Neutrino Decoherence Phys. Rev. Lett. 118, 221801 (2017) Joo Coelho - PowerPoint PPT Presentation

Nonmaximal θ 23 Mixing at NOvA from Neutrino Decoherence Phys. Rev. Lett. 118, 221801 (2017) João Coelho APC Laboratory 22 June 2017 22 Jun 2017 1

Quantum System      U U    1 1 2 2      U U    1 1 2 2 2 2      * * P U U U U        1 1 2 2 2 2 2 2     * * * * P U U U U U U U U U U U U              1 1 2 2 1 1 2 2 2 2 1 1 Classical Quantum Probability Interference 22 Jun 2017 2

Decoherence          U U    1 1 2 2 Entanglement         , U U    1 1 1 2 2 2 Measurement coupled      , U   to environment i i i i 2 2 2 2             * * , , , , P U U U U          1 2 1 1 2 2 2 2 2 2   U U U U     1 1 2 2 Only Classical Probability 22 Jun 2017 3

Density Matrix • Better framework to describe loss of coherence      U U    1 1 2 2      U U    1 1 2 2 Classical   2 * | | U U U   Terms         1 1 2      * 2  | |  U U U    Quantum 2 1 2 Terms     P     Unitary Evolution (Shcroedinger) 22 Jun 2017 4

Modeling Decoherence • What causes decoherence? • Coupling to an environment • Neutrino interactions with matter? • Vacuum fluctuation? (Quantum Gravity) • Very model dependent! • Phenomenological approach: Unitary Non-Unitary Lindblad Equation: Most general Markovian evolution that preserves probabilities even in the environment system 22 Jun 2017 5

Neutrino Oscillations • Neutrinos are created in a superposition of mass states • Time evolution generates flavour oscillations Simple QM     U   i i i   2        iHt P e      2 m L    . ~ . ~ H t E L 2 E 22 Jun 2017 6

Neutrino Decoherence • Interaction with some environment → Mixed states • Time evolution given by Lindblad equation Open QM  Complete Positivity  Trace Preserving  Increasing Entropy  Energy Conserving 22 Jun 2017 7

Effect On Disappearance 22 Jun 2017 8

Nonmaximal Mixing? • NOvA sees nonmaximal mixing with 2.6 sigma • All others are consistent with maximal • T2K especially is in mild tension with NOvA 22 Jun 2017 9

3x3 Systems • Neutrinos come in 3 flavours • Hilbert space can be describe by SU(3) • Expand all operators in generators of SU(3) (Gell-Mann Matrices) Operators as sum SU(3) of generators Simple block-diagonal form System of 9 coupled equations 22 Jun 2017 10

3x3 Systems • Neutrinos come in 3 flavours • Hilbert space can be describe by SU(3) • Expand all operators in generators of SU(3) (Gell-Mann Matrices) In general* 36 parameters! Operators as sum SU(3) of generators Diagonal w/ energy conserv. System of 9 coupled equations 22 Jun 2017 11 † = A j ) *But already assuming increasing entropy (A j

3  Formulas q 23 ORCA JUNO q 12 DUNE q 13 NOvA T2K 22 Jun 2017 12

G 21 Constraints Solar scale oscillations strongly constrain G 21 • Under our assumptions, this implies G 31 ≈ G 32 = G • G 21 < 5.5×10 -25 GeV at 90% C.L. 22 Jun 2017 13

Mimicking Nonmaximal Mixing NOvA 22 Jun 2017 14

Mimicking Nonmaximal Mixing Given G -1 ~ 8600 km Solve 22 Jun 2017 15

Global Fit • Current LBL global fit agrees with NOvA-only prediction  MINOS: Neutrino 2012 talk*  NOvA: PRL 118, 151802 (2017)  T2K: arXiv:1704.06409 [hep-ex] * No new MINOS result has LBL-only values that would be relevant to this analysis 22 Jun 2017 16

Global Fit • Current LBL global fit agrees with NOvA-only prediction • Still weak preference for nonzero decoherence  MINOS: Neutrino 2012 talk*  NOvA: PRL 118, 151802 (2017)  T2K: arXiv:1704.06409 [hep-ex] * No new MINOS result has LBL-only values that would be relevant to this analysis 22 Jun 2017 17

What About Super-K? • Not a lot has been published since early 2000’s Strongest limits we found: G < 3.5 x 10 -23 GeV at 90% CL • • Effect mostly on up-going muon neutrinos  Lisi et al.: PRL 85, 1166 (2000) 22 Jun 2017 18

What About MINOS at HE? • Not a lot of power from MINOS so far, but UNICAMP Group published some positive results in 2014…  Oliveira et al. : PRD 89, 053002 (2014) 22 Jun 2017 19

However… • Strong matter effects may not be trivial to understand • Oliveira’s paper shows some funky behaviour at the reso- nance for some decoherence models • Important questions on usual assumptions of energy con- servation, especially with res- pect to the underlying mech- anism for decoherence • Mass Hierarchy may also play a very important role  22 Jun 2017 20 R. Oliveira: EPJC 76, 417 (2016)

Energy Conservation • Simple constraint equation: • But which H is conserved? – Vacuum? Decoherence is due to neutrino mass measurement (QG-like) – Matter? Decoherence is due to effective neutrino energy (EW-like) • In the paper we assume the latter, but effect is small so both scenarios are reasonably described • Important consequences when matter effects are large 22 Jun 2017 21

Summary • NOvA’s new results indicate some tension in LBL exps • Could this be a sign of decoherence? • Our paper shows there’s still room for speculation • New analyses of existing data at higher energies needed • More studies of relationship with matter effects are likely to be required before looking at atmospheric neutrinos • Read our paper at: PRL 118, 221801 (2017) or https://arxiv.org/abs/1702.04738 22 Jun 2017 22

Thank you! João Coelho Tony Mann Saqib Bashar 22 Jun 2017 23

Cauchy-Schwarz G ij are not independent • • Related by Cauchy-Schwarz inequalities = Any permutation of G   G  G 0 21 31 32 22 Jun 2017 24

Matter Effects V H 0 22 Jun 2017 25

Matter Effects w/o Deco. H eff = H 0 + V  H eff = H 0 - V  22 Jun 2017 26

Matter Effects w/ Deco. H eff = H 0 + V  H eff = H 0 - V  22 Jun 2017 27

Matter Effects 22 Jun 2017 28

Resonances q 23 21 cos2 q 12 31 cos2 q 13 q 12  m 2 q 13  m 2 22 Jun 2017 29

Resonances q 23 NH q 12 q 13 IH 22 Jun 2017 30

Resonances q 23 ORCA JUNO ARCA q 12 DUNE q 13 NOvA T2K 22 Jun 2017 31

Resonance Formulas Depends on sign of  m 2 31 (MH) 22 Jun 2017 32