Neutrino oscillations unlocked
A. Yu. Smirnov
NOW 2022, Ostuni
September 5, 2022
Max-Planck-Institut fur Kernphysik,
Heidelberg, Germany
105 papers with neutrino
oscillation in titles since
September 2021
detection
production
1
Interference:
coherence at
production
propagation,
detection
Wave packets of
the eigenstates of
propagation
i
Vacuum : VEV V(x,t),
interactions of
with VEV
h V
m,
h = h(<
>)
2
Entanglement with
accompanying
particles
Quantum mechanical
effect (superposition,
interference)
Modification of geometry of x-t,
metrics, GR, NO in the GW background
effect of propagation in
space - time
x
x
x
x
V
h
Tests of QM, modification
of QM, evolution equation..
NO:
detection
production
1
Classical fields (e.g. magnetic fields)
2
Matter Particle densities
Oscillating neutrino medium - treatment as open system
h
Effective mass squared
m
2
~
n
~
z
3
increases with decrease of t
U
Interactions with scalar bosons (DM) <
>
From microscopic picture: scattering on individual electrons,
to macroscopic one in terms of effective potentials.
Coherence, entanglement and wave packets
Matter , vacuum and propagation
Space-time localization diagrams
Talks on other aspects
of oscillations
B. Dasgupta,
L. Johns
M. Blasone
LSND
m
41
2
= 1 - 2 eV
2
Reflects computations of oscillation amplitude in QFT,
visualizes various subtle issues
E.Kh. Akhmedov, D. Hernandez,
A.Y.S. 1201.4128 [hep-ph]
|
P
>
=
1
P
|
1
> +
2
P
|
2
>
Produced and propagated neutrino state
where the wave packets
i
P
=
i
P
(x – v
i
t)
v
i
- group velocities
|
D
>
=
1
D
|
1
> +
2
D
|
2
>
i
D
=
i
D
(x – x
D
, t – t
D
)
For simplicity
i
D
(x – x
D
, t – t
D
) =
(x – L)
i
D
(t –t
D
)
Amplitude: projection of propagated state onto detection state:
Detected state
- the detection WP
A (L, t
D
) = <
D
|
P
>
=
i
dt
i
D*
(t –t
D
)
i
P
(L – v
i
t)
L- baseline
interference
Oscillation probability
P (L) = dt
D
|A(L, t
D
)|
2
=
dt
D
[|A
1
(L, t
D
)|
2
+ |A
2
(L, t
D
)|
2
]
+ 2Re dt
D
A
1
(L, t
D
)
*
A
2
(L, t
D
)
A
i
(L, t
D
) =
dt
i
D*
(t –t
D
)
i
P
(L – v
i
t)
Further integration over interval
of baseline L due to finite sizes
of the source and detector
The slopes of bands are
determined by group velocities
- generalized WP
Interference is determined by
overlap of produced WP
A
i
(L, t
D
)
~
i
P
(L – v
i
t
D
)
t
D
<<
t
P
short detection coherence time
i
D
(t – t
D
)
~
(t –t
D
)
t
D
>>
t
P
long detection coherence time
A
i
(L, t
D
)
~
i
D
(L/v - t
D
)
t
D
>> t
sep
restoration of coherence if
two extreme cases
WP’s are determined by localization region of the production process:
overlap of localization regions of all particles involved but neutrinos.
E.Kh. Akhmedov and A.Y.S.
[hep-ph]
The latter is determined by time
between two collisions of N, t
N
x
~ v
t
N
~
X
N
c/v
N
enhancement factor
N
N’ + e
-
+
If N’ and e
-
are not detected or
their interactions can be neglected
E.g. in the
decay,
localization of process is given
by localization of atom N
distance
time
If N’ or/and e
-
are detected or interact, this may narrow their WP’s
and therefore the neutrino WP.
If e
-
is detected during time
interval t
e
< t
N
, the size of
WP
will be determined by t
e
If
e
-
interacts with particles
of medium which have very
short time between collisions
t
coll
, then
x
~
ct
coll
Similar to the EPR paradox
consider
emission and interactions of
e
-
as unique process;
contributions to its amplitude from different interactions regions
appear with random phases
k
- incoherent
A
tot
= A
k
e
i
k
distance
time
t
coll
LSND
m
41
2
= 1 - 2 eV
2
x –t space: separation of wave packets of mass states due
to difference of group velocities
Suppression of interference
damping of oscillations
x
Information is not lost
and can be restored at
detection
Survival probability :
P
ee
= P
ee
+ ½ D(E, L) sin
2
2
cos
D(E, L) = exp [- ½(L/L
coh
)
2
]
Damping factor for Gaussian WP
Coherence length
E
2
m
2
L
coh
=
x
E
~
1/
x
equivalent to integration over
the energy uncertainty
f(E)
x
E
A de Gouvea, V De Romeri,
C.A. Termes, 2104.05806
[hep-ph]
Daya Bay, RENO
KamLAND
Expected
damping
effect
Absence of decoherence (damping) effect means
L << L
coh
Bound on size of the WP
x
> L
m
2
2E
2
Analysis of data:
x
> 2.1 x 10
-11
cm (90% C.L.)
The bound corresponds to the energy resolution of detectors
E
x
~
1/
E
Daya Bay: decoherence due to finite momentum spread
p
Damping effects in various experiments computed
for
x
= 2.1 x 10
-11
cm (as found in A de Gouvea et al).
C.A.Arguelles et al,
2201.05108 [hep-ph]
F.P. An, et al,
1608.01661 [hep-ex]
p
/p < 0.23 (95% C.L.)
for p = 3 MeV:
x
~
1/
E
= 2.8 x 10
-11
cm
JUNO in future may set the limit
p
/p < 10
-2
(95% C.L.)
x
> 2.3 x 10
-10
cm
Decoherence in oscillations active – eV scale sterile
J. Wang et al.
2112.14450 [hep-
ex]
Claims:
- decoherence allows to reconcile BEST result with reactor bounds;
- results of analysis should be presented in two forms: with and
without decoherence
R(E
r
, E) energy resolution in experimental set-up (width
E
):
- spectrum of produced neutrinos (line), or
- energy resolution of a detector
integration over the energy resolution of setup
– another sources of damping
f(E, E) – WP of produced neutrino in energy representation
acts on oscillations, as R does, and can be attached to R(E
r
, E)
Effective resolution function
R
eff
(E
r
, E) = dE R(E
r
, E) |f(E, E)|
2
For Gaussian f and R, R
eff
is also Gaussian with width
E
2
+
E
2
The problem: to disentangle the two contributions
E.Kh. Akhmedov and A.Y.S.
2208.03736[hep-ph]
Source:
-decays of fragments N of nuclear fission
N
N’ + e
-
+
N quickly thermalise
in equilibrium with medium in the moment of
decay
t
he average velocity:
If
N’ and e
-
are not detected or their interactions can be neglected,
localization of
production process is given by localization of N.
x
~ v
t
N
~
X
N
c/v
N
t
N
~
[
AA
n
U
v
N
]
-1
t
N
- time between two collisions of N with other atoms
AA
geometric cross-section
AA
~
(2r
vdW
)
2
Van der Waals radius
v
N
~
[3T/ m
N
]
-1/2
n
U
- number density of Uranium
x
= 2.8 x 10
-3
cm
“short cut” estimation: can be
considered as the upper bound
Duration of
production process
is given by the shortest mean free
time among particles involved
Consideration of x-t localization
of interactions of accompanying
particles.
Chain of k processes of
secondary interactions till
equilibration (thermalization)
t
= t
e
= X
e
/v
e
x
= 2 x 10
-5
cm
X
e
is determined by ionization
of uranium,
eU
Electrons have the shortest
X
e
= (n
U
eU
)
-1
t
~
t
N
/2
k
x
= (5 – 10)x 10
-5
cm
t
e
i
N
A
E + A
e’ + A’
...
x
>>
x
exp
x
= 1.4 x 10
-4
cm
x
/
x
exp
= 10
5
- 10
6
E
~
1 eV
Corresponding energy uncertainty
while energy resolution
E
~
10
5
eV
1.
2.
3.
To be sensitive to WP separation energy resolution
function should be known with better that 10
-5
accuracy
Large
m
2
does not help since oscillatory pattern shows up at L
~
l
but L
coh
~
l
~
1/
m
2
m
2
cancels in damping factor
4.
For Cr source:
5.
Experiments with L
~
L
coh
? Lower energies? Widening lines?
If some additional damping is found, it is due to some
new physics and not due to WP separation
6.
B.J.P. Jones,
2209.00561 [hep-ph]
WP are determined by absolute
localization of parent particle in
the source i.e. wrt other atoms
Integration in non-orthogonal
basis of entangled recoil
Three points appear to undermine that WP separation is unobservable:
Causality violation
The statement is based on figures
which do not correspond to our
computations
We are not making integration
over characteristics of recoil
Nuclear interactions inside
nucleus measure position of
initial particle (nucleon)
Electron interaction decides
light cone should be
constructed differently
In this setup t
N’
>> t
N
recoil does
not affect WP of neutrinos
which is determined by t
N
B.J.P. Jones,
2209.00561 [hep-ph]
Figs do not correspond
to our estimations
No problem with casuality
LSND
m
41
2
= 1 - 2 eV
2
From interactions with individual scatteres to effective
potential (mean field approximation)
e.g., G Fantini,
A.G. Rosso, F. Vissani
1802.05781
E.Kh. Akhmedov
2010.07847 [hep-ph]
A. Y.S. , Xun-jie Xu
Point-like scatterers, a coarse graining –
coordinate space averaging over macroscopic
volumes with large number of particles
Summation of potentials produced by individual
scatteres.
since
~
1/p
<< X
e
make sense to
consider propagation of
neutrino inside atom
For short range interactions r
WI
, localization
of scatterers should be taken into account
X
e
>>
r
WI
, e.g. localization of e in atom
x
n
a
b
V
a
V
b
L
a
L
b
Half – phases:
a
b
a
b
Mixing angles:
Oscillation probability
x
P = [1 - I
2
/(1 – R
2
)] sin
2
(n
)
= arcos R
E. Kh. Akhmedov
I = I(
a
b
,
a
b
) , R = R(
a
,
b
,
a
,
b
)
n – number of periods
For
a
b
<< 1 the probability can be reduced to
P = sin
2
2
m
(V) sin
2
½
(V)
V =
V
a
L
a
+ V
b
L
b
L
a
+ L
b
- averaged potential
Partially ionized atoms as the electron density perturbations
Number density profile of electrons in atom (O, C, He) is non adiabatic
M. Kusakabe
2109.11942 [hep- ph]
Interplay of non-adiabatic evolution and
separation (relative shift) of the WP’s leads to
new effects: additional averaging of oscillations
Applications to Supernova neutrinos
No new effects without WP separation and adiabatic evolution
No new effects for very sharp (step-like) density profile
WP’s are formed at the production (at boundaries)
(t x) = dp f(p)
p
(t x)
If there is no absorption or p-dependent interactions, f(p) does not
change in the process of evolution
Evolution equation
p
(t x) - plane waves
id
/dt - H
= 0,
insert
(t x):
dp f(p) [id
p
/dt - H
p
] = 0
eq for
p
, then integrate over p (which takes care about WP nature)
No effects predicted in
2109.11942 [hep- ph]
Superposition principle and linearity of evolution equation
solve
In t-x space WP can change form in the course of evolution,
but integrated over time result coincides with result in E-p rep.
Y. P. Porto-Silva , A Y S
2103.10149 [hep-ph]
- scattering
H = H (
p
) – non-linear equation ?
A = 81.5
Evolution matrix
Equation for correction
(p,1)
(t) in coordinate representation:
T. Gherghetta A. Sherin
2208.10567 [hep-ph]
U(t, t
p
,
(p)
(t)) = U
0
(t, t
p
) +
U
1
(t, t
p
,
(p)
(t))
(p)
(t) = U(t, t
p
,
(p)
)
(p)
(t
p
)
Produced state
Standard linear
evolution matrix
expansion
parameter
non-linear
correction
(p)
(t) =
(p,0)
(t) +
(p,1)
(t)
id
(1)
(t) /dt = H
0
(1)
(t) + G(t, x,
(0)
)
inhomogeneous term
Weinberg 5D operator
interaction with scalar
state dependent
term
G
P = sin
2
2
sin
2
½
- sin
m
1
- m
2
m
1
+ m
2
‘
4
‘ = A
(m
1
+ m
2
)
2
/v
2
Correction is very small
Schrodinger equation for single particle
q = m
/v
D E Kaplan S Rajendran
2106.10576 [hep-th]
id
(t, x) /dt = H
0
+
d
4
x
1
|
(t
1
, x
1
)|
2
G
r
(t x, t
1
x
1
)
(t, x)
q
2
4
G
r
- retarded Green function for scalar
q – charge, Yukawa coupling constant of
and
get small masses due explicit symmetry breaking by WI via loops
Neutrino vacuum condensate due to gravity. Order parameter
mixing matrix
<
> = <
T
C
>
~
G
= meV -
0.1 eV
Cosmological phase transition at T
~
G
Neutrinos get masses m
~
<
>
Flavor is fixed by weak (CC) interactions and charged leptons
with definite mass generated by usual Higgs field
m
~
U(
)
T
<
> U(
)
T
<
G
Relic neutrinos form bound states
= (
T
)
<
> = diag (
11
,
22
,
33
),
decay and annihilate into
(neutrinoless Universe)
Symmetry of system SU(3)xU(1) spontaneously broken by
neutrino condensate -
are goldstone bosons
G.Dvali , L Funcke,
1602.03191 [hep-ph]
Solar system moves through the frozen string-DW background
with v = 230 km/sec. For 6 years (operation of Daya Bay)
d = vt = 4 x 10
13
m - comparable with expected
Symmetry breaking:
G
1 meV
G.Dvali , L Funcke,
T Vachaspati
2112.02107 [hep-ph]
SU(3)
Z
2
x Z
2
I
global strings
domain walls
Length scale of strings
~
inter-string separation
string-wall
network
= 10
14
m (
/a
G
)
7/2
Travelling around string winds VEV <
> by the SU(3) transformation:
(self-coupling of string field
/scale factor of phase transition)
<
(
S
) > =
(
W
)
T
<
>
(
W
)
(
W
) path - O(3) transformation with angles
W
= (
W
12
,
W
13
,
W
23
).
U = U(
)
(
W
)
After the path
lepton mixing changes as
over length
,
W
= O(1)
Elastic forward scattering of
on background
scalars
with fermionic
mediator
L
L
L
L
Resonance: s =
m
2
E
R
=
A.Y.S. , V. Valera, 2106.13829 [hep-ph]
Effective potential
m
2
2
m
for
at rest the resonance
energy:
V
B
E
0
Wolfenstein
limit
0
resonance
1/E tail
E
R
For small
m
resonance at low,
observable energies
Ki-Yong Choi, Eung Jin Chun,
Jongkuk Kim,
1909.10478 [hep-ph]
S. F Ge and H Murayama,
1904.02518 [hep-ph]
2012.09474 [hep-ph]
|
m
eff
2
|
E
R
,
E << E
R
E
E
R
m
eff
(0) < 5 10
-6
eV: m
eff
(z = 1000)
~
0.15 eV,
m
eff
< 2 10
-4
eV - undetectable
E
For E
R
= 0.01 MeV:
= 0
existing
observations
relic
m
eff
2
~
1 , E >> E
R
y
2
n
4 m
m
eff
2
= constant - checked
down to 0.1 MeV
t
ake E
R
<< 0.1 MeV
KATRIN, E
~
1 eV:
Relic
, E = 10
-4
eV:
m
eff
2
~ 2E
V
B
COSMOLOGY
while VEV = const
m
eff
2
~
n
~
(1 + z)
3
i
ncreased in the past
no problem
Ki-Young Choi, Eung Jin Chun,
Jongkuk Kim, 2012.09474 [hep-ph]
Upper bounds on y from scattering
of neutrinos from SN1987A on DM
with zero C- asymmetry and two
different masses of mediator f
Green band:
m
eff
2
=
m
atm
2
m
< 10
-10
eV
Similar bound from Ly
(relic neutrinos) .
Allowed
values:
m
f
< 10
-3
eV
y
< 10
-9
the corresponding resonance
energy E
R
= 0.01 MeV
C
osmological bound is satisfied
y
m
, eV
allowed
Effect of propagation decoherence (damping) is unobservable in
the present reactor and source experiments. If some additional
damping is found
due to new physics
Space-time localization diagrams visualize (uncover) the key aspects
of neutrino oscillations
Evolution of
state and construction of WP in the momentum space
commute
propagation decoherence is boundary (for linear case)
phenomenon (as well as production and detection decoherence)
Effects of complex structure of vacuum, neutrino condensates,
Non-linear generalization of QM can affect NO
Important study: search for time, space and energy
Dependences of oscillation parameters.
Neutrino oscillations – the tool for explorations of properties of
space and time, subtle aspects of QM fundamental symmetries
(beyond measurements of neutrino parameters)
About 100 papers with “Neutrino oscillations “ in titles
Topics:
Coherence,
Entanglement in neutrino oscillations
Collective neutrino oscillations
Micro vs. macro description
Quantumness, Tests of quantum mechanics
Oscillations in modified metric, gravity
Oscillations in gravitational waves background
Mater, medium effects in presence of new
interactions (long range forces, DM ),
Modification of QM, evolution equation
Effects of
L
orentz invariance violation,
Equivalence principle violation
Parameter symmetries
…
All aspects, components, characteristics of oscillations are under
investigation. They can be classified as…
Unlock the mysteries of neutrino oscillations in vacuum and other media, exploring wave packets, interference, entanglement, and oscillation probabilities. Dive into discussions on matter, vacuum, propagation, and time localization diagrams, shedding light on subtle quantum mechanical effects and tests.
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Presentation Transcript
Neutrino oscillations unlocked A. Yu. Smirnov Max-Planck-Institut fur Kernphysik, Heidelberg, Germany 105 papers with neutrino oscillation in titles since September 2021 NOW 2022, Ostuni September 5, 2022
Oscillations in vacuum Wave packets of the eigenstates of propagation i production detection 1 h 2 x x x x V Interference: coherence at production propagation, detection Vacuum : VEV V(x,t), interactions of with VEV h V m, h = h(< >) Entanglement with accompanying particles NO: Modification of geometry of x-t, metrics, GR, NO in the GW background effect of propagation in space - time Quantum mechanical effect (superposition, interference) Tests of QM, modification of QM, evolution equation..
Oscillations in media production detection 1 h 2 Classical fields (e.g. magnetic fields) Matter Particle densities From microscopic picture: scattering on individual electrons, to macroscopic one in terms of effective potentials. Interactions with scalar bosons (DM) < > Effective mass squared m2 ~ n ~ z3 increases with decrease of tU Oscillating neutrino medium - treatment as open system
Content Matter , vacuum and propagation Talks on other aspects of oscillations B. Dasgupta, L. Johns M. Blasone
m412 = 1 - 2 eV2 Space-time LSND Localization diagrams
time localization diagram Reflects computations of oscillation amplitude in QFT, visualizes various subtle issues E.Kh. Akhmedov, D. Hernandez, A.Y.S. 1201.4128 [hep-ph] Produced and propagated neutrino state | P>= 1P| 1 > + 2P| 2 > where the wave packets iP = iP(x vit) vi - group velocities Detected state | D>= 1D| 1 > + 2D| 2 > iD = iD(x xD, t tD) - the detection WP Amplitude: projection of propagated state onto detection state: L- baseline For simplicity iD(x xD, t tD) = (x L) iD(t tD) A (L, tD) = < D| P>= i dt iD* (t tD) iP(L vit)
Space time localization diagram Oscillation probability P (L) = dtD|A(L, tD)|2 = dtD [|A1(L, tD)|2 + |A2(L, tD)|2] + 2Re dtD A1(L, tD)*A2(L, tD) interference Ai(L, tD) = dt iD* (t tD) iP(L vit) - generalized WP Further integration over interval of baseline L due to finite sizes of the source and detector The slopes of bands are determined by group velocities
Detection two extreme cases tD >> tP tD << tP short detection coherence time iD(t tD) ~ (t tD) long detection coherence time Ai(L, tD) ~ iD(L/v - tD) Ai(L, tD) ~ iP(L vitD) restoration of coherence if Interference is determined by overlap of produced WP tD >> tsep
Production E.Kh. Akhmedov and A.Y.S. [hep-ph] WP s are determined by localization region of the production process: overlap of localization regions of all particles involved but neutrinos. N N + e- + E.g. in the decay, If N and e- are not detected or their interactions can be neglected localization of process is given by localization of atom N distance The latter is determined by time between two collisions of N, tN x ~ v tN ~ XN c/vN time enhancement factor
Entanglement and correlations If N or/and e- are detected or interact, this may narrow their WP s and therefore the neutrino WP. If e- is detected during time interval te < tN, the size of WP will be determined by te tcoll distance If e- interacts with particles of medium which have very short time between collisions tcoll, then x ~ ctcoll Similar to the EPR paradox time consider emission and interactions of e- as unique process; contributions to its amplitude from different interactions regions appear with random phases k - incoherent Atot = Ak ei k
m412 = 1 - 2 eV2 Propagation coherence LSND
Observing propagation decoherence x t space: separation of wave packets of mass states due to difference of group velocities equivalent to integration over the energy uncertainty f(E) E ~ 1/ x x E x Suppression of interference damping of oscillations Survival probability : Pee = Pee + D(E, L) sin2 2 cos Damping factor for Gaussian WP D(E, L) = exp [- (L/Lcoh)2] Coherence length Lcoh = x Information is not lost and can be restored at detection E2 m2
Decoherence of reactor neutrinos A de Gouvea, V De Romeri, C.A. Termes, 2104.05806 [hep-ph] Bound on size of the WP KamLAND Daya Bay, RENO Expected damping effect Absence of decoherence (damping) effect means L << Lcoh Analysis of data: x > 2.1 x 10-11 cm (90% C.L.) The bound corresponds to the energy resolution of detectors E x ~ 1/ E m2 2E2 x > L
Other studies Daya Bay: decoherence due to finite momentum spread p p /p < 0.23 (95% C.L.) for p = 3 MeV: x ~ 1/ E = 2.8 x 10-11 cm F.P. An, et al, 1608.01661 [hep-ex] JUNO in future may set the limit p /p < 10-2 (95% C.L.) J. Wang et al. 2112.14450 [hep- ex] x > 2.3 x 10-10 cm Decoherence in oscillations active eV scale sterile C.A.Arguelles et al, 2201.05108 [hep-ph] Damping effects in various experiments computed for x = 2.1 x 10-11 cm (as found in A de Gouvea et al). Claims: - decoherence allows to reconcile BEST result with reactor bounds; - results of analysis should be presented in two forms: with and without decoherence
Propagation decoherence and energy resolution integration over the energy resolution of setup another sources of damping E.Kh. Akhmedov and A.Y.S. 2208.03736[hep-ph] R(Er , E) energy resolution in experimental set-up (width E ): - spectrum of produced neutrinos (line), or - energy resolution of a detector f(E, E) WP of produced neutrino in energy representation acts on oscillations, as R does, and can be attached to R(Er, E) Effective resolution function Reff (Er , E) = dE R(Er , E) |f(E, E)|2 For Gaussian f and R, Reff is also Gaussian with width E2 + E2 The problem: to disentangle the two contributions
WPs of reactor neutrinos Source: -decays of fragments N of nuclear fission N N + e- + N quickly thermalise in equilibrium with medium in the moment of decay the average velocity: vN ~ [3T/ mN]-1/2 If N and e- are not detected or their interactions can be neglected, localization of production process is given by localization of N. x ~ v tN ~ XN c/vN tN - time between two collisions of N with other atoms tN ~ [ AA nU vN]-1 AA geometric cross-section AA ~ (2rvdW) 2 Van der Waals radius nU - number density of Uranium x = 2.8 x 10-3 cm
Effect of accompanying particles Consideration of x-t localization of interactions of accompanying particles. Duration of production process is given by the shortest mean free time among particles involved Chain of k processes of secondary interactions till equilibration (thermalization) Electrons have the shortest t = te = Xe/ve Xe is determined by ionization of uranium, eU ... E + A e + A A i Xe = (nU eU)-1 N te t ~ tN /2k x = 2 x 10-5 cm x = (5 10)x 10-5 cm short cut estimation: can be considered as the upper bound
Implications 1. x >> xexp x / xexp = 105 - 106 2. Corresponding energy uncertainty while energy resolution E ~ 105 eV To be sensitive to WP separation energy resolution function should be known with better that 10-5 accuracy E ~ 1 eV For Cr source: x = 1.4 x 10-4 cm 3. Large m2 does not help since oscillatory pattern shows up at L ~ l but Lcoh ~ l ~ 1/ m2 m2 cancels in damping factor 4. If some additional damping is found, it is due to some new physics and not due to WP separation 5. Experiments with L ~ Lcoh ? Lower energies? Widening lines? 6.
Comments and replies B.J.P. Jones, 2209.00561 [hep-ph] Three points appear to undermine that WP separation is unobservable: The statement is based on figures which do not correspond to our computations Causality violation Integration in non-orthogonal basis of entangled recoil We are not making integration over characteristics of recoil Nuclear interactions inside nucleus measure position of initial particle (nucleon) WP are determined by absolute localization of parent particle in the source i.e. wrt other atoms
Comments B.J.P. Jones, 2209.00561 [hep-ph] Figs do not correspond to our estimations No problem with casuality Electron interaction decides light cone should be constructed differently In this setup tN >> tN recoil does not affect WP of neutrinos which is determined by tN
m412 = 1 - 2 eV2 Matter vacuum and propagation LSND
From micro to macro picture From interactions with individual scatteres to effective potential (mean field approximation) Point-like scatterers, a coarse graining coordinate space averaging over macroscopic volumes with large number of particles Summation of potentials produced by individual scatteres. For short range interactions rWI, localization of scatterers should be taken into account Xe >> rWI , e.g. localization of e in atom E.Kh. Akhmedov 2010.07847 [hep-ph] A. Y.S. , Xun-jie Xu e.g., G Fantini, A.G. Rosso, F. Vissani 1802.05781 since ~ 1/p << Xe make sense to consider propagation of neutrino inside atom
Modeling with castle wall profile n b a x Half phases: a b Mixing angles: Va Vb La Lb a b Oscillation probability P = [1 - I2/(1 R2 )] sin2 (n ) I = I( a b, a b ) , R = R( a, b, a, b ) E. Kh. Akhmedov n number of periods = arcos R x For a b << 1 the probability can be reduced to P = sin 22 m(V) sin2 (V) Va La + Vb Lb La + Lb - averaged potential V =
WPs and non adiabatic evolution Partially ionized atoms as the electron density perturbations Number density profile of electrons in atom (O, C, He) is non adiabatic Interplay of non-adiabatic evolution and separation (relative shift) of the WP s leads to new effects: additional averaging of oscillations Applications to Supernova neutrinos M. Kusakabe 2109.11942 [hep- ph] No new effects without WP separation and adiabatic evolution No new effects for very sharp (step-like) density profile
Evolution of WPs WP s are formed at the production (at boundaries) (t x) = dp f(p) p(t x) If there is no absorption or p-dependent interactions, f(p) does not change in the process of evolution p(t x) - plane waves Evolution equation insert (t x): id /dt - H = 0, dp f(p) [id p/dt - H p ] = 0 Superposition principle and linearity of evolution equation solve eq for p, then integrate over p (which takes care about WP nature) No effects predicted in 2109.11942 [hep- ph] In t-x space WP can change form in the course of evolution, but integrated over time result coincides with result in E-p rep. Y. P. Porto-Silva , A Y S 2103.10149 [hep-ph] - scattering H = H ( p) non-linear equation ?
linear generalization of QM T. Gherghetta A. Sherin 2208.10567 [hep-ph] Evolution matrix U(t, tp, (p) (t)) = U0(t, tp) + U1(t, tp, (p) (t)) Standard linear evolution matrix expansion parameter non-linear correction (p) (t) = U(t, tp, (p)) (p)(tp) (p)(t) = (p,0) (t) + (p,1) (t) Produced state Equation for correction (p,1) (t) in coordinate representation: id (1)(t) /dt = H0 (1)(t) + G(t, x, (0)) inhomogeneous term Weinberg 5D operator interaction with scalar state dependent term G P = sin 22 sin 2 - sin m1 + m2 4 m1 - m2 Correction is very small A = 81.5 = A (m1 + m2) 2/v2
Casual framework for non linear QM D E Kaplan S Rajendran 2106.10576 [hep-th] Schrodinger equation for single particle q2 id (t, x) /dt = H0 + d4x1 | (t1, x1)|2 Gr(t x, t1 x1) (t, x) 4 Gr - retarded Green function for scalar q charge, Yukawa coupling constant of and q = m /v
Vacuum and properties of oscillations G.Dvali , L Funcke, 1602.03191 [hep-ph] Neutrino vacuum condensate due to gravity. Order parameter < > = < TC > ~ G = meV - 0.1 eV Cosmological phase transition at T~ G Neutrinos get masses m ~ < > Flavor is fixed by weak (CC) interactions and charged leptons with definite mass generated by usual Higgs field m ~ U( )T < > U( ) < > = diag ( 11, 22, 33), mixing matrix Relic neutrinos form bound states = ( T ) decay and annihilate into (neutrinoless Universe) T< G Symmetry of system SU(3)xU(1) spontaneously broken by neutrino condensate - are goldstone bosons get small masses due explicit symmetry breaking by WI via loops
Mixing and topological defects G.Dvali , L Funcke, T Vachaspati 2112.02107 [hep-ph] string-wall network Symmetry breaking: SU(3) Z2 x Z2 I global strings domain walls Length scale of strings ~ inter-string separation = 1014 m ( /aG) G 7/2 1 meV (self-coupling of string field /scale factor of phase transition) Travelling around string winds VEV < > by the SU(3) transformation: < ( S) > = ( W)T< > ( W) ( W) path - O(3) transformation with angles W = ( W12, W13, W23). After the path lepton mixing changes as over length , W = O(1) U = U( ) ( W) Solar system moves through the frozen string-DW background with v = 230 km/sec. For 6 years (operation of Daya Bay) d = vt = 4 x 1013 m - comparable with expected
S. F Ge and H Murayama, 1904.02518 [hep-ph] VEV or refraction on scalar DM? Ki-Yong Choi, Eung Jin Chun, Jongkuk Kim, 1909.10478 [hep-ph] 2012.09474 [hep-ph] Elastic forward scattering of on background scalars with fermionic mediator Effective potential L VB L L Wolfenstein limit L 1/E tail Resonance: s = m 2 for at rest the resonance energy: 0 m 2 2m ER = For small m resonance at low, observable energies resonance A.Y.S. , V. Valera, 2106.13829 [hep-ph] E 0 ER
Effective m2 meff2 ~ 2EVB = 0 1 , E >> ER y2n 4 m | meff 2| meff2 ~ E , E << ER ER existing observations meff2 = constant - checked down to 0.1 MeV take ER << 0.1 MeV relic ER E For ER = 0.01 MeV: KATRIN, E ~ 1 eV: meff < 2 10-4 eV - undetectable meff2 ~ n ~ (1 + z)3 increased in the past COSMOLOGY while VEV = const meff (0) < 5 10-6 eV: meff (z = 1000) ~ 0.15 eV, Relic , E = 10-4 eV: no problem
Bounds on parameters Ki-Young Choi, Eung Jin Chun, Jongkuk Kim, 2012.09474 [hep-ph] Green band: meff2 = matm2 Upper bounds on y from scattering of neutrinos from SN1987A on DM with zero C- asymmetry and two different masses of mediator f y Similar bound from Ly (relic neutrinos) . m , eV the corresponding resonance energy ER = 0.01 MeV Cosmological bound is satisfied Allowed values: mf < 10-3 eV m < 10-10 eV y< 10-9
Summary Neutrino oscillations the tool for explorations of properties of space and time, subtle aspects of QM fundamental symmetries (beyond measurements of neutrino parameters) Evolution of state and construction of WP in the momentum space commute propagation decoherence is boundary (for linear case) phenomenon (as well as production and detection decoherence) Important study: search for time, space and energy Dependences of oscillation parameters.
Landscape of studies 2021 2022 About 100 papers with Neutrino oscillations in titles Coherence, Entanglement in neutrino oscillations Collective neutrino oscillations Micro vs. macro description Quantumness, Tests of quantum mechanics Oscillations in modified metric, gravity Oscillations in gravitational waves background Mater, medium effects in presence of new interactions (long range forces, DM ), Modification of QM, evolution equation Effects of Lorentz invariance violation, Equivalence principle violation Parameter symmetries All aspects, components, characteristics of oscillations are under investigation. They can be classified as Topics:
