Summing up My New Semi-Empirical
Neutrino Physics Ideas from 2016 Year
E. M. Lipmanov, Brighton
1) As in case of light at the
dawn of quantum physics, neutrino special empirical features probably suggest
new fundamental physics, in particular flavor one. Semi-empirical neutrino
mixing angle phenomenology is described by one primary equation
cos^2 (2θ12) + cos^2 (2θ23) + cos^2
(2θ13) = 1+ sin^2 (2θ13), (1)
cos(4θ13) = 1 –
[cos^2 (2θ12) + cos^2 (2θ23)], (1`)
which predicts the magnitude of finite small reactor angle θ13
= ~ 8.5o and suggests deeper physical meaning by accurate quantitative
description of small neutrino mixing deviation, (right side term sin^2 (2θ13)
of Eq. (1)) from geometric SO(3)-symmetry (left side of Eq. (1)). Again, in
analogy with particle-wave duality in case of light, Eq. (1) indicates new
fundamental physics flavor-geometric duality: congruence
of flavor neutrino leading approximation bimaximal mixing angle hierarchy and
flavor neutrino momentum vector leading approximation direction angle hierarchy
-- both at presentations without free parameters.
That quantum-geometric congruence
fact may be also interesting as an empirical example of relation between
neutrino mass state superposition quantum mechanics and outer Euclidean
geometry -- particular evidence of the discussed in the literature general
theoretical ideas of connection between quantum physics and geometry.
2) There is a principal question –
Why is Geometric SO(3)-symmetry of the
realistic neutrino mixing violated? In the framework of Standard Model there is
only one answer: the violation of neutrino mixing geometric symmetry is caused
by the necessary CP-violation of neutrino weak interactions. CP-violation is
the only possible cause of geometric symmetry violation that is absent in 3-space
Euclidean geometry and therefore is absent in the mentioned flavor-geometric
duality.
3) Suggested connection between violation of neutrino mixing
geometric symmetry and CP-violation in the neutrino
Pontecorvo-Maki-Nakagava-Sokata mixing matrix means that θ13-angle is tied to the
Dirac CP-phase ‘d’ in that mixing matrix
|d| = (90^o - 2 θ13).
(2)
Indeed, in combination with (1) the complementary relation
(2) shows possible primary cause of neutrino mixing geometric symmetry violation
as phenomenon of CP-symmetry violation in the neutrino weak interactions as described
by equation
Cos^2 (2θ12) + cos^2 (2θ23) + cos^2 (2θ13) =
1 + cos^2 d. (3)
From that equation, the CP-violating Dirac phase |d| is
maximal |d| = 90^o at leading bimaximal neutrino mixing approximation θ12 = θ23
= 90^o, θ13 = 0.
It should be underlined that despite maximal CP-phase the
factual CP-violation effect at leading bimaximal approximation is zero since
θ13 = 0. But at realistic neutrino mixing θ13 = ~ 8.5^o a prediction follows,
d
= + - (90^o - 2 θ13) = ~ + - (72 – 74)^o,
(4)
and so, a physically observable CP-violation effect in
neutrino physics appears
[sin
θ13 exp(-id)] = ~ [0.15(0.3 + - 0.96i)],
(5)
which is testable and falsifiable in coming neutrino
experiments. If confirmed, those semi-empirical results of weakly violated
neutrino mixing symmetry and CP-violation may influence general fundamentally
new particle physics.
Normal
0
false
false
false
EN-US
X-NONE
X-NONE
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Table Normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
mso-style-parent:"";
mso-padding-alt:0in 5.4pt 0in 5.4pt;
mso-para-margin-top:0in;
mso-para-margin-right:0in;
mso-para-margin-bottom:8.0pt;
mso-para-margin-left:0in;
line-height:107%;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri",sans-serif;
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:minor-bidi;}
