Astrophysical Limits  Neutrino Physics  Neutrino Physics

    
Introduction

Neutrino experiments are at the forefront of the physics because they offer one of the few opportunities at low and intermediate energies to probe the constituents of matter and their interactions. Within the standard model neutrinos are taken to be massless with no electromagnetic interactions and with only two degrees of freedom for each of the e, $\mu$, and $\tau$ family. There is no unambiguous empirical evidence in conflict with this simple picture, but also, there are no fundamental symmetries that would explain this baffling simplicity. The observation of neutrino masses, electromagnetic interactions, or the ``missing'' right-handed components would constitute the long-sought evidence for ``physics beyond the standard model.'' Neutrino masses in the 1-50 eV range would play an important role for cosmological structure formation (Sec. ). However, the bulk of the cosmic dark matter probably consists of some novel weakly interacting species such as the supersymmetric ``neutralinos.'' In many phenomenological ways they resemble massive Majorana neutrinos and are thus included in this report (Sec. ). There are only few efforts to search for anomalous electromagnetic neutrino couplings because the existing astrophysical limits indicate that it will be very difficult to detect such properties (Sec. ). On the other hand, neutrino magnetic dipole or transition moments would have important consequences in supernovae or the early universe, and they would provide clear evidence for physics beyond the standard model. The holy grail of neutrino physics is the quest for their masses. Direct experimental limits are obtained from the phase-space modification of reactions with final-state neutrinos (Sec. ). A far more restrictive constraint of around $50\ \rm eV$ on all flavours obtains from cosmology (Sec. ). This bound applies if neutrinos do not decay fast on cosmological time scales. This possibility requires neutrino interactions beyond the standard model. Thus it appears unlikely that neutrino masses can be discovered by direct kinematical methods with the exception of $\nu_e$ (Sec. ). It is conceivable that $\nu_\mu$ and $\nu_\tau$ masses in the 10 eV regime can be measured from signal dispersion effects of a future galactic supernova (Sec. ). Other than that one must rely on indirect methods to search for neutrino masses below the cosmological limit. The first approach relies on nuclear double beta decay. Recently it has become possible to measure the $2\nu2\beta$ mode in several cases. The unobserved neutrinoless ( $0\nu2\beta$) mode requires the violation of (electron) lepton number by two units. A Majorana mass term would have this effect with an amplitude proportional to $m_{\nu_e,{\rmMajorana}}$. Current $m_{\nu_e,{\rmMajorana}}$ limits are in the neighbourhood of 1 eV (Sec. ). This method requires a neutrino Majorana mass term while all charged fermions have Dirac masses. It is natural, however, to think of Dirac fermions as a pair of mass-degenerate Majorana ones. The absence of the electromagnetic gauge coupling for neutrinos obviates the need for them to be mass degenerate. The unobserved (right-handed) partner could well be very heavy, perhaps with a mass at the grand unification scale. The small masses of the active (left-handed) states are then natural in the framework of the see-saw mechanism. If neutrinos do have masses the flavours probably mix in analogy to the quarks. For example, the electron neutrino would be a superposition of three mass eigenstates m_j,

$$\vert\nu_e\rangle=\sum_{j=1}^3U_{ej}\vert\nu_j\rangle$$ (1.1)

 

with the mixing amplitudes U_ej. In this case, what the $0\nu2\beta$ experiments really measure is the quantity $\langlem_\nu\rangle\equiv\sum_{j} \lambda_j\vert U_{ej}\vert^2m_{j,{\rm Majorana}}$ where $\lambda_j$ is a CP phase equal to $\pm1$, and the sum is to be extended over all two-component Majorana neutrinos that mix with $\nu_e$. Another consequence of neutrino mixing is the phenomenon of flavour oscillations which is the most important indirect method to search for neutrino masses. A neutrino produced as a $\nu_e$ is generally a superposition of three mass eigenstates. Along a beam (z-direction) each of them acquires a phase according to the plane-wave propagation with $e^{-i(E_\nu t-p_\nu z)}$. Because $p_\nu=(E_\nu^2-m_\nu^2)^{1/2}$ the different mass components acquire different phases so that downstream one finds a new superposition. One distinguishes between appearance experiments where one searches for a neutrino flavour different from the one produced at the source, and disappearance experiments where a flux depletion of the originally produced flavour is looked for. In general, U is a $3\times3$ matrix, or even larger if one speculates that new (sterile) neutrino flavours exist. A general discussion of neutrino oscillations is thus quite complicated. We limit our presentation to two-flavour mixing, keeping in mind that a definitive interpretation of experimental results may require more complicated assumptions. Taking $\nu_e$-$\nu_\mu$ mixing as an example, the interaction eigenstates are expressed as

$$\pmatrix{\vert\nu_e\rangle\cr\vert\nu_\mu\rangle\cr}=\pmatr......theta\cr}\pmatrix{\vert\nu_1\rangle\cr\vert\nu_2\rangle\cr}$$ (1.2)

 

in terms of the mass eigenstates $\vert\nu_1\rangle$ and $\vert\nu_2\rangle$, and in terms of the mixing angle $\theta$. The probability for an original $\nu_e$ to appear as a $\nu_\mu$ is

$$p(\nu_e{\to}\nu_\mu)=\sin^2(2\theta)\,\sin^2(\pi L/L_{\rm osc})$$ (1.3)

 

where L is the distance from the source and

$$L_{\rm osc}=\frac{4\pi E_\nu}{\Delta m^2_\nu}=2.48~{\rm m}~\frac{E_\nu}{1~{\rm MeV}}\,\frac{1~{\rm eV}^2}{\Delta m^2_\nu}$$ (1.4)

 

is the oscillation length with $\Delta m^2=m_2^2-m_1^2$. Depending on the source and the detector distance, different experimental techniques are needed to cover various areas in the $\sin^22\theta$- $\Delta m^2$-parameter space. Besides accelerator neutrino beams (Sec. ) and reactors (Sec. ), both solar (Sec. ) and atmospheric neutrinos (Sec. ) have turned out to be extremely important. They exhibit signal characteristics that can be consistently interpreted by oscillations. When the neutrino beam passes through matter, notably in the case of solar and atmospheric neutrinos, the medium modifies the vacuum dispersion relation. The neutrino refractive index depends on the flavour because normal matter contains many electrons but no mu- or tau-leptons. This flavour birefringence modifies the effective mixing angle and effective $\Delta m^2$ as a function of matter density. When these effects are important one speaks of matter oscillations, otherwise of vacuum oscillations. In the Sun, the neutrinos are produced near the center and thus have to pass through a density gradient before they reach the surface. In this case it can happen that the effective $\Delta m^2$ changes sign along the beam, leading to so-called resonant oscillations or the MSW effect. In this situation one must go beyond the simple oscillation probability Eq. (). One can obtain an almost complete flavour conversion even for small mixing angles without parameter fine tuning. The experimental activities on the neutrino physics are carried out at reactors and high energy accelerators, in underground and small scale laboratories. A large part of these activities concern topics pertaining the nuclear physics. Some experiments, such as the double beta decay and the beta decay to search for the neutrino mass, involve directly the nucleus. Some others use experimental techniques typical of the low energy physics as the study of solar neutrinos and dark matter, and the experiments at the reactors. The understanding of the neutrino physics are of fundamental interest not only in the elementary particle physics but also in nuclear physics. Therefore all activities focused to fix the open problems are of great interest for both these fields.