DYNAMICAL PION COLLAPSE &

THE COHERENCE OF NEUTRINO BEAMS

Benjamin J. P. Jones, MIT

Talk at Pheno2015, Pittsburgh, PA

1

2

Here is a neutrino oscillation according to the “standard” plane-wave picture, in mass and flavor spaces:

PLANE-WAVE PICTURE

Source Osc MaxRe(ψ)

P(f)

m1m2

μ

e

3

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)

Re(ψ)

P(f)

Source Osc Max

Kicks in sooner with big Δm2 or small

packet width

m1m2

μ

e

4

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)

5

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

EXTERNAL WAVE-PACKET PICTURE

π Decay Lagrangia

n μ

ν

Specified final state

?Input

Input

Output

Beuthe arxiv:0109119 Akhmedov + Smirnov arxiv:0905.1903

But … now two unknown states, rather than one!

6

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. D91 (2015) 5, 053002 [B.J.P.J.]

WIDTH OF THE INCOMING PION?

πInput

7

Start with some pion density matrix:

FIRST, TRANSLATE INTO THE DENSITY MATRIX PICTURE.

And let it decay:

8

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:

9

To get an idea of the phenomenology, substitute a representative pion density

matrix with Gaussian on and off diagonal position widths:

THE OSCILLATION PROBABILITY

Standard oscillation Classical coherencecondition

Quantum coherencecondition

Know location of source to within 1

osc length

Need WP’s not toseparate

x1

x 2

quantum clas

sica

l

10

What is the coherent pion width?

LOCALIZATION BY SCATTERING

x

ψ

E1

E2

E3

E4

With environmental entanglement the pion has

both a total width and a coherent width

E0

π

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, interferometry, etc)

11

Under some loose assumptions, we can describe what happens to the pion reduced density matrix without

considering the full system DM

OPEN QUANTUM SYSTEMS

E0

π

FT of mom transfer prob dist

quantumcl

assica

l

OPEN QUANTUM SYSTEMS

quantumcl

assica

l

T=0T=1T=2

Between scatters the state evolves according to the free Schrodinger equation

This leads to dispersion (broadening) of both coherent and incoherent widths

13

COHERENCE LENGTHS

Tegmark, arxiv:9310032

Competition of unitary evolution and collapse define a stable coherent width:

To calculate this width for a relativistic pion, we need:1) Scattering momentum transfer probability

distribution + rate2) Method of calculating convergent width in a

relativistic system

14

MOMENTUM TRANSFERS

Derived from photoionization cross section, in a somewhat complicated way

We need photoionization spectrum of beam-pipe gas as input:

Semi-classical model – consider energy losses in a continuum with some complex refractive index and re-interpret in terms of photon exchanges with electrons

Photoioniziation input

Measured drift chamber

fluctuations

Corrected Landau

PAImodel

Allison and Cobb,Ann.Rev.Nucl.Part.Sci 1980. 30:253-98

PAI Model:

15

PAI SANITY CHECK

My PAI model implementati

on

Standard plot of energy losses from the PDG

THE DECOHERENCE FUNCTION

Collapse this

way

16

17

SIMULATING DYNAMICAL COLLAPSE

Time

No longer fits on grid, simulation halts

Start with very

narrow pure state

density matrix evolve / scatter / evolve / scatter / evolve /

scatter…

These ingredients are used to construct a dynamical wave-function collapse MC simulation of the pion evolution:

18

Dispersion winning

Collapse winning

Eq

uilib

riu

m

SIMULATING DYNAMICAL COLLAPSE

(note timescale for collapse)

19

Map out collapsed widths as a function of incoming pion momentum

And substitute into fancy oscillation formula to find coherence loss distance

COLLAPSED WIDTHS

Standard oscillation Classical coherencecondition

Quantum coherencecondition

20

DRUMROLL PLEASE!

21

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!

CONCLUSION

22

BACKUPS

23

24

25

26

Re(ψ)

P(f)

PROPAGATION WITH WAVEPACKETS

Phase velocity is not affected – so neither is oscillation length

No process can make a neutrino of perfectly defined momentum.

Source makes a wave-packet with some momentum and some position width

m1m2

Source Osc Max

μ

e

27

COHERENCE LENGTHS

Calculated analytically by solving a master equation:Tegmark, arxiv:9310032

Competition of unitary evolution and collapse to define a stable width:

YOUNGS TWO-SLIT EXPERIMENT

A

B

scre

en

slit

s

source

Interference pattern:

YOUNGS TWO-SLIT EXPERIMENT

A

B

scre

en

slit

s

source

What if we add an environment?

E0

E0

YOUNGS TWO-SLIT EXPERIMENT

A

B

scre

en

slit

s

source

Switch on the coupling.

The particle becomes entangled with the environment via its interactions

The interference pattern now depends on how much overlap there is between EA, EB

EA

EB

?

YOUNGS TWO-SLIT EXPERIMENT

A

B

scre

en

slit

s

source

Extreme cases :

EA

EB

Fully quantum-mechanical-looking particles

YOUNGS TWO-SLIT EXPERIMENT

A

B

scre

en

slit

s

source

Extreme cases :

EA

EB

Fully classical-looking particles

Diverging entanglements with the environment make quantum-looking systems into classical-looking ones

33

SEEING DECOHERENCE IN PRACTICE

e.g. Talbot Lau interferometry with C70 fullerenes

34

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 ArPrediction from decoherence theory

35

Now consider a superposition of two particle position states, talking to an environment, which is “measuring”

them with some resolution.

POSITION STATES OF A PARTICLE

PA

PB

E0Time

PA

PB

EA

EB

PA

PB

E0 TimePA

PB

EA~EB Narrowly

separated

Widely separated

36

The particle (in superposition of positions) emits a neutrino. Will the neutrino state from each emitter add coherently or

incoherently?

POSITION STATES OF A PARTICLE

PA

PB

E0Time

PA

PB

EA

EB

PA

PB

E0 TimePA

PB

EA~EB Narrowly

separated

Widely separated

ν ν

ν ν

37

POSITION STATES OF A PARTICLE

PA

PB

E0Time

PA

PB

EA

EB

PA

PB

E0 TimePA

PB

EA~EB Narrowly

separated

Widely separated

38

THE ROLE OF THE MUON

Interaction

Detector

Freedom!

Un

itary

evo

luti

on

mean

s th

at

the n

eu

trin

o

doesn

’t c

are

!

μ

μ

μ

ν

ν

ν

See also:Glashow 0810.4602Kayser1110.3047

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 analogue of the EPR thought experiment.

Appendix 1 of the paper gives a very general proof

39

KINEMATICS

Oscillations require i≠j terms to be non-zero.

Can only happen if the pion density matrix is coherently wide enough (δ):

δ

pμ pμ

pν,mipν,mj

pπ pπ+2δij

How should we understand δ?

40

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:

Section 2 of paper

41

CHANGING DECAY ENVIRONMENT