arXiv subjects

W. G. Scott

Publications and source records attributed to W. G. Scott.

30 records · Page 2Linked to original sources

arXiv2002

Mu-Tau Reflection Symmetry in Lepton Mixing and Neutrino Oscillations

We examine the possibility that the lepton mixing matrix may exhibit a strong form of mu-tau universality, in which corresponding elements of the mu- and tau-neutrino flavour eigenstates have equal moduli, and find that it is consistent with present data on neutrino oscillations. We point out that in the Dirac case, this is equivalent to symmetry under mu-tau reflection, ie. the combined operation of mu-tau flavour exchange in the MNS matrix with a CP transformation on the whole leptonic sector. We give the most general form for such a mixing matrix, examine the lepton mass matrices under such a symmetry, and explore the observable manifestations of the symmetry in neutrino oscillations.

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arXiv2002

Neutrino Matter Effect Invariants and the Observables of Neutrino Oscillations

We generalise our previous observation on the invariance of the Jarlskog determinant to matter effects in neutrino oscillations. Within the context of standard neutrino oscillation theory with matter effects, we present the complete set of (five) matter invariant observables for neutrino propagation in matter. We give some examples of their application.

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arXiv2002

Symmetries and Generalisations of Tri-Bimaximal Neutrino Mixing

Tri-bimaximal mixing is a specific lepton mixing ansatz, which has been shown to account very successfully for the established neutrino oscillation data. Working in a particular basis (the `circulant basis'), we identify three independent symmetries of tri-bimaximal mixing, which we exploit to set the tri-bimaximal hypothesis in context, alongside some simple, phenomenologically interesting CP-conserving and CP-violating generalisations.

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arXiv2002

Tri-Bimaximal Mixing and the Neutrino Oscillation Data

Following recent results from the SNO solar neutrino experiment and the K2K long-baseline neutrino experiment, the combined existing data on neutrino oscillations now point strongly to a specific form for the lepton mixing matrix, with effective bimaximal mixing of $ν_μ$ and $ν_τ$ at the atmospheric scale and effective trimaximal mixing for $ν_e$ with $ν_μ$ and $ν_τ$ at the solar scale (hence `tri-bimaximal' mixing). We give simple mass-matrices leading to tri-bimaximal mixing, and discuss its relation to the Fritzsch-Xing democratic ansatz.

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arXiv2001

Nucleon Structure, Duality and Elliptic Theta Functions

Nucleon structure functions are shown to have a qualitative (or `formal') relation to the classical elliptic theta functions. In particular, theta_1'/2 shows a clear resemblance to a non-singlet structure function like xF_3. In the appropriate range the Q^2-dependence of the moments of theta_1'/2 is in near-quantitative agreement with QCD, and at low-Q^2 the moments converge to a common value, as observed experimentally for xF_3. At very high Q^2 (Q^2 -> M_PL), theta_1'/2 -> eta^3(x) (where eta(x) is the Dedekind eta function), while xF_3 in the same limit appears closer to eta^5(x). A comparison of the theta function identity theta_2^4(0)=theta_3^4(0)-theta_4^4(0) with the relation xF_3=Q(x)-Q^-(x) suggests that singlet structure functions have more in common with theta_3 and theta_4. The possibility of interesting large-x/small-x `duality' relations for structure functions emerges naturally from the analysis.

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arXiv2000

Status of Trimaximal Neutrino Mixing

Trimaximal mixing is the mixing hypothesis with maximal symmetry. In trimaximal mixing there remains a still worrying conflict between the large values of $Δm^2$ preferred by the atmospheric fits (possibly supported by the early K2K data) and reactor limits on $ν_e$-mixing. However, the latest solar results do seem to point to energy-independent (ie. `no-scale') solar solutions, like the trimaximal solution.

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arXiv1999

CP and T Violation in Neutrino Oscillations and Invariance of Jarlskog's Determinant to Matter Effects

Terrestrial matter effects in neutrino propagation are T-invariant, so that any observed T violation when neutrinos pass through the Earth, such as an asymmetry between the transition probabilities P(nu_mu -> nu_e) and P(nu_e -> nu_mu), would be a direct indication of T violation at the fundamental level. Matter effects do however modify the magnitudes of T-violating asymmetries, and it has long been known that resonant enhancement can lead to large effects for a range of plausible values of the relevant parameters. We note that the determinant of the commutator of the lepton mass matrices is invariant under matter effects and use this fact to derive a new expression for the T-violating asymmetries of neutrinos propagating through matter. We give some examples which could have physical relevance.

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arXiv1999

Tri-Maximal vs Bi-Maximal Neutrino Mixing

It is argued that data from atmospheric and solar neutrino experiments point strongly to tri-maximal or bi-maximal lepton mixing. While (`optimised') bi-maximal mixing gives an excellent a posteriori fit to the data, tri-maximal mixing is an a priori hypothesis, which is not excluded, taking account of terrestrial matter effects.

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arXiv1999

A Redetermination of the Neutrino Mass-Squared Difference in Tri-Maximal Mixing with Terrestrial Matter Effects

We re-fit for the neutrino mass-squared difference $Δm^2$ in the threefold maximal (ie. tri-maximal) mixing scenario using recent CHOOZ and SUPER-K data, taking account of matter effects in the Earth. While matter effects have little influence on reactor experiments and proposed long-baseline accelerator experiments with $L \simlt 1000 km$, they are highly significant for atmospheric experiments, suppressing naturally $ν_e$ mixing and enhancing $ν_μ - ν_τ$ mixing, so as to effectively remove the experimental distinction between threefold maximal and twofold maximal $ν_μ-ν_τ$ mixing. Threefold maximal mixing is fully consistent with the CHOOZ and SUPER-K data and the best-fit value for the neutrino mass-squared difference is $Δm^2 = (0.98 \pm^{0.30}_{0.23}) \times 10^{-3} eV^2$.

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arXiv1997

Further Evidence for Threefold Maximal Lepton Mixing and a Hierarchical Spectrum of Neutrino Mass-Squared Differences

The phenomenological case for threefold maximal lepton mixing is strengthened by more detailed comparison with existing data. The atmospheric neutrino data are self-consistent and in good agreement with the threefold maximal mixing prediction R = 2/3 (chi-squared/dof = 4.3/5, CL = 51%). Including partially con- tained event data, the zenith angle dependence also points to threefold maximal mixing, ruling-out a range of mixing schemes, including that of Fritzsch and Xing. Accounting for `de facto' uncertainties in solar neutrino fluxes, the solar neutrino data (including HOMESTAKE) are shown to be consistent with threefold maximal mixing (chi-squared/dof = 5.1/3, CL = 16%), as is the upper limit from the LSND appearance experiment. Detailed pred- ictions for forthcoming long-base-line reactor and accelerator experiments are presented.

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arXiv1996

No Mikheyev-Smirnov-Wolfenstein Effect in Maximal Mixing

We investigate the possible influence of the MSW effect on the expectations for the solar neutrino experiments in the maximal mixing scenario suggested by the atmospheric neutrino data. A direct numerical calculation of matter induced effects in the Sun shows that the naive vacuum predictions are left completely undisturbed in the particular case of maximal mixing, so that the MSW effect turns out to be unobservable. We give a qualitative explanation of this result.

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arXiv1994

Generation Permutation Symmetry and the Quark Mixing Matrix

We propose a new discrete symmetry in the generation space of the fundamental fermions, consistent with the observed fermion mass spectrum. In the case of the quarks, the symmetry leads to the unique prediction of a flat CKM matrix at high energy. We explore the possibility that evolution due to quantum corrections leads to the observed hierarchical form of the CKM matrix at low energies.

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