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--- open_problems:hierarchy_puzzle [2017/10/23 11:14]
jakobadmin ↷ Page moved from standard_model:open_problems:hierarchy_problem to open_problems:hierarchy_problem
+++ open_problems:hierarchy_puzzle [2019/02/08 09:23]
129.13.36.189 [Concrete]
@@ Line 1: / Line 1: @@
-====== Hierarchy Problem ======
+====== Hierarchy Puzzle ======
-<tabbox Why is it interesting?>
-<tabbox Layman>
+<tabbox Intuitive>
 <blockquote>
@@ Line 15: / Line 14: @@
 <cite>"A Zeptospace Odyssey" by Guidice</cite></blockquote>
-<tabbox Student>
+<tabbox Concrete>
-[[https://arxiv.org/abs/0801.2562|Naturally Speaking: The Naturalness Criterion and Physics at the LHC]] by G.F. Giudice
+  * [[https://arxiv.org/abs/0801.2562|Naturally Speaking: The Naturalness Criterion and Physics at the LHC]] by G.F. Giudice
+  * http://syymmetries.blogspot.de/2017/06/naturalness-pragmatists-guide.html
+  * http://jakobschwichtenberg.com/hierarchy-problem/
-<tabbox Researcher>
+<tabbox Abstract>
 [[https://inspirehep.net/record/189504/|Fine Tuning Problem and the Renormalization Group
 C. Wetterich]]
-<tabbox Examples>
+<tabbox Why is it interesting?>
+<blockquote>
+ Since long ago [1, 2] physicists have been reluctant to accept small (or
+large) numbers without an underlying dynamical explanation, even when the smallness of a
+parameter is technically natural in the sense of ’t Hooft [3]. One reason for this reluctance
+is the belief that all physical quantities must eventually be calculable in a final theory with
+no free parameters. It would be strange for small numbers to pop up accidentally from the
+final theory without a reason that can be inferred from a low-energy perspective.
---> Example1#
+<cite>https://arxiv.org/pdf/1610.07962.pdf</cite>
+</blockquote>
+<blockquote>
-<--
+Look at the Higgs field φ responsible for breaking electroweak theory. We don’t know its renormalized or physical mass precisely, but we do know that it is of order $M_{EW}$ . Imagine calculating the bare perturbation series in some grand unified theory - the precise theory does not enter into the discussion —starting with some bare mass $\mu_0$ for φ. The Weisskopf phenomenon tells us that quantum correction shifts $μ_0^2$ by a huge quadratically cutoff dependent amount $δμ_0^2 ∼ f^2\Lambda^2 \sim f^2 M_{GUT}^2$ , where we have substituted for $\Lambda$ the only natural mass scale around, namely $M_{GUT}$, and where $f$ denotes some dimensionless coupling. To have the physical mass squared $μ^2 = μ_0^2 + δμ_0^2$ come out to be of order $M_{EW}$, something like 28 orders of magnitude smaller than $M_{GUT}$, would require an extremely fine-tuned and highly unnatural cancellation between $\mu_0$ and $δμ_0$. How this could happen “naturally” poses a severe challenge to theoretical physicists.
---> Example2:#
+**Naturalness**
+The hierarchy problem is closely connected with the notion of naturalness dear to the theoretical physics community. We naturally expect that dimensionless ratios of parameters in our theories should be of order unity, where the phrase “order unity” is interpreted liberally between friends, say anywhere from $10^{−2}$ or $10^{−3}$ to $10^2$ or $10^3$. Following ’t Hooft, we can formulate a technical definition of naturalness: The smallness of a dimensionless parameter η would be considered natural only if a symmetry emerges in the limit η → 0. Thus, fermion masses could be naturally small, since, as you will recall from chapter II.1, a chiral symmetry emerges when a fermion mass is set equal to zero. On the other hand, no particular symmetry emerges when we set either the bare or renormalized mass of a scalar field equal to zero. This represents the essence of the hierarchy problem.
+<cite>page 419 in QFT in a Nutshell by A. Zee</cite>
-<--
+</blockquote>
-<tabbox History>
 </tabbox>

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