lepton mass and neutrino mixings [Archive]

Alejandro

Aug7-04, 05:06 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Minakata, and Smirnov, in hep-ph/0405088, speak about the solar\nneutrino mixing and at the end (point 4) they remark some courious\nrelationsips with CKM angles without quoting sources.\nThey say that sin theta is about the square root of m_mu/m_tau\n\nDoes anybody knows the original reference for this suggestion? Smirnov\nquotes it continously, and sometimes with similar relationships for\nother mixings and masses, it a way such that I am not able to\ndetermine its origin or originality.\n\nIt is specially interesting because an outsider, Hans de Vries,\nhttp://www.chip-architect.com/news/2004_07_27_The_Electron.html\nhas noted that this quotient can be approximated using\nln ( m_tau / m_mu ) = pi - 1/pi\nwhich holds within a 0.029 % (!!!)\n\nSo one can put Mikanata-Smirnov relation as\nln(sin(cabibbo))=-sinh(ln(pi)).\n\nDe Vries notes similar integer combinations for the other two lepton\nquotients; sort of mnemonic resource at least, because they are more\nprecise than usual. Alternatively\none can use integer combinations of hyperbolic sines and cosines\n\nAmusing.\n\nAlejandro Rivero\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Minakata, and Smirnov, in http://www.arxiv.org/abs/hep-ph/0405088, speak about the solar
neutrino mixing and at the end (point 4) they remark some courious
relationsips with CKM angles without quoting sources.
They say that sin \theta is about the square root of m_{mu}/m_{tau}

Does anybody knows the original reference for this suggestion? Smirnov
quotes it continously, and sometimes with similar relationships for
other mixings and masses, it a way such that I am not able to
determine its origin or originality.

It is specially interesting because an outsider, Hans de Vries,
http://www.chip-architect.com/news/2004_07_27_The_Electron.html
has noted that this quotient can be approximated using
ln ( m_{tau} / m_{mu} ) = \pi - 1/\pi
which holds within a .029 % (!!!)

So one can put Mikanata-Smirnov relation as
ln(sin(cabibbo))=-sinh(ln(\pi)).

De Vries notes similar integer combinations for the other two lepton
quotients; sort of mnemonic resource at least, because they are more
precise than usual. Alternatively
one can use integer combinations of hyperbolic sines and cosines

Amusing.

Alejandro Rivero

Thomas Larsson

Aug12-04, 08:30 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\n\narivero@posta.unizar.es (Alejandro) wrote in message news:<1d8a7d98.0408061146.15b32b76@posting.google. com>...\n> It is specially interesting because an outsider, Hans de Vries,\n> http://www.chip-architect.com/news/2004_07_27_The_Electron.html\n> has noted that this quotient can be approximated using\n> ln ( m_tau / m_mu ) = pi - 1/pi\n> which holds within a 0.029 % (!!!)\n>\n\nWe also have\n\n1/alpha = pi + pi^2 + 4*pi^3 = 137.0363038\n\nm_proton / m_electron = 6*pi^5 = 1836.118109\n\n(the second observation is due to Lubos Motl).\n\nProbably means nothing. Or maybe it does.\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>arivero@posta.unizar.es (Alejandro) wrote in message news:<1d8a7d98.0408061146.15b32b76@posting.google.com>...
> It is specially interesting because an outsider, Hans de Vries,
> http://www.chip-architect.com/news/2004_07_27_The_Electron.html
> has noted that this quotient can be approximated using
> ln ( m_{tau} / m_{mu} ) = \pi - 1/\pi
> which holds within a .029 % (!!!)
>

We also have

1/\alpha = \pi + \pi^2 + 4*\pi^3 = 137.0363038

m_{proton} / m_{electron} = 6*\pi^5 = 1836.118109

(the second observation is due to Lubos Motl).

Probably means nothing. Or maybe it does.

Alejandro

Aug23-04, 04:05 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nthomas_larsson_01@hotmail.com (Thomas Larsson) wrote in message news:<24a23f36.0408072208.cf75b1d@posting.google.c om>...\n> arivero@posta.unizar.es (Alejandro) wrote in message news:<1d8a7d98.0408061146.15b32b76@posting.google. com>...\n> > It is specially interesting because an outsider, Hans de Vries,\n> > http://www.chip-architect.com/news/2004_07_27_The_Electron.html\n> > has noted that this quotient can be approximated using\n> > ln ( m_tau / m_mu ) = pi - 1/pi\n> > which holds within a 0.029 % (!!!)\n> We also have\n> 1/alpha = pi + pi^2 + 4*pi^3 = 137.0363038\n> m_proton / m_electron = 6*pi^5 = 1836.118109\n> (the second observation is due to Lubos Motl).\n\nHmm, yes, it seems mostly a exersice about using "pi" instead of\n2 or 10 as a basis for a numerical system. The three quantities\ncould be rewritten\nln(...)= 1 - 0.1\n(we can not "cycle" negative numbers using a non integer basis)\n1/alpha= 40110\nm_p/m_e= 600000\n\nIn this way, the 1/alpha rule seems the least interesting one, because\njust writting 137 contains the same information.\n\nAlejandro\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>thomas_larsson_01@hotmail.com (Thomas Larsson) wrote in message news:<24a23f36.0408072208.cf75b1d@posting.google.com>...
> arivero@posta.unizar.es (Alejandro) wrote in message news:<1d8a7d98.0408061146.15b32b76@posting.google.com>...
> > It is specially interesting because an outsider, Hans de Vries,
> > http://www.chip-architect.com/news/2004_07_27_The_Electron.html
> > has noted that this quotient can be approximated using
> > ln ( m_{tau} / m_{mu} ) = \pi - 1/\pi
> > which holds within a .029 % (!!!)
> We also have
> 1/\alpha = \pi + \pi^2 + 4*\pi^3 = 137.0363038
> m_{proton} / m_{electron} = 6*\pi^5 = 1836.118109
> (the second observation is due to Lubos Motl).

Hmm, yes, it seems mostly a exersice about using "\pi" instead of
2 or 10 as a basis for a numerical system. The three quantities
could be rewritten
ln(...)= 1 - .1
(we can not "cycle" negative numbers using a non integer basis)
1/\alpha= 40110
m_p/m_e= 600000

In this way, the 1/\alpha rule seems the least interesting one, because
just writting 137 contains the same information.

Alejandro

Alejandro

Aug25-04, 07:31 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nthomas_larsson_01@hotmail.com (Thomas Larsson) wrote in message news:<24a23f36.0408072208.cf75b1d@posting.google.c om>...\n> arivero@posta.unizar.es (Alejandro) wrote in message news:<1d8a7d98.0408061146.15b32b76@posting.google. com>...\n> > It is specially interesting because an outsider, Hans de Vries,\n> > http://www.chip-architect.com/news/2004_07_27_The_Electron.html\n> > has noted that this quotient can be approximated using\n> > ln ( m_tau / m_mu ) = pi - 1/pi\n> > which holds within a 0.029 % (!!!)\n> 1/alpha = pi + pi^2 + 4*pi^3 = 137.0363038\n> m_proton / m_electron = 6*pi^5 = 1836.118109\n> (the second observation is due to Lubos Motl).\n> Probably means nothing. Or maybe it does.\n\nTo follow the collection, let me note this other logarithmic formula from\nL. Nottale:\n\nln (m_P/m_e) = (3/8) alpha^(-1)\n\nWhere 3/8 is, I guess, the sin^2 of Weinberg angle, alpha is the fine structure\nconstant, and m_P is Planck mass. Nottale justifies his idea in grounds\nof a variant of double scale relativity. He has some papers on "scale\nrelativity and fractal space time" (BTW, the readers of s.p.r fond of\nbiquaternions and Lanczos electromagnetism, should review Nottale\'s papers).\n\nTo be precise, the equality is 51.528 \\sim 51.388, within 0.3 percent, and\nNottale argues that the discrepance signals a residual mass of\nnon-electromagnetic character.\n\n\n[Moderator\'s note: Numerology in general if off-topic for s.p.r. and this discussion is\nprone to progress further into overly-speculative territory. Participants replying to\nthis thread should make sure that their message is about physics and not just about\nfar-fetched coincidences. -usc]\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>thomas_larsson_01@hotmail.com (Thomas Larsson) wrote in message news:<24a23f36.0408072208.cf75b1d@posting.google.com>...
> arivero@posta.unizar.es (Alejandro) wrote in message news:<1d8a7d98.0408061146.15b32b76@posting.google.com>...
> > It is specially interesting because an outsider, Hans de Vries,
> > http://www.chip-architect.com/news/2004_07_27_The_Electron.html
> > has noted that this quotient can be approximated using
> > ln ( m_{tau} / m_{mu} ) = \pi - 1/\pi
> > which holds within a .029 % (!!!)
> 1/\alpha = \pi + \pi^2 + 4*\pi^3 = 137.0363038
> m_{proton} / m_{electron} = 6*\pi^5 = 1836.118109
> (the second observation is due to Lubos Motl).
> Probably means nothing. Or maybe it does.

To follow the collection, let me note this other logarithmic formula from
L. Nottale:

ln (m_P/m_e) = (3/8) \alpha^(-1)

Where 3/8 is, I guess, the sin^2 of Weinberg angle, \alpha is the fine structure
constant, and m_P is Planck mass. Nottale justifies his idea in grounds
of a variant of double scale relativity. He has some papers on "scale
relativity and fractal space time" (BTW, the readers of s.p.r fond of
biquaternions and Lanczos electromagnetism, should review Nottale's papers).

To be precise, the equality is 51.528 \sim 51.388, within .3 percent, and
Nottale argues that the discrepance signals a residual mass of
non-electromagnetic character.

[Moderator's note: Numerology in general if off-topic for s.p.r. and this discussion is
prone to progress further into overly-speculative territory. Participants replying to
this thread should make sure that their message is about physics and not just about
far-fetched coincidences. -usc]