Light sterile neutrinos effects in processes with electron and muon neutrinos V. V. Khruschov S. V. Fomichev

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Light sterile neutrinos eﬀects in processes with

electron and muon neutrinos

V. V. Khruschov, S. V. Fomichev

NRC Kurchatov Institute, 123182 Moscow, Russia

Abstract

Sterile neutrinos with various masses could be participated in astrophys-

ical and cosmological processes including mixing with active neutrinos, if

exist. It is considered the possible eﬀects of mixing of active and sterile

neutrinos with masses of the order or less than 1 eV. For oscillation pro-

cesses involving electron and muon neutrinos, as well as for beta decay and

neutrinoless double beta decay processes, the contributions of light sterile

neutrinos in the characteristics of these processes are calculated. For this

purpose the estimates of the mixing parameters in the model with three

active and three sterile neutrinos are made taking into account experimen-

tal data. Two cases of sterile neutrinos masses distribution are considered

in detail. The results obtained can be used for interpretation of available

experimental data, and also for predictions of subsequent experimental re-

sults.

Keywords: Neutrino oscillations, Short-baseline anomalies, Sterile neutrinos, Beta

decay, Neutrinoless double beta decay.

PACS: 12.10.Kt; 12.90.+b; 13.35.Hb; 14.60.Pq; 14.60.St; 95.35.+d.

1 Introduction

It is well known that in the framework of the Standard Model (SM) of electromag-

netic, weak and strong interactions of particles a quantitative agreement between

most of experimental and theoretical results was achieved [1]. However, some

data are emerging and increasing in number that cannot be well described within

the framework of the SM. For instance, it relates to oscillations of active neu-

trinos, which have been detected experimentally. Nonzero neutrino masses must

be invoked for their explanation. In this case SM is called as the modiﬁed SM

(νSM). Using the neutrino mass states makes it possible to explain the oscillations

of the known neutrino ﬂavor states, i.e. electron, muon and tau neutrinos (νe,

νµ,ντ) with the help of the Pontecorvo–Maki–Nakagawa–Sakata mixing matrix

UPMNS ≡U. The standard parametrization for matrix Uis given in the review

[1].

In the present paper some peculiarities of neutrino processes are considered.

For their explanation possibly it is necessary to go out beyond not only the SM but

also the νSM. This is especially true in regard to so called neutrino anomalies at

arXiv:2210.03359v3 [hep-ph] 13 Oct 2023

short distances (short baselines, SBL) from the source [2, 3, 4]. The appearance

of these anomalies can be explained perhaps with the eﬀects of new particles,

namely, light sterile neutrinos (LSN) with the characteristic mass scale about

1 eV. Let us mention that three sterile neutrinos with masses of the order of 1 eV

were already introduced in Ref. [5] for the explanation of the LSND anomaly.

Generally a LSN number can be arbitrary. The most using model now is the

(3+1) model with one LSN, but the (3 + 2) and (3 + 3) models are used as well

(see, for example, [6, 7]). Below we consider the LSN eﬀects in processes with

electron and muon neutrinos in the framework of the version of the (3+3) model,

which was elaborated in Refs. [8, 9, 10].

The content of the paper is as follows. Section 2 provides short reference

to SBL neutrino anomalies perceived in a number of experiments [4]. Section 3

contains brief description and some results of the used (3 + 3) model with three

LSN [10]. In Section 4 the test values of the model parameters are proposed taking

into account experimental data. Thereon calculations of the survival probabilities

of electron and muon neutrinos and probabilities of transition of muon neutrinos

to electron neutrinos with the help of the obtained parameter values are carried

out. The calculation results are represented in the graphic form (Figs. 1, 2 and 3).

The eﬀective masses of electron neutrinos, which can be measured in experiments

on beta decay and neutrinoless double beta decay, are also estimated. In the ﬁnal

Section 5 the main results of the paper are discussed.

2 Neutrino data anomalies on small distances

from neutrino sources

In addition to the known standard data on neutrino oscillations for three active

neutrinos, indications are obtained related to anomalous data for SBL neutrino

ﬂuxes in a number of processes. These anomalies cannot be explained by using

the oscillatory parameters for only known active neutrinos. They include the

LSND (or accelerator) anomaly (AA) [11, 12, 13, 14], the gallium (or calibration)

anomaly (GA) [15, 16, 17] and the reactor (antineutrino) anomaly (RA or RAA)

[18, 19, 20, 21, 22, 23]. AA, GA and RA manifest themselves at small distances,

more precisely, at such distances from the source L, when the value of the param-

eter ∆m2L/E is of the order of unity (where Eis the neutrino energy and ∆m2

is the square of the characteristic mass scale of the considered oscillations). ∆m2

is equal to the diﬀerence of the squared masses of the participating neutrinos.

Excluding purely experimental problems, the SBL anomalies can be explained by

the presence of at least one neutrino with a mass of about 1 eV, which does not

interact directly with the νSM gauge bosons, therefore they are called LSN.

AA was noticed ﬁrstly by the LSND collaboration in the reaction with the

transition of a muon antineutrino into an electron antineutrino [11]. Then this

result was conﬁrmed and extended by adding the results of the reaction with

the transition of a muon neutrino into an electron neutrino in the MiniBooNE

experiment [12, 13] and with less signiﬁcance in the MicroBooNE experiment

[14, 24]. GA was discovered during the calibration of detectors for the Ga-Ge

experiment at the SAGE and GALLEX facilities [15, 17] and has been conﬁrmed

in the BEST experiment [25, 26]. Now the conﬁdence level of the AA and GA in

the mentioned experiments lies in the 4 −5σCL interval [24, 25].

After recalculating the values of the antineutrino ﬂux from the reactor, the

theoretical values turned out to be 3% higher than those used before [18, 19]

that led to RA about the 3σlevel [20]. However, it should be noted that the

β-spectra of the decay products of uranium and plutonium isotopes introduce

large systematic uncertainties into the reactor spectra [27].

3 Some propositions and results of the (3+3)

model

In spite of that the SBL anomalies can be explained, as mentioned above, with

the presence only one LSN with the characteristic mass scale about 1 eV, the

number of additional sterile neutrinos with diﬀerent masses, in principle, can be

arbitrary [2, 28, 29]. Phenomenological models with NSN are usually denoted

as (3 + N) models.

(3 + N) models are often used to describe SBL anomalies as well as some

astrophysical data [30]. It is desirable that the Nnumber would be minimal that

is why (3+1) and (3+2) models are mostly used [6]. However, taking into account

the possible left-right symmetry of weak interactions, (3 + 3) models attract

considerable attention (see, e.g. [7, 31]). In this paper, to take into account

the LSN eﬀects, the (3 + 3) model is also used [10], which includes three known

active neutrinos νa(a=e, µ, τ ) and three new (in this case light sterile) neutrinos:

sterile neutrino νs, hidden neutrino νhand dark neutrino νd. Thus, the model

contains six neutrino ﬂavor states and six neutrino mass states, therefore a 6×6

mixing matrix is used. This matrix is dubbed as the generalized mixing matrix or

the generalized Pontecorvo–Maki–Nakagawa–Sakata matrix UGPMNS ≡Umix [8].

Umix can be represented as the matrix product VP , where Pis a diago-

nal matrix containing the Majorana CP-phases ϕi,i= 1,...,5, that is P=

diag{eiϕ1, . . . , eiϕ5,1}. Below we will use only some particular forms of matrix

Umix. In this case, we will denote the Dirac CP-phases as δiand κj, and the

mixing angles as θiand ηj. In doing so, δ1≡δCP,θ1≡θ12,θ2≡θ23 and θ3≡θ13.

Only the normal order (NO) of the active neutrino mass states and the value

δCP = 1.2πwill be considered.

For compactness of formulas, we introduce symbols νband νi′for sterile left

ﬂavor ﬁelds and sterile left mass ﬁelds, respectively. So ﬁelds νbwith index b

contain ﬁelds νs,νhand νd, while i′denotes a set of indices 4, 5 and 6. A total

6×6 mixing matrix Umix can be represented in the form of 3×3 matrices R,T,V

and W:νa

νb=Umix νi

νi′≡R T

V W  νi

νi′.(1)

Let us represent the matrix Rin the form of R=κUPMNS, where κ= 1−ϵ, and ϵ

is a small quantity. The matrix Tin the equation (1) must also be a small matrix

as compared with the Pontecorvo–Maki–Nakagawa–Sakata 3×3 matrix for active

neutrinos UPMNS ≡U(UU+=I). So, active neutrinos mix by means of the U

matrix, as it should be in the νSM, when choosing the appropriate normalization.

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LightsterileneutrinoseffectsinprocesseswithelectronandmuonneutrinosV.V.Khruschov,S.V.FomichevNRCKurchatovInstitute,123182Moscow,RussiaAbstractSterileneutrinoswithvariousmassescouldbeparticipatedinastrophys-icalandcosmologicalprocessesincludingmixingwithactiveneutrinos,ifexist.Itisconsideredthepossib...

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Light sterile neutrinos effects in processes with electron and muon neutrinos V. V. Khruschov S. V. Fomichev

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