arXiv subjects

P. F. Harrison

Publications and source records attributed to P. F. Harrison.

35 records · Page 2Linked to original sources

arXiv2006

Simplified Unitarity Triangles for the Lepton Sector

Encouraged by the latest SNO results, we consider the lepton mixing matrix in the approximation that the nu_2 mass eigenstate is trimaximally (democratically) mixed. This suggests a new parameterization of the remaining mixing degrees of freedom, which eschews mixing angles, dealing instead, directly with the complex parameter U_e3 of the mixing matrix. Unitarity triangles then take a particularly simple form, which we hope will faciltate comparison with experiment.

hep-ph↗

arXiv2006

Real Invariant Matrices and Flavour-Symmetric Mixing Variables with Emphasis on Neutrino Oscillations

In fermion mixing phenomenology, the matrix of moduli squared, P=(|U|^2), is well-known to carry essentially the same information as the complex mixing matrix U itself, but with the advantage of being phase-convention independent. The matrix K (analogous to the Jarlskog CP-invariant J) formed from the real parts of the mixing matrix "plaquette" products is similarly invariant. In this paper, the P and K matrices are shown to be entirely equivalent, both being directly related (in the leptonic case) to the observable, locally L/E-averaged transition probabilities in neutrino oscillations. We study an (over-)complete set of flavour-symmetric Jarlskog-invariant functions of mass-matrix commutators, rewriting them simply as moment-transforms of such (real) invariant matrices.

hep-ph↗

arXiv2006

Radiation shielding for underground low-background experiments

The design task of creating an efficient radiation shield for the new COBRA double-beta decay experiment led to a comprehensive study of commercially available shielding materials. The aim was to find the most efficient combination of materials under the constraints of an extreme low-background experiment operating in a typical underground laboratory. All existing shield configurations for this type of experiment have been found to perform sub-optimally in comparison to the class of multilayered configurations proposed in this study. The method used here to create a specific shield configuration should yield a close to optimal result when applied to any experiment utilising a radiation shield. In particular, the survey of single material response to a given radiation source turns out to give a guideline for the construction of efficient multilayer shields.

nucl-ex↗

arXiv2005

Covariant Extremisation of Flavour-Symmetric Jarlskog Invariants and the Neutrino Mixing Matrix

We examine the possibility that the form of the lepton mixing matrix can be determined by extremising the Jarlskog flavour invariants associated, eg. with the commutator ($C$) of the lepton mass matrices. Introducing a strictly covariant approach, keeping masses fixed and extremising the determinant (Tr $C^3/3$) leads to maximal CP violation, while extremising the sum of the $2 \times 2$ principal minors ($-{\rm Tr} C^2/2$), leads to a non-trivial mixing with zero CP violation. Extremising, by way of example, a general linear combination of two CP-symmetric invariants together, we show that our procedures can lead to acceptable mixings and to non-trivial predictions, eg.\ $|U_{e3}| \simeq \sqrt{2}/3 \sqrt{Δm_{12}^2/Δm_{23}^2} (1-m_μ/m_τ)^2 \simeq 0.07$.

hep-ph↗

arXiv2004

The Simplest Neutrino Mass Matrix

We motivate the simplest ansatz for the neutrino mass matrix consistent with the data from neutrino oscillation experiments, and admitting CP violation. It has only two free parameters: an arbitrary mass-scale and a small dimensionless ratio. This mass matrix exhibits two symmetries, Democracy and Mutativity, which respectively ensure trimaximal mixing of the |nu_2> mass eigenstate, and mixing parameter values |theta_{23}|=45 degrees and |delta|=90 degrees, consistent with bimaximal mixing of the |nu_3> mass eigenstate. A third constraint relates the smallness of |U_{e3}|^2 to that of the mass-squared difference ratio, Delta m^2_sol/Delta m^2_atm, yielding the prediction sin(theta_{13})=sqrt{2 Delta m^2_sol/3 Delta m^2_atm} ~ 0.13 +- 0.03.

hep-ph↗

arXiv2004

Status of Tri/Bi-Maximal Neutrino Mixing

Tri/bi-maximal mixing (TBM) is a specific lepton mixing ansatz, which describes the trend of the current neutrino oscillation data, in particular the recent SNO and KAMLAND results. The significant feature of TBM in this respect is |U_e2|^2=|U_m2|^2=|U_t2|^2=1/3, and we say that the nu_2 is tri-maximally mixed. We have generalised the TBM ansatz to a generic mixing matrix with the nu_2 trimaximally mixed, whereby the neutrino mass matrix in the lepton flavour basis takes the form of a general S3 group matrix (3 x 3 `magic-square'). In exact TBM the charged-lepton mass matrix in the neutrino mass basis (where the neutrino mass matrix is diagonal) takes the form of a general S3 class operator. The neutrino mass matrix in the flavour basis is a particular S3 group matrix which is also an S1 C S2 C S3 group-chain class operator, whereby the neutrino mass eigenstates are distinguished by their `mutativity' (M_i = +/-1) and `democracy' (D_i = 0,3) which are both good quantum numbers in exact TBM.

hep-ph↗

arXiv2003

Exact Matter-Covariant Formulation of Neutrino Oscillation Probabilities

We write the probabilities for neutrino oscillations in uniform-density matter exactly in terms of convention-independent vacuum neutrino oscillation parameters and the matter density. This extends earlier results formulating neutrino oscillations in terms of matter-, phase-, and trace-invariant quantities.

hep-ph↗

arXiv2003

Permutation Symmetry, Tri-Bimaximal Neutrino Mixing and the S3 Group Characters

We postulate that the neutrino mass matrix in the lepton flavour basis is an S3 group matrix in the natural representation of S3. This immediately requires one neutrino to be trimaximally mixed, as suggested by the solar neutrino data. We go on to postulate that the charged-lepton mass matrix in the neutrino mass-basis is an S3 class matrix in the natural representation of the S3 class-algebra, leading to exact tri-bimaximal mixing, which is compatible with data overall. The tri-bimaximal mixing matrix is seen to be closely related to the S3 character table, and is properly the S2 C S3 table of induction coefficients, where the S2 corresponds to symmetry under mu-tau interchange in the lepton flavour basis.

hep-ph↗

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.

hep-ph↗

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.

hep-ph↗

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.

hep-ph↗

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.

hep-ph↗

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.

hep-ph↗

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 $Δm^2 = (0.98 \pm^{0.30}_{0.23}) \times 10^{-3} eV^2$.

hep-ph↗

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.

hep-ph↗

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.

hep-ph↗

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.

hep-ph↗