Folks,
Please find another version of the short and long Energy Frontier reports attached. This version incorporates input from
Soeren, Markus, Sally, and Chip. More changes are still required, so please send it your requests. We have to finalize
this report in the next few days.
I believe that i am now up to date on making changes, so if changes you recommended have not been made, you need to write to
me again.
Please refer to changes by line number and version number. There are now 3 versions in play 10-3, 10-11, and 10-12.
If you have not started reading yet, read the 10-12 version.
Best wishes,
Michael
p.s. I have accepted all changes, modified in response to the complaint, or written back with a query except in one case.
Markus recommended a large rewriting of section 1.2.2 (Naturalness). I like the current version better. Markus' version
is below. The two versions are very different in tone. Please give your recommendations.
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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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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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more changes to the EF report:
these changes are listed by line number in the 10-3 versions of the short and long reports.
Short document
--------------
Major changes:
46 Chip requests to restore the earlier language for item 2. Note
that this specifically calls out studies of W, Z, top. I hope
copy/pasted this formuation of the three prongs into the long
report in the two places that the list is given, so that all
three appearances are identical
Nontrivial changes:
Number updates:
Long document
-------------
Major changes:
190, 1175 see the comment on the change to the short document above
376 Largely rewritten section on searches for additional Higgs bosons,
incorporating new results supplied by the NP group and merging these
with the Higgs group's original discussion.
1163-1169 Rewritten, hopefully in better accord with our general discussion of
conclusions. If you are not happy, suggest specific changes or alternatives.
Nontrivial changes:
41 Markus Luty wanted a reference here to the hierarchy problem
52 Markus criticized this sentence, but I left it unchanged. He wanted this to refer
specifically to the hierarchy problem, but there are many more reasons to be
uncomfortable with fundamental scalar fields.
154-55 Change in response to Markus' comments. But, I think it is important to
retain words denigrating naturalness.
71-78 updated outline of the document, suggested by Soeren
450 Soeren questions whether the discrepancy in mW is significant. The current discrepancy is 1.4 sigma. mW has been high for a long time at this level, and it certainly bother Tevatron folks. I put "1-2 sigma"; this is the fluctuation over time. Any suggestions?
587 Clarification requested by Soeren
723 clarification requested by Soeren
740 clarification requested by Soeren
782 clarification requested by Soeren
827 paragraph moved to just before 1.8.1 thank you Soeren
833-841 paragraph rewritten in response to Soeren's comments
846 new version of the figure and caption
887 new version of the figure and caption
900 new version of the figure caption
1046 change in response to Sally's request
1061 change in response to Sally's request
Number updates:
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