What does {mu}-{tau} symmetry imply about neutrino mixings?

Journal Article · Wed Mar 01 04:00:00 EST 2006 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PhysRevD.73.055014· OSTI ID:20776901

Fuki, Kenichi; Yasue, Masaki ^[1]

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1. Department of Physics, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji, Tokyo 192-0397 (Japan)

The requirement of the {mu}-{tau} symmetry in the neutrino sector that yields the maximal atmospheric neutrino mixing is shown to yield either sin{theta}{sub 13}=0 (referred to as C1)) or sin{theta}{sub 12}=0 (referred to as C2)), where {theta}{sub 12(13)} stands for the solar (reactor) neutrino mixing angle. We study general properties possessed by approximately {mu}-{tau} symmetric textures. It is argued that the tiny {mu}-{tau} symmetry breaking generally leads to cos2{theta}{sub 23}{approx}sin{theta}{sub 13} for C1) and cos2{theta}{sub 23}{approx}{delta}m{sub {center_dot}}{sup 2}/{delta}m{sub atm}{sup 2}({identical_to}R) for C2), which indicates that the smallness of cos2{theta}{sub 23} is a good measure of the {mu}-{tau} symmetry breaking, where {delta}m{sub atm}{sup 2} ({delta}m{sub {center_dot}}{sup 2}) stands for the square mass difference of atmospheric (solar) neutrinos. We further find that the relation R{approx}sin{sup 2}{theta}{sub 13} arises from contributions of O(sin{sup 2}{theta}{sub 13}) in the estimation of the neutrino masses (m{sub 1,2,3}) for C1), and that possible forms of textures are strongly restricted to realize sin{sup 2}2{theta}{sub 12}=O(1) for C2). To satisfy R{approx}sin{sup 2}{theta}{sub 13} for C1), neutrinos exhibit the inverted mass hierarchy, or the quasi degenerate mass pattern with |m{sub 1,2,3}|{approx}O({radical}({delta}m{sub atm}{sup 2})), and, to realize sin{sup 2}2{theta}{sub 12}=O(1) for C2), there should be an additional small parameter {eta} whose size is comparable to that of the {mu}-{tau} symmetry breaking parameter {epsilon}, giving tan2{theta}{sub 12}{approx}{epsilon}/{eta} with {eta}{approx}{epsilon} to be compatible with the observed large mixing.

• OSTI ID: 20776901
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 5 Vol. 73; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COSMIC NEUTRINOS
MASS DIFFERENCE
MIXING
MUONS
NEUTRINO OSCILLATION
REST MASS
SOLAR NEUTRINOS
SYMMETRY
SYMMETRY BREAKING
TAU PARTICLES
WEINBERG ANGLE