## Wednesday, 27 June 2012

### String Phenomenology: Day 2

Here are some of the highlights from day 2 of the conference, as I saw it.

Gordy Kane continued to describe his recent collaboration with Bobby Acharya and others (see the post about day 1), focussing on their prediction of the Higgs mass. Specifically, they claim to predict that the Higgs should sit between about 122 and 129 GeV, and most likely at about 125 GeV. This time, the animosity towards these claims was a lot more apparent. Some of the varied objections made by various people are as follows:

• This 'prediction' was first discussed at around the time that the rumours of a 125 GeV Higgs began to circulate last year. Obviously this makes a lot of people suspicious, although Kane insists that they had not heard any such rumours at the time they were doing the calculation.
• They don't have an explicit compactification which realises the various features they claim to be 'generic'. This doesn't actually both me too much; if their arguments about the necessary moduli masses etc. are correct, then it is perfectly valid to assume these features, and see what they imply. There don't seem to be any reasons for the necessary compactifications to not exist.
• Related to the above is the robustness of the high-energy boundary conditions they assume for the renormalisation group flow. These are absolutely crucial for the Higgs mass. (Edit: Here I am talking about the soft SUSY breaking parameters.)
One thing which is clear is that the majority of people in the field do not 'believe' the statements by Kane et al. The broad consensus seems to be that they are overselling the genericity of their models in string theory, and that their work is probably better described as string-inspired bottum-up model-building.

Michael Ratz discussed R-symmetry as a solution to the mu problem. I can't say much more than his abstract, other than to point out that in these models, the R-symmetry is broken at the electroweak scale, in contrast to models that I (and many other people) have worked on, in which fermion masses and the mu term are generated without breaking R-symmetry.

There were a number of other interesting talks, including many by people I consider friends, but I don't want to discuss them all, so to be fair I will not discuss any!

1. According to Acharya, Kane, and Kumar, “The enormity of the landscape has led to the popular, but incorrect, view that string theory has no predictive power …”
http://arxiv.org/pdf/1204.2795.pdf “Compactified String Theories — Generic Predictions for Particle Physics”
If we take “popular” to mean “popular with respect to the scholarly community of physicists with PhDs” then how popular is the anti-string viewpoint? Would it be fair to say that 20% are pro-string, 60% are neutral on string, and 20% are anti-string?
Consider 3 questions on the sociology of string theory:
(1) Are there about 2,000 string theorists in the contemporary world?
(2) How many people in today's world have PhD in physics and what % of them have a favorable opinion of string theory?
(3) Among Nobel prize winners in physics, who might be the 3 best critics of string theory and who might be the 3 strongest supporters of string theory?

2. I believe that the compactifications where the lightest moduli are O(1)*m_{3/2} have been explicitly constructed. As for the Higgs mass, during the last String Pheno meeting Kane demonstrated essentially the same plot as in the paper, which was about 5 months before the 125 GeV Higgs rumor appeared. The robustness of the soft SUSY breaking parameters at the high scale is probably the least understood, I agree. I think that in the G2-MSSM case, which they tend to refer to all the time, the soft terms are computed fairly robustly, except for the B\mu term and the supersymmetric mu-term, which is the main reason for Kane et al for not being able to pin down tan\beta precisely. For other classes of compactifications I think it all depends on how SUSY is broken. Warped sequestering in KKLT-type scenarios gives light scalars as well as gauginos, but Kane calls these cases 'non-generic', which is probably true since sequestering is definitely hard to achieve in string theory. So, to summarise, I would agree that the moduli - gravitino mass relation is generic, however, I'm not so certain about generalising the G2-MSSM results, which seem fairly robust to me, to other compactification scenarios.

3. Certainly compactifications exist with moduli at and below the gravitino mass; the important question is whether this is always true. I think the claim is that it is true whenever any moduli are stabilised in a SUSY-breaking way.

If the $G_2$ scenario is correct, then that's fine for me (I see no reason to demand that things work the same way in all corners of the 'landscape'?), as long as we start seeing some explicit singular $G_2$ manifolds with the right properties. Bobby tells me that a lot of progress is being made on this, so we might not have to wait too long.

4. Hi Rhys, Could you please elaborate on the progress Bobby was telling you about? As far as I understand, one needs a supersymmetric three cycle, supporting the hidden sector gauge theory, that is Poincare dual to the co-associative four form in order to stabilise all the moduli in the way they propose.

1. Apparently a large class of explicit compact $G_2$ spaces is currently under construction; presumably this will allow for systematic searches for those with desirable properties, as has been ongoing with Calabi-Yau threefolds for a number of years.

2. Thanks, Rhys! This is very interesting!

5. This is an interesting discussion! Hope the blog sticks around for a while.

The argument that moduli fields have masses of order $m_{3/2}$ applies, I think, generically. The argument was given by de Carlos, Casas, Quevedo, and Roulet in 1993. They, like most of the other literature, state that they're assuming moduli get masses only from supersymmetry breaking, in which case it's clear that the moduli masses are order $F/M_{Pl}$. But if you look at their argument, it really applies even to scenarios like KKLT where moduli stabilization is supersymmetric. The point is that even if the moduli are stabilized independently of supersymmetry breaking, the requirement that the cosmological constant is canceled relates different terms in the potential, and so you can't make the moduli much heavier than $m_{3/2}$ without fine-tuning. I tried to clarify this in a paper last year, but it's more or less explicit in their paper, if you ignore their statement that moduli masses come from SUSY-breaking.

So, the moduli problem is real if $m_{3/2} < 30$ TeV, and the only solutions that make much sense to me are tuning it away or a late period of thermal inflation. Thermal inflation really doesn't work very well, and fine-tuning is problematic too. Personally, then, I find the case that cosmology requires $m_{3/2} > 30$ TeV pretty persuasive.

The link to particle physics is more complicated. It's also pretty generic to have gaugino masses a loop factor below $m_{3/2}$: it happens whenever the moduli in the gauge kinetic function are stabilized only by nonperturbative effects. (I count what Acharya et al. call tree-level contributions to the gaugino masses as loops for this purpose -- if you rewrite the moduli dependence in terms of the gauge couplings determined by the moduli VEVs, they look like loop factors.) The trickier part seems to be the scalars, since in other settings people have found that they also have suppressed masses.

There's also the possibility that, in special cases like with no-scale structure, the gaugino masses can be much more than even loop-suppressed, allowing TeV-scale soft masses with $m_{3/2} \gg$ TeV, which could restore the possibility of a thermal cosmology for dark matter abundance, etc.

In short, I think it's useful to separate the parts of the argument that seem to follow from completely general effective field theory considerations-- like moduli masses near or below $m_{3/2}$ and gaugino masses suppressed relative to $m_{3/2}$ -- from the parts that appear to depend on details of moduli stabilization and the string construction, like exactly how much gaugino masses are suppressed and whether or not scalar masses are suppressed.

1. Hi Matt. Thanks for the kind words; I'm not a very conscientious blogger, but I'll certainly try to continue!

I completely agree with your last paragraph in particular; for this reason, I'll be checking out the papers you mentioned (I also need to improve my understanding of cosmology, for many reasons...)

6. Dear Matt, I think that their statement about the masses of the lightest moduli and their relation to m_{3/2} contains a qualifier, namely, a nearly Minkowski vacuum. The claim is that in a generic case it is very hard to achieve a susy preserving *nearly Minowski* vacuum in N=1 D=4 sugra with all moduli stabilised. Even the KKLT proposal can't stabilise *all* the moduli in a susy preserving way for realistic vacua because some moduli will not appear in the superpotential due the presence of chiral matter in the visible sector, of which you are probably well aware. So, the modulus, which corresponds to \alpha_{GUT} in the visible sector would have to be stabilised by a different mechanism. In the proposal of Acharya et al the problem of chirality is automatically evaded because they use a rather special hidden sector three-cycle in the superpotential, which is Poincare dual to the co-associative four form, but since it generically does not intersect other three cycles since we are in seven dimensions the problem of chirality vs moduli stabilisation is not really a problem in their context. It is those linear combinations of moduli, which do not enter the superpotential, that after susy breaking and tuning the CC end up being the lightest moduli. The moduli that do appear in the superpotential always end up being the heavier ones, by one or two orders of magnitude.

7. I just found my way here.

I think its worth pointing out, if only for historical accuracy, that Gordon Kane's predictions for the Higgs mass were taking place well before there were any rumors of a 125 GeV Higgs. All the main content of the research was presented a year ago. I downloaded the presentation back then, and it predicted a Higgs mass of "about 127 GeV". This was also blogged by Motl at the time. You can clearly see in the presentation that all the basic features of the paper that appeared around the same time as the rumor were there.

http://conferencing.uwex.edu/conferences/stringpheno2011/documents/kane.pdf
http://motls.blogspot.com/2011/08/string-phenomenology-2011-gordon-kane.html

1. Thanks Cliff. I was aware of this (in fact, Kane showed his Higgs mass slide from last year again), but can't remember when people might have got the first whiff of a 125 GeV Higgs. In any case, I think this is somewhat moot; if people think there is a problem with the arguments/calculations, they need to point them out explicitly.

8. The videos of talks are up. I just watched both Bobby's and Gordy's talks. Some of the questions baffled me as, for example the statement by Antoniadis, about many examples where moduli are stabilised supesymmetrically and decouple from the gravitino mass. Excuse me, by the gravitino mass for such vacua is generically huge, unless you fine-tune the fluxes, plus the Kahler moduli must also be stabilised and then the cosmological constant must be tuned. It's true that the complex structure and the axio-dilaton in Type IIB can be fixed by fluxes but the point which he and many people are still missing is that not all the moduli can be stabilised in that way while giving a nearly zero cosmological constant! Furthermore, some Kahler moduli can never enter the superpotential even non-perturbatively if the corresponding divisor has chiral intersections, so they can never be stabilised supersymmetrically! This paper http://arxiv.org/abs/arXiv:0711.3389 is five years old, and it's just incredible that there are senior people, who are actively working in this field, and who are still unaware of this problem! Also, I don't understand what the big fuss about the Higgs mass is. Isn't is pretty obvious that having a slightly split MSSM superpartner spectrum would automatically result in a heavy Higgs somewhere between 120 and 130 GeV? It's been known for about five years that the G2 construction of Acharya et al gives such a split spectrum with scalars O(10-100)TeV. So, that particular range for the Higgs mass is a natural consequence of that spectrum and I have no idea why people are suddenly questioning this. There are certainly some assumptions that go into this, e.g. the MSSM spectrum, but they clearly state all of them in the paper as well as the talks. I did have a problem with Gordy's statement that there are no free parameters, and that they predict tan\beta to be exactly 10, which is clearly BS, because in the next few minutes he started talking about varying some parameters. These kinds of statements is what annoys a lot of people but I still think that Acharya, Kane et al deserve much credit for sticking with these split susy models with heavy scalars, instead of trying to massage them into some more conventional MSSM scenarios, eg with light stops, etc.

1. The whole atmosphere baffled me a bit. People seemed adamant that Kane et al. are wrong, but nobody seemed to have a valid reason.

I agree, they are quite clear about the assumptions they are making. The "no parameters" thing is a bit strange though. Surely the soft terms depend somewhat on the particular compact $G_2$ space one chooses; in the absence of a concrete example, then, we get a family of low energy theories, with parameters...

The biggest concern I have is with the apparent fine-tuning (they are simply fixing $M_Z$ to its experimental value). They have arguments that the fine-tuning is a lot less that it naively seems to be, but I haven't understood them.

9. During the discussion after Kane's talk Kiwoon Choi, after seeing the slide with the spectrum, says with regard to the Higgs mass that "It's not surprising at all", which I completely agree with.
I liked Sven Krippendorf's question about the constraint on the hidden sector gauge group rank difference Q-P>=3 in the G2 scenario, and what happens to the Higgs mass for Q-P=4 since in that case the gravitino mass jumps from O(10)TeV to O(10^12)GeV. He seems to think that this would lead to the Higgs mass higher than 140 GeV or even 200 GeV, and therefore there is no firm prediction for the Higgs mass. I'm not sure if Sven will read this, but the answer to his question is rather simple. For Q-P=4 the gravitino, and therefore the all scalars and gauginos become as heavy as O(10^12) GeV because for Q-P=4 gauginos at tree-level are only suppressed relative to m_{3/2} by a factor of 20 or so. The mu-term is also as heavy as m_{3/2}. As a result of such MSSM spectrum there will be no radiative electroweak symmetry breaking, eg. the up-type Higgs mass squared will never go negative, so there is no non-zero Higgs vev and no Standard Model Higgs boson. This is precisely what distinquishes the G2-MSSM scenario from a generic split SUSY model. The only case where radiative electroweak symmetry breaking is possible is for the minimal allowed value of Q-P=3, which also automatically gives a O(10-100)TeV gravitino mass. All values Q-P>3 will have no electroweak symmetry breaking and no Standard Model Higgs, hence they are irrelevant.

1. Thanks for that.

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