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View Full Version : hierarchy problem and see-saw mechanism


Ilja Schmelzer
Dec2-04, 06:18 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>Is the following description of the hierarchy problem\nand the see-saw mechanism more or less reasonable?\nCan somebody correct the errors?\n\n1.) If we consider electroweak symmetry breaking in the\nstandard model, a straightforward renormalization gives\nthe observable gauge bosons W_+, W_-, Z, very large\nmasses, much larger than the observed masses. To obtain\nthe observed masses is, in principle, possible, but it requires\nsome strange fine-tuning of the non-renormalized parameters.\n\n2.) A similar fine-tuning is necessary to explain the very small\nneutrino masses.\n\n3.) The see-saw mechanism is some proposed mechanism which\nallows to explain this fine-tuning for the case of neutrinos.\nIt works in such a way that the observable neutrinos with\nsmall masses have some partners with large masses (which are\nthe right-handed neutrinos).\n\n4.) The key idea is that for a 2x2 matrix with values a_ij of the\nsame order it is quite natural to have one eigenvalue of the\nsame order but the second one may be very small without\ntoo much fine tuning.\n\nIlja\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">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>Is the following description of the hierarchy problem
and the see-saw mechanism more or less reasonable?
Can somebody correct the errors?

1.) If we consider electroweak symmetry breaking in the
standard model, a straightforward renormalization gives
the observable gauge bosons W_+, W_-, Z, very large
masses, much larger than the observed masses. To obtain
the observed masses is, in principle, possible, but it requires
some strange fine-tuning of the non-renormalized parameters.

2.) A similar fine-tuning is necessary to explain the very small
neutrino masses.

3.) The see-saw mechanism is some proposed mechanism which
allows to explain this fine-tuning for the case of neutrinos.
It works in such a way that the observable neutrinos with
small masses have some partners with large masses (which are
the right-handed neutrinos).

4.) The key idea is that for a 2x2 matrix with values a_{ij} of the
same order it is quite natural to have one eigenvalue of the
same order but the second one may be very small without
too much fine tuning.

Ilja

MP
Dec3-04, 04:49 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>"Ilja Schmelzer" &lt;Ilja.Schmelzer@FernUni-Hagen.de&gt; wrote in message\nnews:comqjk\\$fah\\$1@beech.fernuni-hagen.de...\n&gt; Is the following description of the hierarchy problem\n&gt; and the see-saw mechanism more or less reasonable?\n&gt; Can somebody correct the errors?\n&gt;\n&gt; 1.) If we consider electroweak symmetry breaking in the\n&gt; standard model, a straightforward renormalization gives\n&gt; the observable gauge bosons W_+, W_-, Z, very large\n&gt; masses, much larger than the observed masses. To obtain\n&gt; the observed masses is, in principle, possible, but it requires\n&gt; some strange fine-tuning of the non-renormalized parameters.\n&gt;\n&gt; 2.) A similar fine-tuning is necessary to explain the very small\n&gt; neutrino masses.\n&gt;\n&gt; 3.) The see-saw mechanism is some proposed mechanism which\n&gt; allows to explain this fine-tuning for the case of neutrinos.\n&gt; It works in such a way that the observable neutrinos with\n&gt; small masses have some partners with large masses (which are\n&gt; the right-handed neutrinos).\n&gt;\n&gt; 4.) The key idea is that for a 2x2 matrix with values a_ij of the\n&gt; same order it is quite natural to have one eigenvalue of the\n&gt; same order but the second one may be very small without\n&gt; too much fine tuning.\n\nThis is how I have memorized it, after reading a couple of papers\nabout the subject. But I\'m not an expert in electroweak theory, nor\nin neutrino physics. Therefore I can only offer you that, on the\nshallow level of my understanding of these matters, I would have\n"parroted" the subject in the same way, maybe with different\nwords ;-)\n\nMP\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">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Ilja Schmelzer" <Ilja.Schmelzer@FernUni-Hagen.de> wrote in message
news:comqjk$fah$1@beech.fernuni-hagen.de...
> Is the following description of the hierarchy problem
> and the see-saw mechanism more or less reasonable?
> Can somebody correct the errors?
>
> 1.) If we consider electroweak symmetry breaking in the
> standard model, a straightforward renormalization gives
> the observable gauge bosons W_+, W_-, Z, very large
> masses, much larger than the observed masses. To obtain
> the observed masses is, in principle, possible, but it requires
> some strange fine-tuning of the non-renormalized parameters.
>
> 2.) A similar fine-tuning is necessary to explain the very small
> neutrino masses.
>
> 3.) The see-saw mechanism is some proposed mechanism which
> allows to explain this fine-tuning for the case of neutrinos.
> It works in such a way that the observable neutrinos with
> small masses have some partners with large masses (which are
> the right-handed neutrinos).
>
> 4.) The key idea is that for a 2x2 matrix with values a_{ij} of the
> same order it is quite natural to have one eigenvalue of the
> same order but the second one may be very small without
> too much fine tuning.

This is how I have memorized it, after reading a couple of papers
about the subject. But I'm not an expert in electroweak theory, nor
in neutrino physics. Therefore I can only offer you that, on the
shallow level of my understanding of these matters, I would have
"parroted" the subject in the same way, maybe with different
words ;-)

MP