The wrong turn of string theory: our world is SUSY at low energies

[mitchell porter]

Massless QCD spontaneously breaks part of chiral symmetry (http://www.nikhef.nl/pub/theory/academiclectures/sm06_three.pdf). And in a standard model with no Higgs and massless fermions, the quark condensates do have the right quantum numbers to break electroweak symmetry a little - see Quigg and Shrock, II.A.1 and II.B.1. Here's an informal description of the resulting physics (also see this talk by Quigg).

 

[lpetrich]

From PDF page 20, the nonperturbative-QCD ground state has

<\bar Q_L \cdot Q_R> = <\bar u_L u_R + \bar d_L d_R + \cdots>

How would the quark fields "know" which ones to pair up with in the massless case? In the massive case, it's easy: the mass eigenstates.

 

[mitchell porter]

It seems (see page 20 of Wilczek's latest) that the degenerate ground states of massless QCD are indexed by unitary matrices (the matrix elements being VEVs like <\bar q_{jL} q_{kR}>, j and k flavor indices), and that the quark fields would be defined as the operator basis which diagonalizes the matrix.

 

[mitchell porter]

Alejandro's revisit to Koide 1981 (publication, preprint) in the other thread prompts me to outline yet another what-if scenario.

In Koide 1981 there are three generations of preons. In each generation, there is a subquark doublet with color charge, a subquark doublet with subcolor charge (subcolor is an extra SU(3) interaction), and a subquark "h", also with subcolor charge. (The left-handed part of the doublets is a weak doublet, the right-handed part is two weak singlets.)

One generation of SM leptons consists of the subcolor-charged doublet coupled to an subcolor-antisymmetric combination of two "h" subquarks, producing a lepton which is a subcolor singlet. One generation of SM quarks consists of the color-charged doublet coupled to a subcolor-singlet meson "h-hbar", producing particles which are subcolor singlets but color triplets. Koide admits the model doesn't explain why the doublet and the meson are bound together.

Curiously, this is the reverse of the sbootstrap, in the following sense. In Rivero 2005, quarks are associated with diquarks and leptons with mesons. In Koide 1981, leptons are associated with di-preons and quarks with pre-mesons.

Can we build the sbootstrap out of subcolor, but with "diquarks" in quarks and "mesons" in leptons? Here one faces the usual stumbling block that in the sbootstrap, we seem to be building quarks out of themselves. So I propose to proceed as follows. We are to think of the SM as dual to a model containing six quarks only, which we shall label t', b', c', s', u', d'. We are to think of t' as massive and the other five as massless.

Finally, we suppose that these dual quarks all have subcolor charge as well as color charge, and that there is a further dual-quark doublet n1, n2 ("n" for neutral), with subcolor charge, but no color charge or electromagnetic charge.

Now we can proceed in imitation of Koide, but in reverse. SM leptons combine n1, n2 with ordinary-color dual-mesons, producing particles that are color singlets and subcolor singlets. SM quarks combine n1, n2 with color-antisymmetric dual-diquarks in the anti-triplet representation, producing particles that are also subcolor singlets, but which are color anti-triplets, just like the original form of "hadronic supersymmetry". Or rather, SM quarks are "partially composite"; they are mixtures of the original dual-quarks with these quark-like subcolor-baryons.

So we have a duality between a model with six "dual quarks", one heavy and five massless, and no leptons; and a model with six quarks and six leptons of various masses. If we think of these as superfields, one might even suppose that this is a duality between two models of mass generation discussed recently in the thread, the "radiative" model in which only the top has a tree-level mass and all other SM fermions get their masses through loop effects, and the "circulant" model in which there are 3 or 6 higgses (the emergent sleptons) producing circulant mass matrices. (And perhaps the n-quarks are subcolor gauginos, and perhaps there will be a stringy model of the "subcolor baryons".)

 

[arivero]

Mitchell, have you noticed in the bibliography on composite Higgs equations such as

y_{u,d}\sim \lambda_{u,d}\lambda_q \sqrt {N/4\pi}

? I guess that the lambdas are a kind of square roots of mass.

 

[arivero]

How does the condensation "technicolor" work for the electroweak group? If I understand it, we need to give mass to three vector particles and produce three goldstone bosons. Thus the real comparision is not to flavour SU(3), that produces an octect of goldstones, but to flavour SU(2), and then the triplet of pions should be a triplet of higgses H+, H-, H0, and another three degrees of freedom are eaten to give mass to the rho.

I think that the role of the "u,c terminated strings" in the sBootstrap is a even more retorted version of this, involving pairs of particles instead of particle/antiparticle, and some B-L juggling to adjust the charges. But it is amazing that then the top condensate is not involved ever in the Higgs mechanism. Does the sBootstrap have some hidden role for the top condensate, or we are really so strict about not allowing it to bind to any object in any situation?

 

[arivero]

"u,c terminated strings" ... and some B-L juggling to adjust the charges.

The point is that Q = T3 + (B-L)/2.

So if we uncouple B-L, a quark only offers an electric charge from T3, this is +1/2 for the up quark, -1/2 for the down. The T3 can be R or L.

So you see, uu, uc and cc could produce three Q=+1 bosons very nicely, and the antiparticles the corresponding Q=-1 But the problem is that we need to have two Q=0 bosons in the pack.

The most obvious way is to have one of them, say c, with a T3=-1/2. But then it should have B-L equal to 7/3 to compensate, for instance keeping B=1/3 but L=-2 instead of 0. Either that, or some other mechanism I am missing yet.

Had we such mechanism, we had a prediction of a higgs sector from condensates with a neutral H0 and two charged H+ H-

 

[mitchell porter]

I think the idea is unlikely. However, I will point out Mohapatra et al on an up-type sextet diquark Higgs. Your diquark Higgs might also need a B-L spurion to work.

There was a paper proposing that the 125 GeV boson is in fact a mixture of toponium and bottomonium. (Interestingly, the other mixed eigenstate has a mass close to 325 GeV, where there were anomalies last year.) One could look for a connection with topcolor, topcolor-assisted technicolor, and/or pion-Higgs models.

 

[arivero]

Mohapatra et al

Somehow the academics now how to get their stuff published. Not that they get more impact that us, although.

I am pretty sure that it is possible to do the first part, to get rid of colour and B-L on the argument that they are pure vector forces. The problem remains of genning a neutral boson out of it.

 

[arivero]

I think the idea is unlikely. However, I will point out Mohapatra et al on an up-type sextet diquark Higgs.

It is interesting that in this kind of models the uu diquarks have different mass scale than the dd. I guess that it is related to the different scales of electrons and neutrinos in the lepton side of the model.

 

[mitchell porter]

There is no fundamental dd diquark in that model. The "diquark" here is a scalar with a diquark coupling, not a QCD diquark.

If you follow the references back, the 2007 paper cites a 1998 paper which cites a 1980 paper which talks about Higgses made of bound states of fermions. It doesn't call them diquark Higgses. Actually I can't parse the figure in that paper; it seems the Δ_R,44 is the scalar with a VEV, then it has an interaction with three other scalars, and then they interact with quarks and induce a ΔB=2 transition. So the "diquarkness" might be hiding in that diagram somewhere. But that's the best I can do, in the search for a diquark Higgs which is a genuine QCD diquark.

Another consideration is that QCD diquarks are not gauge invariant. A diquark condensate breaks the gauge symmetry, it's involved with phenomena like color-flavor locking and color superconductivity. I can imagine that such exotic phenomena play a role in the appearance of QCD scales in the Koide triplets, e.g. maybe they help to hide a second confining SU(3) interaction, as in the amended version of Koide 1981 that I proposed. But I do think a chiral condensate (qqbar, not qq) is a more plausible way to get EWSB.

In sbootstrap language, diquark -> squark and meson -> slepton. There's a small literature on sneutrino Higgses, but I can't see anything at all about a "squark Higgs". (There is some stuff out there, about squark condensates and CFL in holographic QCD.) But this difference of opinion shouldn't be too much of a problem, the big picture probably involves both chiral condensates and diquark condensates and we'll have to understand both.

 

[lpetrich]

So this is about some particle in a 6 (20) representation of QCD SU(3)?

That is a symmetric square of the fundamental representation, 3 (10); its antisymmetric square is 3* (01).

Since hadron states are all color singlets (colorless), a 6 needs to combine with a 6* (02), like its antiparticle, or a 3 (10) and an 8 (11), like a quark and a gluon:

6(20) * 6*(02) = 27(22) + 8(11) + 1(00)
6(20) * 3(10) = 10(30) + 8(11)
8(11) * 8(11) = 10(30) + 10*(03) + 27(22) + 8(11) + 8(11) + 1(00)

To combine with the quarks and yield integer electric charges, it must have antiquark-like electroweak quantum numbers, with
(weak hypercharge) = (weak isospin) + 1/3 + (integer)

 

[lpetrich]

Let's see about Georgi-Glashow 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.

 

[arivero]

So this is about some particle in a 6 (20) representation of QCD SU(3)?

Yes and no. The particles in these articles come from usual GUT theory. The ones in the sBootstrap comes from a 15 of SU(5) flavour, still to be seen if it is relevant to see them also as SU(3) colour antitriplets.

 

[arivero]

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

 

[mitchell porter]

"A Higgslike Dilaton". There have been many such Higgs-vs-dilaton 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.

 

[arivero]

"A Higgslike Dilaton". There have been many such Higgs-vs-dilaton 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.

Big guys in the paper. And then it shows how half-baked our speculations are, if you consider the difficulties they have to formulate a decently realistic model. But it is encouraging that they consider partial compositeness as a part of the play.

 

[mitchell porter]

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 field-theoretic 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 susy-breaking from a whole new sector where the breaking originates is completely standard; it's "single-sector supersymmetry breaking" which is the unusual alternative to mediated susy-breaking.

By contrast, the papers which introduce the sbootstrap hardly talk about susy-breaking. 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 pion-like (and in fact all the leptons are "superpartners" of pion-like quark-antiquark 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 three-generation model, there are only two "families". This isn't yet a serious phenomenological model, it's a toy model of how symmetry-breaking messenger particles (here, some of the new scalars) could carry flavor and yet not cause detectable flavor-changing neutral currents. The physics that results depends greatly on the specific vacuum and on renormalization-group 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 Koide-type 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.

 

[mitchell porter]

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 b \bar b and t \bar t. And Christopher Hill, inventor of "topcolor", observes that the "top-Higgs system" has a susy-like 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?

 

[arivero]

Two unorthodox top/Higgs papers today.

Well, as a minimum, it shows that Perimeter and Fermilab have an allowance for exotic thoughts

 

[arivero]

The peculiar arrangement of SU(4), or U(1)xSU(3) multiplets noticed in the Koide thread

https://www.physicsforums.com/showthread.php?t=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 B-L, 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.

 

[mitchell porter]

Two recent papers, by authors already mentioned in this thread, which derive a Higgs sector in a sbootstrap-friendly 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 pion-like 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 Higgs-like condensates. Presumably future work will aim to get the whole CKM matrix from the quark bilinears of a three-generation 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 M5-brane, 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 Kitano-Nakai scenario, in which new strong couplings occur at high energy. "As in the Nambu–Jona-Lasinio model for the chiral symmetry breaking, whether or not a condensation forms depends crucially on how the theory is cut-off, and thus discussion requires a UV completion of the theory."

 

[arivero]

The peculiar arrangement of SU(4), or U(1)xSU(3) multiplets noticed in the Koide thread
https://www.physicsforums.com/showthread.php?t=551549&page=6

Back to this, let's approach diquark masses with the mass of the heaviest quark, or the QCD mass if it is heavier than the quarks themselves. Then we can add mesons and diquarks to the "SU(4) arrangement".

\begin{array}{lllll}<br /> ?, t_{rgb}&amp; &amp; &amp; &amp; \\<br /> ?, b_{rgb}&amp; B^+,B_c^+ &amp; bu, bc&amp; bb, bs, bd &amp; \\<br /> \tau, c_{rgb} &amp; D^+, D_s^+&amp; sc,dc \\<br /> \mu, s_{rgb} &amp; \pi^+, K^+&amp; su, du&amp; ss, sd, dd \\<br /> ?, d_{rgb} \\ <br /> e, u_{rgb}\end{array}

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

\begin{array}{lllllll}<br /> &amp;\nu_?, t_{rgb}&amp; &amp; &amp; &amp; \\<br /> &amp;\nu_?, b_{rgb}&amp; B^+,B_c^+ &amp; bu, bc&amp; bb, bs, bd &amp; \eta_b, \stackrel{b\bar s,b\bar d}{\bar bs,\bar bd} \\<br /> \stackrel{\bar c\bar c}{cc},\stackrel{\bar c\bar u}{cu}&amp;\tau, c_{rgb} &amp; D^+, D_s^+&amp; sc,dc &amp; &amp; \eta_c, \stackrel{c\bar u}{\bar cu}\\<br /> \stackrel{\bar u\bar u}{uu}&amp;\mu, s_{rgb} &amp; \pi^+, K^+&amp; su, du&amp; ss, sd, dd &amp; K^0,\pi^0, \stackrel{s\bar d}{\bar sd}\\<br /> &amp;\nu_?, d_{rgb} \\ <br /> &amp;e, u_{rgb}\end{array}

It is sort of symmetric, in a pleasant way. Wish I knew what to do about it.

 

[mitchell porter]

We can adapt an earlier idea for the sbootstrap to Pati-Salam. The earlier idea is that there is a fundamental QCD-like 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 Pati-Salam sbootstrap, the prescription is almost the same, except that the leptons already exist as the "nth color" in the fundamental QCD-like 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.

 

[arivero]

http://higgs.ph.ed.ac.uk/sites/default/files/Higgs_RR.pdf

Rattazzi is near to discover the sBootstrap if he continues this kind of enquiries.

 

[mitchell porter]

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 model-building. 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 "super-paradigm" 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 non-susy 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 symmetry-breaking, 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 "five-flavor" 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 tail-chasing 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".

 

[arivero]

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

<br /> \begin{array}{||l|l|llll||} <br /> \hline<br /> \stackrel{\bar c\bar c}{cc}&amp;<br /> \nu_2, b_{rgb}, e, u_{rgb}&amp; <br /> B^\pm,B_c^\pm &amp; <br /> \stackrel{\bar b\bar u}{bu}, \stackrel{\bar b\bar c}{bc}<br /> &amp; \stackrel{\bar b \bar s}{bs}, \stackrel{\bar b\bar s}{bd} &amp; <br /> B^0, B^0_c, \bar B^0, \bar B^0_c \\ <br /> \stackrel{\bar c\bar u}{cu}&amp;<br /> \tau, c_{rgb} , \nu_3, d_{rgb}&amp;<br /> D^\pm, D_s^\pm&amp;<br /> \stackrel{\bar s\bar c}{sc},\stackrel{\bar d\bar c}{dc} &amp; <br /> \stackrel{\bar b\bar b}{bb},\stackrel{\bar d\bar d}{dd} &amp;<br /> \eta_b, \eta_c, D^0, \bar {D^0}\\ <br /> \stackrel{\bar u\bar u}{uu}&amp;<br /> \mu, s_{rgb} , \nu_1, t_{rgb}&amp;<br /> \pi^\pm, K^\pm&amp; <br /> \stackrel{\bar s\bar u}{su}, \stackrel{\bar d\bar u}{du}&amp;<br /> \stackrel{\bar s\bar s}{ss}, \stackrel{\bar s\bar d}{sd}&amp;<br /> \eta_8, \pi^0, K^0, \bar K^0 \\<br /> \hline<br /> \end{array}<br />

 

[mitchell porter]

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 Pati-Salam, 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 quark-antiquark 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: flavor-flavor, color-color, and flavor-color. As usual, each stack will have a corresponding symmetry (e.g. SU(N) for some N), the flavor-flavor strings will be singlets under the color group, the color-color strings (the bosonic states of which are the gluons) are singlets under the flavor group, and the flavor-color strings transform under both groups.

Also, the flavor-color 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 flavor-flavor and color-color strings can be found anywhere within their respective stacks, because the branes are parallel and so the inter-brane distance is the same everywhere. To my mind this poses a major barrier to the idea of placing a flavor-color string and a flavor-flavor 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 brane-stack. 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.

 

[mitchell porter]

I'll sketch how something like this could work. We'll use nine D3-branes in a space of three large dimensions, and six small and compact dimensions. Geometrically it can be just like Kaluza-Klein, except that each local copy of the KK manifold has nine special points scattered throughout it, the places where the nine D3-branes 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 six-dimensional 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 D3-branes) 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.

 

[mitchell porter]

We have a number of threads right now on getting the Higgs mass from Planck-scale boundary conditions. The common idea is that there is no new physics between the weak scale and the Planck scale. The best-known 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 right-handed neutrinos with keV Majorana mass, left-handed 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 Planck-scale 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 boson-fermion 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 type-0 version of the brane-stack constructions I discussed here a few weeks ago, could provide a "non-susy sBootstrap" in which we have mesinos but not gauginos.

So perhaps we might want a type-0 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 SW-like 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.

 

[arivero]

As for the relationship between the above folding and the S4 generalisation of Koide, I find that they are two solutions of the eight S4 simultaneus equations that seem relevant:

<br /> \begin{array}{|ll|}<br /> \hline<br /> 3.64098 &amp; 0 \\<br /> 1.69854 &amp; 1.69854 \\<br /> 0.12195 &amp; 0.12195 \\<br /> \hline<br /> \end{array}<br /> \dots<br /> \begin{array}{|ll|}<br /> \hline<br /> b &amp; u \\<br /> d &amp; c \\<br /> s &amp; t \\<br /> \hline<br /> \end{array} <br /> \dots<br /> \begin{array}{|ll|}<br /> \hline<br /> 3.640 &amp; 3.640 \\<br /> 1.698 &amp; 1.698 \\<br /> 0.1219 &amp; 174.1 \\<br /> \hline<br /> \end{array}<br />

The one on the left appears when looking for zero'ed solutions; the one on the right appears in the resolvent of the system when looking for zero-less solutions; so both of them are singled-out very specifically even if, being doubly degenerated, they are hidden under the carpet of a continuous spectrum of solutions.

To be more specific: a S4-Koide system on the above "folded" quark pairings should be a set of eight simultaneous Koide equations, for all the possible combinations: bds, bdt, bcs, bct, uds, udt, ucs, uct. A double degenerated solution of such S4-Koide system lives naturally inside a continuum: the equation K(M1,M2,x)=0, with M1 and M2 being the degenerated masses, has multiple solutions for x, and any two of them can be used to build the non-degenerated pair of the folding.

The solution in the left is one of the possible solutions having at least a zero; up to an scale factor, there are only four of them. I have scaled it to match with the solution in the right.

The solution in the right is one of the solutions obtained by using the method of polynomial resolvents to solve the system of eight equations (actually, we fix a mass and then solve the four equations containing such fixed mass). It is scaled so that its higher mass coincides with the top mass.

For details on the calculation of the solutions, please refer to the thread on Koide.

 

[mitchell porter]

Some recent thoughts:

As with mainstream supersymmetry, I see the sbootstrap's situation as still being one where there is such a multitude of possibilities that it is hard even to systematically enumerate them. The difference is that a mainstream susy model consists of a definite equation and a resulting parameter space that then gets squeezed by experiment, whereas a sbootstrap "possibility" consists of a list of numerical or structural patterns in known physics which are posited to have a cause, and then an "idea for a model" that could cause them. It may be that some part of sbootstrap lore is eventually realized within a genuinely well-defined model that will then make predictions for MSSM objects like gluinos, or it may be that it will be a "minimalist" model that is more like SM than MSSM. (As for the Koide waterfall, that is such a tight structure, it seems that any rigorous model that can reproduce it is going to be sharply predictive - but there may still be several, or even many, such models.)

Today I want to report just another "idea for a model". It's really just a wacky "what if"; I don't know that such a model exists mathematically; but I'd never even look for it if I didn't have the schematic idea. The idea is just that there might be a brane model in which the top yukawa is close to 1 both in the far UV and in the far IR, and that this is due to a stringy "UV/IR connection".

The reason to think about this is as follows. The discussion of whether the Higgs mass might be in a narrow metastable zone, has yielded the perspective that it might be worth considering the top yukawa and the Higgs quartic coupling at the same time. The latter goes to 0 in the UV, the latter goes very close to 1 in the IR.

But Rodejohann and Zhang have observed that with massive neutrinos, the top yukawa can approach 1 at high energies as well (see pages 14 and 15; the minimum is roughly 0.5, reached at about 10^15 GeV). And high energies are where a coupling might naturally take a simple value like 1. So what if there's a brane model where the top yukawa is 1 in the far UV, for some relatively simple reason, and then it is also near 1 in the far IR, because of a UV/IR relation that we don't understand yet? String theory contains UV/IR relations (scroll halfway down for the discussion); none of them appear to be immediately applicable to this scenario; but such relations are far from being fully understood.

At the same time, I think of Christopher Hill's recent papers (1 2, it's basically the same paper twice), in which he first restricts the SM to just the top and the Higgs, and then considers a novel symmetry transformation, which he likens to a degenerate form of susy. At high scales he ends up with the relation that the Higgs quartic equals half of the square of the top yukawa - which is not what I'm looking for. Then again, he also ends up with Higgs mass equals top mass, with the difference to be produced by higher-order corrections. So perhaps his model, already twisted away from ordinary supersymmetry, can be twisted a little further to yield a Rodejohann-Zhang RG flow for the top yukawa, as well as a Shaposhnikov-Wetterich boundary condition for the Higgs quartic.

One might want to see whether this can all be embedded in something like the "minimal quiver standard model" (MQSM), which is not yet a brane model, but it is a sort of field theory that can arise as the low-energy limit of a brane model; and the MQSM is the simplest quiver model containing the SM.

Finally, to round things out, one might seek to realize the sbootstrap's own deviant "version of susy" here too, perhaps by using one of the brane-based "ideas for a model" already discussed in this thread.

 

[mitchell porter]

Krolikowski has some preon musings (relegated to gen-ph) which resemble the sBootstrap. He wants to get the color-triplet SM quarks and color-singlet SM leptons by combining color-triplet preons; but he has to suppose that the preons are a fermion and a scalar boson, in order for the composite to be a fermion, whereas the sBootstrap combines two fermions and then supposes that the phenomenological fermions are superpartners of the resulting composites.

Curiously, in an attempt to explain the up-down mass ratio, he inadvertently provides a new perspective on the Koide-Brannen phase: 2/9 = (1/3)² + (1/3)². He is squaring the electromagnetic charges of the preons for an up quark, on the hypothesis that the mass is a self-energy effect. (The analogous quantity for down is then 5/9, then leading to an up:down mass ratio of 2:5, not too far from the observed 1:2; but he acknowledges that the argument then doesn't work for all the other fermion masses...) I wonder if this completely elementary formula could be motivated in some other context, to explain the Koide-Brannen phase for e,μ,τ?

 

[arivero]

For a different turn... what about the SO(8) in the representations of elementary states of superstring theory?

It seems unvoidable because it comes from taking lorentz group SO(9,1) and decomposing to SO(8)xSO(1,1). So once the worldsheet takes the (1,1) part, the rest must be SO(8). In fact, it seems unrelated to the 7-sphere nor octonions nor other Kaluza Klein thingies.

Could it be posible to have still a "8" representation but under a different group? Of course I am thinking SO(5)xSO(4) or even better, SU(3)xSO(4).

 

[mitchell porter]

There is another installment from Bruno Machet (previously discussed at #149, #172). Machet wants to build the Higgs sector entirely from meson VEVs, with no additional fundamental scalars. John Moffat tried to do the same (#169), and probably there is older literature.

On this thread, #150 forward, there was some discussion of the conventional perspective: without a Higgs, the qqbar condensate will still add mass to W and Z, but they will be MeV-scale, not GeV-scale.

Such works are potentially complementary to the sBootstrap. In the sBootstrap we start with five light quarks, and get all the SM fermions as "superpartners" of the resulting diquarks and mesons, with the uu-type diquarks left over, playing no role in this correspondence, and also no theory of what the Higgs is.

I think I see four possibilities:

1) The Higgs originates outside the sBootstrap combinatorics, e.g. it really is an independent elementary scalar.

2) The uu-type diquarks make up the Higgs field. This is Alejandro's often-expressed dream, but it has the problem that the +4/3 charge has to be mysteriously screened somehow.

3) The Higgs comes from the scalar sector being explored by Machet and Moffat.

4) We could seek inspiration in the recently observed Zc(3900): perhaps the Higgs is a tetraquark! - of the form u u ubar ubar.

 

[mitchell porter]

Some recent papers:

1) A new proposal for quark-lepton unification which resembles Pati-Salam, but with different relations between the mass matrices.

2) The latest from Harald Fritzsch, on making H, W, Z from preons he calls "haplons". It seems unlikely; but what if we thought of the haplons as branes, and the composites as strings ending on them?

3) New d=4 non-susy vacua from F-theory. As Lubos mentions, susy appears if you compactify further, to d=3, so this is a case of hidden supersymmetry; which is why it is relevant to this thread... Also see these old musings by Witten 1 2.

4) Via arivero elsewhere, I have learned of Alejandro Cabo, who wants to get the quark masses from the top quark, via a cascade effect involving condensates; again a theme already explored in this thread. Some of the relevant papers have two "Alejandro Cabo"s as authors, so I am not sure who's in charge, but if you just go to arxiv and look through all the papers with author:cabo, you will find them. Apart from the obvious (titles which refer to quark masses), anything about "modified QCD" would also be part of the program. Especially interesting from the Koide perspective is the appearance of the democratic matrix, e.g. on page 5 here. A. Cabo has also given two talks at pirsa.org on this subject.

 

[MTd2]

4) Via arivero elsewhere, I have learned of Alejandro Cabo, who wants to get the quark masses from the top quark, via a cascade effect involving condensates; again a theme already explored in this thread. Some of the relevant papers have two "Alejandro Cabo"s as authors, so I am not sure who's in charge, but if you just go to arxiv and look through all the papers with author:cabo, you will find them. Apart from the obvious (titles which refer to quark masses), anything about "modified QCD" would also be part of the program. Especially interesting from the Koide perspective is the appearance of the democratic matrix, e.g. on page 5 here. A. Cabo has also given two talks at pirsa.org on this subject.

Talking about Koide relations, do you know Jay Yablon?

http://vixra.org/author/jay_r_yablon

His results are insanely precise for a rather simple method. I'd not say theory though. He calculates stuff differently and get it all too exactly to be good.

 

[mitchell porter]

I have seen his work. The papers which provide formulas for nuclear binding energies in terms of quark masses are a new frontier for physics numerology... What I thought was interesting, is that it is possible at all - e.g. (his starting point) the fact that the deuteron binding energy, and the mass of the up quark, are of the same order of magnitude. In reality, that binding energy ought to be some function of m_u, m_d, m_s, and alpha_strong, that we would currently need lattice QCD techniques to estimate. But I wonder if there is some heuristic argument that apriori it should be within an order of magnitude of the first-generation quark masses? That might be a good question for Physics Stack Exchange or for the HEP forum here... Incidentally, these binding energies also occasionally get mentioned by Arkani-Hamed (and I assume others) as evidence for finetuning in nature - if you look at the effective field theory of nucleons, apparently the parameters are finetuned to several orders of magnitude.

 

[MTd2]

3) New d=4 non-susy vacua from F-theory. Susy appears if you compactify further, to d=3, so this is a case of hidden supersymmetry; which is why it is relevant to this thread... Also see these old musings by Witten [URL="http://arxiv.org/abs/hep-th/9409111"]1 2.

Don't you think it is a nice finding? That is, in the real world, SUSY does not exist, other than a math trick, and string theory is fine with that?

 

[MTd2]

The papers which provide formulas for nuclear binding energies in terms of quark masses are a new frontier for physics numerology...

He justifies his treatment in lengthy papers from standard theory, like QCD. I don't think that is not numerology at all. You have to see if his approximation arguments for QCD are OK. Certainly, it yields results that are OK.

 

[mitchell porter]

Don't you think it is a nice finding? That is, in the real world, SUSY does not exist, other than a math trick, and string theory is fine with that?

String theory has many neglected and disputed corners without supersymmetry. One thing that's interesting here, is that this is F-theory and very mainstream. But in these vacua, SUSY is still there at the highest energies i.e. the compactification scale. It's just different from the usual model-building in string phenomenology, which is to look for something whose low-energy limit has an N=1 supersymmetry that is then broken. Here even that is bypassed, and SUSY is solely a high-scale phenomenon (if I understand correctly).

He justifies his treatment in lengthy papers from standard theory, like QCD. I don't think that is not numerology at all. You have to see if his approximation arguments for QCD are OK. Certainly, it yields results that are OK.

It has only the barest of connections to QCD that I can see. He hardly considers the quantum theory at all, piles guess upon guess (ansatz upon ansatz), freely introduces extra quantities like the Higgs VEV and the CKM matrix into his formulae...

 

[MTd2]

In reality, that binding energy ought to be some function of m_u, m_d, m_s, and alpha_strong, that we would currently need lattice QCD techniques to estimate. But I wonder if there is some heuristic argument that apriori it should be within an order of magnitude of the first-generation quark masses?

He is making a new paper due many requests on further enlightenment. So, if you want to ask question, that's the time!

http://vixra.org/abs/1307.0135

 

[member 11137]

He is making a new paper due many requests on further enlightenment. So, if you want to ask question, that's the time!

http://vixra.org/abs/1307.0135

Since that thread is discussing string theory and SUSY in a kind of fictive and positive competition, I would like to bring a modest contribution in the actual debate and directly ask if the documents pointed here can help the scientific community:
http://www.vixra.org/author/thierry_periat
In a kind of constructive emulation, I would also appreciate any feedback. So far my understanding, a discussion about the vacuum is probably concerning regions with low energies (this is at least the classical and well accepted vision - coming into the debate from the "theory of relativity" viewpoint side). Except if errors (calculations) have been done in one of the proposed documents, the concept of string is not in opposition with the one of vacuum (consequently with the existence of regions with a low energy level). The embarassing consequence is the necessity to accept a dynamical vision for these regions but as far I am well-informed, the 2013 recent analysis of the data coming from the Planck satellite allows a dynamical dark energy...

 

[fzero]

He justifies his treatment in lengthy papers from standard theory, like QCD. I don't think that is not numerology at all. You have to see if his approximation arguments for QCD are OK. Certainly, it yields results that are OK.

Referring to the paper in the Hadronic Journal (which is full of crackpot papers, sorry to say), he bases the whole numerics on postulating that the quark wavefunctions are Gaussian with a width equal to their reduced Compton wavelength. For the up quark, using $m_u\sim 2.3~\mathrm{MeV}$ as Yablon does, the reduced Compton wavelength is $\lambda_u \sim 0.012~\mathrm{fm}$. However, the proton charge radius is $\sim 0.88~\mathrm{fm}$, so the quark ansatze has nothing whatsoever to do with reality.

It's unilluminating to further sift through his classical manipulations or try to point to the large quantum corrections that he waves his hands around (current quark masses are set by the weak scale and unnaturally small Yukawa couplings, whereas the hadronic masses are set by the QCD scale). Instead it suffices to see that the picture of the nucleon that he sets as an input is completely different from what we observe.

I have seen his work. The papers which provide formulas for nuclear binding energies in terms of quark masses are a new frontier for physics numerology... What I thought was interesting, is that it is possible at all - e.g. (his starting point) the fact that the deuteron binding energy, and the mass of the up quark, are of the same order of magnitude. In reality, that binding energy ought to be some function of m_u, m_d, m_s, and alpha_strong, that we would currently need lattice QCD techniques to estimate. But I wonder if there is some heuristic argument that apriori it should be within an order of magnitude of the first-generation quark masses? That might be a good question for Physics Stack Exchange or for the HEP forum here... Incidentally, these binding energies also occasionally get mentioned by Arkani-Hamed (and I assume others) as evidence for finetuning in nature - if you look at the effective field theory of nucleons, apparently the parameters are finetuned to several orders of magnitude.

As I mentioned above, the current masses of the quarks are set by the EW scale (with a huge fine-tuning) and have nothing to do with strong physics. There should be no heuristic argument why properties of the deuteron should be closely related to the current masses.

 

[mitchell porter]

The basic coincidence here is that the QCD scale and the electroweak scale are within an order of magnitude or two of each other. I believe I've seen attempts to explain this anthropically.

One theme of this thread is that the weak interactions and the leptonic sector might be emergent from a strongly coupled supersymmetric theory. There, the benchmark of success might be, to explain the coincidence of scales causally and naturally.

Finally, Koide aficionados have noticed that the basic mass scale in Carl Brannen's reformulation of the Koide formula, is very close to the "constituent" masses of the first-generation quarks. A Brannen-style formulation of Koide's relation, derives particle masses from a common mass scale, and an angle. So it's rather amazing that arivero gets the s,c,b masses by applying Brannen's formula for e,mu,tau, but tripling both the mass scale and the angle. Tripling these parameters might have some rationale involved in working with color triplets (quarks) rather than color singlets (leptons); and then there's the simple fact that three times the constituent quark mass scale, gives you the nucleon mass scale!

So I consider it very rational to at least entertain the possibility that these relations derive from some sort of super-QCD or extended QCD that underlies the standard model... though even if that's true, proving it might have to await future advances in QCD itself, that would make it transparent why quantities such as the nucleon mass and the pion mass have the values they do.

 

[fzero]

The basic coincidence here is that the QCD scale and the electroweak scale are within an order of magnitude or two of each other. I believe I've seen attempts to explain this anthropically.

The QCD scale depends most strongly on the coefficient of the one-loop beta function, which only depends on the number of colors and flavors. Quark masses are a very small effect, but would be the leading way for the EW scale to feed into the QCD scale. I can imagine that it's possible to set anthropic bounds, but I'm not sure that the ratio of the QCD and EW scales is the most important consideration when compared to the fine-structure constant, for example.

One theme of this thread is that the weak interactions and the leptonic sector might be emergent from a strongly coupled supersymmetric theory. There, the benchmark of success might be, to explain the coincidence of scales causally and naturally.

Finally, Koide aficionados have noticed that the basic mass scale in Carl Brannen's reformulation of the Koide formula, is very close to the "constituent" masses of the first-generation quarks. A Brannen-style formulation of Koide's relation, derives particle masses from a common mass scale, and an angle. So it's rather amazing that arivero gets the s,c,b masses by applying Brannen's formula for e,mu,tau, but tripling both the mass scale and the angle. Tripling these parameters might have some rationale involved in working with color triplets (quarks) rather than color singlets (leptons); and then there's the simple fact that three times the constituent quark mass scale, gives you the nucleon mass scale!

This is also numerology. These particles interact, so any dynamical relationship between masses should involve their values at the same energy scale. The Koide-type relations are between pole masses, which have no logical reason to be directly related to one another by a consistent dynamical formula. The difference between pole masses and $\overline{\mathrm{MS}}$ masses might be small for the leptons, but it is not for the up quarks.

I suspect that these are just as coincidental as the fact that the running fine-structure constant is numerically the same as the Higgs mass to within a % or so: $\alpha^{-1}(m_H) \approx m_H/\mathrm{GeV}$.

 

[MTd2]

These particles interact, so any dynamical relationship between masses should involve their values at the same energy scale. The Koide-type relations are between pole masses, which have no logical reason to be directly related to one another by a consistent dynamical formula.

Is nature logical?

 

[member 11137]

... These particles interact, so any dynamical relationship between masses should involve their values at the same energy scale. The Koide-type relations are between pole masses, which have no logical reason to be directly related to one another by a consistent dynamical formula...

But as indicated in arXiv:hep-ph 0505220v1 25 May 2005 (end of page 1 and at the beginning of page 2), these pole masses are co-related in such a way that an angle can be introduced between two vectors: (1, 1, 1) and (m1, m2, m3). This motivates the vision of what one is encouraged to call "directional masses" (masses defining a spatial direction) and at the end this is suggestively asking for the existence of a link between these masses (taken all together) and some underlying geometrical structure... Since the geometrical structure is dynamic within the theory of relativity (Einstein)...

 

[mitchell porter]

the leading way for the EW scale to feed into the QCD scale

I actually had the other direction in mind: e.g. that QCD is embedded in some sort of technicolor where there is a composite Higgs whose properties are correlated with those of the hadronic sector; or, standard model QCD is part of an SQCD whose susy-breaking is transmitted to an independent Higgs sector and determines part of its scalar potential.

As for relations between different energy scales, UV/IR mixing in noncommutative field theory leads me to think that they can exist; though perhaps not in an ordinary field-theoretic framework.

 

[arivero]

The difference between pole masses and $\overline{\mathrm{MS}}$ masses might be small for the leptons, but it is not for the up quarks.

I suspect that these are just as coincidental as the fact that the running fine-structure constant is numerically the same as the Higgs mass to within a % or so: $\alpha^{-1}(m_H) \approx m_H/\mathrm{GeV}$.

I usually do not like when people compares adimensional numerology with dimensional-based numbers, but well, just in this case it is reasonable, and you have a point here, because it is true that fixing a substraction scheme is as arbitrary as fixing a unit. Now, it is good to remember that in adimensional numerology the units are canceled out, and similarly we could find equations which are independent of the substraction scheme, or at least have a very weak dependency.

You have probably not noticed that the final relationship that Porter was mentioning is a relationship between pole masses. Input masses are only the mass of electron and muon, then you get the tau, then the factor three to pass to a Koide equation in quark sector for s,c,b, then Koide equation again to get t from c,b,t, and the final result is 173.264 GeV, to be compared with pdg mass, 173.07 ±0.52 ±0.72 GeV at the time of this post.

Yes it is true that the intermediate results for s, c and b are very near of the $\overline{\mathrm{MS}}$ values given in the tables, but you do not need to buy it in the same package; you can stick to pole mass and still get a fine prediction, 173.26 GeV.