We reconsider the possibility that the masses of the three light neutrinos of the Standard Model might be almost degenerate and close to the present upper limits from Tritium β decay and cosmology. In such a scenario, the cancellations required by the latest upper limit on neutrinoless double-β decay enforce near-maximal mixing that may be compatible only with the vacuum-oscillation scenario for solar neutrinos. We argue that the mixing angles yielded by degenerate neutrino mass-matrix textures are not in general stable under small perturbations. We evaluate within the MSSM the generationdependent one-loop renormalization of neutrino mass-matrix textures that yielded degenerate masses and large mixing at the tree level. We find that m νe > m νµ > m ντ after renormalization, excluding MSW effects on solar neutrinos. We verify that bimaximal mixing is not stable, and show that the renormalized masses and mixing angles are not compatible with all the experimental constraints, even for tan β as low as unity. These results hold whether the neutrino masses are generated by a see-saw mechanism with heavy neutrinos weighing ∼ 10 13 GeV or by non-renormalizable interactions at a scale ∼ 10 5 GeV. We also comment on the corresponding renormalization effects in the minimal Standard Model, in which m νe < m νµ < m ντ . Although a solar MSW effect is now possible, the perturbed neutrino masses and mixings are still not compatible with atmospheric-and solar-neutrino data.

The conclusions of the Physics Working Group of the International Scoping Study of a future Neutrino Factory and super-beam facility (the ISS) are presented. The ISS was carried out by the international community between NuFact05, (the 7th International Workshop on Neutrino Factories and Super-beams, Laboratori Nazionali di Frascati, Rome, 21-26 June 2005) and NuFact06 (Ivine, CA, 24-30 August 2006). The physics case for an extensive experimental programme to understand the properties of the neutrino is presented and the role of high-precision measurements of neutrino oscillations within this programme is discussed in detail. The performance of second-generation super-beam experiments, beta-beam facilities and the Neutrino Factory are evaluated and a quantitative comparison of the discovery potential of the three classes of facility is presented. High-precision studies of the properties of the muon are complementary to the study of neutrino oscillations. The Neutrino Factory has the potential to provide extremely intense muon beams and the physics potential of such beams is discussed in the final section of the report.

We explore interpretations of the anomaly observed by H1 and ZEUS at HERA in deep-inelastic e + p scattering at very large Q 2 , in terms of possible physics beyond the Standard Model. Since the present data could be compatible with either a continuum or a resonant solution, we discuss both the possibilities of new effective interactions and the production of a narrow state of mass M ∼ 200 GeV with leptoquark couplings. We compare these models with the measured Q 2 distributions: for the contact terms, constraints from LEP 2 and the Tevatron allow only a few choices of helicity and flavour structure that could roughly fit the HERA data. The data are instead quite consistent with the Q 2 distribution expected from a leptoquark state. We study the production cross sections of such a particle at the Tevatron and at HERA, the latter in the cases where it is produced from either a valence or a sea quark. The absence of a signal at the Tevatron disfavours the likelihood that any such leptoquark decays only into e + q. We then focus on the possibility that the leptoquark is a squark with R-violating couplings. In view of the present experimental limits on such couplings, the most likely production channels are e + d →c L or perhaps e + d →t, with e + s →t a more marginal possibility. We point out that thec L could have competing branching ratios for R-conserving and R-violating decay channels, whereast decays would be more likely to be dominated by one or the other. Possible tests of our preferred model include the absence both of analogous events in e − p collisions and of charged current events, and the presence of detectable cascade decays whose kinematical signatures we discuss. This model could also make an observable contribution to K → πνν and/or neutrinoless ββ decay. We also discuss the possible implications for the Tevatron and for e + e − →qq and neutralinos at LEP 2.

The universal behavior of superconductors near the phase transition is described by the three-dimensional field theory of scalar quantum electrodynamics. We approximately solve the model with the help of nonperturbative flow equations. A first-or second-order phase transition is found depending on the relative strength of the scalar versus the gauge coupling. The region of a second-order phase transition is governed by a fixed point of the flow equations with associated critical exponents. We also give an approximate description of the tricritical behavior and briefly discuss the crossover relevant for the onset of scaling near the critical temperature. Final confirmation of a second-order transition for strong type-II superconductors requires further analysis with extended truncations of the flow equations.

Motivated by the data from Super-Kamiokande and elsewhere indicating oscillations of atmospheric and solar neutrinos, we study charged-lepton-flavour violation, in particular the radiative decays µ → eγ and τ → µγ, but also commenting on µ → 3e and τ → 3µ/e decays, as well as µ → e conversion on nuclei. We first show how the renormalization group may be used to calculate flavour-violating soft supersymmetrybreaking masses for charged sleptons and sneutrinos in models with universal input parameters. Subsequently, we classify possible patterns of lepton-flavour violation in the context of phenomenological neutrino mass textures that accommodate the SuperKamiokande data, giving examples based on Abelian flavour symmetries. Then we calculate in these examples rates for µ → eγ and τ → µγ, which may be close to the present experimental upper limits, and show how they may distinguish between the different generic mixing patterns. The rates are promisingly large when the soft supersymmetry-breaking mass parameters are chosen to be consistent with the cosmological relic-density constraints. In addition, we discuss µ → e conversion on Titanium, which may also be accessible to future experiments.

We study CP violation in the lepton sector of the supersymmetric extension of the Standard Model with three generations of massive singlet neutrinos with Yukawa couplings Y ν to lepton doublets, in a minimal seesaw model for light neutrino masses and mixing. This model contains six physical CP-violating parameters, namely the phase δ observable in oscillations between light neutrino species, two Majorana phases φ 1,2 that affect ββ 0ν decays, and three independent phases appearing in Y ν Y ν † , that control the rate of leptogenesis. Renormalization of the soft supersymmetry-breaking parameters induces observable CP violation at low energies, including T-odd asymmetries in polarized µ → eee and τ → ℓℓℓ decays, as well as lepton electric dipole moments. In the leading-logarithmic approximation in which the massive singlet neutrinos are treated as degenerate, these low-energy observables are sensitive via Y ν † Y ν to just one combination of the leptogenesis and light-neutrino phases.We present numerical results for the T-odd asymmetry in polarized µ → eee decay, which may be accessible to experiment, but the lepton electric dipole moments are very small in this approximation. To the extent that the massive singlet neutrinos are not degenerate, low-energy observables become sensitive also to two other combinations of leptogenesis and light-neutrino phases, in this minimal supersymmetric seesaw model.result [2] encourages this possibility, since it further favours the large-mixing-angle (LMA) solution to the solar-neutrino deficit [13].As mentioned above, processes that violate charged-lepton flavour can provide important complementary information on the leptonic CP-violating phases. These may be measured using intense sources of stopped muons. The SINDRUM II experiment is designed to be sensitive to B(µT i → eT i) ∼ 10 −14 [14], and the MECO project would be sensitive to B(µAl → eAl) ∼ 10 −16 [15]. The experiment with the sesitivity Br(µ → eγ) ∼ 10 −14 is proposed at PSI [16]. The PRISM project [6,17] and the front ends of neutrino factories now under consideration at CERN [18] and elsewhere will provide beams of low-energy muons that are more intense by several orders of magnitude than any of the present facilities. This will enable the construction of stopped-muon experiments able to probe LFV processes with sensitivities Br(µ → eγ) ∼ 10 −15 , Br(µ → eee) ∼ 10 −16 . The latter sensitivity opens the way to measuring the T-odd, CP-violating asymmetry A T (µ → eee).

Supersymmetry with R-parity violation ͑RPV͒ provides an interesting framework for naturally accommodating small neutrino masses. Within this framework, we discuss the lepton-flavor violating ͑LFV͒ processes →e␥, →eee, and →e conversion in nuclei. We make a detailed study of the observables related to LFV in different RPV models, and compare them to the expectations of R-conserving supersymmetry with heavy right-handed neutrinos. We show that the predictions are vastly different and uniquely characterize each model, thus providing a powerful framework for experimentally distinguishing between different theories of LFV. In addition to the obvious possibility of amplified tree-level generation of →eee and →e conversion in nuclei, we find that even in the case where these processes arise at the one-loop level, their rates are comparable to that of →e␥, in clear contrast to the predictions of R-conserving models. We conclude that, in order to distinguish between the different models, such a combined study of all the LFV processes is necessary, and that measuring P-odd asymmetries in polarized →eee can play a decisive role. We also comment on the intriguing possibility of RPV models yielding a large T-odd asymmetry in the decay of polarized →eee.

Motivated by the Super-Kamiokande atmospheric neutrino data, we discuss possible textures for Majorana and Dirac neutrino masses within the see-saw framework. The main purposes of this paper are twofold: first to obtain intuition from a purely phenomenological analysis, and secondly to explore to what extent it may be realized in a specific model. We comment initially on the simplified two-generation case, emphasizing that large mixing is not incompatible with a large hierarchy of mass eigenvalues. We also emphasize that renormalization-group effects may amplify neutrino mixing, presenting semi-analytic expressions for estimating this amplification. Several examples are then given of three-family neutrino mass textures which may also accommodate the persistent solar neutrino deficit, with different assumptions for the neutrino Dirac mass matrices. We comment on a few features of neutrino mass textures arising in models with a U (1) flavour symmetry. Finally, we discuss the possible pattern of neutrino masses in a 'realistic' flipped SU (5) model derived from string theory, illustrating how a desirable pattern of mixing may emerge. Both smallor large-angle MSW solutions are possible, whilst a hierarchy of neutrino masses appears more natural than near-degeneracy. This model contains some unanticipated features that may also be relevant in other models: the neutrino Dirac matrices may not be related closely to the quark mass matrices, and the heavy Majorana states may include extra gauge-singlet fields.2 We note that a sterile neutrino with ∆m 2 1,4 ∼ 1eV 2 is sometimes postulated in order to accommodate the data from short-baseline neutrino experiments. Such a possibility may be realized [18] within some variants of the models we are examining, e.g., flipped SU(5), which include additional light neutral singlets as well as the three ordinary neutrinos. However, we do not discuss such scenarios here.