Fluctuating physic as a new type physics for LHC and successors

  I have been absent from this blog for a long time, basically since the LHC bumb went away, but not from physics. In the last days Sabinne Hossenfelder has been again doing posts against the idea of making new coliders as, for example Why a larger particle collider is not currently a good investment. I had already written a post, years ago, saying that it is necessary to make new coliders, and hope that  Europeans and Chinese make one.

  The topic of this entry is somewhat related to the LHC bumb. Let's remember the affair, an statistical in the LHC as around 3.5 $$ \sigma $$ was found and a lot of  paper trying to find an explanation for it were published. A few mounts later the LHC published new data and the fluctuation had gone away.  The usual interpretation was that the fluctuations were of pure statistical nature, which, of  course, is the most rational interpretation, but here I wonder if beyond the standard model at least part of the new physic is a new kind of physic and that signal,, pointed that new kind of physic.

   Before that fluctuations some others had been found, but with minor statistical significance, to later vanish.. Also, since them another ones had been found, and some have gone away also while a few others are waiting for new data to determine their fate.

Well, clearly statistical fluctuations are something that are very common, and it is not at all surprising to find them. In fact that is the reason of the $$ 5 \sigma$$ criteria to claim a discovery, and even this very high statistical significance could become not enough with the very large amount of data that the LHC is getting, according to some claims in Tomasso Dorigo's blog.

To understand why I use the expression "new kind of physic" we must wonder what we understand as a particle. In particle physics we have quantum fields, and they create particles. That particles created by the field have a definite mass, charge (under whatever gague group it is charged) and cross section of production but, could it be otherwise?

Well, if I wrote this entry is because I am considering that possibility. In that case maybe we have "erractic" particles that are defined by the possibility that their properties (mass, charge and coupling constants to standard model particles) can vary in time and/or space.

The idea of varying coupling constants is not new and goes back to Dirac, but usually it was considered that the considered coupling constants were the standard model ones, specially, the $$ \alpha$$ electromagnetic constant. My idea is that, someway, the standard model could be stable, but the should be new (low energy, in the sense of well bellow the planck energy, but still high energy for the earth colliders) physics could be unstable, with fluctuating characteristics. In his recent papers about the issue of whether string theory allows or not the existence of a deSitter vacua he mentions the possibility that the coupling constants of physic beyond the standard model  could variate, but has not gone too far on it. .Lubos also has said in some posts that that variations should be related to moduli and they would have inconvenient statistical properties in cosmological data. That means that I am aware that there could be difficulties with the proposal, but still I think it is interesting to say a few things more about it.

To understand how this could happen we must go to string theory, but, in order to get it somewhat easier, we coould begin by the kaluza-klein scenario. As is well known there there we have a single extra dimension compactified in a circle. There a scalar field fit the relation

$$  p_\mu p^\mu - \frac{n^2}{R^2}=0 $$

 That implies

$$ m_n=\frac{\mid n\mid }{R} $$

If the scalar field is a self interecting one, thorough a $$ \lambda\pi^4$$ (or maybe another power, it is not  really relevant) the 4d coupling constant is related to the 5d one by

$$ \lambda_4=\frac{1}{R} \lambda_5 $$

Where V is the "volume" of the extra dimension, in this case $$ V= 2 \phi R $$

Well, now it comes the key ingredient, the way that we assign a value to R. It is a well known problem that was resolved assigning an scalar field to the geometrical moduli of the compactified space (in this simple case the radius of the cylinder) and a potential to the moduli so that the actual radius corresponds to the minimum of the potential of the moduli field. Still moduli stabilisation is a difficult issue. Usually the potential is generated by fluxes associated to the antisymmetric fields arising in string theory and sourced in branes. Still to get an stabilisation of all moduli is something that one put's by hand to avoid runaways, and to get defined values of the quantities but the question is that maybe we are prejudicing and that, in general, not all of them the  are stabilised and that the physics beyond the standard model is not constant.

 In a simple K-K scenario a variation of the radio doesn't give a grate variation of the masses and constants.  If we change $$  R \mapsto R + \Delta R $$ the the mass changes as

$$ \Delta m_n= \frac{\mid n \mid }{R + \Delta R}=\mid  n \mid \left (  - \frac{1}{R^2} \Delta R  + o \left (  \Delta R^2 \right ) \right ) $$

In more general settings that Kaluza Klein the details are different in heterotic, F-theory, "plain braneworld" type II A, etc, but the dependence of the coupling constants on the inverse of the volume of the extra space  remains true. In fact the mere KK mechanism is not too much the key ingredient determining the new physics and everything is more involved. One must first get a compactification that makes that the remaining supersymmetry is N=1  and later to chose some symmetry breaking mechanism, usually through a superpotential, and part of the characteristics of the low energy physics is fixed by that superpotential (others depend on the topology of the compatification space, and even in the metric, which  is generally unknown, even in the simplests cases)  The superpotential usually has perturbative and not perturbative contributions (instantons) but still depends in the geometry of the compactificated space.

 I tried to do all the details  in a generic scenario, the one described in a Dust and all paper from 2008  The LHC String Hunter's Companion but at last I considered that not being a payed investigator it didn't worth the effort.

But, in fact, the new physic searched by the LHC were not only superpartners or particles associated to new gague groups, usually some new U(1). Some star predictions for the LHC were micro black holes and Kaluza-Klein tower of the graviton in the Lisa Randall braneworlds scenario, and also that phsyic depends on the size of an extra dimension, which was assumed to have a fixed value. Still more interesting, in that scenarios the extra dimension was expected to have a size a lot bigger than the usual compactification scale. Previous to the braneworld there was the ADD scenarios, that is mathematically simplest.

 In ADD the cross section to form a black hole in a collision of energy E is:

$$ \sigma (E) \sim \frac{1}{V_n M_*^{n+2} }\left ( \frac{E}{\sqrt{V_n M_*^{n+2} } }    \right )  ^\alpha  $$

 Here $$ M_* $$ is true the (4+n) dimensional Planck scale (the 4d one would Mpl) The relation between them is different in ADD and in RS. In RS the relation  is:

 $$ M^2_{pl}= \frac{V_n}{M_*^{n+2}} $$

In ADD is:

$$ M^2_{pl} = \frac{M_*^3}{k}(1-e^{-2\pi k R} ) $$

The key ingredient is again present, the cross section depends on the size of the extra dimension. If this extra dimension size varies with time, the cross section of production of black holes is not constant. Even if it varies in space and not in time we have that as the earth moves in space it will move to zones with different value of the size, and them of the cross section.

 I haven't searched in deep for the formula giving the dependence of the kaluza klein tower of the graviton but I am sure that it also depends on that size.


As I said at some point I am aware that maybe there are possible issues with the "erratic particles" scenario, and may be it is impossible in string theory anyway. For sure there are people that know string theory far better than me that could explain the issues in the improbable case that they consider that my proposal deserves their attention.  And even if the scenario could be viable I have not made any estimation of what the variations of the sizes could be expected to be, nor the exact influence in a concrete realistic model of the variations of the measurable masses and coupling constants or whatever associated to the size variations.

One possible way to get that estimation could relay in cosmological considerations, but my knowledge of string cosmology is too bad to even try to purchase that objective. The only thing that I could conjecture is that maybe some properties of dark matter are fluctuating, and, perhaps, that could explain the very controversial claim of DAMA/LIBRA observation of an annual modulation of dark matter detection.

 But, going very weird, we could think that physics beyond the standard model is not described by string theory but that, still, the properties of that new physic are not constant.

In any case the only really important thing is the LHC is searching for new physic in the conventional way, expecting that the characteristic of the new physic is as stable as the characteristics of the standard model physics, but may be that is a wrong starting point. Maybe there is something special in the standard model that makes it robust against fluctuations, but the same thing doesn't apply to the extra physics.

 If true the people doing search for new physics should design a way to distinguish between statistical fluctuations of the type they are actually considering and another ones that are generated because the actual new physic is fluctuating. My knowledge of such issues is so null that I can even give a gimp of how they would do it.

And, to end my return to bloging, and the main reason for it: please, ignore Sabine campaign and build the FCC or whatever new collider you can!


P.S. I haven't mentioned it in the post, but there is a very important aspect in this scenario. The fluctuations in the new physic would not be random but there would be important correlations. One toy model is one in which there could be to possible particles A and Be to be produced in a collision. A would have certain value Qa of a certain charge (that would not be fluctuating) and a mass that maybe fluctuates among a central value $$ Ma= MCa \pm  \Delta Ma$$ and the same for the particle B. The cross section of production would depend in many factors, but, mainly, in some coupling constant that would fluctuate. The key point would be that according to the coupling variations one would have periods where the production of A would be much more favourable, and another where the production of B would be the preferred one, and periods in between, giving some characteristic pattern. If there are more particles and coupling constants involved the pattern would be more complicated, but still there would be one, and maybe that kind of patterns would make the search simpler that if the fluctuations would be pure random.

P.S. 2 In the type of scenario I describe (see Mitchel comment for the suggestion of an slighthly different one) I think that string theory would gain because if correlated fluctuations are detected some aspects of the goemetry of the compatification could be inferred form low energy physics, something not quite possible in the standard wisdom.