tag:blogger.com,1999:blog-8666091.post4194796642491541744..comments2021-07-18T19:54:06.055+02:00Comments on The Reference Frame: Could the Koide formula be real?Luboš Motlhttp://www.blogger.com/profile/17487263983247488359noreply@blogger.comBlogger21125tag:blogger.com,1999:blog-8666091.post-36221143945060728042015-05-07T06:29:16.948+02:002015-05-07T06:29:16.948+02:00There are a couple of functions of masses of vario...There are a couple of functions of masses of various particles, numbers called Q, that are a priori guaranteed to be between 0 and 1. And it's said that they're equal to 2/3 or 3/4 within some accuracy.<br /><br /><br />It is not a big deal at all. The interval 0-1 is covered by neighborhoods of numbers we can write analytically - like rational numbers. The probability that an expression Q is exactly 2/3 or exactly 3/4 with the accuracy of 0.0001 may be just 1/10,000, but the probability that one finds *some* similarly accurate quantification of *some* ratio of this kind is almost 100% because there are many numbers that are about as interesting as 2/3 or 3/4 and because the ratio Q may be written in many different ways, too.<br /><br /><br />The other formulae are even more meaningless. For example, there is one ratio involving quarks c,b,t. This is literally adding apples and oranges. Some of them are lower quarks, one of them is upper quark, and no generation of quarks is fully represented.<br /><br /><br />This coincidence really says nothing else that sometimes if we compute a random function of three random parameters, the random result we obtain is sometimes close to 2/3 or 3/4. What a surprise. It's guaranteed to happen sometimes.<br /><br /><br />All your excitement about this stuff is irrational.Luboš Motlhttp://motls.blogspot.com/noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-86562080022108336572015-05-07T06:23:42.164+02:002015-05-07T06:23:42.164+02:00This comment of yours makes no sense because the e...This comment of yours makes no sense because the energy of a physical system is always a *real* number - the Hamiltonian is a Hermitian operator.<br /><br /><br />Balmer found the correct parameterization of the energy differences in the hydrogen atom itself not coupled to the electromagnetic field - an idealized system that is a good approximation for the hydrogen most of the time because the coupling to the external electromagnetic field is weak enough.<br /><br /><br />So these energy differences had to be real. The actually calculable "points" are complex because the excited states are unstable but they may be well approximated by the real problem.<br /><br /><br />In the strongly coupled case, however, the widths are routinely of the same order as the energies. The real and imaginary parts are comparable - at least to the extent for them to severely reduce the accuracy of the numerological formulae claimed to be surprising. <br /><br /><br />That shows that something is conceptually wrong with this whole line of reasoning.<br /><br /><br />The comparison with Balmer is inadequate because of the "amount of surprise" in the numerological accidents. Balmer had much more numerological evidence - many lines that agree with a simple natural formula.<br /><br /><br />This Koide stuff only gives one ratio right, only a few digits, and the formula for it is much less natural and unique.Luboš Motlhttp://motls.blogspot.com/noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-42297171655126808202015-05-07T05:51:55.803+02:002015-05-07T05:51:55.803+02:00Also, long as I am complaining, I point out: if yo...Also, long as I am complaining, I point out: if you had been around back when Blamer did his numerology, and you'd said "Ha! Really there is no such thing as energy differences because there also are line widths caused by finite lifetimes so those energy differences actually are complex not real numbers!" and therefore dismissed Balmer's findings as bullshit numerology, you'd have prevented the discovery of quantum mechanics. Congratulations.Warren Smithnoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-31513145402374489652015-05-07T05:10:50.626+02:002015-05-07T05:10:50.626+02:00wikipedia has an article on the Koide formula
htt...wikipedia has an article on the Koide formula<br /><br />http://en.wikipedia.org/wiki/Koide_formula<br /><br /><br /><br />and it claims that the same formula also holds for the masses of the 3 heaviest quarks, and ditto for the 3 lightest quarks, to within today's experimental errors. Not just the 3 leptons as you discussed.<br />And I suppose it also holds for the 3 neutrino masses to within today's experimental errors although that is purely since those experimental errors are enormous :).<br />Is that right? Because if so, it makes it sound pretty amazing when you put it that way. And your jive about the imaginary parts of the "masses" does not affect this if we agree to use |mass|,for example, because the imaginary parts are so small compared to the real parts.<br /><br /><br />So does all that cause your sneering to up-convert?<br />There have been prior examples in physics such as Balmer and the speed of light, where such numerology actually succeeded even though according to the laws of physics known at those times, these numerological facts were inexplicable. It does seem like rest masses are very complicated under the laws of physics as currently understood, but if all 4 of the Koide formulae really hold<br />and keep holding, then I'd think there must be something to it...Warren Smithnoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-17283905082935065172015-04-18T14:29:35.827+02:002015-04-18T14:29:35.827+02:00With pdg 2014, let me update on Koide tuples now i...With pdg 2014, let me update on Koide tuples now including of experimental error. <br /><br />The original tuple:<br />e mu tau = 0.666 658 25 pm 0.000 009 04, 0.93 sigmas<br /><br />The Waterfall tuples:<br />tbc = 0.6696 pm 0.0011, 2.72 sigmas<br />cb(-)s = 0.6759 pm 0.0049, 1.89 sigmas<br />bs0 = 0.6632 pm 0.0054, 0.63 sigmas<br />s0d= 0.7004 pm 0.0094, 3.59 sigmas<br /><br />Other tuples:<br />sud= 0.5655 pm 0.0163, 6.20 sigmas<br />bsu = 0.6225 pm 0.0072, 6.13 sigmas<br />bsd= 0.7297 pm 0.0044, 14.3 sigmas<br /><br />I should add (c+b+s)/(e+mu+tau) = 3, which experimentally is 2.947 pm 0.021, so 2.5 sigmas away, and invites to consider a slightly higher mass for c quark.alejandro riveronoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-61260251274140183312014-10-03T19:32:05.403+02:002014-10-03T19:32:05.403+02:00I have this topic in the backburner (quark-hadron ...I have this topic in the backburner (quark-hadron susy is more interesting to me, nowadays) but I happened to be invited to try a virtual lecture for an in2p3 institute and as a byproduct there is a new set of slides including the published bibliography in the topic (and indeed renormalization group objections). Uploaded at slideshare http://www.slideshare.net/alejandrorivero/koide2014talkalejandro riveronoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-83198581104193693502014-07-20T21:31:42.913+02:002014-07-20T21:31:42.913+02:001776.96894(7) is the predicted mass of tau from cu...1776.96894(7) is the predicted mass of tau from current values as of May 2014. <br /><br />"The pre-BESIII paper PDG value for the tau lepton mass is 0.93 sigma less than the original Koide's rule value. The new BESIII value for the tau lepton mass is 0.33 sigma less than the original Koide's rule value."<br /><br />So as of mid 2014, Koide is still predicting accurately.<br /><br />http://dispatchesfromturtleisland.blogspot.ca/2014/05/experiments-reaffirm-original-koides.htmltomandersennoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-16012913273792646472013-04-02T01:21:13.110+02:002013-04-02T01:21:13.110+02:00sqrt(mass) makes sense for masses that are distrib...sqrt(mass) makes sense for masses that are distributed in a disc. Then mass = k*r**2, so sqrt(mass) is a dimension (the constant divides out in Koide), and the Koide formula could be telling us that these particles are disc shaped.<br /><br /><br />Not likely, perhaps, but the Koide formula can be interpreted physically.tomandersennoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-49887811371217360062012-11-12T03:08:06.978+01:002012-11-12T03:08:06.978+01:00173.18 ± 0.56 ± 0.75 is now final word from Tevat...173.18 ± 0.56 ± 0.75 is now final word from Tevatron. Most recent CMS, from V.A. slides in the HCP2012, is 173.36 ± 0.38 ± 0.91. This is only with the 5 fb dataset, a previous CMS/Atlas combination this summer was also of the same order, 173.3 ± 0.5 ± 1.3. Lets see what happens with Atlas.Alejandro Riverohttp://profiles.google.com/al.riveronoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-71948087381577603812012-07-24T01:20:51.139+02:002012-07-24T01:20:51.139+02:00Another thing... composite Higgs, as well as some ...Another thing... composite Higgs, as well as some variants coming from 5D, have the yukawa coupling as a product of two other coefficients. So in such cases there is really a "square root of the masses" directly in the Lagrangian.Alejandro Riverohttp://www.facebook.com/alejandro.riveronoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-3579846325068284682012-07-07T03:21:05.618+02:002012-07-07T03:21:05.618+02:00I sketched a prezi presentation http://prezi.com/e...I sketched a prezi presentation http://prezi.com/e2hba7tkygvj/koide-waterfall/ on Koide chainsAlejandro Riverohttp://profiles.google.com/al.riveronoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-9428831106330137402012-07-05T15:08:22.465+02:002012-07-05T15:08:22.465+02:00New numbers on the mass of the top: 173.18 ±0.94 G...New numbers on the mass of the top: 173.18 ±0.94 GeV, from arxiv:1207.1069 CDF/D0 combination. Koide ladder calculation from vixra:1111.0062v2/arxiv:1111.7232, is 173.263947(6) GeV.Alejandro Riverohttp://profiles.google.com/al.riveronoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-89679610148005387062012-01-18T20:18:46.085+01:002012-01-18T20:18:46.085+01:00The mass of a fourth lepton that would be predicte...The mass of a fourth lepton that would be predicted by Koide's formula has, IIRC, been ruled out experimentally. It would be on the same order of magnitude of mass as a bottom quark, since the charm and strange quarks have masses on the same order of magnitude as the muon and tau, but the exclusion range from experiment for new charged fermions is on the same order of magnitude as the much heavier top quark.<br /><br />Thus, Koide's formula if extended, predicts that there is not a fourth or higher generation of fundamental fermions.Andrew Oh-Willekehttps://www.blogger.com/profile/02537151821869153861noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-52031480189260570922012-01-17T16:21:49.089+01:002012-01-17T16:21:49.089+01:00I saw the Koide formula some years and found it in...I saw the Koide formula some years and found it interesting. Plus it is close to 0.001 * 666 , which is evil but only one in a thousand :P<br /><br />Wether there is a deeper truth or not...I don't know! I would like however to ask something.<br />Supose there is a fourth lepton, not yet discovered, what would it's mass be? Should the formula still work with adding another mass?Konstantinos Tsoukalashttps://www.blogger.com/profile/10380054297299118216noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-75349432158994737412012-01-17T13:25:12.491+01:002012-01-17T13:25:12.491+01:00Well, you did not notice Koide equation till this ...Well, you did not notice Koide equation till this week, it seems, so please forgive me if I did not notice it till 2005, and all the masses had already been measured.<br /><br />Actually, tau is a prediction. The current value was measured in 1992. Previously, and in the age when Koide produced his equation, it was quoted a bit about 1.78 or even 1.80 MeV. In fact, Koide work is a good example that a prediction does not grant success. It is amusing that a lot of internet arguments go about predictions vs postdictions, when at the end that the important point of calculations during evaluation of theories is its use to discard them, not its use to accept them.<br /><br />Let me note also that nobody claims, afaik, that this set of equations has a closed non perturbative origin without further corrections. It is just claimed that in this simple form they already do a huge step towards matching the mass values.<br /><br />Still, I am amazed of your way to look at the data and your argument , "Some of them don't work at all, some of them work at 10%". Lets check again. Besides the tau, when we take as start points the best measured masses, electron and muon, we get that:<br /><br />- Strange is inside of the evaluation and 8% from the average.<br />- Charm is in the border of the evaluation and 5% from the average.<br />- Bottom is inside 1-sigma and <br /> and 0.2% of the central value.<br />- Top is inside 1-sigma and 0.2% of the central value too. <br /><br />But it is true that for the first generation:<br /><br />Up does not work, and<br />Down is inside the estimate (4.1-5.7), but at 11.3% above the average.<br /><br />So it seems that your protest reduces to the low triplet U,D,S.<br /><br />You are right to protest here. In fact I am a bit amused that Rodejohann and Zhang put this triplet in the valid set. It seems that they argue RG to do all the comparisons in some GeV scale, and then it works better. But it is also possible, as I said, to postulate that the Koide prediction, whatever its underlying physics, give us the masses before mixing. With an ad-hoc mixing with M=185 MeV, we should get<br />U'=U+DS/M= 2.67 MeV<br />D'=D+US/M= 5.32 MeV<br />S'=S+UD/M= 92 MeV<br />This kind of mixings were proposed time ago as a solution to the strong CP problem, setting U=0 to conjure out the problem and then getting the real masses from the mix. Instantons were the main candidate for it.<br /><br />Ah, other thing... When you say:<br /><br /> "given the limited interval in which the ratio may a priori be."<br /><br />... I am a bit puzzled about what "a priori" are you thinking about. Obviously it is something different that (0,infinite), and surely you are thinking in something coming from GUT or some limit where yukawas of leptons and quarks are equal and generations keep simple rations across them, and then the running down fixes the possible "limited interval". As far as I remember, you have never blogged about this; it could do a nice post by itself.Alejandro Riverohttps://www.blogger.com/profile/16181521111080562335noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-90559251574750563702012-01-17T12:14:12.173+01:002012-01-17T12:14:12.173+01:00Dear Alejandro, these are not really predictions b...Dear Alejandro, these are not really predictions because you knew the results when you were inventing these silly contrived rules. And they don't work, either. Every sane person knows that they're coincidences. Once the tau mass will be measured more accurately, it will be 5 sigma away from your deluded "predictions".<br /><br />The quarks are not worth talking about at all. Some of them don't work at all, some of them work at 10% which is a very likely outcome even a priori, given the limited interval in which the ratio may a priori be.<br /><br />So this whole program is utter failure. I can't believe you don't see that.Luboš Motlhttps://www.blogger.com/profile/17487263983247488359noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-24903291377507959852012-01-17T11:56:47.764+01:002012-01-17T11:56:47.764+01:00Er, Lubos, have you checked the numbers lately?
...Er, Lubos, have you checked the numbers lately? <br /><br />Tau is 1776.82 ± 0.16 Our prediction 1776.97 <br /><br />And s,c,b,t are respectively<br />100.2 ± 2.4 average, 80-130 evaluation. Our prediction,92.28<br />1.294 ± 0.004 average, 1.18-1.34 evaluation. Our prediction, 1.3596<br />4.19 −0.06+0.18 Our Prediction, 4.198 <br />172.9 ± 0.6 ± 0.9 GeV Our Prediction 173.264<br /><br />If they do not fit, what do you call a fit? Note that the more stressed measures are the ones for which the pdg has not confidence, giving also an equivalent estimate. Only the charm seems to be a bit in the extreme of the estimate.<br /><br />It is true that Koide ladder fails to obtain the mass of the up quark. But it errs a right side, it predicts an up mass near to zero and a down mass in the right order so that the standard arguments of second order corrections, instantons or like, could be applied. I do not consider it a success because it implies a new input, but exactly this kind of correction has been around in the literature by some time, and it is still to be settled via lattice. If you buy it, a new parameter allows to fix right values for down and up too.<br /><br />As for why should we have alternating quarks, well, it is the original HHW situation, with (u,d,s) meeting Koide formula in the breaking where the mass of up quark is zero. The real question is why the leptons are not alternating with neutrinos. Well, perhaps they are, and the mu neutrino has the same Dirac mass that the muon. Or perhaps it is just an effect of the composite theory that transported the formula to the lepton sector. The alternation between quarks of different kinds was used in the primitive literature to try to fix a CKM parameter; the corresponding parameters in the lepton sector work differently, so it is not so surprising if a situation is "alternating" while the other is "generation-wise".Alejandro Riverohttps://www.blogger.com/profile/16181521111080562335noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-27249563415739504222012-01-17T08:50:55.955+01:002012-01-17T08:50:55.955+01:00Alejandro, fine, so do you agree that the numerolo...Alejandro, fine, so do you agree that the numerology doesn't work for quarks, not even on the numerological level? All the numbers are totally different than they should be.<br /><br />Even if the numbers worked, and they didn't, it would be extraordinarily stupid to look for coincidences involving c,s,b quarks. They're 3 out of 6 flavors; some of them are down-type quarks but "c" is an up-type quark. You're clearly mixing apples and oranges. <br /><br />It makes absolutely no sense to find exact patterns constraining 3 random quarks out of the 6 flavors.<br /><br />And it probably makes no sense for me to talk to you because you apparently viscerally hate rational as well as scientific reasoning.Luboš Motlhttps://www.blogger.com/profile/17487263983247488359noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-81678413050946197062012-01-17T01:44:39.436+01:002012-01-17T01:44:39.436+01:00So, prediction-wise, the current built is:
Take t...So, prediction-wise, the current built is:<br /><br />Take the mass of electron and muon<br /> <br />me = 0.510998910± 0.000000013 <br />mμ = 105.6583668± 0.0000038<br /><br />and use Koide to calculate the mass of tau. <br /><br />m = 1776.96894(7) MeV<br /><br />(I am putting inside the hamburger buns the error of the "prediction", given the errors in the only two physical inputs, electron and muon)<br /><br />second step, assume the orthogonal Koide triplet (this implies a factor three in mass and other factor three in angle) to predict the masses of strange, charm and bottom:<br /><br />ms = 92.274758(3) MeV<br />mc = 1359.56428(5) MeV<br />mb = 4197.57589(15) MeV<br /><br />third step, assume again Koide as usual to produce the mass of the top from charm and bottom<br /><br />mc as above<br />mb as above<br />mt = 173.263947(6) GeV<br /><br />Even to me it is hard to swallow, because in my usual frame of mind I expect that the top mass is natural, yukawa order 1, while all the others are yukawa zero.<br /><br />Well, four and five, just to see, go ladder down with Koide with mc and ms as input, getting m_up, amd then ms and up as input, getting md. This is the most dissapointing result:<br />mu = 0.0356 MeV<br />md = 5.32 MeV<br />It is possible to go into serious values by adding some mixing, instanton or whatever. Let M be its scale, then we could produce<br />ms'= ms + mu md / M<br />mu'= mu + ms md / M<br />md'= md + mu ms / M<br />this is an old trick that nowadays is suppossed to be ruled out by lattice QCD.Alejandro Riverohttps://www.blogger.com/profile/16181521111080562335noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-46876377921295154702012-01-17T01:25:13.128+01:002012-01-17T01:25:13.128+01:00Thanks to take the time to write about this. Actua...Thanks to take the time to write about this. Actually I am surprised you did... no much news, this week?<br /><br />The first occurrence I known of this kind of formula is not from Koide but <a href="http://inspirehep.net/record/130343?ln=en" rel="nofollow">by Harari, Haut, and Weyers in Phys.Lett. B78 (1978) 459</a>, in the context of Cabibbo angle. They propose a discrete symmetry for a very peculiar Higgs sector that aims to explain other coincidency, that of Cabibbo angle and the mass quotient of down and strange quarks. They single out a particular breaking where mass of up quark is zero and the other quotient,(mass_down/mass_strange) is (2-sqrt(3))/(2+sqrt(3). You can see that such triplet fulfills the formula.<br /><br />The startpoint for Koide work was to try to explain Cabibbo angle from the point of view of composite models of quarks and leptons. Then such composites implied an extra condition in the lepton sector, and he used it to predict the tau lepton. This is the status up to today: with the electron and muon mass as input, Koide formula predicts mass of tau lepton within one sigma.<br /><br />One year ago, in one of the typical struggles to extend this formula to neutrinos, <a href="http://inspirehep.net/record/885923?ln=en" rel="nofollow"> Rodejohann and Zhang Phys.Lett. B698 (2011) 152-156</a> remarked that the mass values of the sequence top, bottom, charm were not in disagreement with Koide's formula. With foresight, we could have been inspired in the 1978 paper and thought that for triplets of quarks it was important to have one of a different family, if only to build the two mass quotients you refer to. But instead we got lost, thinking family-wise.<br /><br />Given the observation of Rodejohann and Zhang, it was natural to look again, and you can construct it as if we had been five or six years pestering on the topic, but do not worry, we have had time to think on other topics. Whatever, it happens that the next of the sequence, bottom, charm and strange, also goes into the error bar umbrella of the strange quark IF we use the negative square root. By itself, it does not mean a lot, because the mass of s has a huge error bar. But the interesting point is that the new triplet was also almost orthogonal to the lepton triplet. I noted this point in <a href="http://arxiv.org/abs/1111.7232" rel="nofollow">arxiv:11117232</a>Alejandro Riverohttps://www.blogger.com/profile/16181521111080562335noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-25198828892364373402012-01-16T23:34:12.847+01:002012-01-16T23:34:12.847+01:00If it is merely a coincidence, why are their simil...If it is merely a coincidence, why are their similar top-bottom-charm, bottom-charm-strange, and charm-strange-down triples, and why is there a three to one relationship between the charged lepton triples and the b-c-s triple?Andrew Oh-Willekehttps://www.blogger.com/profile/02537151821869153861noreply@blogger.com