Signature of a higgselss/bootstrap model at LHC.

[MTd2]

I tried to ask Tommaso Dorigo and he doesn't know how to answer. So, it is something very non-conventional and so it suits this BSM forum.

So, I ask you people, what would be the signature of a higgselss/bootstrap model at LHC?

 

[arivero]

Three spin 1/2 chiral gauginos, pairing with W+,W- and Z.

 

[MTd2]

I was thinking more along the lines of "nothing but the SM". Like, a quark condensate. How would we see a quark condensate, for example?

 

[arivero]

Point is, the only way i see to do the bootstrap is including supersymmetry. In the bootstrap model, all the particles are composites of all the others. With supersymmetry, we can put some order and postulate that all the particles in the bosonic sector are composites of all the fermionic sector. With the known masses and forces of the standard model, the binding force is qcd and then only the five light quarks contribute, and the bootstrap can be built. Quark condensates in some sens, if you wish.

With this context, no argument for the higgs appears. But as the W+, W- and Z are massive and need to be supersymmetric, each of them pairs with two extra scalars and a chiral fermion (in the traditional thinking, one of the scalars bosons is eaten for the zero heliciry of the spin 1 massive gauge boson, and the other one goes to the higgs quintet of MSSM). The scalars are composites, so the only real candidate for detection is the chiral fermion.

 

[MTd2]

Oh, you mean your supersymmetric model, udscb-t? How would be a composite gaugino?

 

[arivero]

Yep, that is the only thing you can not build from the udscb composites, and it is spin 1/2, so it is a good signature.

Still, the signature is probably model independent. If you want supersymmetry you need the gauginos, if you want bootstrap and supersymmetry, the bosons will be composites, of some model, and only the gauginos are there to be detected.

I doubt you can get general bootstrap only, without susy. I think that at some moment in the late sixties it was hinted that the solutions for such general boostrap where trivial or non existent.

 

[MTd2]

But why do you need a gaugino, when you have have bosons with opposite charges and you can arrange them in 1-1+1-1...=1/2spin

An infinite number of them would make a gaugino. So, you have a strings quarks and gauginos of W's

 

[arivero]

But why do you need a gaugino, when you have have bosons with opposite charges and you can arrange them in 1-1+1-1...=1/2spin

An infinite number of them would make a gaugino. So, you have a strings quarks and gauginos of W's

I have never thought of using the regularization ofhttp://mathworld.wolfram.com/DirichletEtaFunction.html" to do a sum of alternating spin. Just for historical interest, did you read of it somewhere or got the idea yourself. And in any case, when? Is it a suggestion already done in the sixties?

btw, given that some public can feel disconfort with divergent series it is interesting to remark that their math is well undestood. Given a sum rule applied to the infinite series 1 -1 +1 -1 +..., any other result can be reached by inserting zeros. For instance 1 + 0 - 1 + 1 + 0 - 1 + 1 +0 - 1 + ... will produce a different sum.

 

[MTd2]

I have never thought of using the regularization ofhttp://mathworld.wolfram.com/DirichletEtaFunction.html" to do a sum of alternating spin. Just for historical interest, did you read of it somewhere or got the idea yourself. And in any case, when? Is it a suggestion already done in the sixties?

I had the idea the instant you wrote that message. But that was not a coincidence! I was studying something similar not related to that. To tell you the truth, I was thinking about how getting fermions from bosons for the last 3 years... And I had the idea when I read your post

About obtaining the sum... Well, you have to organize the sum in a proper order it to get a proper result. The regularization works because you are using *time ordered* operators! :)

We, so you have to align those W spins so that they give you 1/2. Not necessarily like in a time orders. Perhaps in an order of distance, like the regularization is done in a crystal lattice. I was thinking more like in putting them within infinite shells.

 

[mitchell porter]

Since we are talking about gauginos, I will report another very recent paper which I believe adds some plausibility to Alejandro's ideas, without telling us exactly how to realize them.

http://arxiv.org/abs/1105.1510" that "The reader will recognize that our magnetic spectrum resembles a supersymmetric one, however, the magnetic theory is not supersymmetric since we do not invoke supersymmetric relations among its spectrum and couplings."

In this http://arxiv.org/abs/1105.1510" , they study various fixed points of this nonsupersymmetric dual, and find one where the gaugino coupling evolves like the gauge coupling; so they call it emergent supersymmetry. It must be the adjoint quark, "lambda", which is the emergent gaugino in their model (the paper does not spell this out). It's not the field that is emergent, it's the behavior of the coupling; it's because the coupling of the "lambda" field matches the coupling of the gauge field that it acts like a gaugino field.

I have never had much of an opinion about the gauginos in Alejandro's model, because we don't see any such particles. What has impressed me is the matching among known objects. I was not (and am not) convinced that the theoretical realization of the correspondence will necessarily involve gauginos. In the gauge-gauge duality here, there is an adjoint quark on both sides of the duality, so it's not as if we have an emergent adjoint quark, constructed from other variables. Apart from the change in the gauge group, what happens in the duality is that the fundamental quarks in the "electric" theory are replaced by new fundamental quarks in the "magnetic" theory, and one or two extra fields appear. In other words, for this emergent supersymmetry via Seiberg duality to occur, one still has to have matter in the adjoint representation on both sides of the duality, and no such matter is known in the real world.

Then again, I have tended to think of Alejandro's correspondence as a way to realize supersymmetry which is wholly disjoint from the usual conception, in which we keep looking for massive superpartners at ever higher energies. Instead, I took the point to be that some form of supersymmetry might already exist right in front of us, connecting Standard Model elementary fields with certain QCD composites. I suppose it's possible to take a hybrid approach, and say that the Standard Model already contains supersymmetry, but that some of the usual bestiary of massive superparticles (in this case, gauginos) do remain to be discovered, as new fundamental degrees of freedom at higher energies.

So that we don't stray entirely from the original topic of this thread (which is an important topic), let me point out the reference, on page 4 of 1105.1510, to "minimal walking technicolor models", which are said to have similar properties and to be of phenomenological interest. It's asserted in http://arxiv.org/abs/hep-ph/0607191" that 'Higgsless models may be viewed as dual to models of dynamical symmetry breaking akin to “walking technicolor”' - they mean Higgsless models in which unitarity of W-W scattering is preserved by the existence of W' bosons, which can arise as KK states in an extra dimension, or in some related way in a "deconstruction" model where the existence of an extra dimension is approximated by having a discrete number of copies of the d=4 theory (the copies are like slices through a discretized fifth dimension... that is, in the continuum limit the fields exist throughout five dimensions, but when the fifth dimension is discretized into a stack of surfaces, you get those fields existing on each discrete surface, so it's as if you have a set of copies of the four-dimensional version of the fields).

Maybe you could even connect deconstruction to this newly-discovered "eta-function regularization"... ;-)

 

[arivero]

To add some stuff:

- "eta-function regularisation" is really used in classical lectures in string theory, it appears instead of the infamous "zeta-function" argument for D=26 when you add fermions, then you must substract the boson series from the fermion series before to regularise it, and at the end you get an alternating series, where the argument of consistence gives you D=10 instead of D=26. But in the idea of MTd2 you don't get the minus sign from the fermions, instead you look for an alternating sum of bosonic angular momenta. This beast is new. although some of it remembers to the panic of Heisenberg after hearing of spin 1/2 particles, he went to say that "if we open the door to spin h/2, tomorrow we will open to spin h/4 or 3h/7 or whatever, and at the end to every rational number".

- I am into gauginos because my model has six composites without any assignation to fermionic partners, the uu uc cc and antiparticle, which keep worrying me, as they need either to be assigned or truncated out. Now it is fascinating when you read about the massive gauge supermultiplet of N=1 SUSY and you discover that it has two new scalars just because of susy, independently of the existence or not, of the Higgs.

The mechanism for a N=1 massive gauge supermultiplet is very understable, when you think about it . The massless supermultiplet is just the gauge boson, with two helicities, and the gaugino, compensating them. If you want it to get mass without breaking susy, you must arrange such that the limit m->0 recovers a set of massless supermultiplets including this one. Now, look for the minimal adition: the fact is that you must add a new helicity to the gauge boson because now it will have +1, 0 and -1 states. But this new helicity news a partner, and the less you can doo is to add a chiral fermion. And then this chiral fermions carries two states, and forces you to add a new scaler. So at the end the supermultiplet of a massive Z particle (or a W or a Z) contains a massive vector boson with three helicities, two chiral fermions of two helicities each and one scalar. In the massless limit they will separate into a massless Z and "zino" on one side, and a chiral fermion and two scalars in the other.

I apologize if I indiced some confusion in my initial answer. As you see, for each gauge particle there are not one but two chiral fermions, one coming from the massless theory, other coming from the mass. This is further confused in the usual presentations of the SSM because normally the MSSM is buiilt directly, so confident people is about the Higgs model. Moreover, you can try to build dirac fermions out these chiral ones, and then I guess it is different for Z0 than for W+ W-, and probably the basis where electroweak SU(2) x U(1) symmetry is unbroken gives you a better presentation.

 

[MTd2]

CORRECTION

But why do you need a gaugino, when you have have bosons with opposite *charges* and you can arrange them in 1-1+1-1...=1/2spin

I meant opposite spins.

 

[arivero]

CORRECTION
I meant opposite spins.

It was understood :-D But your "subsconscient slip" signals how slippery the theory of sums of divergent series is. I'd prefer to have it as a last resource, and hope that the LHC has some explanation for these spin 1/2 particles.

 

[MTd2]

Well the slippery was in relation to the charge/spin coincident value 1 of the Ws :) There is no slippery here because I simply don't know how to physically arrange the spins to get that sum, but I think that is awesome. So, I want to invent a way. I was thinking something like an anti correlation between occupation of states vs. density of states of BE and FD statistics.