Reply to Comment on Damping of neutrino oscillations decoherence and the lengths of neutrino wave packets Evgeny Akhmedov1and Alexei Y. Smirnov1y

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Reply to “Comment on “Damping of neutrino oscillations, decoherence and the lengths of

neutrino wave packets””

Evgeny Akhmedov1, ∗and Alexei Y. Smirnov1, †

1Max-Planck-Institut f¨

ur Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany

(Dated: October 5, 2022)

In arXiv:2209.00561 [1] our treatment [2] of eﬀects of particles emitted together with neutrinos on

neutrino wave packets is criticized on several grounds. We show here that this criticism is based on

misinterpretation of our results and is invalid. Our conclusions and, in particular, the conclusion that

neutrino wave packet separation eﬀects are unobservable in reactor and neutrino source experiments,

remain unchanged.

In [1] it has been claimed that our treatment of damp-

ing of neutrino oscillations in sec. 3 of [2] is inconsistent

as it (i) suﬀers from causality violation, (ii) involves inte-

gration over non-orthogonal basis and (iii) inadequately

considers the localization of the particles involved in neu-

trino production process. The author presumes that

these points undermine our conclusion that decoherence

by wave packet (WP) separation cannot be observed in

reactor and neutrino source experiments. We demon-

strate here that the ﬁrst of the above claims is based

on an incorrect interpretation of the space-time diagram

serving to illustrate our treatment, the second claim crit-

icizes a calculation we have never done and the third one

stems from misinterpretation of the localization of the

neutrino production process.

I. CAUSALITY

It is claimed in [1] that our analysis of damping of neu-

trino oscillations implies the possibility of superluminal

signals and thus leads to causality violation. To illustrate

this point, the author considers a two-stage thought ex-

periment, in which initially neutrinos are produced in

electron captures in a low-density gas, so that the in-

teractions of the daughter nuclei with the surrounding

particles of the medium can be neglected. This leads to

relatively long neutrino WPs and no decoherence by WP

separation observed in the detector. Then, at some “de-

cision making time” t0, one compresses the gas in the

source with a piston, leading to strong localization of the

daughter nucleus N0and much shorter neutrino WPs; as

a result, an observer at the detector position should see

decoherence eﬀects. However, according to the claim in

[1], this happens outside the future light cone with the

origin at the point of N0interaction soon after t0, as the

light signal from this point would reach the neutrino de-

tector after the neutrino detection process has already

been over. This would mean causality violation.

The above argument is based on the incorrect space-

time diagrams in Figs. 1 and 2 of [1] which do not cor-

∗Email:akhmedov@mpi-hd.mpg.de

†Email:smirnov@mpi-hd.mpg.de

respond to our calculations. Our analysis in [2] is based

on a consideration of mean free times of the particles

involved in the neutrino production process. We have

demonstrated that the production time is determined by

the shortest among the mean free times taof all the in-

volved particles. In the cases considered in [1], these are

the mean free times of either electron (Fig. 1)1or of the

parent nucleus N(both panels of Fig. 2), but not of N0.

Thus, in all the diagrams of [1] the mean free time tN0

of the daughter nucleus corresponds to the times when

the neutrino production process has already been over.

In such circumstances the interactions of N0are irrele-

vant; they cannot (and do not) aﬀect the outcome of the

neutrino detection experiment.

Consider now the situation when tN0< tN(see Fig. 1

of this Reply). In this case the scattering of N0is rel-

evant and it determines the length σxof the neutrino

WP: σx=ctN0. Simple geometrical considerations then

show that, for baselines Lexceeding the coherence length

Lcoh = (2E2/∆m2)σx(which means that the WPs of the

neutrino mass eigenstates ν1and ν2have separated by

more than their length σxbefore reaching the detector),

the arrival of the slower neutrino mass eigenstate ν2at

the neutrino detector position will be inside the future

light cone. This means that no causality violation arises

in this case.

Figure 2 of [1] actually corresponds to the situations

when the duration τof the individual processes of scatter-

ing of the daughter nucleus N0on the surrounding atoms

of the source rather than mean free time of N0determines

the length of the neutrino WP. (The author does not say

this explicitly, but this follows from his ﬁgure). Note that

such an approach is by itself fully legitimate, except that

the time intervals τhave to be found rather than loosely

assumed to be small or large, depending on the density of

the system. This approach was mentioned in the end of

sec. 3 of our paper [2] as an alternative to the approach

we have elaborated. If implemented, it could in principle

1Note that the light cone in Fig. 1 of [1] is plotted incorrectly:

since the produced electron has in this case the shortest time of

free propagation, the light cone should originate from the point

of interaction with the surrounding atoms of the electron and not

of N0.

arXiv:2210.01547v1 [hep-ph] 4 Oct 2022

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ReplytoCommentonDampingofneutrinooscillations,decoherenceandthelengthsofneutrinowavepackets""EvgenyAkhmedov1,andAlexeiY.Smirnov1,y1Max-Planck-InstitutfurKernphysik,Saupfercheckweg1,69117Heidelberg,Germany(Dated:October5,2022)InarXiv:2209.00561[1]ourtreatment[2]ofeectsofparticlesemittedtogetherw...

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Reply to Comment on Damping of neutrino oscillations decoherence and the lengths of neutrino wave packets Evgeny Akhmedov1and Alexei Y. Smirnov1y

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