Study of invisible neutrino decay and oscillation in the presence of matter with a 50 kton magnetised iron detector

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1 Study of invisible neutrino decay and illation in the presence of matter with a kton magnetised iron detector S. Choubey a,b,c, S. Goswami d, C. Gupta b,d, Lakshmi.S.Mohan d, T. Thakore e a Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad, India b KTH Royal Institute of Technology, AlbaNova University Center, Stockholm, Sweden, c Homi Bhabha National Institute, Mumbai, India, d Physical Research Laboratory, Navrangpura, Ahmedabad, India e Louisiana State University, Baton Rouge, LA sandhya@hri.res.in,sruba@prl.res.in,chandang@prl.res.in, phipf@smail.iitm.ac.in,tarakstar@gmail.com The sensitivity to the invisible decay of the mass eigenstateν in the presence of Earth matter effects is studied. Only the charged current interactions of atmosphericν and ν for kton year exposure of a future magnetised iron detector at INO are analysed. The analysis with erved muon energy in the range would give a constraint ofτ /m >. s/ at % CL with this exposure. Hereτ is the lifetime andm is the mass ofν, when it is the heaviest. The effect of decay on the precision measurement of sin θ and m and neutrino mass hierarchy are also studied. Since the presence of decay affects the illation amplitude rather than its phase, it is seen that the precision on sin θ worsens whereas that on m is not much affected. Sensitivity to hierarchy also worsens slightly in the presence of the invisible decay of ν. PoS(NuFact) The th International Workshop on Neutrinos from Accelerators-NUFACT - September, Uppsala University, Uppsala, Sweden Speaker. Currently at Indian Institute of Technology Madras, Chennai c Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives. International License (CC BY-NC-ND.).

2 . Introduction Flavour illations of neutrinos have been established from the ervation of neutrino illations at various energies and baselines by different experiments over the world. Currently, the major open questions in neutrino illation physics are neutrino mass hierarchy, octant of the mixing angle θ and the value of the CP phase δ CP. The Iron Calorimeter () detector [, ] at the proposed India-based Neutrino Observatory (INO) is an atmospheric neutrino experiment aiming to study the illation parameters by probing the Earth matter effects on the propagation of atmospheric neutrinos. The main goal of is to determine neutrino mass hierarchy and to perform precision measurements on sin θ and m. New physics phenomena are expected to change the illation probabilities and will affect the number of erved events. Hence illation experiments can be used to study the sensitivity to the new physics parameter itself. The presence of the new physics parameter will also affect the determination of the standard illation parameters and thus creating new degeneracies. Here we investigate one such phenomenon namely the invisible decay of the mass eigen state ν while its travel from its production point to the detector. For this simulation study we have used charged current ν and ν events obtained with kton year exposure of INO to atmospheric neutrinos whose illation probabilities in matter are modified by the invisible decay model we consider. Here the mass eigen state ν is considered to decay invisibly via ν ν s + J, where J is a pseudo-scalar and ν s is a sterile neutrino; and illations in the presence of full -flavour matter. Since ν s does not mix with the three active neutrinos, the mixing matrix U in vacuum will be: c c s c s e iδ U = c s s s c e iδ c c s s s e iδ s c, (.) s s c s c e iδ s c c s s e iδ c c wherec ij = cosθ ij,s ij = sinθ ij ; θ ij are the mixing angles andδ is the CP violating phase. Three-flavour evolution equation in the presence of Earth matter, with invisible decay is: M = i d ν dt = ] [UM U +A CC ν, (.) E A cc m, and A CC =, (.) m iα PoS(NuFact) where E is the neutrino energy, α = m /τ is the decay constant in units of, m is the mass ofν andτ its rest frame life time. The conversion factor used to makeα to have the units of is/s =.. Matter potential is A cc = G F n e E =. ρ(gm/cc) E(G), (.) where,g F is the Fermi constant andn e is the electron number density in matter andρis the matter density. For anti-neutrinos, the sign of A cc and the phaseδ in Eq. (.) will be reversed.

3 . Why use an atmospheric neutrino experiment to probe α? Since the decay term appears in the illation probabilities in the form exp(αl/e), no decay corresponds to α =. The effect of α for various values of L/E are shown in Fig. ; here exp(αl/e) vs L/E is plotted for α =,, and. The values of α to which a given experiment spanning a specified L/E range is sensitive to, can be understood from here. The red (blue) shaded region in Fig. indicates the L/E range covered by the narrow band NOνA neutrino beam with L = km and E = G (atmospheric neutrinos at a baseline L = km and E =. G). It can be seen from the figure that NOνA s sensitivity is limited to larger values of α; i.e and for which the exponential terms shows substantial departure from the no decay value of exp(αl/e) =. Since atmospheric neutrino illation experiments span an L/E range of [., ] (km/g), they will be sensitive to a wider range of α from. Larger L/E values will be sensitive to smaller values of α and vice versa. Since INO is an atmospheric neutrino detector and has good exposure, it is well suited to probe a phenomenon like invisible neutrino decay. As seen from Fig. could be sensitive to even α of the order of. The sensitivity to low α values come from low energies, while the higher energies will help in ruling out the larger values of α. exp( αl/e) α = α = α = α = L/E (km/g) Figure : The value of exp(αl/e) as a function of L/E for different values of α - from left to right -,, and respectively. The red shaded region denotes thel/e range accessible with NOνA narrow band neutrino beam (E = G), the dashed blue shaded region indicates the range forl= km, when E is in the range. G. PoS(NuFact). Three flavour neutrino illation probabilities with α The three flavour illation probabilities in Earth matter, for a baseline of km in the presence of invisible decay are shown in Fig.. The values of parameters used to generate the illation probabilities are : δ CP = ; θ =. ; θ =,, ; θ =. ; m =. ( ); m =. ( ); α =,, ( ). Several things can be understood from the figure. For a given value ofθ,α = corresponds to the no decay case. The effect of decay is to reduce the illation probabilities at maxima

4 P P e E ν (G) E ν (G) P P e E ν (G) α =, θ = α =, θ = α =, θ = α =, θ = α =, θ = α =, θ = α =, θ = α =, θ = α =, θ = E ν (G) Figure : From left to right P matt, Pmatt, Pe matt and P matt for L = km and with different θ and α. NH is taken as the true hierarchy. and elevate at minima, thus causing a damping effect. When α is very large say, illations are completely washed out. The larger the value of α, the more the dampening will be. Also the effect is more at lower energies. Since the relative change in P (P e ) due to decay is more than that in P ( P e ), the contribution to the α sensitivity χ will be more from ν (ν ). But P and P being the dominant channels at, the major contribution to α sensitivity will come from ν events in the present study. Since the effect ofα is to alter the amplitude of the illations, it will affect the measurement of θ which also alters the illation amplitudes. This creates a degeneracy between α and θ. i.e, θ in the first octant combined with a larger (smaller) value of α can give a probability similar to that with θ in second octant + a smaller (larger) value of α for P and P (P e and P e ). This combined effect affects the sensitivity(discovery potential) to(of) α and the precision measurement onθ. PoS(NuFact). Sensitivity toα Sensitivity studies to α are done with ν and ν charged current events obtained with kton years exposure of INO. The details of the numerical simulations and χ analysis can be found in [, ]. Analyses with fixed parameters as well as marginalisation in the σ ranges of these parameters were performed. Since there is no real data, the data events are simulated with

5 Lakshmi.S.Mohan a true set of parameters and then fitted with theory events by varying the parameter values. For the sensitivity study of α, data was simulated with α = and is fitted with theory with different non-zero values of α. The number of illated events for different α =,,, in different bins ofe are shown in Fig.. No.of illated events, α =, α = h h h h h h Entries, α = Entries Mean... Mean.,.. α RMS... = RMS..., α =, α = =.. G cosθ No.of illated events, α = h h h h h ν h, α = Entries, α = Mean..... RMS ν......, α =, α =, α = =.. G cosθ No.of illated events, α, α ν h h h h h h, α = Entries Entries Entries Entries Mean Mean. Mean.,.. α = Mean.. RMS RMS. RMS... RMS., α. =, α = cosθ = =.. G = No.of illated events, α, α = h h h h ν h Entries, α h = Entries Mean... ν. Mean, α.. RMS =... RMS.., α =, α =.. G cosθ Figure : Oscillated ν and ν events for each E bin as a function of cosθ for α =, and. Only up-coming events (illated) are shown here. The sensitivity of kton year exposure of with NH (IH) as the true hierarchy is shown in Fig.. Previous analyses [, ] had obtained a bound of α <. (τ /m >. s/) at % C.L, with charged current and neutral current events. For true NH, analysis with charged current ν and ν events only give bounds of α <. (τ /m >. s/) at % CL with all parameters fixed. With marginalisation over θ,θ and m the limit at % CL is α <. (τ /m >. s/) for true NH. This is two orders of magnitude tighter than the bounds given by the previous MINOS and TK analyses [, ]. The results for true IH are similar, with % CL limits of α <. (τ /m >. s/) for fixed parameters andα <. (τ /m >. s/) with marginalisation. E =. G, NH, ktonyr, with decay in theory Fixed parameters α ( ) (test) E =. G, NH, ktonyr, with decay in theory Fixed parameters τ /m (s/) (test) E =. G, IH, ktonyr, with decay in theory Fixed parameter α ( ) (test) E = = =. G, IH, ktonyr, with decay in theory Fixed parameter τ /m (s/) (test) PoS(NuFact) Figure : Expected sensitivity of to neutrino decay with true NH (first and second from the left) and true IH (third and fourth from the left). The expected χ is shown as a function of α (test) (panels and ) and τ /m (test) (s/) (panels and ) with kton-yr exposure of.. Precision measurement of sin θ and m in the presence of decay The effect of the presence of invisible decay on the precision measurement of sin θ and m is also studied. Since decay affects the amplitude of illations, it is expected that the

6 Lakshmi.S.Mohan precision measurement on θ will be affected. For these analyses, both data and theory are simulated with decay. The value of α is taken as in data and kept at this value in theory for fixed parameter analysis and varied in the range[. ] for marginalised analysis. The comparison with no decay case is also made. The results are shown in Fig.. E =. G, ktonyr, NH, fixed parameters Oscillation only Invisible decay + illation, decay in data and theory sin θ E =. G, ktonyr, NH, marginalised, decay in data and theory Oscillation only, α = Invisible decay + illation, α = sin θ m ( ) E =. G, ktonyr, NH, fixed parameters Oscillation only Invisible decay + illation, with decay in data and theory E =. G, ktonyr, marginalised Oscillation only Invisible decay + illation, with decay in data and theory m ( ) Figure : From left to right : Precision on sin θ (left-set) and m (right-set) in the presence and absence of invisible decay for fixed parameters and with marginalisation. The value of decay parameter α in data is taken to be. For the fixed parameter case eventhough the relative σ precision on sin θ with α = and are similar,.% for the former and.% for the latter, the parameter space shifts to the higher sin θ side in the with decay case. This can be understood from Fig.. No.of illated events Oscillated events: E =.. G, h h, θ Entries h h h h = Entries Entries Mean ν, θ..... = Mean. RMS.. RMS RMS ν...., θ = E (G) α =, θ =, θ =, θ = No.of illated events Oscillated events: E =.. G,, θ h h h = h h Entries Entries Entries h, θ = Mean Mean... Entries Mean.. RMS RMS... Mean RMS.., θ =. RMS., θ = E (G) α =., θ =, θ = PoS(NuFact) Figure : Oscillated ν events as a function of E for (left) α = and (right) α = for θ =, and. When there is decay, the difference between the events with θ in the first octant and those with θ = is more than that with θ in the second octant and those with θ =. This causes the parameter space to shift towards the higher θ side. When marginalisation is done, the precision without and with decay are.% and.% respectively. Hereα can be varied in theory to match the theory events with the data generated with true θ =. The precision on m remains the same both in the absence and presence of invisible decay. For fixed parameters the relative σ on m is.% whereas with marginalisation it is.%.

7 . Conclusions The sensitivity to invisible neutrino decay with kton year exposure of is studied. The analysis with only charged current ν and ν events give a bound of α <. (α <. ) at % CL for fixed parameters (marginalised case), assuming true NH. This is two orders of magnitude tighter than the bounds on α given by the previous analyses with charged and neutral current events. This means that if we include the analysis of neutral current events also, should be able to put an even better bound on α. The effect of the presence of decay on the precision of sin θ and m was also studied; it was found that the precision on sin θ worsens in the presence of invisible decay since it is related to the amplitude of illations which the decay also affects. Acknowledgments Prof. Amol Dighe, Prof. D. Indumathi, Prof. S. Uma Sankar and Prof. Jim Libby. LSM acknowledges Nandadevi and Satpura clusters, part of IMSc, Chennai computing facility and thanks the organisers of NUFACT, Anushree Ghosh, Monojit Ghosh and Sushant Raut. References [] Kumar, A., Vinod Kumar, A.M., Jash, A.et. al., Invited review: Physics potential of the detector at the India-based Neutrino Observatory (INO), Pramana - J Phys : (). [] M. S. Athar et al., India-based Neutrino Observatory: Project Report. Volume I., INO-- (). [] S. Choubey, S. Goswami, C. Gupta, S. M. Lakshmi and T. Thakore, Sensitivity to neutrino decay with atmospheric neutrinos at INO, (), arxiv:hep-ph/.. [] Lakshmi. S. Mohan, D. Indumathi, Pinning down neutrino illation parameters in the sector with a magnetised atmospheric neutrino detector: a new study, Eur. Phys. J. C, (), arxiv:hep-ph/.. [] R. A. Gomes, A. L. G. Gomes, O. L. G. Peres, Constraints on neutrino decay lifetime using long-baseline charged and neutral current data, Physics Letters B (). [] M. C. Gonzalez-Garcia, Michele Maltoni, Status of illation plus decay of atmospheric and long-baseline neutrinos, Physics Letters B, - (), arxiv:hep-ph/.. PoS(NuFact)