# What is wrong with the standard model at 1 or 2 TeV?

1. Sep 29, 2008

### JohnStanton

Every now and then one reads that the
standard model does not work for
energies above 1 or 2 TeV.

Can anybody explain where this statement
comes from?

As far as I understand, there are no
deviations of the standard model form
experiment. There is only the issue
of Higgs mass being sensitive to
higher order perturbative corrections.
But is that sufficient to derive the 2 TeV
number? Or is there another reason?

John

2. Sep 29, 2008

Staff Emeritus
A theory can be wrong in two ways. It can either be inconsistent with experiment, or inconsistent with itself. The SM has this second problem.

The problem is that the process $$W_L + W_L \rightarrow W_L + W_L$$ has a predicted probability of interaction that exceeds 1 around 1 TeV. This is clearly nonsensical, so something new has to happen.

3. Sep 29, 2008

### hamster143

I think you want to say that $$W_L + W_L \rightarrow W_L + W_L$$ scattering amplitudes don't behave nicely for all energies unless Higgs is lighter than 1 TeV.

Higgs isn't "new". Higgs is an integral part of SM. Not having a Higgs would be new.

4. Sep 30, 2008

### JohnStanton

Yes, I meant that the Higgs is part of the standard model. Does you comment mean that
there is definitely no problem with the standard model, if the Higgs exists?

John

5. Sep 30, 2008

### malawi_glenn

Define "problem"

6. Sep 30, 2008

Staff Emeritus
There is no inconsistency in the SM if the Higgs exists. Whether or not it agrees with the higher energy data that will be available when the LHC turns on is an open question. There are also questions that the SM doesn't answer and we'd like to know - why fermion masses vary by 10-13 orders of magnitude is one of them.

7. Sep 30, 2008

### fermi

I agree, but this leaves the John Stanton's original question unanswered. In other words, if the Higgs is lighter than 1 TeV, all is well in SM (but not pretty perhaps.) On the other hand, we must now answer what goes wrong if the Higgs exists but heavier than 1 TeV. Especially, if it is much heavier than 1 TeV. Only that would answer the original question properly, and I would like hear that explanation myself too. If the W+W scattering violate unitarity bounds at some large Higgs mass, that mass must be computable exactly. Is it not so?

8. Sep 30, 2008

### hamster143

"Simplest" SM with Higgs heavier than 1 TeV is incompatible with observations. Precision measurements of heavy quark and boson masses constrain SM Higgs to be lighter than approx. 250 GeV.

9. Sep 30, 2008

Staff Emeritus
Not exactly. There are two unknowns. One is the Higgs mass, and the other is the energy scale where the W scattering remains sensible. The mass of the Higgs depends on how high a scale you want the theory to still work - the Planck scale? The GUT scale? 10 TeV? Given one value, someone (other than me) can calculate the other.

10. Sep 30, 2008

### fermi

Yes, I know, but this is an experimental bound which comes from the best known values of various masses and mixing angles. As such, I think it is tighter than the so-called unitarity bound. I was also under the impression that the W+W elastic scattering would violate the unitarity at some Higgs mass above 1 TeV. (Vanadium50 mentioned the same thing earlier.) If true, this second restriction is not an experimental bound, but a fundamental theoretical limit. I would like to know how this latter limit is obtained, and if we may be able to accurately calculate the lowest Higgs mass which violates unitarity in the W+W elastic scattering. Do you know any papers or books where this computation is explicitly carried out?

11. Sep 30, 2008

### Haelfix

"There is no inconsistency in the SM if the Higgs exists."

You could probably argue that the Landau pole is really the only last glaring theoretical inconsistency (though it exists only at ridiculously high energy scales), and maybe the absense of gravity too.

However i'd say the SM is already falsified experimentally, b/c it cannot accurately predict cosmological constraints (no dark matter, issues with baryogenesis and so forth), thus it must be viewed as an effective theory regardless.

12. Sep 30, 2008

### Haelfix

13. Oct 1, 2008

### fermi

Thank you, I checked the W+W elastic scattering in the references you provided. It includes the mass computation I hoped to see, and I was excited. Unfortunately, I don't think the partial wave analysis employed in the mass computation is correct. (The scattering amplitude computation by first order perturbation is fine; what follow this computation however, borders speculation.) Perhaps I don't fully appreciate it. Interestingly, the article itself concludes with the remark: "The limit can not be taken all too serious(ly) since it drives the pertubative approach of partial waves into the region of non-pertubative analysis where |a0| = $\cal$O (1) . "

Does this mean the so called TeV unitarity bound is a mirage?

14. Oct 2, 2008

### Haelfix

Hi Fermi,

Yea the limit itself gets into mildly shaky mathematical territory, I wouldn't trust the number exactly, but then again its close modulo factors on the order 1. There is probably more detailed computations found in the literature/textbooks if you look for them, but indeed the systems do become strongly coupled and its a very hard problem to really get precise analytic control off.

You should however come away with the notion that whatever the theoretical upper bound is, its still squarely in the range of what the LHC can probe. Moreover modern electroweak precision tests tends to put the best fits somewhere between 115-175 GeV or so, so we should know one way or the other relatively soon and this whole discussion will become academic.

15. Oct 2, 2008

Staff Emeritus
No, it means before the calculation becomes nonsense, it becomes what is called "non-pertrubative", which means difficult and quite sensitive to ordinarily irrelevant details of the calculation.

This kind of behavior is hardly new - calculating the Curie temperature of iron from first principles, just to pick a random example, is also difficult. Happens all the time.

16. Oct 3, 2008

### JohnStanton

Fine Tuning and the Higgs mass - not necessary?

The 4 page paper arXiv:0712.0402
by Pivovarov and Kim provides a different
opinion than most. It is quite new (Phys Rev D,
July 2008) and says in its summary:

---
Let us summarize our findings. Taking into account
higher order perturbative corrections does not change
the basic fact: radiative corrections to the electroweak
scale are growing fast with cutoff. At 1.2 TeV the correction
to the intermediate bosons mass squared is about
a half of the total mass squared. Is it new physics that
half of the observable mass scale is due to radiative corrections
is a matter of convention. We consider such a
situation as deserving the title of new physics. To say
the least, perturbation theory looks jeopardized in such
circumstances. Beyond perturbation theory, we still do
not know any mechanism that would provide for small
masses of the scalar particles.

On the other hand, if some unknown mechanism provides
for small mass of scalar particles, perturbation theory
is quite able to explain relative stability of the scalar
mass against small variations in fundamental parameters.
We demonstrated that there is no fine tuning problem in
the theory of quantum scalar field, and derived inequality
(16) in the Standard Model restricting the Higgs boson
mass. Phenomenological consequences of this restriction
will be studied elsewhere.
---

So they say that there is NO *fine tuning problem*
for the Higgs mass, in contrast to most other authors.

In the abstract, they write; "We conclude that higher
order perturbative corrections take care of the fine tuning
problem, and, in this respect, scalar field is a natural system."
So they even say that there is no *naturalness problem*.

They only have the problem that the mechanism that
keeps the Higgs mass small is unknown. (The *hierarchy
problem*.) Most other authors disagree, giving
all 3 problems for the Higgs. Who is right?

John

17. Oct 3, 2008

### JohnStanton

Re: Fine Tuning and the Higgs mass - not necessary?

I found a post by Haelfix in 2004 where he says:

---

It's just hidden naively b/c of the assumptions in the scheme (1/epsilon divergences etc) gobbling up the physical quantities of interest. eg It's only in pure SDM valid at all scales where the above claim is true.. there really isn't a hierarchy problem per se unless you assume *something else*.

---

Does the Planck scale count as something else, or does the above statement mean that
if in nature there is only the standard model and the Planck scale, then there is no hierarchy problem?

Could one make the hierarchy problem go away?

John

18. Oct 3, 2008

### Haelfix

Yea that post I wrote a long time ago, is perhaps worded a little strange, but had to do with the fact that the hierarchy problem is invisible in dimensional regularization.

In a way, if there is no Planck scale, or GUT scale or some other physical scale of note, you won't see the unnatural ratios. There will be a problem of principle of course (where is gravity, where does the Higgs field VeV come from, etc), but technicallly what I wrote is accurate if dubious on physical grounds.