Markus,
line 164: I made the change to:
We do have a hint from the principle of ``naturalness.''
line 184, 188: Yesterday, Kaustubh suggested
The corresponding naturalness bounds for one-significant-figure cancellations
are
and
This gives a bound for one-significant-figure cancellation
Is this OK with you?
Thanks,
Michael
-------------------------------------------------------------------------------------------
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/
---------------------------------------------------------------------------------------------
________________________________________
From: [log in to unmask] [[log in to unmask]] On Behalf Of Markus A. Luty [[log in to unmask]]
Sent: Monday, October 14, 2013 9:25 AM
To: Ashutosh Kotwal
Cc: Peskin, Michael E.; snowmass-ef
Subject: Re: [SNOWMASS-EF] more about the naturalness section -- please read and reply
The main difference that I was trying to make from the version of Michael and Chip was to avoid the impression that I got from their version that naturalness is not a legitimate concept. I was trying to emphasize that it is something we actually do every day when we are faced with a scientific problem, namely dimensional analysis. I felt that the current version made it seem something mysterious.
Since there seems to be no consensus among the conveners that the different approach in my version is preferred, I agree with Michael that the original version remains the default.
I would then request the following small changes:
Line 164: Please remove the phrase "slippery principle." This is unnecessarily florid and makes it sound like naturalness is not something to be taken seriously. I would suggest no adjective at all:
We do have a hint from the principle of "naturalness."
The fact that it says "hint" makes it clear that this is not a precise concept.
Lines 184-185: "The corresponding naturalness bounds are" > "The corresponding bounds suggested by naturalness are"
Line 188: "This gives the bound" > "This suggests the bound"
The idea is to make it clear that naturalness "bounds" are not not sharp boundaries.
Markus Luty
============================================
Physics Department
University of California, Davis
One Shields Avenue
Davis, CA 95616
Phone: +1 530 554 1280
Skype: markus_luty
On Mon, Oct 14, 2013 at 7:46 AM, Ashutosh Kotwal <[log in to unmask]<mailto:[log in to unmask]>> wrote:
hi all,
Its clear we all agree there are no guarantees. Its hard to make an incisive argument for the slope of the prior distribution for the amount of fine tuning, But its not unreasonable that there is some slope (i.e. all else being the same, less fine tuning is preferred over more fine tuning). In the end, this is a decision-making criterion, not a prediction. Its a reason to bet a certain way. The past is a guide: people thought SU(5)-motivated proton decay was a good bet, and people thought the top quark should be 30 GeV and tristan (or even Petra before that) had a good chance to see it. So these projects were done.
As Chip said, at 1 TeV we are in the game and there is a good chance we will win.
I will add one comment about the bet placed on the Higgs for the LHC (SSC). In the absence of Higgs, we always say "unitarity would be violated in longitudinal Vector boson scattering". But as an experimentalist who is not motivated by quantum mechanics arguments, I would say that observing this "unitarity violating" cross section is actually very hard. All it says is that the amplitude A has a condition that Im(A) > |A|^2 (factor of 2 somewhere maybe). But A is pretty small and its really hard to see this rising cross section at high VV mass…
In other words, the Higgs was again a bet on nature choosing the easy solution and not the hard solution to find. And we won this bet.
I am ok with betting on ~ 1 TeV new particles. Especially when the LHC is already on the field…we just have to step up to the plate. Are we really going to turn our back on this game (might I add "again?') ?
regards,
Ashutosh
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
>
> -------------------------------------------------------------------------------
>
>
> 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
>
> ------------------------------------------------------------------------------------
> -------------------------------------------------------------------------------------------
> 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<tel:1-%28650%29-926-3250>
> 2575 Sand Hill Road fax: 1-(650)-926-2525<tel:1-%28650%29-926-2525>
> Menlo Park, CA 94025 USA www.slac.stanford.edu/~mpeskin/<http://www.slac.stanford.edu/~mpeskin/>
> ---------------------------------------------------------------------------------------------
> ________________________________________
>
> 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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