A4 SYMMETRY AND NEUTRINOS

2008 ◽  
Vol 23 (21) ◽  
pp. 3366-3370 ◽  
Author(s):  
ERNEST MA
Keyword(s):  
Family Symmetry ◽  
History Of ◽  
Discrete Family

I recount briefly the history of neutrino tribimaximal mixing and the use of the discrete family symmetry A 4 in obtaining it.

scholarly journals ANOMALY OF DISCRETE FAMILY SYMMETRIES AND GAUGE COUPLING UNIFICATION

2007 ◽  
Vol 16 (05) ◽  
pp. 1463-1478
Author(s):  
TAKESHI ARAKI
Keyword(s):  
Planck Scale ◽  
Gauge Coupling ◽  
Baryon Number ◽  
Discrete Symmetry ◽  
Lepton Number ◽  
Supersymmetric Model ◽  
Family Symmetry ◽  
Fundamental Scale ◽  
Integral Measure ◽  
Discrete Family

Anomaly of a discrete symmetry is defined as the Jacobian of the path-integral measure. Assuming that anomaly at low energy is cancelled by the Green–Schwarz (GS) mechanism at a fundamental scale, we investigate possible Kac–Moody levels for anomalous discrete family symmetries. As the first example we consider discrete abelian Baryon number and Lepton number symmetries in the minimal supersymmetric standard model with see-saw mechanism, and find that the ordinary unification of gauge couplings is not consistent with the GS conditions, indicating a possible existence of further Higgs doublets. Next we consider the recently proposed supersymmetric model with Q6 family symmetry. In this model, the GS conditions are such that the gauge coupling unification appears close to the Planck scale.

LIVING THE ENLIGHTENMENT AND THE FRENCH REVOLUTION: JAMES WATT, MATTHEW BOULTON, AND THEIR SONS

1999 ◽  
Vol 42 (1) ◽  
pp. 157-182 ◽  
Author(s):  
PETER M. JONES
Keyword(s):  
Eighteenth Century ◽  
Cultural History ◽  
French Revolution ◽  
Steam Engine ◽  
The West ◽  
The Enlightenment ◽  
West Midlands ◽  
History Of ◽  
James Watt ◽  
Discrete Family

This article is a contribution to the cultural history of English Enlightenment. It examines the formation of a discrete ‘family’ of philosophes in the West Midlands who maintained close links with their counterparts on the continent. Birmingham's role as a magnet for ‘industrial tourists’ in the second half of the eighteenth century helped to propagate the influence of this local intelligentsia who were mostly members of the Lunar Society. None the less, it is argued that the activities of the Society correspond more closely to an Enlightenment than to a proto-industrial pattern of inquiry. The events of 1789 in France disrupted this philosophic ‘family’. Their impact is explored through the medium of a real family; that of James Watt, the engineer, who came to Birmingham to manufacture the steam engine in partnership with Matthew Boulton. The vicissitudes of the Watt family, and of other prominent members of the Lunar Society, are unravelled to illustrate the dilemmas faced by men raised in the values of the Enlightenment when confronted with the reality – and the proximity – of a far-reaching political revolution.

scholarly journals Discrete family symmetry from F-theory GUTs

2014 ◽  
Vol 2014 (9) ◽  
Author(s):  
Athanasios Karozas ◽  
Stephen F. King ◽  
George K. Leontaris ◽  
Andrew K. Meadowcroft
Keyword(s):  
Family Symmetry ◽  
Discrete Family

scholarly journals Neutrino tri-bi-maximal mixing from a non-Abelian discrete family symmetry

2007 ◽  
Vol 648 (2-3) ◽  
pp. 201-206 ◽  
Author(s):  
I. de Medeiros Varzielas ◽  
S.F. King ◽  
G.G. Ross
Keyword(s):  
Family Symmetry ◽  
Discrete Family

scholarly journals Discrete family symmetry, Higgs mediators and θ 13

2012 ◽  
Vol 2012 (12) ◽  
Author(s):  
Ivo de Medeiros Varzielas ◽  
Graham G. Ross
Keyword(s):  
Family Symmetry ◽  
Discrete Family
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