# Weinberg: `superparticles don't need Higgs to give them mass'

1. Jul 21, 2012

### w4k4b4lool4

Hi All,

I've been watching the Weinberg youtube video:

and I have two questions.

1) He says at some point that although there is a symmetry which wants the standard model particles to be massless (and which is then spontaneously broken by the Higgs mechanism), this symmetry does not imply the same for the superpartners ... it's not unnatural that these are heavier. In particular, the symmetries of the Standard Model would make the W^-+, Z^0, e^-, neutrinos, quarks, etc., massless if it weren't for the action of the Higgs. That symmetry however does not make the winos, zinos, selectrons, sneutrinos, etc., massless, so they don't need the Higgs to give them mass, they could have any mass you like, and so in particular they could have very large masses; so it's quite natural that they would be much heavier than the other particles.

Does anyone know why the superpartners don't need the action of the Higgs to give them mass??

2) There is a real mystery as to why the Higgs isn't much much heavier than the other particles. [He mentioned before that the Higgs mechanism doesn't give mass to the Higgs.] SUSY provides a possible answer: the Higgs is paired by SUSY with particles of spin 1/2 called Higgsinos, and there are mechanisms that would keep the Higgsinos light, except for the breaking of SUSY, which like the other symmetries of the SM has to be spontaneously broken. So that's another plus for SUSY.

What mechanisms could he be referring to that would keep the Higgsinos light?

Wakabaloola

Last edited by a moderator: Sep 25, 2014
2. Jul 21, 2012

### fzero

I gave up on trying to listen to the talk, since Weinberg seemed to have stopped talking into the microphone sometime before getting to the part you're referring to. Nevertheless, I think he was discussing some well-known topics, so my educated guess below should be accurate.

In the minimal supersymmetric version of the Standard Model (MSSM), there is a unique SUSY-preserving mass term for the Higgs fields known as the $\mu$-term. However, it turns out that the $\mu$-term gives a positive mass-squared contribution to the scalar potential, whereas the Higgs mechanism requires a "wrong-sign" mass term in order to have an electroweak symmetry breaking (EWSB) vacuum state. So the only way to have a viable Higgs mechanism is to add additional mass terms that break SUSY, such that the sum of all contributions to the scalar potential leads to the necessary negative sign mass term.

These additional mass terms are usually called the soft SUSY breaking terms, or soft terms. The nomenclature soft refers to the fact that these terms have positive mass dimension, so at high energies, where we can neglect them as small parameters, SUSY is restored. The MSSM is agnostic about where these terms come from. There are extensions of the model where they are explained in terms of spontaneous SUSY breaking, but in the MSSM they are just treated as free parameters.

The soft terms are precisely the terms which give rise to masses for the superpartners. However, after EWSB, the Higgs mechanism usually generates additional contributions to the masses. However, these contributions are expected to be small in comparison to the scale of the soft terms.

The Higgsino mass also depends strongly on the values of $\mu$ and the soft terms. Keeping the Higgsinos light means explaining why $\mu$ is small compared to the Planck scale, which is known as the $\mu$-problem, which is a type of hierarchy problem.

A somewhat generic way to explain a small value of $\mu$ is to postulate that $\mu$ is the expectation value of a new scalar (super)field. It is possible to introduce this field into the MSSM potential in such a way that $\mu$ is set to a value whose order of magnitude is the same as the soft terms.

Last edited by a moderator: Sep 25, 2014
3. Jul 21, 2012

### w4k4b4lool4

Wow, so you are saying that SUSY is not compatible with SSB, and that one needs to break SUSY in order to incorporate it, that's remarkable! Is this specific to MSSM?

This doesn't sound very natural ..

I see! So does this mean that these soft terms actually do break the symmetry of the underlying theory (as opposed to the "spontaneous" breaking of the symmetry, where the symmetry is still present in the underlying theory but not present in the particular solutions of interest)?

Can you please mention the (or some of the) extensions you are referring to?

I see. So is it correct to say that the Higgs particle(s) still couple universally to all massive particles, but for the superpartners the contribution of the Higgs coupling to their masses is subdominant?

So a hierarchy problem is still there, but has been reincarnated ...

I see.

Thank you very much fzero! Your response has been most enlightening ...
Wakabaloola

4. Jul 21, 2012

### fzero

The key point is that the electroweak theory is chiral, so we can't just arbitrarily write down mass terms for the fields. SUSY puts extra constraints, which is why you need a 2nd Higgs doublet in the MSSM (in order to avoid anomalies and to write down necessary Yukawa couplings).

There are certainly SUSY models that have spontaneous breaking of gauge symmetry without breaking SUSY. These usually involve superpotentials for nonchiral matter. In the MSSM, we can't write down any such terms given the chiral charges under the electroweak gauge group. It is possible to add new fields to the model to find SUSY vacua, but it doesn't seem to be well-motivated. It certainly appears (from the nonobservation of superpartners so far) that if SUSY exists at all, it has to be broken above the scale of EWSB.

It's not, but it's not really worse than the situation in the SM. There the mass in the scalar potential is also just a parameter with no explanation as to its value.

The soft terms break SUSY, but preserve the SM gauge group, at least over a small range of energies $\Lambda_{EW} < E < \Lambda_{SUSY}$. So EWSB can be spontaneous, but no underlying mechanism for SUSY breaking is assumed in what we call the MSSM.

It turns out that it's difficult to use the fields of the MSSM alone to break SUSY and keep the SM gauge symmetries intact, as well as end up with a reasonable mass spectrum.

Therefore many models of SUSY breaking do it in a "hidden sector." Namely, we call the MSSM fields the "visible sector" and add new fields (and perhaps gauge interactions) as a "hidden sector." With suitable choices, spontaneous SUSY breaking is easy to accomplish in the hidden sector. The effects of the hidden sector get communicated to the visible sector by "messenger fields" that would appear in loop diagrams involving the visible sector fields.

One possibility for the messenger field is gravity, since all fields must participate in gravitational interactions. This scenario is known as gravity-mediated SUSY breaking. Another possibility is that there is a new gauge interaction that is either weak in strength or broken at some scale above the electroweak scale. This is called gauge-mediated SUSY breaking.

It's certainly seems true that the MSSM Higgs contribution to the masses of the superpartners is subdominant in reasonable sections of parameter space. Exactly how the Higgs couples to regular matter isn't so easily decided. There we have the problem of explaining why the lightest leptons and quarks are so light compared to the top quark. It could be that some of these Yukawa couplings are actually zero and the observed masses are explained by loop and nonperturbative effects.

The $\mu$ hierarchy problem is still a problem, but it's a bit softer than the SM one. Namely, if we generate $\mu$ at some intermediate scale between $\Lambda_{EW}$ and $M_P$, then SUSY probably protects its value above $\Lambda_{SUSY}$. Without SUSY, there must still be a precise cancellation between the bare Higgs mass and any radiative corrections that has to survive over a presumably large range of energy scales. It's difficult to imagine how to explain this without SUSY.

5. Jul 22, 2012

### w4k4b4lool4

Thanks for your very interesting responses fzero.
I'll need to think about these carefully to understand the implications.
Wakabaloola

6. Jul 23, 2012

### docbillnet

I've seen reference elsewhere that if a Higgs particle were too massive, then eventually once you had a Higgs created with sufficient energy, it's self interaction would cascade into an increasing set of massive Higgs spreading out at the speed of light. I have no idea if that analysis is correct. But the reference I've seen sets an upper limit for the Higgs mass for that not to happen just about at the same value CERN is measuring for the Higgs mass. So if the analysis is correct, the Higgs has the mass value it does, because it cannot be any larger. A universe which had a more massive Higgs would not exist long enough for someone to come along and measure it.

In regards to SUSY particles, lets first worry about whether they exist before worrying about such details.

Bill

Last edited by a moderator: Sep 25, 2014
7. Jul 23, 2012

### fzero

You have the mass bound backwards. The upper bound on the mass of the Standard Model Higgs is set by the Landau pole. In perturbation theory, the Higgs quartic coupling receives large quantum corrections from loop diagrams involving top quarks. At some high energy scale $\Lambda$, the quartic coupling will become infinite, signaling the need for new physics to repair the theory. An upper bound on the Higgs mass can then be set as a function of $\Lambda$. For small values $\Lambda\sim 10^{3}~\mathrm{GeV}$, the upper bound is $m_h \lesssim 600~\mathrm{GeV}$. Larger values of $\Lambda$ decrease the bound.

For small Higgs masses, the quartic coupling can actually run to a negative value at some high scale. If the quartic coupling were negative, the Higgs potential would not be bounded from below, so the EW vacuum would presumably not be stable. If the scale of new physics was again around $\Lambda\sim 10^{3}~\mathrm{GeV}$, the bound is $m_h \gtrsim 70~\mathrm{GeV}$. Larger values of $\Lambda$ increase the bound. $m_h \sim 126~\mathrm{GeV}$ is a borderline value if there is no new physics before around $10^{16}~\mathrm{GeV}$. This thread includes some recent references that are relevant.

8. Jul 23, 2012