Neutrino overview

PROCEEDINGS SUPPLEMENTS

ELSEVIER

Nuclear

Physics B (Proc. Suppl.) 114 (2003) 125-140

www.elsevier.com/locate/npe

NEUTRINO OVERVIEW Jos~ Bernab~u D e p a r t m e n t of Theoretical Physics and IFIC, University of Valencia and CSIC These lectures discuss the possibilities for the origin of neutrino mass terms, as well as the evidence for masses and mixings from atmospheric and solar neutrino oscillations. The programme includes: 1.- Introduction 2.- Dirac versus Majorana neutrinos 3.- Effective Lagrangian approach 4.- Absolute Neutrino Masses 5.- Neutrino Oscillations 6.- Atmospheric Neutrinos 7.- Solar Neutrinos 8.- Outlook

1. I n t r o d u c t i o n Neutrinos have been a source of scientific discoveries in the last few years. In 1998 the SuperKamiokande (SK) experiment in J a p a n presented evidence of oscillations in atmospheric neutrinos[I]. In 1991 and 1992, the SNO (Sudbury Neutrino Observatory) experiment in Canada presented crucial results[2] t h a t solve the historical solar neutrino problem, again in terms of oscillations a m o n g the various neutrino species. The expectations generated by these discoveries in the scientific community are due, not only to the beauty of the physics involved in the quant u m mechanical phenomena of neutrino oscillations and the need to provide masses and mixings to the different neutrinos, but also to the hope t h a t these effects could be the first window to new physics beyond the Standard Model of elementary particles, describing the building blocks of matter and the fundamental interactions. Neutrinos play a very important role as probes in many fields of subatomic and subnuclear physics, as well as in astrophysics and cosmology. This probe is unique in the sense t h a t covers the exploration of distances from 10 -33 cm, in physics at the Planck energy scale of 10 +19 GeV, to the cosmological distances of 10 +28 cm in the present Universe. Such an immense reso0920-5632/03/$ - see front matter © PII S0920-5632(02)01900-X

2003 Elsevier Science B.V.

lution power of neutrinos to probe from element a r y particles to the entire Universe, due to the knowledge of their weak interaction with matter, contrasts however with the lack of knowledge on their intrinsic properties. Only recently we are observing phenomena which are sensitive to neutrino masses as well as to the mixing among the various neutrino species. Still we do not know whether neutrinos are Dirac or Majorana particles, with neutrinos and antineutrinos as different particles or as a unique rigorously neutral particle free of all kinds of charges. In Section 2 we discuss the possible neutrino mass terms, as well as the flavour mixing which is expected for both Dirac and Majorana particles. In Section 3 we use an effective Lagrangian approach which leeds to the dimension -5 operator for the lepton sector and to an effective see-saw result for the masses of Majorana neutrinos. Neutrinoless Double Beta Decay and Tritium Single Beta Decay are sensitive to absolute neutrino masses and the information provided by these processes is presented in Section 4. Section 5 discusses neutrino flavour oscillations, both in vacuum and in matter. In Section 6 we study the implications of atmospheric neutrino results for neutrino masses and mixings. Section 7 is devoted to solar neutrinos. Present conclusions, open problems and proposals for the near future All rights reserved.

126

J, BernabOu/Nuclear Physics B (Proc. Suppl.) 114 (2003) 125-140

are given in Section 8.

2. D i r a c v e r s u s M a j o r a n a N e u t r i n o s Neutrinos, contrary to other fermions, do not participate in parity conserving vector interactions QED and QCD, and only the left-handed UL field is active for weak interactions. There is no need of introducing the right-handed uR field as an independent field. If one does it, against the standard model choice, and a global lepton number is imposed as an exact symmetry, the UR only suffers the Yukawa interaction

£(~') = - v ~ - ~ L M(~')~'R~ + h.c. v

(1)

where ~L is the left-handed lepton doublet, uR is the right-handed neutrino singlet and ~ is the charge- conjugated of the scalar doublet, v is the vacuum- expectation- value of the neutral scalar field and M (~) is the mass matrix in flavour space. The form (1) is dictated by SU(2) x SU(1) electroweak gauge invariance. Under spontaneous symmetry-breaking, one sees t h a t

£(") ~-- --ULM(U)VR + h.c. mt288

(2)

and M (v) is a Dirac mass term. In this alternative, neutrinos would be similar to quarks: the analogous[3] to the CKM matrix would contain 3 mixing angles and 1 phase as physical parameters. Besides Eq. (1), the U R ' s do not appear elsewhere. With the global U(1) - symmetry, neutrinoless double/3eta decay would be thus rigorously forbidden in Nature. If uR does not exist as an independent field, we can ask: Is it possible, with only UL, to generate a non-vanishing neutrino mass? For the chiral/,I L field, its charge conjugated u~ is right-handed, so that one can write a Majorana mass term[4] f(Maj) 1 mass = --TVL

+ h.c.

(3)

For neutrinos, Eq. (3) is not, only Lorentz invariant, but also SU(3) cotour x U(1) ¢.m. invariant. It is thus a priori legal, contrary to all other charged fermions. The requirement of anticommutation for the quantum fermion fields leads to the symmetry condition M r = M for the Majorana mass nlatrix. M is, in general, a complex symmetric nmtrix and it can be diagonalized by means of a unitary matrix V according to

M = VmV

(4)

r

with m the diagonal matrix of mass eigenvalues. Eq. (3) can be written in terms of the fields X with definite mass

1

x

--

+ (v*.L)

(5)

For Majorana neutrinos, the physical neutrinos of definite mass are true neutral particles, with no conserved global lepton number. If a lepton number L is introduced, Eq. (3) transports two units of the lepton charge A L = 2, so t h a t neutrinoless double/3-decay would be allowed. The selfconjugate condition (5) of the X field does not allow the rephasing invariance, so that two relative phases[5] among the three neutrinos cannot be rephased away. The V matrix contains then 3 mixing angles and 3 phases as physical parameters. Two of the phases, however, can only be apparent when the process contains the genuine A L = 2 Majorana neutrino propagation. The Majorana mass t e r m (3) cannot be obtained in the standard model by spontaneous s y m m e t r y breaking of a SU(2) xU(1) gauge invariant Yukawa interaction: One would need a scalar triplet instead of the standard scalar doublet. This theory is not very attractive today: a scalar triplet at the electroweak scale runs into difficulties with the invisible Z-width. One concludes that the standard model predicts a vanishing mass neutrino.

J. Bernab&,/Nuclear Physics B (Proc. Suppl.) 114 (2003) 125-t40

3. Effective Lagrangian approach In the last 30 years one has seen a deep evolution in the understanding of quantum field theory, so that the requirement of renormalizability is taken today with a less dogmatic philosophy: it only means that shorter distances new physics is irrelevant at present energies. Take the particle content of the standard model without UR, and ask what is the lowest dimension non-renormalizable operator which still keeps the SU(2) x V(1) gauge invariance. The answer to this question is unique, given by the dimension5 operator[6] in the leptonic sector

(6) where ~ = i~-2~ c = i~-2C-~ T. We can say properly that Eq. (6) represents the first window to physics beyond the standard model. The symmetric matrix F T = F induces mixing in flavour space. The coupling ~ is the remnant of new physics at higher energies and fixes its scale. Eq. (6) generates, in addition to lepton flavour violation, A L = 2 transitions. After spontaneous symmetry breaking, Eq. (6) leads to a Majorana mass term (3) for neutrinos, with the mass matrix

righthanded uR. An alternative to it is suggested by the Fierz-reordered form of the effective Lagrangian (6)

The last bracket has the same transformation property of a scalar triplet, so that a very heavy Higgs triplet will do the job as well. The seesaw model[7] is most natural in the framework of grand unified theories such as SO(10)[8], or in left-right symmetric models[9], in wich the right-handed u n acquires a large Majorana mass as part of the symmetry breaking scenarios. But it also operates in the standard SU(2) x V(1) gauge invariant model, extended to include a heavy uR [10]. The most general mass terms compatible with symmetry include the left-right Dirac mass, generated by the standard spontaneous symmetry breaking in the Yukawa coupling, and a Majorana mass for right-handed neutrinos. As uR is sterile (electroweak singlet), this last term introduced by hand keeps the SU(2) x U(1) gauge invariance. We have

v2

(7)

We conclude that the new physics mechanism leads to massive Majorana neutrinos. Eq. (7) provides a simple and attractive explanation of the smallness of neutrino mass: it is of order V with respect to the mass of the other fermions. It relates the smallness of m . with the existence of a higher energy scale A, compared with the electroweak scale represented by the vacuum expectation value v = 174 GeV. The effective Lagrangian approach cannot unveil the origin of A, because the shorter distance physics has been integrated out. We will discuss below the see-saw model based on the introduction of very heavy

(8)

£eff= -~--~

D-M £mass

M = -~- F

127

=

1 --~Rrr~DVL -- ~ ' ~ R m R (UR) c + h.c.

=

_ _2

1

)c M n n

+

(9)

where the last equality follows from organizing the left handed fields (twice the number of families) as

nL

----

(,R) c

, M =

mD

mR

(10)

For the one-family case, let us discuss the limit The diagonalization of the 2x2 real symmetric matrix M leads to two Majorana neutrinos with masses ?riD < ' ~ m R .

J. Bernab~u/Nuclear Physics B (Proc. Suppl.) 114 (2003) 125-140

128

e

ml ~ m ~ , mR

m2~mR

(11)

x Vk

and definite CP eigenvalues rh = - 1 , r/2 = + l . T h e mixing angle is hierarchical 0 " ~mDR . Neglecting this small admixture between "active" and "sterile" neutrinos, the Majorana fields with definite mass are ,q -- i - L - i ( . L ) c ,

~2 -~ - R + (-R) c

(la)

mR

for the active and sterile 3x3 neutrino mass matrices, respectively. The subsequent diagonalization of the light neutrino mass matrix mL leads to active Majorana neutrinos with an expected hierarchy in the spectrum and the mixing among the three families. 4. A b s o l u t e

Figure 1.

(12)

corresponding to a light neutrino with mass m l < < m D and a heavy neutrino with mass m2 :>> m D . The scale mD is representative of the electroweak scale. The solution (11)-(12) is a realization of the general result obtained with the effective Lagrangian approach, with the high mass scale A represented here by mR. The mass Lagrangian of Eq. (9) violates global lepton number only by the Majorana mass term mR. One thus connects the smallness of the light neutrino mass to lepton number violation at the high mass scale. The results for one family can be generalized, so that mD and mR are matrices of dimension the number of families, Block-diagonalization of M gives. - , m rD, m L ~-- - - m D m R

Nucl. Phys.

76As

0* 2*

0÷ 76Se

Figure 2.

It becomes allowed for Majorana neutrino virtual propagation. It is described by the diagram of Fig. 1 as a second order weak interaction amplitude. It becomes a source of nuclear unstability for selected even-even nuclei in which the single beta decay is energetically forbidden. I show the level diagram corresponding to the decay of 76Ge in Fig.2. The flavour neutrino propagation is here

.~L ( < ) -rL (z2)

Neutrino Masses

"ekTX-k

If neutrinos are Majorana particles, the best known way to distinguish them from the Dirac case is the search for neutrinoless double ~3eta d e cay/3/30. [ll] (A,Z)

--+ ( A , Z + 2) + e -

+e-

(14)

(15) (Xl) Xk

k

=

Z V g a2r n k ~ _-~i

f daP eiP(*, x2) 1 - -27 5 C p2 _ m2k

k

If m k are small, when compared to the momenta relevant for nuclear physics excitations, the

J. Bernabku/Nuclear Physics B (Proc. Suppl.) 114 (2003) 125-140

Isotope neutrino masses can be neglected in the denom- E x p e r i m e n t KlapdorO1 7SGe inator of the propagator. T h e amplitude of the Aalseth02 76Ge process is then factorized in its different ingrediM i D B D - ~4)2 13°Te ents BelliO1 136Xe Table 1 Amp [~f~0v] = (m,) (Phase Space) ×

>((Nuclear Physics)

(17) k

where Vek is for Majorana neutrinos. This result shows t h a t the main ingredient to produce an allowed (j3~) ov is the massive Majorana neutrino character. Without mixing, the process is allowed. In the presence of mixing, there are contributions of the different physical neutrinos (k-index) to (my), contributions which can cancel each other. Even with CP-conserving interactions, the contributions of different CP eigenvalues ~k appear as (my> = ~

IVo~l2 m ~

T~I~2(y) > 1.9x1025 > 1.57x1025 > 2.1x1023 > 7x10 ~3

( m , ) (eV) < 0.35 < 0 . 3 3 - 1.35 < 0.85 - 2.1 < 1 . 4 - 4.1

(16)

The quantity of primary interest in neutrino physics is the average neutrino mass

(my> =

129

We know that, due to mixing, this weak state has no definite mass. I will call the effective mass leading to a distorsion of the beta spectrum m E. For "allowed" nuclear transitions, the nuclear matrix elements do not generate any energy dependence, so t h a t the electron spectrum is given by phase space alone ! dN = CpE(Q - T ) x / ( Q - T) 2 - m ~ F ( E ) ¥ dT

(19)

where E = T + m ~ , Q is the maximum energy and F(E) the Fermi function which incorporates final state interactions. The decay 3 H - ~ 3 H e + e - + F e is a superallowed transition with a very small energy release Q-18.6 keV. In the Kurie plot

(18)

k

For CP-violating interactions, there are 2 relative CP phases (out of 3) which intervene in (m~). T h e result (17) shows the dependence of the amplitude with the absolute neutrino masses mk [12]. T h e experimental situation is confusing at present. T h e best (/3/3)ov limits involve active source experiments[13, 14] and four of them are given in Table 1. There is a recent reanalysis of the 1990-2000 data of the Heidelberg-Moscow experiment [first line of Table1], which claims an "evidence" for 0~2f~ decay[15]. T h e analysis depends crucially of the selection of a small energy interval[16] for the 2/3 signal around the correct energy of the 7SGe decay. Depending on the choice, one can reach up t o a 2a-effect. T h e direct or kinematic search of the neutrino mass is based on[17] the hard part of the beta spectra in 3H single beta decay. With an abuse of language, this search was historically leading to an upper limit t o the electron neutrino mass.

K(T)

=-

dN

1

(20)

a non-vanishing m E provokes a distorsion from the straight-line T-dependence at the end point of the spectrum, in such a way that mf~=0 =~Tm~x = Q whereas m E # 0 =*zT~a~ = Q-m E. This is shown in Fig. 3

The experimental spectrum is fitted by m~ and many other parameters (Q, background term, normalization, ...). The most precise Troitsk and Mainz experiments[18, 19] give no indication in favour of m~ # 0. One has the upper limit m~ ~ 2 eV.

130

J Bernab$u/Nuclear PhysicsB (Proc. Suppl.) 114 (2003) 125-140

K(T)

ourselves to active left-handed z~'s without any demand for light sterile neutrinos. If the neutrino is prepared at t = 0 as v~, its propagation in vacuum leads to

'~'""""""~"-...,,..

"

~

Q

(~k . . . . ,

m

iEktv

(24)

s

The transition probability t h a t (24) is observed, at a distance L_~4, as v~ is given by Figure 3.

P (z/a~ P/3) The equivalent mass mz is a function of two mixings and three masses mz = f ( I V ~ l 2 , me)

(21)

which depends on the overlap of the three channels s; associated with the definite mass neutrinos. In the present situation, for which the energy resolution A E is much larger than all mass differences, the appropriate expression for m z is quadratic

m~ "-"E

k

IV~I2m~

(22)

One has to emphasize that this direct analysis in 3H /3eta decay is independent of whether neutrinos are Dirac or Majorana particles.

5. N e u t r i n o Oscillations The most sensitive method to prove that neutrinos are massive is provided by neutrino oscillations[20]. These phenomena are quantum mechanical processes based on masses and mixing of neutrinos. If the weak interaction states (greek indices) do not coincide with the mass eigenstates (latin indices) one has the coherent superposition v~

= E V~kVk

k

(23)

where v~ can be either Dirac or Majorana particles. For the present discussion, we will limit

X(e

k
(25)

where E is the neutrino energy and Am2kj the square mass differences of the physical neutrinos.One observes t h a t the physical observable (25) contains four V's- matrix elements in order to satisfy the invariance under rephasing of the neutrino states. One realizes that the conditions L Am~j-~

< < 1,Vk # j

(26)

lead immediately to P(v~ --~ vZ) _~ 5 ~ . In order to observe neutrino oscillations, in addition to mixing, one needs at least one A m 2 with A m 2 ~> E . T h e characteristic oscillating phases go like L/E. The flavour preparation and detection by means of charged current interactions leads to the classification of neutrino oscillation experiments into two types: 1) Appearance Experiments, with t~Z ~ z/a;2)Disappearance Experiments, measuring the survival probability P ( v a ---* z/a). Pure neutral current detection at distance L does not discriminate among flavours, so t h a t it is insensitive to neutrino oscillations. If the detection is by means of a process with interference between charged currents and neutral currents, the result is a neutrino oscillation experiment 3) Superposition of 1)4-2). This last strategy allows for an effective appearance experiment even for low energy ~c(z/e) such as produced by reactors

J. Bernab~u /Nuclear Physics B (Proc. Suppl.) 114 (2003) 125-140

(the sun). The superposition 3) is, in general, energy dependent, so that one can tune[21] the proportion of appearance versus disappearance behaviours. The reader can check that, for antineutrinos prepared from 7r--decay, the detection of ~e + P --* e + + n corresponds to a pure appearance experiment. For solar neutrinos, the detection u~ + d --* e - + p + p selects a disappearance experiment. On the contrary, the detection of solar neutrinos by means of uz + e- --* e- + uz is an example of the combination 3). In going from v to P, the mixing matrix changes from V to V*. The use of eq. (24) for the oscillating amplitude then says that C P T invariance implies

C P T =~ A(-~ ~ -~; t) = A* (a ~ 13; - t )

is an odd function of t. Due to the equality A(I3 --* a; t) = A*(a --+ /3; - t ) , the second term of (31) can be written as IA(a --*/3; - t)l 2 and the proof is completed. One has to emphasize, however, that this property is valid only for an hermitian Hamiltonian responsible of the time evolution, as it is the case for stable neutrinos. For an oscillation between two neutrino types, the mixing matrix of Eq. (23) is real and orthogonal

~

cP~

(28)

IA(a--*t3; t)l

(29)

t)[ =

There are important consequences of these relations[22]: 1) CP-, or T-, Violation can be seen in Appearance Experiments only. For a Disappearance Experiment, one has A* (a --* a; - t ) = A(a --* a; t), so that Eq. (27), asuming CPT-invariance, leads to the CP-invariance equality (29). 2) The CP- odd probability D~Z -~ JA(a --, ~; t)l 2 - IA(~ ~ ;

,(u

--*

u ' ) - - 2 sin220

1-cos

p(.

-~

.) = 1 - P ( . -~ .')

Am2L ~

-5V-

)

(33)

With two intervening parameters (Am 2, sin 2 28), the analysis of neutrino oscillation experiments was presented in two-dimensional "exclusion" plots. The general mixing for three families contains three angles and one CP-phase, accompanying two independent mass differences. All these ingredients have to have an active participation in order to generate CP violating observables[22, 23]. An interesting factorization of the matrix V is given by

1 0 V =

×

0 -s13e- ~

1 0

0/

0

023

823

0

--823

C23

0 c13

X

-812 0

c12 0

0 1

(30)

(34)

is unique for three flavours, i.e., De, = D,~ = D ~ . This is not so for the CP-even probability. 3) The T-odd probability

As we will see below, the left matrix is probed by atmospheric neutrinos and long-base-line neutrino beams, the right matrix by solar neutrinos and possibly by reactor experiments. The main question at present is the search of appropriate

T~Z -

t)l 2

(32)

( . ' # ~)

[A03-~a;t)l-IA(a~t3;t)

[A(~-~;

sin 0 ) cos0

and there is no room for CP-, or T-, nonconserving observables. The appearance and survival probabilities are given, correspondingly, by

(27)

I [A(-~ ~-~; t)[ = lA(a -~-~; t)[

cos 0 -sin0

V=

The (free) phase of the quantum CPT-operator is rephasing invariant, so that it can be chosen once for all. On the contrary, the phase of the CPor T-operators is rephasing variant and cannot be fixed for its matrix elements. The requirements for T, or CP, invariance are then written as

r

131

IA(a ~ / 3 ; 0] 2 - IA(B -~ a; t)l 2

(31)

J Bernabdu/Nuclear Physics B (Proc. Suppl.) 114 (2003) 125-140

132

In Vacuma

2 - 1 ..................

2 ~

1

In 1Vhfler

/\ Me

e. C

Figure 5. Figure 4.

experiments to probe the middle matrix: we will discuss this point in Section 8. In a medium, the electron-neutrinos u~ acquire an extra inertia due to the extra charged current interaction with the electrons of matter, described by the first diagram of Fig, 4 Neutral current interaction is universal for ux, with X = e, #, ~'. Contrary to the interaction with electrons, there is no difference for interactions with protons or neutrons for active neutrinos. As a consequence, the forward electronneutrino propagation acquires an extra phase coming from < Hcc >, with an amplitude which adds coherently to its propagation in vacuum. The effective hamiltonian in the extreme relativistic limit is, in the flavour basis,

{ oi i/} oo

+

sin 2 20 =

4s2c2 ; (O¢ -- cos 20) 2 -4- 482C2

a a = ~'-~m2(37)

and to a change in the spectrum as depicted in Fig. 5 Eq. (37) shows the possibility of a Resonant MSW-behaviour[24] at an anergy ER solution of the relation a = cos 20. In going from u to ~, the m a t t e r - t e r m changes sign a --~ - a , so t h a t the MSW-resonance will be apparent either for neutrinos iff cos20 > 0 or for antineutrinos iff cos20 < 0. In matter, the physical domain of the mixing is the entire quadrant 0 ° < 0 < 90 °. The appearance probability P @¢ --* u ' ) = sin2 20sin 2 A

(38)

(35)

0 0

where the potencial is given by

a = GFv/-~N ~ V-- 2E

of electrons, which contributes coherently to forward scattering, so t h a t -~Pe7o~Pe ~ ~p+ ~ ~p~ is the Number Operator. In the case of two families (ue,u I) for solar neutrinos, and constant Ne , the diagonalization of H leads to an effective mixing

(36)

with N~ the electron number density. The result (36) comes from the vector charge density

has the following features: 1) ON-resonance, sin 2 20 ---* 1 whereas the effect of level-crossing in matter leads, except for the resonance-width, to 2x --* 0. As a consequence, the resonance will not be apparent in Eq. (38) unless one goes to extremely long base-lines, compared with the inverse width. 2) OFF-resonance, where the oscillating phase 2x = A (1 - a ) , with A the oscillating phase in vacuum, has a distorsion of the L / E - b e h a v i o u r .

J Bernab~u/Nuclear Physics B (Proc. Suppl.) 114 (2003) 125-140

K

p, He... k r ~ , K± vl~/

1 ~------~,--~.,wv I

v~/~vc

e±

L= 10-30Km

71 ~--~1

,.T~T - • --r.-.-,~--r-r-v~-r~.

~........ r"" ~ "~ "T'v'r

e-like

~t

°i

IIII/llll~llXl/lllllll Z/~

133

--

.1,

:" :::i •

~

I

l,~lll

!

~

,

i

:l,i|

i

I

,

kkll,l

L = up to 13000 Km

Figure 6.

/

.~i

................

~,£_ _ _ _

/

6. Atmospheric Neutrinos The interaction of a primary cosmic ray in the upper layers of the atmosphere results in the development of a hadronic shower. This leads to a flux of neutrinos from charged pion and muon decay, as indicated in Fig.6, These neutrinos have energies ranging from -O.1GeV to several GeV. Their interaction rate is of the order of 100/y for a target mass of 1 Kton. Since a uu is produced from both r i and p~ decay, and a u~ from #± decay only, one expects the ratio between the uu and ue fluxes on Earth to be equal to 2 if both 7r± and #± decay in the atmosphere. This is a good approximation for neutrinos with energies lower than 3 GeV. At higher energies, this ratio increases. Calculations of atmospheric neutrino fluxes have an uncertainty of the order of +30%, but the uncertainty on the predicted uu/Ue ratio is believed to be of the order of 4-5% [25]. Underground experiments have measured the atmospheric neutrino fluxes by detecting quasielastic interactions in nuclei.

u~(u~)+n--~ v.

+ p

the order of 0.6 ( see the discussion in Ref. [26] ). The baseline L of the atmospheric neutrinos from the production point to the detector varies enormously with the zenith angle 0. Also, the higher the neutrino energy, the better the outgoing charged lepton follows the incident neutrino direction. Measurements of the zenith angle distributions are a sensitive way to search for neutrino oscillation with variable neutrino energies and baselines, without a need to compare with (u,/u~) predicted! Fig. 7 shows the up-down asymmetry obtained by the Super-Kamiokande collaboration [1]. The asymmetry is defined as (U - D)/(g + D), where U(D) is the number of events with cos0 < - 0 . 2 ( c o s 0 > 0.2). While for electron events the asymmetry is consistent with zero, for muon events its absolute value increases with energy and reaches a value around -0.4 above 1

GeV.

#-(e-)+p (e+) + n

Figure 7.

(39)

The comparison between the measured and predicted u~/u~ ratio leads to a double ratio R ==-((u~/~e) measured) / ((uu/~e) predicted) of

Conventional interpretations of the up-down asymmetry can be excluded and one is led to the existence of a new phenomenon. Its most plausible interpretation is the occurrence of u u oscillations, leading to ur or to a new type of "sterile" neutrino u~. For two-neutrino mixing u v - uT,

134

J Bernab~u/Nuclear Physics B (Proc. Suppl.) 114 (2003) 125-140

the best fit values of the parameters are [27] Am322 = 3 x 10-3eV 2, tan 2 023 = 1

(40)

A u u - Us oscillation can be distinguished from the oscillation to an "active" neutrino by studying neutral current interaction. Oscillations to an active neutrino do not change the rate of these events, whereas us has neither charged nor neutral-current interactions. In the SuperKamiokande experiment, the reaction u + N --* u + 7r° + N was studied. One concludes that us cannot be the partner of u , in a two neutrino mixing, although some mixing of us in a three (or four) neutrino mixing is still allowed[28]. Matter effects for neutrinos traversing the E a r t h affect u , - us oscillations, contrary to u , - u~- oscillations with no matter effects.

spectrum of solar neutrinos. The main pp cycle, responsible for 98.5% of the Sun luminosity, involves the following reactions

p+p

~

e+ + u ~ + d

p+d

~

",/+3He

~

4He + p + P

3He + 3He

(45)

These reactions (45) represent 85% of the pp cycle. The remaining 15% involves the following sequence

3He +4 H e

---* "7 +7 B e

e- +7 B e

---* Ue +7 Li

p+rLi

~

(46)

4He+4He

In about 2 × 10 - 3 of the cases, there is a third sequence starting from 7Be

7. S o l a r N e u t r i n o s There are several nuclear fusion reactions occurring in the Sun core, all having the net effect

p+rBe 4!o __,4 H e + 2e + + 2u~

(41)

These reactions are followed by the annihilation of the two positrons with two electrons, so the average energy emitted by the Sun in form of electromagnetic radiation is

8B 8Be

=

--~

8Be + e + + ue

~

4He +4 H e

(47)

The initial tYp reaction of Eq. (45) is sometimes (0.4%) replaced by p+e-

Q

--~ , y + 8 B

+p--~d+u~

(48)

( 4 r a p - MH~ + 2m~) c 2 - (E(2u~))

"~ 2 6 M e V

(42)

where (E (2Ue)) --~ 0 . 6 M e V is the average energy carried by the two neutrinos. As the Sun luminosity is measured to be Lo = 2.4 × 1 0 3 9 M e V / s

(43)

one can calculate from Q and Lo the rate of Ue emission from the Sun dg(ue) 2no 1038s_ 1 d---~ - - - Q - = 1.8×

(44)

From this rate, one can obtain the solar ue flux on Earth ¢~ _~ 6.4 x 101°cm-2s -1 The Standard Solar Model (SSM), developed and updated[29] by Bahcall, predicts the energy

The neutrinos produced in each sequence will be denoted by upv,UBe , UB, and vv~v. In Fig.8, the ve flux is shown as a function of energy, as predicted by the SSM. The Upp flux is the dominant component. However, neutrino cross-sections increase with energy, so these neutrinos are not easy to detect. It is interesting to point out that solar neutrinos arrive on Earth in 500s, whereas it takes 106 years for the energy transport from the Sun core to its surface. Thus the Sun luminosity which is measured at present is associated with neutrinos which reached the Earth one million years ago. Is this a problem? The Sun, which is a star in the main sequence, has no appreciable change of properties over ~ 108 years. The Solar neutrino experiments are:

J. Bernab~u/Nudear Physics B (Proc. Suppl.) 114 (2003) 125-140 ~._tch~..

135

~ - ~ r r'. ~No ,

o @ z

Neutrino Energy (MeV)

Figure 9. Figure 8. tering 1) T h e H o m e s t a k e e x p e r i m e n t . [ 3 0 ] Solar neutrinos were detected for the first time by Davis and collaborators in the Homestake gold mine (South Dakota, USA). The method, proposed by Pontecorvo, consists in measuring the production rate of 37A from u'~ +37 C1 ~ e- +3v A

(49)

The neutrino energy threshold for this reaction is 0.814MeV, so this reaction is not sensitive to the upp component, as shown in Fig. 8. It has become customary to express the solar neutrino capture rate in Solar Neutrino Units or SNU (1SNU = 1 capture/s from 1036 nuclei). The result of the Homestake experiment, averaged over more than 20 years of data taking, is Re×p (37C/) = 2.56 ± 0.23 S N U

(50)

whereas the rate predicted by SSM is Rth (37C/) = 7.7 ± 1.1 S N U . This comparison is presented in the first column in Fig. 9. 2) S u p e r - K a m t o k a n d e [ 3 1 ] This is a real time experiment using an underground detector installed in the Kamioka mine in Japan. The inner detector, filled with 32 Ktons of water, is used as an imaging Cerenkov counter. Solar neutrinos are detected by the elastic scat-

ux + e- ~ ux + e:-

(51)

which is suppressed by --~ 1/6 for u~ and u~ with respect to u~. The threshold is about 5 M e V , so the experiment is only sensitive to uB. The detected electron from (51) has a very strong directional correlation with the incident neutrino. This property is used to demonstrate the solar origin of the events, as shown in Fig. 10, which displays the angular distribution between the electron direction and the Sun-to-Earth direction at the time of the event. The peak at cos Os~n -- 1 is due to solar neutrinos The Super-K experiment measures a flux-ratio of 0.45 ± 0.02, to be compared with the SSM prediction of 1.0 ± 0.18, as indicated in the second column of Fig. 9. 3) G a l l i u m e x p e r i m e n t s [ 3 2 , 33, 34] Two experiments, GALLEX and SAGE, have measured the rate of the reaction u~ +71 Ga _.71 Ge + e-

(52)

which has a neutrino energy threshold of 0.23 M e V and is sensitive to the upp contribution. GALLEX, installed in the Gran Sasso underground laboratory in Italy, uses 30.3 tons of Gallium dissolved in H C1. SAGE, installed in the Baksan underground laboratory in Russia, uses

136

J Bernab~u/Nuclear Physics B (Proc. Suppl.) 114 (2003) 125-140 ~

~

solar nmdstno e y e i n g !

occurs, with a good measurement of ~ energy spectrum and some directional sensitivity 1 - ~ cos Osun. The main feature of SNO is its capability to detect the neutral current reaction

Mar P e a k above S M e Y SK4

/

0.1 -.

.

14,q6day5,0-20MeV

-- ,"-<

-o.,,

%

-"

o

0.465 4- O . O 0 5 ( s t a t ) _ ~ : ~ l ~ C s y s .

--

22.5M

J - "'~

N C : ~ + d --* ~ + p + n •

which has the same cross section for all three neutrino flavours and thus measures the total SB /]B flux from the Sun. Any significant difference between the neutrino fluxes as measured from reactions (54) and (55) is an unambiguous proof of neutrino oscillations. The electron elastic scattering reaction

o.5 ~ 2 ) x

ES : ~ + e

Figure 10.

57 tons of metalic Gallium. In both radiochemical experiments, 71Ge is extracted after some time, as it was for 37At in the Homestake experiment. The atomic X-rays emitted from 71Ge decay, through e - +71 Ge _~7] Ga + u~, are detected in order to provide evidence for 71Ge production by solar neutrinos. The 71Ge production rate from solar neutrinos is measured to be

R(r'Ga)

=

74 4-7 S N U , G A L L E X + G N O

R(rlGa)

:

75 4-7 S N U , SAGE

(53)

where GNO is the continuation of GALLEX experiment. T h e SSM prediction is 129 4-8 SNU, and the comparison is shown in the third column of Fig. 9. The comparison, shown in Fig. 9 for the three columns, between the Rates predicted by SSM versus the Experiments constitutes the historical Solar Neutrino Problem. 4) SNO[35, 2] The Sudbury Neutrino Observatory (SNO) is a neutrino detector installed in a mine near Sudbury in Canada. The detector contains --~ 1 Kton of high purity heavy water surrounded by ,-~ 8 Ktons of ultra-pure water for shielding purposes. In heavy water, the charged current reaction + p+ p

(54)

--* v~ + e -

(56)

is sensitive to all ~ types, but it presents an enhanced sensitivity to ~ . As we know, (56) has a strong directional correlation, but it is a low statistics experiment. T h a main point of SNO is thus t h a t cc

(sT)

_

v~ + u~ + u~

NC

the Charged-Current to Neutral-Current ratio is a direct signature for neutrino oscillations. The C C / E S ratio CC ES

C C : ~,e + d ~ e -

(55)

~

=

~ +0.15(~

+ ~z)

(58)

could also show significant effects. From a sample of CC

:

1967.7 +61"9 events -60.9

NC

:

576.5 +49.5 events -48.9

ES

:

263 •6+26"4 - 2 5 . 6 events

(59)

the SNO-collaboration has performed a shape constrained analysis to extract the SB tJB fluxes, with an energy threshold of 5 M e V . The result is ¢ c c (u~)

:

CNC (ux)

=

1 76 +0.06 4-0.09 x 106cm-2s -1 " -0.05 5 09 +0.44 +0.46 " --0.43 --0.43 × 106cm--2s-1

¢ES (ux)

=

2 "39 +0.24 --0.23 4-0.12 X 106cm-2s 1

(60)

I Bernab#u/Nuclear Physics B (Proc. Suppl.) 114 (2005) 125-140

137

8. O u t l o o k LMA

Maximal mixing

o

We have seen that there is convincing and consistent evidence for neutrino oscillations coming from atmospheric and solar neutrino data. A zeroth-order approximation for the mixing matrix is

LOW

doesn't L~I

0O% ~L

116"1,C L

"4 ~

'41 "2.11 !

-t,S -1 ~

v

IIJ| I

k,e(m, e)

=

All SNO, SK D/N spectra; Ga, CI, SSM but 8B free.

(*

1

0 1

~

--~

)

(62)

The value dpNC (Vx) is in agreement with the predicted flux by SSM! From the result (60), one is able to extract the appearance flux of vu,~ as detected at the neutrino arrival

taking both 82a and 812 to be maximal. We know that there are significant deviations for 012 which are important to be settled. The first test of the solar neutrino solution will come from the Japanese Reactor Experiment KAMLAND[37]. KAMLAND aims at detecting the Fe produced by five nuclear reactors located at distances between 150 and 210 km from the detector at Kamioka. The V~, with an average energy of 3 M e V , are detected by measuring the e + signal from the reaction

¢ (vu,r)

P~ + p --* e + + n

Figure 11.

=

3.41 4- 0 "45 +0.48 - 0 . 4 5 × 106cm-2s-]

(61)

The result (61) is a proof, by many standard deviations, of the fiavour change in the travel of neutrinos from the Sun to the Earth! One notes from Eq. (60) that the actual redepletion is about 1/3. This is, in fact, consistent with the deficit observed by the Davis experiment. The flux measured by Super-K, of the order of 1/2 of that of the SSM, is now understood as coming from the additional vu,r fluxes which contribute to elastic scattering. The analysis of all solar neutrino data: SNO, SK, Ga, C1, with the constraint of the SSM except for the SB flux which is left free, is presented in Fig. 11 in terms of a two-neutrino mixing between ve and v , a superposition of v~ and vr which cannot be distinguished by solar neutrino experiments. The large-mixing-angle solution, associated with the MSW matter effects in the Sun, is favoured[36]. This LMA-MSW result gives Am~2 = 8 × lO-~eV 2 < < Am~a and a mixing 012 which, although large, is not maximal (as it was for O2a). !

(63)

followed by the late 3' signal from the neutron capture reaction n + p --* d + 7, which occurs after neutron thermalization. Because of its large distance from the reactors and the low 7~ energy, KAMLAND is sensitive to A m 2 > 7 × 10-6eV 2 and sin220 > 0.1, a region which includes the LMA-MSW, large A m 2 solar neutrino solution. BOREXINO is an experiment[38] near to start at the Qran Sasso Laboratory. The aim is to detect v~ - e- elastic scattering with an energy threshold as low as 0.25MeV. The experiment is thus sensitive to the Vs~ component of the solar neutrino flux (E = 0.86MeV) and thus to the energy dependence which is expected from matter effects in solar neutrino oscillations. The verification of the atmospheric neutrino oscillation results will come from long baseline experiments at accelerators. The sensitivity of searches for v ~ - u~ oscillations will be increased to reach A m 2 as low as l O - 3 e V 2 using vp beams of well known properties. The K2K experiment [39], using neutrinos from the decay of 7r and K mesons produced by the KEK 12 G e V

138

J. Bernab~u/Nuclear Physics B (Proc. Suppl.) 114 (2003) 125-140

proton synchrotron and sent to the SK-detector at a distance of 250 km, is in operation. The beam energy is low, so that the main items are the disappearance rate and the distorsion of the energy spectrum. The MINOS experiment will use two detectors, one at Fermilab[40], the other located at the Soudan mine. Both detectors are iron-scintillator sandwich calorimeters with a toroidal magnetic field in the iron plates. The experiment can provide therefore muon charge discrimination. The main aim, in a disappearance experiment, is the precise determination of the neutrino oscillation parameters and observe the characteristic L/Edependence. The measurement of the N C / C C ratio will be very important to discriminate between different oscillations. The distance from Fermilab to Soudan is 730 Km. The CNGS project[41] consists of a neutrino beam from the CERN 450 G e V SPS sent to the Gran Sasso Laboratory at a distance of 732 Km. Two detectors, OPERA[42] and ICARUS[43], are under construction to search for T production in an appearance experiment from a u~-beam. This detection will test the main flavour oscillation, uu - u r , suggested by present atmospheric neutrino results. The main pending question in the determination of the mixing matrix V is the size, if any, of V~3. This 013- ingredient is fundamental in order to have a physical CP-phase 6 to generate CP-, and T-, violating observables in neutrino oscillations. Although other approaches could be also significant to reach some conclusions on 013, an appearance neutrino oscillation experiment u u - ue looks superior. Up to know, the CH00Z disappearance experiment ~e - r e at a nuclear reactor provides[44] the upper bound ]Veal <~ 0.2. The value of 013 is the fundamental input in taking decisions on long-term projects, like neutrino factories[45] based on muon storage rings. The wrong sign # - induced by ue - uu oscillations from #+ decay is the main channel envisaged by these studies. One question which cannot be settled by neutrino oscillations in vacuum is the form of the spectrum for massive neutrinos, either hierarchical or inverted, as shown in Fig.12.

.3 /~]ll 2

VS

2

Am: 3

Figure 12.

The interference with medium effects sees the sign of A m 2. It is based in that, in going from u to U, the potential changes sign a --* - a . It has been suggested[46] to measure the muon-charge asymmetry for atmospheric neutrinos from below, in order to reach baselines of at least 7000 Km able to make apparent the MSW-resonance induced by a non-vanishing 813. A magnetized iron detector, like MINOS or MONOLITH, is mandatory for these studies and a mass of about 100 Kton is necessary to reach enough sensitivity[47]. To conclude, let me emphasize that neutrino flavour oscillations cannot distinguish whether neutrinos are Dirac or Majorana particles. Although Theory probably prefers u~s as Majorana particles, the answer can only come from the observation of a process which includes the AL = 2 Majorana neutrino propagation.

9. A C K N O W L E D G E M E N T S I would like to thank the Organizers of the XXX International Meeting on Fundamental Physics at Jaca for the pleasant atmosphere and the stimulating meeting. This work is supported by the Grant AEN99-0962 of the Spanish CICYT.

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