DYNAMICAL PION COLLAPSE THE COHERENCE OF NEUTRINO BEAMS
DYNAMICAL PION COLLAPSE & THE COHERENCE OF NEUTRINO BEAMS Talk at Pheno 2015, Pittsburgh, PA Benjamin J. P. Jones, MIT 1
PLANE-WAVE PICTURE Here is a neutrino oscillation according to the “standard” plane-wave picture, in mass and flavor spaces: Source Osc Max Re(ψ) m 1 m 2 P(f) μ e 2
PROPAGATION WITH WAVEPACKETS We know that really its not a plane wave. Wave-packets can separate. After that, system is incoherent (no L or E depedence) Source Osc Max Re(ψ) m 1 m 2 P(f) μ e Kicks in sooner with big Δm 2 or small packet width 3
IS THIS IMPORTANT? Could this affect standard or sterile neutrino phenomenology? To find out, We need to know the speed of separation (easy), and the wave-packet width (not so easy) 4
EXTERNAL WAVE-PACKET PICTURE Important progress was made by Beuthe, Akmedov +Smirnov : They calculated neutrino state emerging from a pion of a specified width, alongside a specified detected muon Input ? ν π Decay Lagrangian But … now two unknown states, rather than one! μ Output Input Specified final state Beuthe arxiv: 0109119 5 Akhmedov + Smirnov
WIDTH OF THE INCOMING PION? Input π The usual approach: Wave our hands and make something up! The width of the incoming pion wave-packet “must” be: 1. The inverse of its mass width 2. The mean-free path between collisions 3. Something to do with its form factor / physical size 4. The length of the decay pipe 5. Very small / big / … something? It can be calculated without hand-waving / arbitrary scale assumptions, and it turns out that none of the above are the correct answer: Phys. Rev. D 91 (2015) 5, 053002 [B. J. P. J. ] 6
FIRST, TRANSLATE INTO THE DENSITY MATRIX PICTURE. Start with some pion density matrix: And let it decay: 7
REDUCING, TRACING, MEASURING…. Density matrix for entangled muon-neutrino system emerging from general pion state ρπ Tracing out the muon and apply a flavor measurement operator at baseline L: 8
l ca x 2 m tu cl a an ss i qu THE OSCILLATION PROBABILITY To get an idea of the phenomenology, substitute a representative pion density matrix with Gaussian on and off diagonal position widths: Standard oscillation Classical coherence condition Know location of source to within 1 osc length x 1 Quantum coherence condition Need WP’s not to separate 9
LOCALIZATION BY SCATTERING What is the coherent pion width? E 0 E 2 π ψ E 3 E 4 E 1 Repeated bombardment of scatterers encodes information about the pion into the environment. Coherence of neutrino emission from spatial parts of the WF is then suppressed by environmental entanglements. Basic principle of environmentally induced decoherence (used in quantum computing, x With environmental entanglement the pion has both a total width and a coherent width 10
OPEN QUANTUM SYSTEMS E 0 cl as s m tu an qu ic al Under some loose assumptions, we can describe what happens to the pion reduced density matrix without considering the full system DM π FT of mom transfer prob 11 dist
OPEN QUANTUM SYSTEMS Between scatters the state evolves according to the free Schrodinger equation This leads to dispersion (broadening) of both coherent and incoherent widths cl as s m tu an qu ic al T=0 T=1 T=2
COHERENCE LENGTHS Competition of unitary evolution and collapse define a stable coherent width: Tegmark, arxiv: 9310032 To calculate this width for a relativistic pion, we need: 1) Scattering momentum transfer probability distribution + rate 2) Method of calculating convergent width in a relativistic 13
MOMENTUM TRANSFERS PAI Model: Semi-classical model – consider energy losses in a continuum with some complex refractive index and re-interpret in terms of photon exchanges with electrons Derived from photoionization cross section, in a somewhat complicated way We need photoionization spectrum of beam-pipe gas as input: Allison and Cobb, Ann. Rev. Nucl. Part. Sci 1980. 30: 253 -98 Measured drift chamber fluctuations Photoioniziation input Corrected Landau PAI model 14
PAI SANITY CHECK My PAI model implementation Standard plot of energy losses from the PDG 15
THE DECOHERENCE FUNCTION e ps la ol C ay w is th 16
SIMULATING DYNAMICAL COLLAPSE These ingredients are used to construct a dynamical wave-function collapse MC simulation of the pion evolution: Start with very narrow pure state density matrix No longer fits on grid, simulation halts Time evolve / scatter / evolve / scatter… 17
SIMULATING DYNAMICAL COLLAPSE Equilibrium Collapse winning Dispersion winning (note timescale for collapse) 18
COLLAPSED WIDTHS Map out collapsed widths as a function of incoming pion momentum And substitute into fancy oscillation formula to find coherence loss distance Standard oscillation Classical coherence condition Quantum coherence condition 19
DRUMROLL PLEASE! 20
CONCLUSION There will be no coherence loss effects for active neutrinos from accelerator neutrino beams anywhere on Earth There may be coherence loss effects for heavy sterile neutrinos, but not observable in SBN experiments Previous analyses and sensitivities are meaningful (phew!) This work demonstrates a rigorous prediction of when neutrinos become incoherent, using a new approach: the open quantum system picture of neutrino beams There are other neutrino sources where the effects are still unknown : reactors, decay-at-rest, etc. Those sound like fun to think about next! 21
BACKUPS 22
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PROPAGATION WITH WAVEPACKETS No process can make a neutrino of perfectly defined momentum. Source makes a wave-packet with some momentum and some position width Source Osc Max Re(ψ) m 1 m 2 P(f) μ e Phase velocity is not affected – so neither is oscillation length 26
COHERENCE LENGTHS Competition of unitary evolution and collapse to define a stable width: Calculated analytically by solving a master equation: Tegmark, arxiv: 9310032 27
YOUNGS TWO-SLIT EXPERIMENT A source Interference pattern: screen slits B
YOUNGS TWO-SLIT EXPERIMENT What if we add an environment? A E 0 B E 0 screen slits source
YOUNGS TWO-SLIT EXPERIMENT Switch on the coupling. A The particle becomes entangled with the environment via its interactions EA ? source EB screen slits B The interference pattern now depends on how much overlap there is between EA, EB
YOUNGS TWO-SLIT EXPERIMENT Extreme cases : A EA Fully quantummechanical-looking particles source EB screen slits B
YOUNGS TWO-SLIT EXPERIMENT Extreme cases : A EA Fully classical-looking particles source EB screen slits B Diverging entanglements with the environment make quantum-looking systems into classical-looking ones
SEEING DECOHERENCE IN PRACTICE e. g. Talbot Lau interferometry with C 70 fullerenes 33
Environmental gasses are bled into the vacuum chamber. These cause scattering interactions. Entanglements generated with the environment encode “which way” information and suppress coherent superpositions. 3*10 -8 mbar 5*10 -7 mbar Ar Prediction from decoherence theory 34
POSITION STATES OF A PARTICLE Now consider a superposition of two particle position states, talking to an environment, which is “measuring” them with some resolution. E 0 Time P A P B E 0 P A EB P A Time P B EA Widely separated P B EA~EB P A P B Narrowly separated 35
POSITION STATES OF A PARTICLE The particle (in superposition of positions) emits a neutrino. Will the neutrino state from each emitter add coherently or incoherently? ν E 0 Time P A P B E 0 P A EA Widely separated EB P A Time P B ν P B EA~EB P A Narrowly separated P B ν ν 36
POSITION STATES OF A PARTICLE E 0 Time P A P B E 0 P A EB P A Time P B EA Widely separated P B EA~EB P A P B Narrowly separated 37
The existence of the muon is very important. It is a part of the final state. Only neutrino trajectories which “go with the same muon” can interfere coherently. Once the muon leaves the interaction point, its role in the process is complete. Its subsequent interactions / measurement cannot affect neutrino oscillation phenomenology (see: causality) This is a consequence of unitarily, and an exact Appendix 1 of theofpaper givesthought a very general analogue the EPR experiment. Unitary evolution means that the neutrino doesn’t care! THE ROLE OF THE MUON μ Freedom! ν μ Interaction ν μ Detector ν See also: Glashow Kayser 0810. 4602 38 1110. 3047
KINEMATICS Oscillations require i≠j terms to be non-zero. Can only happen if the pion density matrix is coherently wide enough (δ): How should we understand δ? pμ pπ δ pμ pπ+2δij pν, mi pν, mj 39
NOW WITH NEUTRINO MASSES: Build total density matrix for muon-neutrino system emerging from general pion state ρπ Trace out the muon to get neutrino reduced DM: Use it for oscillation physics: 40 Section 2 of paper
CHANGING DECAY ENVIRONMENT 41
- Slides: 41