Kaustubh,
Thank you. I have made the changes (2), (3), (4). You will see them in the next edition.
Michael
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Michael E. Peskin [log in to unmask]
HEP Theory Group, MS 81 -------
SLAC National Accelerator Lab. phone: 1-(650)-926-3250
2575 Sand Hill Road fax: 1-(650)-926-2525
Menlo Park, CA 94025 USA www.slac.stanford.edu/~mpeskin/
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From: Kaustubh Sadanand Agashe [[log in to unmask]]
Sent: Sunday, October 13, 2013 2:34 PM
To: Raymond Brock; Peskin, Michael E.
Cc: snowmass-ef
Subject: RE: [SNOWMASS-EF] more about the naturalness section -- please read and reply
Here is my 2 cents worth on this issue:
(1). Maybe I am missing something, but I actually do not see any significant difference (of spirit) between what Markus wrote and what's in draft right now:
specifically, Markus's last paragraph says "...it is clear that the degree of tuning required to obtain $m_h \ll M$ grows quadratically with $M$..."...
which implies that new physics (which cures Higgs mass divergence) at 1 TeV is less-tuned (by a factor of ~25)/more natural (and thus perhaps "more preferred" by Nature?) than at 5 TeV...
(2). ...it's just that in the draft version, it's made even more quantitative...by suggesting that fine-tuning should be "limited" to not worse than an order (or two)
of magnitude...
So, if we keep Eq. 1.5 of the draft version, then I would like to suggest that it come along with a caveat written in the **same** line, i.e., something like "assuming tuning at worst 10%"...
(3). It's of course true that in most SUSY models studied, Higgsino mass (mu-term) contributes at **tree**-level to Higgs mass and thus is required to be below ~200 GeV by
above criterion of naturalness...
...but there is a possibility that Higgsino mass is a SUSY **breaking** term...in which case it only contributes to Higgs mass at **loop**-level and thus can be larger for same level of naturalness: see,
for example, sec. IV on page 15 onwards of
http://arxiv.org/pdf/1110.6670.pdf
So, could we add a qualifier in line # 179-180 of Oct. 12 draft...something like "In most/typical" SUSY models, ..."?
(4). In line # 186, instead of specifically mentioning Little Higgs", could we just say "In models in which the Higgs boson is a composite **(pseudo) Nambu**-Goldstone boson..."?
That way it includes several models such as little Higgs, Higgs as A_5 (or the "deconstructed" version of the latter)...
Kaustubh
________________________________________
From: [log in to unmask] [[log in to unmask]] on behalf of Raymond Brock [[log in to unmask]]
Sent: Sunday, October 13, 2013 4:48 PM
To: Peskin, Michael E.
Cc: snowmass-ef
Subject: Re: [SNOWMASS-EF] more about the naturalness section -- please read and reply
Hi
This is fun, isn't it! Not your normal sort of scientific exchange...
Surely just the fact that there is such a discussion on Naturalness is proof of its fuzziness and baggage. What I think it's fair to say is that there have been attempts to quantify it, but those formal attempts have been relatively focused in only one direction, right? I think of Giudice and specifically SUSY as reviewed by Feng a while ago. I could be wrong about that. But in any case what I've read about this leads to an actual quantitive measure as a derivative at which one might declare a threshold - above unnatural, below, natural. The \mu in SUSY is that. It's precise enough an definition that JoAnne et al. can actually pick a number in their fits and use it as a criterion.
I don't think we're at that level in this discussion, nor do I interpret Michael's original and recent writing to be that fiercely precise in concept. We talked about this when we were writing and I believe we sort of agreed that here "naturalness" the word is meant to be closer to the colloquial feel, than the really quantitative impression. Forgive me, Michael if I remember this discussion wrongly? But in any case, I interpret his paragraphs - and of course they are his - to be in that spirit. So I was happy.
What I think is distinct about 1 TeV that doesn't hold for 5 TeV. or 4.3 TeV or 15.8 TeV... is that there are hints that point at 1 TeV as the point when it gets interesting. At 1 TeV, the mass correction terms come very close to cancellation. At 1 TeV, the WIMP dark matter idea becomes an interesting topic relative to other thresholds.
Said another way, if the LHC had been built in order to be sensitive to a scale of new physics at 500 GeV, we'd have said that it missed the mark and that to do that would have not taken advantage of the few hints that Nature's so far provided that point at 1 TeV as where it gets interesting for more than one reason.
So to me, it's not that new physics is guaranteed at 1 TeV, but that it would be pretty ho-hum less than that and that 1 TeV qualifies as the entry fee necessary to look for new physics. In that sense 5 TeV is also interesting as it's above that interesting 1 TeV threshold.
Am I making any sense here? 1 TeV is where it gets interesting, not where there are guarantees...and in that sense it's distinct from almost any other "number."
At least, that's how I have comforted myself up to this moment with this whole thing.
best
Chip
On Oct 13, 2013, at 4:21 PM, "Peskin, Michael E." <[log in to unmask]<mailto:[log in to unmask]>>
wrote:
Dear Colleagues,
Sally has a very nice analysis of the difference between the naturalness sections of the long report
(section 1.2.2) proposed by me and by Markus. The current draft was agreed upon between Chip
and me before we sent it to you, but I will take responsibility for its attitude. Sally's reply to my
email yesterday is pasted in below. I sent Markus' version yesterday, and it appears again below.
Anyone who wants to weigh in on this -- especially to object to what is in the current draft -- should write
back by Monday morning if possible. My attitude is that if I have an honest difference of opinion with one
of the conveners, I should win, but if I have an honest difference of opinion with most of the conveners,
their (your) opinion should win. So, let us all know your opinion by replying to snowmass-ef.
I do think it is important to say that it is more likely to find the first new particles at 1 TeV than at 5 TeV.
Otherwise, why is LHC so highly motivated?
Thanks,
Michael
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The naturalness sections that Michael and Marcus wrote reflect honest
differences of scientific opinion. Michael is trying to quantify naturalness
and Marcus is arguing that this isn't really well defined. From what Marcus
wrote, the reader would infer that 5 TeV is just as likely as 1 TeV for new
particles so we should look at as high an energy as possible. From what Michael
wrote, you would take home that 1 TeV new particles are much more likely
than 5 TeV.
I subscribe to Marcus's view, but as long as the naturalness section which
Michael wrote refrains from saying that there must be particles at 1 TeV,
I'm ok.
Sally
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Michael E. Peskin [log in to unmask]<mailto:[log in to unmask]>
HEP Theory Group, MS 81 -------
SLAC National Accelerator Lab. phone: 1-(650)-926-3250
2575 Sand Hill Road fax: 1-(650)-926-2525
Menlo Park, CA 94025 USA www.slac.stanford.edu/~mpeskin/<http://www.slac.stanford.edu/~mpeskin/>
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________________________________________
from Markus:
Lines 152-196. I do not think that naturalness is a "bothersome hint" or a "slippery principle." I think it can be explained in very basic physical terms. I suggest the following:
"Naturalness" is at bottom the use of dimensional analysis to estimate unknown parameters. If a quantity such as the Higgs mass is sensitive to a physics associated with a mass $M$, then dimensional analysis suggests that the Higgs mass should be of order $M$. Of course, this does not take into account the possibility that this dependence is absent, in which case we expect to have a good reason why this sensitivity is absent, such as a symmetry or some kind of decoupling.
Decades of theoretical work in quantum field theory has shown that elementary scalar masses are generically sensitive to physics at higher scales, and only three mechanisms have been established that can avoid this sensitivity. These are supersymmetry, (SUSY), Higgs compositeness, and extra dimensions. Each of these predict a rich spectrum of new states at the scale where the new structure becomes apparent. In SUSY, these consist of the superpartners of all known particles, while in both composite and extra-dimensional models we expect towers of massive resonances. (The fact that the phenomenology is qualitatively similar is the first sign that extra-dimensional models are in fact a realization of Higgs compositeness, a fascinating and deep equivalence that was discovered in string theory and has propagated to particle phenomenology and back again to fundamental theory.)
These mechanisms allow the Higgs mass to be calculated from other more fundamental parameters, and they confirm the expectations of naturalness in the sense that the Higgs mass is indeed sensitive to the new particles associated with SUSY or compositeness. The Higgs mass therefore cannot be much smaller than the scale $M$ of new particles predicted in these models. The Higgs mass can be much smaller than $M$ only if there is an unexplained accidental cancellation, or "fine tuning."
We can see the naturalness problem even without knowing what the new fundamental physics is. If we simply assume that there is *some* new physics at a scale $M$ we can estimate the sensitivity of the Higgs mass to new physics at the scale $M$ by computing quantum loops in the standard model with a cutoff of order $M$. The parameter in the Higgs potential then receives corrections of order
Eq. (1.4) with $M$ instead of $\Lambda$
where $g_{Htt}$ is the same Yukawa coupling as in (1.2), $\alpha_w$ and $\lambda$ are the couplings of these particles, and $\theta_w$ is the weak mixing angle. Note that all terms are proportional to $M^2$, simply as a result of the fact that it is the Higgs mass squared that appears in the Lagrangian. Experience with many specific models teaches us that if there is new physics at the scale $M$, (1.4) gives a reasonable estimate of the contribution of new physics at the scale $M$ to the Higgs mass. The suppression factors in (1.4) mean that the natural expectation for the scale $M$ is that it cannot exceed the Higgs mass by about a factor of 10.
Although there is no general agreement on how to quantitatively measure the (un)naturalness of a given model, it is clear that the degree of tuning required to obtain $m_h \ll M$ grows quadratically with $M$. This means that if we increase the sensitivity to heavy particle masses by a factor of 10, we increase our probing of naturalness by a factor of 100. This provides a very strong motivation to for searches at the largest possible energies.
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Michigan State University
Biomedical Physical Sciences
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