научная статья по теме NEUTRINO ELECTROMAGNETIC PROPERTIES Физика

Текст научной статьи на тему «NEUTRINO ELECTROMAGNETIC PROPERTIES»

= ЭЛЕМЕНТАРНЫЕ ЧАСТИЦЫ И ПОЛЯ

NEUTRINO ELECTROMAGNETIC PROPERTIES

© 2009 C. Giunti1)*, A. I. Studenikin2)**

Received January 22, 2009; in final form, May 7, 2009

The main goal of the paper is to give a short review on neutrino electromagnetic properties. In the introductory part of the paper a summary on what we really know about neutrinos is given: we discuss the basics of neutrino mass and mixing as well as the phenomenology of neutrino oscillations. This is important for the following discussion on neutrino electromagnetic properties that starts with a derivation of the neutrino electromagnetic vertex function in the most general form, that follows from the requirement of Lorentz invariance, for both the Dirac and Majorana cases. Then, the problem of the neutrino form factor definition and calculation within gauge models is considered. In particular, we discuss the neutrino electric charge form factor and charge radius, dipole magnetic and electric and anapole form factors. Available experimental constraints on neutrino electromagnetic properties are also discussed, and the recently obtained experimental limits on neutrino magnetic moments are reviewed. The most important neutrino electromagnetic processes involving a direct neutrino coupling with photons (such as neutrino radiative decay, neutrino Cherenkov radiation, spin light of neutrino and plasmon decay into neutrino—antineutrino pair in media) and neutrino resonant spin-flavor precession in a magnetic field are discussed at the end of the paper.

PACS:14.60.St, 13.15.+g

1. INTRODUCTION

The neutrino is a very fascinating particle which has remained under the focus of intensive investigations, both theoretical an experimental, for a couple of decades. These studies have given evidence of an ultimate relation between the knowledge of neutrino properties and the understanding of the fundamentals of particle physics. The birth of the neutrino was due to an attempt, by W. Pauli in 1930, to explain the continuous spectrum of beta-particles through "a way out for saving the law of conservation of energy" [1]. This new particle, called at first the "neutron" and then renamed the "neutrino", was an essential part of the first model of weak interactions (E. Fermi, 1934). Further important milestones of particle physics, such as parity nonconservation (T.D. Lee, C.N. Yang, and L. Landau, 1956) and the V—A model of local weak interactions (E. Sudarshan, R. Marshak, 1956; R. Feynman, M. Gell-Mann, 1958), as well as the structure of the Glashow—Weinberg—Salam standard model, were based on the clarification of the specific properties of the neutrino. It has happened more than once that a novel discovery in neutrino

!)infn, Section of Turin, University of Turin, Italy.

2)Department of Theoretical Physics, Moscow State University, Russia.

E-mail: giunti@to.infn.it E-mail: studenik@srd.sinp.msu.ru

physics stimulates far-reaching consequences in the theory of particle interactions.

The neutrino plays a crucial role in particle physics because it is a "tiny" particle. Indeed, the scale of neutrino mass is much lower than that of the charged fermions (mVf < mf, f = ). The weak and electromagnetic interactions of neutrinos with other particles are really very weak. That is a reason for the neutrino to fall under the focus of researchers during the latest stages of a particular particle physics evolution paradigm when all of the "principal" phenomena have been already observed and theoretically described.

Neutrino electromagnetic properties, that is the main subject of this paper, are of particular importance because they provide a kind of bridge to "new physics" beyond the standard model. In spite of reasonable efforts in studies of neutrino electromagnetic properties, up to now there is no experimental confirmation in favor of nonvanishing neutrino electromagnetic characteristics. The available experimental data in the field do not rule out the possibility that neutrinos have "zero" electromagnetic properties. However, in the course of the recent development of knowledge on neutrino mixing and oscillations, supported by the discovery of flavor conversions of neutrinos from different sources, nontrivial neutrino electromagnetic properties seem to be very plausible.

The structure of the paper is as follows. In the first part of the paper we summarize what we really

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ud s c b t

e , t

i I

i_i_i_i_i_i_i_i_i_i_i_l_

_l_I_I

10-4 10-2 100 102 104 106 108 1010 1012

m, eV

Fig. 1. Order of magnitude of the masses of leptons and quarks.

know about neutrinos: the basics of neutrino mass and mixing are discussed, as well as the phenomenology of neutrino oscillations. This introductory part is important for understanding the second part of the paper that is devoted to electromagnetic (in the sense mentioned above still "unknown") properties of neutrinos. We start discussing neutrino electromagnetic properties deriving the neutrino electromagnetic vertex function in the most general form for both the Dirac and Majorana cases. Then, we consider the neutrino electric charge form factor and charge radius, magnetic, electric and anapole form factors. We discuss the relevant theoretical items as well as available experimental constraints. In particular, the neutrino magnetic and electric moments, in both theoretical and experimental aspects, are discussed in detail. In Section 3, the most important neutrino electromagnetic processes involving the direct neutrino couplings with photons (such as neutrino radiative decay, neutrino Cherenkov radiation, spin light of neutrino and plasmon decay into neutrino— antineutrino pair in media) and neutrino resonant spin-flavor precession in a magnetic field are discussed.

2. WHAT WE KNOW ABOUT NEUTRINO

In the Standard Model of electroweak interaction, forged in the 60's by Glashow, Weinberg, and

Salam [2—4], neutrinos are massless by construction (see [5]). This requirement was motivated by the low

experimental upper limit on the neutrino mass (see

Fig. 1) and by the theoretical description of neutrinos through massless left-handed Weyl spinors in the two-component theory of Landau, Lee and Yang, and

Salam [6—8], which prompted the V—A theory of

charged-current weak interactions of Feynman and

Gell-Mann, Sudarshan and Marshak, and Saku-

rai [9-11].

The masslessness of neutrinos in the Standard Model is due to the absence of right-handed neutrinos, without which it is not possible to have Dirac mass terms, and to the absence of Higgs triplets, without which it is not possible to have Majorana mass terms. In the following we will consider the extension of the Standard Model with the introduction of three right-handed neutrinos. We will see that this

seemingly innocent addition has the very powerful

effect of allowing not only Dirac mass terms, but also Majorana mass terms for the right-handed neutrinos which induce Majorana masses for the observable neutrinos.

The table shows the values of the weak isospin, hypercharge, and electric charge of the lepton and Higgs doublets and singlets in the extended Standard Model under consideration. For simplicity, we work in the flavor basis in which the mass matrix of the charged leptons is diagonal. Hence, e, ¡, t are the physical charged leptons with definite masses. The three singlet neutrinos are often called sterile, since they do not take part in weak interactions, in contrast with the standard active neutrinos ve, v„, vT.

2.1. Dirac Mass Term

The fields in the table allow us to construct the Yukawa Lagrangian term

3

¿Y = - + H.C., (1)

a=e,^,T k=l

where Y is a matrix of Yukawa couplings and $ = = ia2$*. In the Standard Model, a nonzero vacuum expectation value of the Higgs doublet,

(*) =

1 I 0

71

(2)

induces the spontaneous symmetry breaking of the Standard Model symmetries SU(2)L x U(1)y ^ ^ U(1)q. In the unitary gauge, the Higgs doublet is given by

$(x) =

1

V2

0

,v + H (x)

(3)

where H(x) is the physical Higgs field. From the Yukawa Lagrangian term in Eq. (1) we obtain the neutrino Dirac mass term

Ct

v

71

Y ^2YakVaLVSkR + yi.C. (4)

a=e,^,T k=l

Since the matrix Y is, in general, a complex 3 x 3 matrix, the flavor neutrino fields ve, v^, vT do not

v

2

v

3

Eigenvalues of the weak isospin I, of its third component I3, of the hypercharge Y, and of the charge Q = I3 + Y/2 of the lepton and Higgs doublets and singlets in the extension of the Standard Model with the introduction of right-handed neutrinos

/ h Y g

Left-handed lepton doublets LaL SE M 1/2 1/2 -1 0

\aL J -1/2 -1

Right-handed charged-lepton singlets oir 0 0 -2 -1

Right-handed neutrino singlets Vsr 0 0 0 0

Higgs doublet 1/2 1/2 + 1 1

w -1/2 0

Note. a = e, ß, t and s = s1, s2, s3.

have a definite mass. The massive neutrino fields are obtained through the diagonalization of LD. This is achieved through the transformations

3 3

vaL = UakUkL, UsiR = E V3kUkR, (5)

k=1

k=1

with unitary matrices U and V which perform the biunitary diagonalization

(6)

with real and positive masses mk. The resulting diagonal Dirac mass term is

k=1

£d = - rrikVkLVkR + H.c. 3

^rrijMvk,

(7)

k=1

with the Dirac fields of massive neutrinos vk = vkL +

+ VkR.

2.2. Dirac—Majorana Mass Term

In the above derivation of Dirac neutrino masses we have implicitly assumed that the total lepton number is conserved. If this assumption is lifted, neutrino masses receive an important contribution from the Majorana mass term of the right-handed singlet neutrinos,

1

Cr = Ö E ^IrC]M^S]R + H.c.

(8)

k,j=1

where C is the charge-conjugation matrix. The mass matrix MR is complex and symmetric.

The Majorana mass term in Eq. (8) is allowed by the symmetries of the Standard Model, since right-handed neutrino fields are invariant. On the other hand, an analogous Majorana mass term of the left-handed neutrinos,

U = \ Y. + H.c., (9)

a,f3=e,^,r

is forbidden, since it has I3 = 1 and Y = —2. There is no Higg

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