Systematic uncertainties in long baseline neutrino oscillations for large θ 13

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1 Systematic uncertainties in long baseline neutrino oscillations for large θ 13 Pilar Coloma Center for Neutrino Physics at Virginia Tech Based on P. Coloma, P. Huber, J. Kopp and W. Winter, [hep-ph] Flux Measurement and Determination in the Intensity Frontier Era Neutrino Beams Pittsburgh PACC, Dec 8, 2012

2 Outline Introduction to precision in θ 13 and δ Introduction to the problem of systematics for large θ 13 Possible ways to reduce their impact Simulation details Results Comparison, key systematics, effect of luminosity

3 ( θ 13 ) ± [ Precision in θ 13 (1 Â)2 sin 2 ((1 Â) ) ] 1 θ 13 N ± neutrino/antineutrino

4 ( θ 13 ) ± [ Precision in θ 13 (1 Â)2 sin 2 ((1 Â) ) ] 1 θ 13 N ± Statistical limit: N ± N ± Systematics on the signal: θ 13 ( θ 13 ) ± const Background error: N ± N ± θ13 2 ( θ 13 ) ± θ 13 N ± const ( θ 13 ) ± 1/θ 13

5 Precision in θ 13 Statistical limit: θ 13 θ 13 1 θ 13 Systematics on the signal: 1σ (1 dof) 100 θ 13 θ 13 const Background error: θ 13 θ 13 1 θ 2 13 P. Coloma, A. Donini, E. Fernández-Martínez and P. Hernández, [hep-ph]

6 Precision in δ CPV discovery potential vs precision:

7 Precision in δ VACUUM ( δ) ± f [ ] equal nu and nubar events 1 sin( δ) less nubar than nu events on-peak off-peak 0 Π 2 Π 3 Π 2 0 Π 2 Π 3 Π 2 2 Π

8 Precision in δ VACUUM MATTER ( δ) ± f [ ] 1 sin( δ) ( δ) ± f[â, ] 1 ( ) sin  δ 1  on-peak vacuum off-peak matter 0 Π 2 Π 3 Π 2 0 Π 2 Π 3 Π 2

9 Precision in δ 1) Mild θ 13 dependence 2) Strong δ dependence for BB350 due to no disappearance data 3) CPV discovery potential related to precision around 0,π: more favorable for setups in vacuum and with similar number of nu/nubar events 1σ (1 dof) GLoBES Coloma, Donini, Fernández-Martínez, Hernández, [hep-ph]

10 The starting point NOvA+T2K+Daya Bay 1,2,3σ (2 dof) 1σ (1 dof) GLoBES 3.0 θ 13 =8.8 Huber, Lindner, Schwetz, Winter, [hep-ph] Coloma, Donini, Fernández-Martínez, Hernández, [hep-ph]

11 Impact of systematics Coloma, Fernández-Martínez, [hep-ph]

12 Impact of systematics Atmospheric Solar P Θ CP Interference L E km GeV Coloma, Fernández-Martínez, [hep-ph]

13 Impact of systematics Atmospheric Solar P Θ CP Interference L E km GeV Coloma, Fernández-Martínez, [hep-ph] Huber, Mezzetto, Schwetz, [hep-ph]

14 An example Possible ways to reduce the effect of systematics: 1) measure final flavor cross sections at a near detector. If this cannot be done, put constraints on ratios between cross sections for different flavors Day, McFarland, [hep-ph] (see also Debbie s talk) 2) measure intrinsic background at near detector 3) use data from disappearance channels at the far detector

15 An example µ e ν e ν µ FD: ν e ν µ

16 An example µ e ν e ν µ FD: ν e ν µ Mu- V far Matter Xsec

17 An example µ e ν e ν µ FD: ν e ν µ Mu- V far Matter Xsec ND: ν µ ν µ

18 An example µ e ν e ν µ FD: ν e ν µ Mu- V far Matter Xsec ND: ν µ ν µ Mu- V near Vac Xsec

19 An example µ e ν e ν µ FD: ν e ν µ Mu- V far Matter Xsec ND: ν µ ν µ ν µ ν µ Mu- V near Vac Xsec Mu+ V near Vac Xsec

20 An example µ e ν e ν µ FD: ν e ν µ Mu- V far Matter Xsec ND: ν µ ν µ ν µ ν µ Mu- V near Vac Xsec Mu+ V near Vac Xsec FD: ν µ ν µ ν µ ν µ

21 An example µ e ν e ν µ FD: ν e ν µ Mu- V far Matter Xsec ND: ν µ ν µ ν µ ν µ Mu- V near Vac Xsec Mu+ V near Vac Xsec FD: ν µ ν µ Mu- V far Matter Xsec ν µ ν µ Mu+ V far Matter Xsec

22 Simulation details (details in [hep-ph])

23 Simulation details (details in [hep-ph])

24 Simulation details theoretical constraint (details in [hep-ph])

25 Simulation details theoretical constraint (details in [hep-ph])

26 Simulation details χ 2 = r,i 2 (T r,i ( Θ, ξ) O r,i + O r,i ln + k ( ξk σ k ) 2 O r,i T r,i ( Θ, ξ) ) GLoBES software used A near detector has been explicitly simulated for all experiments Correlations are fully taken into account between different channels (unless otherwise stated) Systematic uncertainties introduced as nuisance parameters Marginalization performed over all parameters No degeneracies considered. Normal hierarchy assumed. sin 2 2θ 13 =0.1 hep-ph/ , hep-ph/

27 More simulation details No energy dependent effects included (nuclear effects, for instance) All errors included as norm errors. However, different independent errors considered for the different cross section regimes: effective shape error Near detector is assumed to be sufficiently far away so that the spectrum is identical to the far detector (1-2 km) Near and far detector are assumed to be identical (except for the treatment of NC backgrounds) No tau backgrounds are included (very little impact for CPV, though) see Zeller s and Morfin s talks Donini, Gomez Cadenas, Meloni, [hep-ph]

28 The setups

29 General comparison How far do we want to get? Fraction of CKM 2011 at 1Σ NF10 NF5 BB350 BBSPL WBB T2HK LBNE mini NOvA 2020 Fraction of CPV at 3Σ GLoBES GLoBES sin 2 2Θ 13 Coloma, Huber, Kopp, Winter, [hep-ph]

30 Sys and near detectors WBB no ND no ND,unc all off matter uncertainty off intrinsic background off RES cross section ratio off 2exposure Fraction of 0.5 Coloma, Huber, Kopp, Winter, [hep-ph] no ND no ND,unc LBNE mini all off matter uncertainty off intrinsic background off RES cross section ratio off 2exposure T2HK no ND no ND,unc all off QE cross section ratio off intrinsic background off 2exposure GLoBES 2012

31 Sys and near detectors no ND no ND,unc NF10 all off matter uncertainty off flux off Ν Μ DIS cross section off 2exposure Fraction of 0.5 Coloma, Huber, Kopp, Winter, [hep-ph] no ND no ND,unc no ND no ND,unc NF5 BBSPL all off SPL flux uncertainty off intrinsic background off QE cross section ratio off 2exposure all off matter uncertainty off fiducial mass off flux off 2exposure GLoBES

32 Exposure vs systematics Variation between optimistic and conservative assumptions: 100 at 1Σ Fraction of NF10 10 BB350 T2HK WBB 10 5 CKM GLoBES Coloma, Huber, Kopp, Winter, [hep-ph]

33 Exposure vs systematics Variation between optimistic and conservative assumptions: 100 at 1Σ Fraction of NF5 BBSPL NOΝA LBNE mini 10 Full LBNE 5 CKM GLoBES Coloma, Huber, Kopp, Winter, [hep-ph]

34 Conclusions The precision on θ 13 obtained at Daya Bay will most likely not be exceeded by any beam experiment. For δ the situation is more complicated, though: ideally, an experiment in vacuum would have the best reach for CPV; however, this is not optimal for precision... maybe a combination of the two? Low energy setups are generally more affected by systematics theoretical assumptions on cross section ratios are critical (Exception! BB+SPL)

35 Conclusions The impact of a ND does not seem so relevant if data from disappearance at the FD is used (under certain assumptions!) migration due to nuclear effects is not included if NP is present, a ND is crucial we assume only norm errors (an effective shape error is done for the xsecs only) effectiveness of this method depends on the statistics In some cases, it may a be better path to increase statistics than reduce systematics... LENF is the only facility able to achieve similar precision to quark sector

36 Backup

37 Impact of systematics Systematics become a problem for large q13 since the leading term in the probability grows quadratically P ± eµ = X ± sin 2 2θ 13 + Z + Y ± cos θ 13 sin 2θ 13 cos ( ±δ 31L 2 )

38 Impact of systematics Variation between optimistic and conservative assumptions: 1.0 at 1Σ 1.0 NF Fraction of BB350 Fraction of WBB Fraction of T2HK GLoBES Coloma, Huber, Kopp, Winter, [hep-ph]

39 Impact of systematics Variation between optimistic and conservative assumptions: 1.0 CPV at 3Σ NF Fraction of BB350 Fraction of WBB Fraction of T2HK sin 2 2Θ sin 2 2Θ 13 GLoBES sin 2 2Θ 13 Coloma, Huber, Kopp, Winter, [hep-ph]

40 Mass hierarchy Mass hierarchy may be obtained through: T2K+NOvA+INO [hep-ph] Atmospheric data at future exps [hep-ex] PINGU [hep-ph] Daya Bay II hep-ph/ combination of precise reactor+lbl data hep-ph/ or a combination of all of them!

41 Present oscillation facilities Discovery potential at the 90% CL Huber, Lindner, Schwetz, Winter, [hep-ph]

42 Present oscillation facilities T2K+NOvA+INO (50kt/100kt; low/high res) sin 2 2θ 13 =0.09 T2K+NOvA only Blennow, Schwetz, [hep-ph]

43 Previous hints on q13 θ 13 θ 13 Previous hints from global fits pointed to nonzero q13... Solar data KamLAND González-García, Maltoni,Salvado, [hep-ph]