tag:blogger.com,1999:blog-7307840825023135484.post2765688244589433761..comments2012-02-07T15:48:38.662+13:00Comments on Arcadian Pseudofunctor: Theory Update 11Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.comBlogger21125tag:blogger.com,1999:blog-7307840825023135484.post-42640336295165353642010-10-25T15:40:58.795+13:002010-10-25T15:40:58.795+13:00That is, the number of generations ($= 3$) gives a...That is, the number of generations ($= 3$) gives a sine value, and if we use this angle with a tan function (like in my mixing matrices) then it gives the $\sqrt{2}$.Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-63922751996280289432010-10-25T15:37:21.000+13:002010-10-25T15:37:21.000+13:00Ah, the $0.615$ seems to come from the inverse sin...Ah, the $0.615$ seems to come from the inverse sine of $1/ \sqrt{3}$. That links the $2$ and the $3$ then.Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-50953433939004454472010-10-25T15:30:55.283+13:002010-10-25T15:30:55.283+13:00Oh, and in the mixing matrix, the parameter $1$ gi...Oh, and in the mixing matrix, the parameter $1$ gives an angle of 45 degrees. The $\sqrt{2}$ instead gives an angle of $0.615$ radians, whatever that means.Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-13418192496647909392010-10-25T13:28:46.313+13:002010-10-25T13:28:46.313+13:00After some thought, yes, it could be that the 45 d...After some thought, yes, it could be that the 45 degrees angle is a redherring. The "angle with 1,1,1", sqrt(2/3), has really two different pieces: the sqrt(3) comes from the number of families, and the sqrt(2), is the size of the symmetry breaking, as it appears very naturally in eq 46 of Brannen's.Alejandro Riverohttp://www.blogger.com/profile/16181521111080562335noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-34045426111000463192010-10-24T09:16:08.312+13:002010-10-24T09:16:08.312+13:00Alejandro, I believe it was Hans de Vries who firs...Alejandro, I believe it was Hans de Vries who first pointed the triangle out, some years ago. And yes, there are many ways to look at the $\sqrt{2}$ geometrically ... but two dimensions at a time, please!Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-74130498853892026362010-10-24T07:25:20.977+13:002010-10-24T07:25:20.977+13:00Ok, I see what puzzles me of the triangle interpre...Ok, I see what puzzles me of the triangle interpretation: that there is not a clear role for the sqrt(2) in the radius of the circle, while in Foot's interpretation is the mark of an angle of 45 degrees with the unbroken "halfmass vector".Alejandro Riverohttp://www.blogger.com/profile/16181521111080562335noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-6680399590161599272010-10-24T06:32:37.916+13:002010-10-24T06:32:37.916+13:00Ok, it is http://www.brannenworks.com/koidehadrons...Ok, it is http://www.brannenworks.com/koidehadrons.pdf formula 46Alejandro Riverohttp://www.blogger.com/profile/16181521111080562335noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-45517285869288519822010-10-24T06:25:08.201+13:002010-10-24T06:25:08.201+13:00Actually, who was the first one suggesting the tri...Actually, who was the first one suggesting the triangle presentation of Koide's angles, and in which paper or blog entry? I guess it was Carl, but I am not sure, it is the first time I see it.Alejandro Riverohttp://www.blogger.com/profile/16181521111080562335noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-834270510997873282010-10-22T12:38:39.086+13:002010-10-22T12:38:39.086+13:00So according to PDG, we just need to down scale $\...So according to <a href="http://pdg.lbl.gov/2010/tables/rpp2010-sum-quarks.pdf" rel="nofollow">PDG</a>, we just need to down scale $\mu$ a little bit.Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-20669312124802826742010-10-22T12:29:52.915+13:002010-10-22T12:29:52.915+13:00Oh, I didn't bother actually looking up the la...Oh, I didn't bother actually looking up the latest top quark estimates. I'm sure the experimentalists can do that, and fix up the Koide fits if necessary.Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-22985644812696393702010-10-22T10:49:18.212+13:002010-10-22T10:49:18.212+13:00compare to the mass of top quark.compare to the mass of top quark.Ullahttp://www.blogger.com/profile/16634036177244152897noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-28720815258200356402010-10-22T10:27:45.004+13:002010-10-22T10:27:45.004+13:00One other possibility for the down quarks is to se...One other possibility for the down quarks is to set $r$ at the average of $r(2/27) = 1.76$ and $r(2/9) = \sqrt{2}$. Then at $\mu = 710$ and $\theta = 5/54$ the triplet is:<br /><br />$4728$ MeV, $80.57$ MeV, $4.85$ MeV<br /><br />At least the experimental bounds really are testing these different scenarios.Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-37196280773705883602010-10-22T10:12:53.054+13:002010-10-22T10:12:53.054+13:00... or maybe we should try to put the down quarks ...... or maybe we should try to put the down quarks on the big triangle?Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-12271945278785694802010-10-22T09:38:33.272+13:002010-10-22T09:38:33.272+13:00Actually, no, the down quarks work best at $1.76$,...Actually, no, the down quarks work best at $1.76$, which comes from the phase $\theta = 2/27$ in the relation<br /><br />$r = \sqrt{2} \sin (5 \pi/6 - 2/9 + \theta) / \sin (\pi/6)$<br /><br />Then the best Koide fits give us:<br /><br />1. up quarks at $\mu = 22990$,<br />$174.553$ GeV, $1.271$ GeV, $2.054$ MeV<br /><br />2. down quarks at $\theta = 4/27$, $\mu = 635$,<br />$4771$ MeV, $79.8$ MeV, $5.8$ MeV<br /><br />and the down quark set really pushes the experimental limits, as before.Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-29930486889275222232010-10-22T08:30:11.216+13:002010-10-22T08:30:11.216+13:00Cool, Dave. Yes, I was a bit rough with the scale ...Cool, Dave. Yes, I was a bit rough with the scale choice above. And I think the down quark radius should be reselected from the phase choice. It was the down quarks that did not quite fit the 1.76 before.Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-25849243916377344212010-10-22T03:18:34.562+13:002010-10-22T03:18:34.562+13:00Using the known relationship:
Mt/sqrt2=(cosOw+sin...Using the known relationship:<br /><br />Mt/sqrt2=(cosOw+sinOw)Mz <br />(Ow is Wienberg angle)<br /><br />to scale the Top mass, we have: <br /><br />2.05MeV 1.27GeV 174.55GeVDavenoreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-89433170523421852602010-10-21T22:39:44.393+13:002010-10-21T22:39:44.393+13:00Good to have a clear prediction. Wikipedia gives ...Good to have a clear prediction. Wikipedia gives the recent bounds on masses (see <a href="http://en.wikipedia.org/wiki/Current_quark_mass" rel="nofollow">this</a>). The most recent estimates for u and d quark masses are 5 and 20 MeV.<br /><br />I assume that the order of masses is t,u, c and b,d, s and unit is GeV.<br /><br /><br />For d the prediction would be at the lower boundary of 2-15 MeV range. For s 71.639 MeV is below 100-130 MeV. For b prediction would be in the required range.<br /><br />For U type quarks the predictions would be by order of magnitude too small as compared to the lower bounds.Matti Pitkänenhttp://tgd.wippiespace.com/public_html/noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-71232272235316806222010-10-21T17:59:25.985+13:002010-10-21T17:59:25.985+13:00So the bigger triangle is completely defined by th...So the bigger triangle is completely defined by the ansatz of phases: sending the $2/9$ for leptons to $2/27$ for the quarks. Presumably we could keep dividing angles by $3$ and come up with an infinite sequence of Koide eigenvalue triplets this way, with the $r$ factor always determined by inscribing.Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-29155832922880705082010-10-21T17:48:22.213+13:002010-10-21T17:48:22.213+13:00Note that for both leptons and quarks, the triangl...Note that for both leptons and quarks, the triangle side length $L$ obeys<br /><br />$(L/r)^2 = 3$Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-37592918441140464822010-10-21T15:10:46.489+13:002010-10-21T15:10:46.489+13:00So plugging this $1.7603$ into the Koide formula, ...So plugging this $1.7603$ into the Koide formula, and choosing a suitable scale, we get the masses:<br /><br />1. up quarks, at a phase of $2/27$:<br />$17159.144$, $0.202$, $124.905$<br /><br />2. down quarks, at a phase of $4/27$:<br />$4282.462$, $5.201$, $71.639$Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-58289044113577505342010-10-21T14:41:43.890+13:002010-10-21T14:41:43.890+13:00Not to mention the CKM matrix ... recall that the ...Not to mention the CKM matrix ... recall that the (offset by 1) Koide eigenvalues could be expressed in terms of a cosine and sine, when we wrote them out with mixing matrix coefficients. So that is what these $x$ and $y$ parameters are about. <br /><br />Ok, now there must be several billion people on the planet who could figure this out ... except maybe the string theorists.Keahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.com