
#163
Jul3012, 07:17 AM

P: 514

Let's see about GeorgiGlashow SU(5).
24(1001) = (8,1,0) + (1,3,0) + (1,1,0) + (3,2,6/5) + (3*,2,6/5) 5(1000) = (3,1,1/3) + (1,2,1/2) 10(0100) = (3,2,1/6) + (3*,1,2/3) + (1,1,1) 10*(0010) = (3*,2,1/6) + (3,1,2/3) + (1,1,1) 5*(0001) = (3*,1,1/3) + (1,2,1/2) To get 6 and 6* QCD states, one can use 15(2000) = (6,1,2/3) + (3,2,1/6) + (1,3,1) 15*(0002) = (6*,1,2/3) + (3*,2,1/6) + (1,3,1) and similar decompositions for 40(1100), 50(0200), 45(1010), etc. GG automatically makes every color singlet have integer electric charge. One can go further, in the likes of SO(10) and E6, but one gets even more extra particles. 



#164
Jul3012, 09:47 AM

PF Gold
P: 2,884





#165
Sep312, 03:57 AM

PF Gold
P: 2,884

Funny. The guy in the left corner in the Strings 2008 closing lecture (the one with the blue shirt) seems to be busy thinking about orientability of the worldsheet and diverse wrappings. I had not noticed it before.
http://cdsweb.cern.ch/record/1121966 



#166
Sep1612, 07:55 PM

P: 748

"A Higgslike Dilaton". There have been many such Higgsvsdilaton papers. This one examines the situation where the theory is supersymmetric and the SM fermions are partly composite (i.e. are mixtures of elementary and composite fields with the same quantum numbers), a scenario discussed several times in this thread.




#167
Sep1712, 10:20 AM

PF Gold
P: 2,884





#168
Oct112, 10:55 AM

P: 748

Ramond et al had a paper, "On Mixing Supersymmetry and Family Symmetry Breakings", in which "extra family partners of the Higgs particles act as messengers for both supersymmetry and family symmetry breakings". It's mildly interesting to contemplate how the waterfall and/or sbootstrap might be realized in a framework like this, because this is a serious, calculable fieldtheoretic model.
The first thing to note is that it talks about supersymmetry breaking, and also how it is accomplished. There are several new scalar fields in the Higgs sector, and one of them is postulated to be coupled to a hidden sector where supersymmetry is broken. This messenger field then acquires vevs which break susy (and family symmetry), and the breaking is then transmitted to the rest of the visible sector (MSSM plus new scalars). This transmission of susybreaking from a whole new sector where the breaking originates is completely standard; it's "singlesector supersymmetry breaking" which is the unusual alternative to mediated susybreaking. By contrast, the papers which introduce the sbootstrap hardly talk about susybreaking. In fact, among the inspirations for the sbootstrap are coincidences like the similarity of the muon mass and the pion mass. Another question hanging over the sbootstrap is how much of conventional thinking about supersymmetry it wishes to take on. In the conventional MSSM, the muon is the superpartner of certain sleptons, and the pion is still a QCD composite and has no relation to those sleptons at all. In the sbootstrap, one supposes that the muon is the superpartner of something decidedly pionlike (and in fact all the leptons are "superpartners" of pionlike quarkantiquark combinations). So it seems that something like the MSSM is supposed to be emergent from something like SQCD. (An alternative approach might be to say that the MSSM has its normal interpretation  sleptons and pions are fundamentally different  but that it has a peculiar hidden N=2 supersymmetry, with the sbootstrap correspondence being the emergent second supersymmetry.) Second, let's consider the role that family symmetry plays in the sbootstrap and the Koide waterfall, and then in Ramond et al. Alejandro describes the sbootstrap as featuring an SU(5) global flavor symmetry, and family symmetries have also featured in many attempts to explain the Koide formula. The family symmetry considered in Ramond et al is discrete and very simple, the permutation group S3, and so is the model; it's not even a threegeneration model, there are only two "families". This isn't yet a serious phenomenological model, it's a toy model of how symmetrybreaking messenger particles (here, some of the new scalars) could carry flavor and yet not cause detectable flavorchanging neutral currents. The physics that results depends greatly on the specific vacuum and on renormalizationgroup effects. These technicalities would be relevant for any serious attempt to embed sbootstrap and waterfall in such a model, and at first glance they don't look very friendly for the generation of Koidetype relationships, but a real assessment on that score awaits a deeper analysis, especially of the "focusing mechanism" which, for certain vacuum alignments, produces phenomenologically convenient cancellations. So overall this is an interesting class of model to examine, for potential implementations of sbootstrap and waterfall, because by design it addresses the issue (neglected by us) of how the symmetries get broken. 



#169
Nov1312, 03:29 AM

P: 748

Two unorthodox top/Higgs papers today. John Moffat continues his series suggesting that LHC's new boson is not a Higgs, but rather a pseudoscalar meson, a mixture of [itex]b \bar b[/itex] and [itex]t \bar t[/itex]. And Christopher Hill, inventor of "topcolor", observes that the "topHiggs system" has a susylike dilatation symmetry, which he uses to explain a web of relations between the top yukawa, the Higgs mass, and the Higgs VEV.
These papers should be considered in conjunction with Bruno Machet's attempt to build Higgs doublets out of quark bilinear condensates (#149) and with "A Higgslike Dilaton" (#166). With respect to the sbootstrap, Moffat and Machet remind us that the "mesons" and "diquarks" of the correspondence might be condensates (but what is the superpartner of a condensate?), and Hill reminds us that an unorthodox "supersymmetry" may be at work. Also, these papers remind us that there remain many relatively elementary constructions that have never been considered. One more thought. In Hill's paper, he argues that alongside top yukawa being close to 1, LHC has revealed that the Higgs quartic coupling is close to 1/4. Numerologically I am reminded of Yukinari Sumino's scheme for cancelling QED corrections to the Koide relation, which requires that the coupling of the new family gauge bosons is approximately 1/4 of the QED coupling. Sumino had no explanation for this relation; could Hill's new symmetry do the job? 



#170
Nov1312, 04:20 PM

PF Gold
P: 2,884





#171
Dec1712, 06:13 AM

PF Gold
P: 2,884

The peculiar arrangement of SU(4), or U(1)xSU(3) multiplets noticed in the Koide thread
http://www.physicsforums.com/showthr...=551549&page=6 could be related to the problems to put the higgs scalar under the same symmetries that the other scalars in the sboostrap. Remember that we had to our disposal three scalars from the 15 and other three from the 15 irreps of SU(5). In our quark mnemonics, it is uu, uc, cc, uu, uc, cc (using the underscore to mean antiparticle). For such thing to be able to produce integer uncoloured charges, we need the mass/higgs mechanism to be blind to colour and blind to BL, so that all the electric charge of these objects come from the electroweak isospin. Thus here is the first connection to the other thread: the multiplets of equal mass are for the charges for which the sBootstrap Higgs, if it is there, needs to be blind. The second connection is even foggier: in the other thread, either the strange quark or the muon seem to need an opposite quantum number in order to fit in a SU(4) multiplet. Here it is either the up quark or the charm quark which seem to need some opposite value to sum zero in the uc combination. 



#172
Dec2412, 01:54 AM

P: 748

Two recent papers, by authors already mentioned in this thread, which derive a Higgs sector in a sbootstrapfriendly way:
Bruno Machet continues his series "Unlocking the Standard Model" (see #149), in which the idea seems to be that the Higgs will come from pionlike vevs. As discussed e.g. in #151, in a Higgsless SM, the W and Z will still acquire masses from pion vevs, but at the wrong energy scale. Machet nonetheless wants a version of this to work. In this, his third paper in the series, he considers two generations of quarks, and claims to get the Cabibbo angle from his Higgslike condensates. Presumably future work will aim to get the whole CKM matrix from the quark bilinears of a threegeneration model. Of the multitude of scalar and pseudoscalar mesons that appear, he states (page 4) that some of the scalars will be the Higgs, and the rest should correspond to the observed mesons. Kitano and Nakai's "Emergent Higgs from extra dimensions" aims to get the Higgs (and the masses of the Higgs and the top) from a deconstructed compactification of the d=6 (2,0) theory to four dimensions. This paper is certainly replete with connections to interesting topics. The (2,0) theory is the worldvolume theory of the M5brane, so it's central to current advances in theoretical QFT. Their deconstructed version (deconstruction here means that the extra dimensions are approximated by a lattice, so e.g. a circle becomes a ring of sites with a copy of the d=4 SM fields at each site, coupled via the links in the ring, as in a quiver theory) is said to resemble topcolor (see page 3). There's much more I could talk about and I may have to return to this paper. But for now I'll remark on the possibility that perhaps something like Machet's model, which naively shouldn't work, could be produced by a KitanoNakai scenario, in which new strong couplings occur at high energy. "As in the Nambu–JonaLasinio model for the chiral symmetry breaking, whether or not a condensation forms depends crucially on how the theory is cutoff, and thus discussion requires a UV completion of the theory." 



#173
Jan313, 01:58 PM

PF Gold
P: 2,884

[tex]\begin{array}{lllll} ?, t_{rgb}& & & & \\ ?, b_{rgb}& B^+,B_c^+ & bu, bc& bb, bs, bd & \\ \tau, c_{rgb} & D^+, D_s^+& sc,dc \\ \mu, s_{rgb} & \pi^+, K^+& su, du& ss, sd, dd \\ ?, d_{rgb} \\ e, u_{rgb}\end{array}[/tex] It is tempting to think that in this "midly broken susy", the two lower mass levels are actually massless, so that SUSY does not need to kept the pairing at the same mass; it could be that the partners of d are the charmed diquarks, while the partners of up have been lost in the same mixing that breaks t and c partners. Adding neutrinos and the missed diquarks, the table is a bit more complex. With some small abuse of notation, we could write the "after mild breaking" sBootstrap as [tex]\begin{array}{lllllll} &\nu_?, t_{rgb}& & & & \\ &\nu_?, b_{rgb}& B^+,B_c^+ & bu, bc& bb, bs, bd & \eta_b, \stackrel{b\bar s,b\bar d}{\bar bs,\bar bd} \\ \stackrel{\bar c\bar c}{cc},\stackrel{\bar c\bar u}{cu}&\tau, c_{rgb} & D^+, D_s^+& sc,dc & & \eta_c, \stackrel{c\bar u}{\bar cu}\\ \stackrel{\bar u\bar u}{uu}&\mu, s_{rgb} & \pi^+, K^+& su, du& ss, sd, dd & K^0,\pi^0, \stackrel{s\bar d}{\bar sd}\\ &\nu_?, d_{rgb} \\ &e, u_{rgb}\end{array}[/tex] It is sort of symmetric, in a pleasant way. Wish I knew what to do about it. 



#174
Jan413, 12:18 AM

P: 748

We can adapt an earlier idea for the sbootstrap to PatiSalam. The earlier idea is that there is a fundamental QCDlike theory with six flavors of quark, five light and one heavy; the five light quarks form fermionic composites, "diquarkinos" and "mesinos"; and the mesinos are the leptons, while the diquarkinos mix with the fundamental quarks to give us the phenomenological quarks.
For PatiSalam sbootstrap, the prescription is almost the same, except that the leptons already exist as the "nth color" in the fundamental QCDlike theory, so in this version the mesinos are mixing with preexisting degrees of freedom, just like the diquarkinos. It's probably best to think of the fundamental theory as having N=1 supersymmetry (at least), and to think of these composites as superfields. 



#175
Jan1013, 04:11 PM

PF Gold
P: 2,884

http://higgs.ph.ed.ac.uk/sites/defau...s/Higgs_RR.pdf
Rattazzi is near to discover the sBootstrap if he continues this kind of enquiries. 



#176
Jan1713, 08:57 AM

P: 748

On the Koide thread we have started to discuss textures and symmetries that could produce the waterfall pattern, and it's beginning to sound like orthodox modelbuilding. But it's still not clear to me how to naturally descend from the sbootstrap to the waterfall. Supersymmetric theories are more complicated, including their methods of mass generation, and the "superparadigm" which in my opinion most resembles the sbootstrap  Seiberg duality  doesn't offer obvious concrete guidance.
However, I have a few thoughts arising from one of the nonsusy paradigms for modeling the masses. As described e.g. on page 2 here, one may imagine that SM yukawas arise from a democratic matrix plus a correction. The democratic matrix has eigenvalues (M,0,0), and the correction can make the smaller eigenvalues nonzero. So consider an approach to the sbootstrap in which we begin with six flavors of chiral superfield, and in which some fundamental, democratic mechanism of mass generation produces a single heavy flavor. Now suppose that the five light flavors form meson superfields which mix with the fundamental superfields, as previously posited. It seems that we then have a mass matrix which starts with SU(6) symmetry and then has a correction with SU(5) symmetry; something which is ripe for further symmetrybreaking, perhaps down to a waterfall pattern. There are still conceptual problems. The democratic matrix usually appears as a Yukawa matrix, but one doesn't usually think of the Higgs as fundamental in the sbootstrap. Also, the usual "fiveflavor" logic of the sbootstrap is motivated by the fact that the top decays before it can hadronize; but that decay is mediated by the weak interaction, which doesn't yet play a role in the scenario above. There's also the problem that the combinatorics of the sbootstrap employs the electric charges of the quarks, but if we impose those from the beginning, then we can't have the exact SU(5) or SU(6) flavor symmetry. So there may need to be some conceptual tailchasing before a logically coherent ordering and unfolding of the ingredients is found. On the other hand, I wonder if some version of the cascades discussed earlier in this thread (page 9, #132 forwards) can produce an iterated breakdown of symmetry in the mass matrix. We could start with one heavy quark and five light, then the diquarkinos and mesinos induce corrections to the mass matrix, which in turn affect the masses of the diquarkinos and mesinos, breaking the symmetry further. Also of interest: "Strongly Coupled Supersymmetry as the Possible Origin of Flavor". 



#177
Feb113, 03:46 PM

PF Gold
P: 2,884

I have put around an example about how the supermultiplets could be, before the susy breaking. Surely it is not the right mix, but it could be a reference to try to build a pure susy model. http://vixra.org/abs/1302.0006
[tex] \begin{array}{llllll} \hline \stackrel{\bar c\bar c}{cc}& \nu_2, b_{rgb}, e, u_{rgb}& B^\pm,B_c^\pm & \stackrel{\bar b\bar u}{bu}, \stackrel{\bar b\bar c}{bc} & \stackrel{\bar b \bar s}{bs}, \stackrel{\bar b\bar s}{bd} & B^0, B^0_c, \bar B^0, \bar B^0_c \\ \stackrel{\bar c\bar u}{cu}& \tau, c_{rgb} , \nu_3, d_{rgb}& D^\pm, D_s^\pm& \stackrel{\bar s\bar c}{sc},\stackrel{\bar d\bar c}{dc} & \stackrel{\bar b\bar b}{bb},\stackrel{\bar d\bar d}{dd} & \eta_b, \eta_c, D^0, \bar {D^0}\\ \stackrel{\bar u\bar u}{uu}& \mu, s_{rgb} , \nu_1, t_{rgb}& \pi^\pm, K^\pm& \stackrel{\bar s\bar u}{su}, \stackrel{\bar d\bar u}{du}& \stackrel{\bar s\bar s}{ss}, \stackrel{\bar s\bar d}{sd}& \eta_8, \pi^0, K^0, \bar K^0 \\ \hline \end{array} [/tex] 



#178
Feb113, 06:27 PM

P: 748

A major conceptual problem for the sbootstrap has been, how to get elementary and composite fields in the same superfield. But I notice that the string concepts of "flavor branes" and "color branes" can bring them closer. The flavor branes would be labeled dusc... and the color branes rgb..., and a single quark is a string between a flavor brane and a color brane (e.g. a red up quark is a string between up flavor brane and red color brane); and a meson is a string between two flavor branes. And if we employ PatiSalam, then all the leptons also have a color, the "fourth color".
According to the sbootstrap, a lepton is the fermionic superpartner of some meson or quarkantiquark condensate. The immediate problem for achieving this within the framework above is that it seems to involve pairing up different types of strings. Usually, you suppose that the flavor branes form one stack, the color branes form a different stack, the two stacks lie at different angles in the extra dimensions, and there are three types of string: flavorflavor, colorcolor, and flavorcolor. As usual, each stack will have a corresponding symmetry (e.g. SU(N) for some N), the flavorflavor strings will be singlets under the color group, the colorcolor strings (the bosonic states of which are the gluons) are singlets under the flavor group, and the flavorcolor strings transform under both groups. Also, the flavorcolor strings are found most naturally in the vicinity of the intersection between the flavor stack and the color stack, because that is where the distance is shortest and thus the tension is smallest. But flavorflavor and colorcolor strings can be found anywhere within their respective stacks, because the branes are parallel and so the interbrane distance is the same everywhere. To my mind this poses a major barrier to the idea of placing a flavorcolor string and a flavorflavor string in the same multiplet. What if, instead of using intersecting brane stacks, we just have one big stack, and then move the branes apart into two groups, while keeping them parallel? This is already a standard method of breaking a symmetry group  the gauge bosons corresponding to strings between the two parts of the stack are the ones that are heavy, because they are longer. Now we would have that G_{flavor} x G_{color} is a subgroup of G_{big}, the symmetry group of the original, unseparated branestack. Then we would suppose that the branes of the big stack are separated from each other in the extra dimensions (while remaining parallel) in such a way as to produce the desired mass spectrum  with the flavor branes clustered together in one group, the color branes in another, and the distances within and between the groups tuned appropriately. 



#179
Feb113, 07:22 PM

P: 748

I'll sketch how something like this could work. We'll use nine D3branes in a space of three large dimensions, and six small and compact dimensions. Geometrically it can be just like KaluzaKlein, except that each local copy of the KK manifold has nine special points scattered throughout it, the places where the nine D3branes pass through that copy of the KK space.
Basically, we would think of three of the points as being close together, and the other six scattered around them in sixdimensional space. The three branes that are close together (in fact, on top of each other) are the color branes. Because they are on top of each other, the SU(3)_{color} gauge symmetry is unbroken. But the other six branes are scattered around and the SU(6)_{flavor} gauge symmetry is completely broken. The quark superfields are strings connecting the 3 coincident points with any of the 6 scattered points, and the meson superfields are strings connected the 6 scattered points with each other. And to get them into the same supermultiplets, you restore the symmetry by moving all 9 points so they are on top of each other. So far I've said nothing about the weak interaction, and in fact I think it will require a doubling of the branes  or of the flavor branes at least. For each flavor there will be two branes, a "left brane" and a "right brane", for the two chiral components. Once again, this is a quite standard idea. Hypercharge is no problem, it's just a particular U(1) subgroup. And I suppose we can hope that the desired arrangement of branes is produced dynamically, e.g. by relaxation from cosmological initial conditions. It's surely too much to hope for, that some version of this would actually work. But I think it's remarkable that mathematically, this is genuine orthodox string theory. You could define a particular geometry for the Type IIB string (which is the one that has D3branes) and calculate its spectrum. edit: Wait, I forgot we were getting leptons from a fourth color. So there are four color branes, four "color points" in the KK space, but one of them is displaced a little from the others  the breaking of SU(4)_{color} to SU(3)_{color}. A single quark is a string connecting a flavor brane to an rgb color brane, and a lepton is a string connecting a flavor brane to the fourth color brane. 



#180
Feb1313, 09:16 PM

P: 748

We have a number of threads right now on getting the Higgs mass from Planckscale boundary conditions. The common idea is that there is no new physics between the weak scale and the Planck scale. The bestknown version is that of Shaposhnikov and Wetterich (SW), who managed to land very close to the observed mass by postulating that the "neutrino minimal standard model + gravity" is "asymptotically safe". However, I think the most elegant proposal is the "conformal standard model" of Meissner and Nicolai, who observe that the classical theory is conformally invariant except for the quartic Higgs term, and who propose therefore that the fundamental theory has conformal symmetry and that this quartic term is generated by the conformal anomaly.
I note that in the world of high theory now, the really interesting symmetry is superconformal symmetry, the combination of supersymmetry and conformal symmetry. And since the sBootstrap, like the conformal standard model, is an exercise in theoretical minimalism, I have to wonder if there could be a "superconformal standard model" combining both? Supersymmetry is normally regarded as wildly incompatible with the minimalist idea of "no new physics between weak scale and Planck scale". We already know that we need physics beyond the original standard model with massless neutrinos; the "neutrino minimal standard model" manages to obtain all this below the weak scale, though at the price of unnatural finetuning (dark matter comes from righthanded neutrinos with keV Majorana mass, lefthanded neutrino masses from very small yukawas). One might suppose that including supersymmetry would be even harder, or just impossible. One approach would be supersplit supersymmetry: all the superpartners have Planckscale masses. But what about the sBootstrap alternative: supersymmetry is there, but it's only very weakly broken? In a sense that's the longrunning theme of this thread  the quest for ways to embed the sBootstrap pattern within a genuinely supersymmetric theory. The gauginos are the main technical problem that I see. One possibility is that we can just do without them by using Sagnotti's type 0 string theory, which is nonsupersymmetric but arises from the superstring, and which can apparently inherit a degeneracy of bosonfermion masses. Armoni and Patella use type 0 open strings to construct a form of "hadronic supersymmetry" (pairing mesons and baryons)  see page 8 for their general remarks on the type 0 theory. Meanwhile, Elias Kiritsis has sought to obtain a holographic dual for (nonsusy) QCD using type 0 strings. We have discussed the mesinos from holographic QCD several times; perhaps a type0 version of the branestack constructions I discussed here a few weeks ago, could provide a "nonsusy sBootstrap" in which we have mesinos but not gauginos. So perhaps we might want a type0 brane stack which classically has conformal symmetry, but in which the Fermi scale is anomalously generated (as in the conformal standard model). Meanwhile (bringing in ideas from the Koide thread), there's also a discrete S4 symmetry producing a Koide waterfall, with the top yukawa equal to 1 and the up yukawa equal to 0... The waterfall produces the quark mass ratios, the SWlike mechanism produces the Fermi scale. The leptons are fermionic open strings between the flavor branes in the brane stack (mesinos)... It's all still a delirium, but perhaps we're getting there. 


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