Impact of systematic uncertainties on neutrino oscillation analysis

Transcript

1 Impact of systematic uncertainties on neutrino oscillation analysis Erica Vagnoni INFN & UNIVERSITÀ DEGLI STUDI ROMA TRE Dipartimento di Matematica e Fisica NuFact Quy Nhon, Vietnam August 2016 Phys.Rev. D92 (073014), A. M. Ankowski, O. Benhar, P. Coloma, P. Huber, C.-M. Jen, C. Mariani, D. Meloni, E.V. Phys.Rev. D92 (091301), A. M. Ankowski, P. Coloma, P. Huber, C. Mariani, E.V. Phys.Rev. D93 (113004), A. M. Ankowski, O. Benhar, C. Mariani, E.V Erica Vagnoni NuFact 2016 August / 16

2 Introduction Neutrinos are produced as tertiary decay products Neutrino has a low cross section ( cm 2 ) ν l + A l + X Neutrino cross section for 12 C as a nuclear target σ/eν (cm 2 /GeV) (a) 2 4 E ν (GeV) RFG SF NOMAD SciBooNE T2K on-axis T2K off-axis (b) 2 4 E ν (GeV) total DIS res 2p2h QE 6 8 Erica Vagnoni NuFact 2016 August / 16

3 The kinematic method The generic final state resulting from neutrino-nucleus scattering in charged current, can be described by a state of N nucleons and M mesons ν l (k ν ) + A(p) l (k l ) + N(p ) + M(h ) and the energy of the incoming neutrino can be reconstructed as E kin ν = W 2 m 2 l + 2(M ɛ n)e l (M ɛ n ) 2 2(M ɛ n E l + k l cos θ l ) The reaction mechanism is assumed to be quasi-elastic like (ν l (k ν ) + n(p) l (k l ) + p(p )) The struck nucleon is assumed to be at rest W 2 is assumed to be equal to M 2 for meson-less events and to M 2 otherwise Erica Vagnoni NuFact 2016 August / 16

4 2p 2h cross section uncertainties The contribution coming from multi-nucleon mechanism is not negligible To account for 2p 2h effects an effective approach has been suggested M A > 1.03GeV σ/eν (cm 2 /GeV) (a) T2K off-axis T2K on-axis SciBooNE NOMAD σ/eν (cm 2 /GeV) (b) genie+νt M A = 1.2 GeV E ν (GeV) E ν (GeV) 6 8 Erica Vagnoni NuFact 2016 August / 16

5 The calorimetric method The generic final state resulting from neutrino-nucleus scattering in charged current, can be described by a state of N nucleons and M mesons ν l (k ν ) + A(p) l (k l ) + N(p ) + M(h ) and the energy of the incoming neutrino can be reconstructed as E cal ν = ɛ n + E l + N (E pi M) + i M j E hj ɛ n = 34 MeV average single-nucleon separation-energy Note that mesons enter with the total energy, while for nucleons only the kinetic energy contribute Can be applied to any type of CC reactions Erica Vagnoni NuFact 2016 August / 16

6 The calorimetric method The generic final state resulting from neutrino-nucleus scattering in charged current, can be described by a state of N nucleons and M mesons ν l (k ν ) + A(p) l (k l ) + N(p ) + M(h ) and the energy of the incoming neutrino can be reconstructed as E cal ν = ɛ n + E l + N (E pi M) + i M j E hj HOWEVER an accurate reconstruction of hadrons poses a formidable experimental challenge Neutrons are likely to escape detection Any undetected meson results as an underestimation of neutrino energy of 135 MeV Erica Vagnoni NuFact 2016 August / 16

7 Energy contribution Energy contribution (%) 50 (a) (b) muon antineutrino muon neutrino 4 6 n p π ± π 0 8 For the calorimetric reconstruction it is important to estimate the energy contribution coming from different species of hadrons In QE range the contribution of protons (neutrons) is dominant for neutrinos (anti-neutrinos) In the region of resonant and non-resonant pion production, charged pions gives the largest contribution At E ν 1.5 GeV neutrons contribute less than 15% to the (anti)neutrino energy Eν (GeV) Erica Vagnoni NuFact 2016 August / 16

8 Energy reconstruction: Strategy Neutrino events are analyzed within two different assumptions Perfect reconstruction: with the exception of neutrons, all produced particles are observed, and their measured energies are equal to the true ones Erica Vagnoni NuFact 2016 August / 16

9 Energy reconstruction: Strategy Neutrino events are analyzed within two different assumptions Perfect reconstruction: with the exception of neutrons, all produced particles are observed, and their measured energies are equal to the true ones Realistic reconstruction: neutrons are assumed to escape detection and detector effects are taken into account the measured energies and angles are smeared with respect to the true ones by a finite detector resolution [ ( ) 1 f(x meas) = exp 1 2 ] (x meas x true) 2πσ(xtrue) 2 σ(x true) detection efficiencies (energy independent) and thresholds are taken into account Thresholds for mesons (20 MeV) and protons (40 MeV) Efficiencies for π 0 (60%), for other mesons (80%) and for protons (50%) Erica Vagnoni NuFact 2016 August / 16

10 Migration Matrices Define the probability that an event with a true neutrino energy in the bin j ends up being reconstructed in the energy bin i: M ij N(Ei rec, Ej true ) Detector effects affect the probability for a neutrino event to be reconstructed in the correct energy bin Finite energy resolutions smear the measured energies Imperfect efficiencies and finite thresholds result in an energy partially carried away by undetected particles PDF Erec,Etrue 1.45 GeV Calorimetric Method CCQE Ν Μ Perfect Rec. Realistic Rec. Gaussian Smear. PDF Erec,Etrue 3.45 GeV Calorimetric Method CCDIS Ν Μ Perfect Rec. Realistic Rec. Gaussian Smear E rec GeV E rec GeV Erica Vagnoni NuFact 2016 August / 16

11 Migration Matrices Define the probability that an event with a true neutrino energy in the bin j ends up being reconstructed in the energy bin i: M ij N(Ei rec, Ej true ) Detector effects affect the probability for a neutrino event to be reconstructed in the correct energy bin Finite energy resolutions smear the measured energies Imperfect efficiencies and finite thresholds result in an energy partially carried away by undetected particles Calorimetric Rec., Ν Μ E Ν DIS 1.0 Kinematic Rec., Ν Μ E Ν DIS E Ν 0.15EΝ E Ν 0.2EΝ 0.1 Σ GeV 0.6 Σ GeV QE 0.4 QE Etrue GeV Etrue GeV Erica Vagnoni NuFact 2016 August / 16

12 Oscillation analysis The extraction of the oscillation parameters is linked to the event rate N i β = E i ν + Eν E i ν de ν σ νβ (E ν ) P αβ ({Θ}, E ν )φ να (E ν ) the event rate distribution is affected by detector capabilities the true rate is generated including experimental features implemented in the construction of the migration matrices Ni true = M X ij Nj X X j where X describes the interaction channel the aim is to reproduce an event distribution obtainable with realistic experimental setup Erica Vagnoni NuFact 2016 August / 16

13 Oscillation analysis The extraction of the oscillation parameters is linked to the event rate N i β = E i ν + Eν E i ν de ν σ νβ (E ν ) P αβ ({Θ}, E ν )φ να (E ν ) the event rate distribution is affected by detector capabilities the fit is performed using a linear combination of the matrices obtained of the realistic and perfect reconstruction { } (1 α)m X,real ij + αm X,perf ij Nj X N fit i = X α is a purely phenomenological parameter j this phenomenological approach is useful to quantify the impact of the incorrect estimation of detectors effect on the oscillation analysis Erica Vagnoni NuFact 2016 August / 16

14 Oscillation analysis The oscillation analysis is performed in the disappearance channel ν µ ν µ, using the software GLoBES The χ 2 analysis is such that χ 2 ( m 2 31, θ 23 ) χ 2 ( m 2 31, θ 23 ) χ 2 best fit < 2.30 The pull method is used, with Gaussian priors for each systematic error a 20% bin-to-bin uncorrelated systematic uncertainty a 20% overall normalization uncertainty, which is bin-to-bin correlated A near detector is used The oscillation parameters used are m 2 21 m 2 31 θ 12 θ 23 θ 13 δ ev ev deg deg 8.5 deg Erica Vagnoni NuFact 2016 August / 16

15 Experimental setup Low energy setup (LE) with a narrow-band off-axis beam. The neutrino flux is peaked around 600 MeV with a baseline L = 295 km High energy setup (HE) with a broadband on-axis beam. The flux is peaked at 1 2 GeV and the baseline is L = 1000 km Φ ΝΜ arb. units LE setup, 295 km HE setup, 1000 km E Ν GeV Number of un-oscillated events in the energy window under study [0.3, 2] GeV for LE and [0.3,4] GeV HE QE 2p2h res DIS total LE 49% 28% 21% 2% 4891 HE 26% 11% 37% 26% 4456 Erica Vagnoni NuFact 2016 August / 16

16 Disappearance analysis: ν µ ν µ Results for the calorimetric method Erica Vagnoni NuFact 2016 August / 16

17 Disappearance analysis: ν µ ν µ Results for the kinematic method Erica Vagnoni NuFact 2016 August / 16

18 Appearance analysis We consider ν µ ν e & ν µ ν e A wide band neutrino beam is considered with L = 1300 km The background is smeared according to a Gaussian with σ(e ν ) = 0.15 E ν The signal efficiency is set to 80% Erica Vagnoni NuFact 2016 August / 16

19 Appearance analysis We consider ν µ ν e & ν µ ν e A wide band neutrino beam is considered with L = 1300 km The background is smeared according to a Gaussian with σ(e ν ) = 0.15 E ν The signal efficiency is set to 80% PDF Erec for Etrue 2.95 GeV DIS events Ν e The true rate is generated with realistic detector capabilities In the ideal case the neutrino energy would be smeared according to a Gaussian distribution E rec GeV σ(e ν ) = a + b E ν + ce ν Erica Vagnoni NuFact 2016 August / 16

20 Appearance analysis We consider ν µ ν e & ν µ ν e A wide band neutrino beam is considered with L = 1300 km The background is smeared according to a Gaussian with σ(e ν ) = 0.15 E ν The signal efficiency is set to 80% PDF Erec for Etrue 2.95 GeV DIS events Ν e E rec GeV The true rate is generated with realistic detector capabilities In the ideal case the neutrino energy would be smeared according to a Gaussian distribution The fit is performed using a linear combination of the above cases Erica Vagnoni NuFact 2016 August / 16

21 Appearance analysis N fit i = X N true i j = X j { (1 α)m X,real ij M X,real ij N X j } + αm X,gauss ij Nj X Erica Vagnoni NuFact 2016 August / 16

22 Appearance analysis N fit i = X N true i j = X j { (1 α)m X,real ij M X,real ij N X j } + αm X,gauss ij Nj X Calorimetric Method Realistic Resolution Correct Result Χ 2 bf dof Χ 2 bf dof Χ 2 bf dof Effects of the missing energy 90% α = % α = % α = Contours for Χ Wide Band Beam, L 1300 km of the missing energy correctly accounted for Θ 13 Erica Vagnoni NuFact 2016 August / 16

23 Effect of the 2p 2h cross-section uncertainties The analysis was aimed at quantifying the impact of the uncertainties of the neutrino - nucleus cross section in the 2p 2h sector Two different approaches have been considered: An effective approach using an increased value of the axial mass M A = 1.2 GeV 2p 2h events simulated using GENIE Erica Vagnoni NuFact 2016 August / 16

24 Effect of the 2p 2h cross-section uncertainties The analysis was aimed at quantifying the impact of the uncertainties of the neutrino - nucleus cross section in the 2p 2h sector Two different approaches have been considered: An effective approach using an increased value of the axial mass M A = 1.2 GeV 2p 2h events simulated using GENIE Erica Vagnoni NuFact 2016 August / 16

25 Conclusions Conclusions Two different energy reconstruction techniques have been used: the reconstruction based on the kinematics of the outgoing lepton and the one based the calorimetric method Detectors effects have been taken into account The impact of the nuclear model used for 2p 2h processes has been estimated Erica Vagnoni NuFact 2016 August / 16

26 Conclusions Conclusions Two different energy reconstruction techniques have been used: the reconstruction based on the kinematics of the outgoing lepton and the one based the calorimetric method Detectors effects have been taken into account The impact of the nuclear model used for 2p 2h processes has been estimated Bias in the extraction of oscillation parameters Effects of incorrect estimation of detector performances Effects of incorrect estimation of missing energy Effects of 2p 2h cross section uncertainties Erica Vagnoni NuFact 2016 August / 16

27 Backup Erica Vagnoni NuFact 2016 August / 8

28 Migration Matrices Define the probability that an event with a true neutrino energy in the bin j ends up being reconstructed in the energy bin i with events generated with GENIE M ij N(Ei rec, Ej true ) Calorimetric MM (QE) Kinematic MM (QE) [GeV] ν E rec [GeV] ν E rec ν E [GeV] true ν E [GeV] true 0 Erica Vagnoni NuFact 2016 August / 8

29 χ 2 analysis The χ 2 values, in the energy bin i and for the detector D is calculated as ( ) χ 2 O i,d i,d = 2 T i,d (θ, ξ) O i,d + O i,d ln. T i,d (θ, ξ) T i,d is the fitted rate T i,d = (1 + ξ φi + ξ n )N i (θ) ξ nuisance parameters N i(θ) is the event rate for a given energy bin computed with the test values θ O i,d is the effective observed rate and depends only on the oscillation values used as true input values { ( ) 2 ( ) 2 } χ 2 = min χ 2 ξ φi ξ n ξ i,d(θ, ξ) + + σ φ σ n i,d Erica Vagnoni NuFact 2016 August / 8

30 Gaussian Smearing The behavior of the standard deviation, as a function of true neutrino energy can be fitted with a given function. The fitting function chosen is σ(e ν ) = a + b E ν + ce ν, with a, b, c > 0, and the energy resolution R(E ν, E ) E ν E R(E ν, E 1 ) = σ(e ν ) 2π e 2σ 2 (E ν ). Erica Vagnoni NuFact 2016 August / 8

31 Gaussian Smearing Σ EΝ Σ EΝ EΝ EΝ 0.6 Real. setup QE E Ν GeV EΝ 0.6 Real. setup DIS E Ν GeV Σ EΝ Σ EΝ EΝ EΝ 0.6 Real. setup res E Ν GeV EΝ 0.6 Real. setup 2p2h E Ν GeV Erica Vagnoni NuFact 2016 August / 8

32 2p 2h uncertanties Discrepancies in neutrino energy reconstruction distribution at E ν = 0.6 GeV in the CCQE channel comparing muon neutrino and muon anti-neutrino 6 (a) genie+νt M A = 1.2 GeV 6 (b) D(E ν rec ) (1/GeV) 4 2 D(E ν rec ) (1/GeV) Eν rec (GeV) Eν rec (GeV) Erica Vagnoni NuFact 2016 August / 8

33 2p 2h uncertanties Discrepancies in neutrino energy reconstruction distribution at E ν = 0.6 GeV in the CCQE channel comparing muon neutrino and muon anti-neutrino 6 (a) genie+νt M A = 1.2 GeV 6 (b) D(E ν rec ) (1/GeV) 4 2 D(E ν rec ) (1/GeV) Eν rec (GeV) Eν rec (GeV) Erica Vagnoni NuFact 2016 August / 8

34 2p 2h uncertanties σ (cm 2 ) 1.6 (a) E ν (GeV) T2K off-axis T2K on-axis NOMAD MINERvA MiniBooNE MiniBooNE/ σ (cm 2 ) 1.2 (b) E ν (GeV) genie+νt M A = 1.2 GeV Erica Vagnoni NuFact 2016 August / 8

35 Erica Vagnoni NuFact 2016 August / 8