, MeV τ=10 -9 τ=10 -10 τ=10 -11 effect does not exceed 2σ

40. 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-201140V.A.Duk, INR RAS

41. 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-201141V.A.Duk, INR RAS

42. Fit (shape) systematics MC shape is not perfect Errors of simultaneous fit scaled to χ 2 =1 New |U µh | 2 has larger error Additional error is treated as shape systematics Dominant source QFTHEP-201142V.A.Duk, INR RAS m = 80 MeV τ = 10 -10 sec x |U µh | 2 |U µh | 2 = (0.9 ± 0.5)*10 -5 |U µh | 2 = (0.7 ± 0.8)*10 -5 |U µh | 2 x

43. 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-201143V.A.Duk, INR RAS

44. 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-201144V.A.Duk, INR RAS

45. 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-201145V.A.Duk, INR RAS

46. Systematics of a cut on x Varying number of stripes in the final fit Fitting dependency of |U µh | 2 on x slope multiplied by stripe width gives error estimation ε syst < 0.2 ε stat QFTHEP-201146V.A.Duk, INR RAS x-stripe number |U µh | 2

47. Setting UL on |U µh | 2 QFTHEP-201147V.A.Duk, INR RAS upper line – total error bottom line – statistical error only τ=10 -11 τ=10 -10 τ=10 -9 UL (95% C.L.) m νh, MeV

48. 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 m νh, MeV |U µh | 2

49. Preliminary results |U µh | 2 < (4-6) x 10 -5 (95% CL) for τ=10 -9 sec |U µh | 2 < (1-2) x 10 -5 (95% CL) for τ=10 -10 sec |U µh | 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-201149V.A.Duk, INR RAS

50. conclusions Heavy sterile neutrino ν h is proposed for LSND/KARMEN/MiniBoone anomaly explanation: 40 MeV < m(ν h ) < 80 MeV, 10 -11 sec < τ(ν h ) < 10 -9 sec, 10 -3 < |U μh | 2 < 10 -2 ν h can be effectively searched for in kaon decay K→µν h (ν h →νγ) First preliminary limits on |U µh | 2 are obtained from K‾→ µ‾ ν γ decay at ISTRA+ setup: |U µh | 2 < (4-6) x 10 -5 (95% CL) for τ=10 -9 sec |U µh | 2 < (1-2) x 10 -5 (95% CL) for τ=10 -10 sec |U µh | 2 < (1.5-2) x 10 -5 (95% CL) for τ=10 -11 sec more detailed study is in progress QFTHEP-201150V.A.Duk, INR RAS

51. QFTHEP-201151V.A.Duk, INR RAS THANK YOU!

52. Back-up slides QFTHEP-201152V.A.Duk, INR RAS

53. LSND: oscillation interpretation QFTHEP-201153V.A.Duk, INR RAS

54. Neutrinos in LSND and KARMEN QFTHEP-201154V.A.Duk, INR RAS

55. Full list of cuts QFTHEP-201155V.A.Duk, INR RAS

56. General formula for decay rate QFTHEP-201156V.A.Duk, INR RAS Taken from: D.Gorbunov, M.Shaposhnikov. JHEP 0710:015,2007

57. (х, cosθ μγ ) correlations QFTHEP-2011 τ=10 -9 sec τ=10 -11 sec m=40MeV m=80MeV Kπ2Kπ2Kμ3Kμ3 cos θ ~ 1/E γ for large ν h mass (similar to π 0 ) х х х х х х cosθ μγ 57V.A.Duk, INR RAS