tag:blogger.com,1999:blog-7315236707728759521.post8348288478948386798..comments2024-06-20T14:04:53.133-06:00Comments on Dispatches From Turtle Island: New Koide-Like Formula For Quark MassesAndrew Oh-Willekehttp://www.blogger.com/profile/02537151821869153861noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-7315236707728759521.post-669178364351244452012-06-22T16:47:30.643-06:002012-06-22T16:47:30.643-06:00She also: http://arxiv.org/abs/1205.4068, a more r...She also: http://arxiv.org/abs/1205.4068, a more recent Koide formula generalization paper focused on estimating neutrino masses.andrewhttps://www.blogger.com/profile/08172964121659914379noreply@blogger.comtag:blogger.com,1999:blog-7315236707728759521.post-51676508359248542392012-01-09T21:33:45.075-07:002012-01-09T21:33:45.075-07:00I should correct my parenthetical remark about the...I should correct my parenthetical remark about the meaning of the phase parameter - I mean the delta0 in equation 3 of arxiv:1111.7232. The way I described it is wrong, its geometric interpretation is a little more complex. But the main point is that it's a very important angle in discussions about the Koide relation, and it's a different angle to the one which Foot introduced.Mitchellhttps://www.blogger.com/profile/10768655514143252049noreply@blogger.comtag:blogger.com,1999:blog-7315236707728759521.post-57444605989206421882012-01-09T21:16:31.568-07:002012-01-09T21:16:31.568-07:00Andrew wrote
"In this generalization, the ar...Andrew wrote<br /><br />"In this generalization, the arccosine of the Koide formula for leptons implies an angle theta lepton, of pi/3 and the arccosine of the Koide forumla for quarks implies an angle theta quark of pi/4."<br /><br />No, they're actually much closer than that. In each case you have a three-dimensional angle of pi/4 and then a six-dimensional generalization of pi/3. <br /><br />In each case, there are three heavy particles and three light particles. For the leptons, the heavy particles are e-mu-tau, and the light particles are the neutrinos. For the quarks, the heavy particles are c-b-t, and the light particles are d-u-s. e-mu-tau and c-b-t are conventional Koide triples, which satisfy Foot's d=3 geometric relation. <br /><br />(By the way, while talking about angles, let us take care to note the difference between these angles - the angle between the mass vector and the "democratic vector" (1,1,1...) - and the "phase" parameter, which has to do with the directions of the components of the mass vector, in the plane perpendicular to the democratic vector.)<br /><br />When we go from three dimensions to six dimensions (i.e. from three masses to six masses), we are no longer considering the angle between (M1,M2,M3,0,0,0) and (1,1,1,0,0,0), but the angle between (M1,M2,M3,0,0,0) and (1,1,1,1,1,1). Evidently (I haven't bothered to do the calculation) the angle between the mass vector and the democratic vector goes from pi/4 towards pi/3 with the jump in dimensions. Then, introducing the three lighter masses (M1,M2,M3,m1,m2,m3) makes that angle almost exactly pi/3.Mitchellhttps://www.blogger.com/profile/10768655514143252049noreply@blogger.comtag:blogger.com,1999:blog-7315236707728759521.post-17935379669156728972012-01-09T14:22:01.026-07:002012-01-09T14:22:01.026-07:00Thanks for your dispatch! Let me add that the note...Thanks for your dispatch! Let me add that the note is now available both in <a href="http://arxiv.org/abs/1111.7232" rel="nofollow">arxiv:1111.7232</a> and <a href="http://vixra.org/abs/1111.0062" rel="nofollow">vixra:1111.0062</a>. Vixra allows to add comments in the abstract page. <br /><br />Most probably I will not pursue publication in the short term; the first try proved that there are some issues basically of scholarly style. A lot of work is already from other authors, it must be reviewed because the topic is not well known anymore, and then the letter must evolve into an article; a time consuming task that I can not afford by now.Alejandro Riverohttps://www.blogger.com/profile/16181521111080562335noreply@blogger.com