Hierarchy problem: Difference between revisions

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Over the past decade{{timeframe|date=December 2024}} many scientists<ref>{{cite journal |last1=Fowlie |first1=Andrew |last2=Balazs |first2=Csaba |last3=White |first3=Graham |last4=Marzola |first4=Luca |last5=Raidal |first5=Martti |date=17 August 2016 |title=Naturalness of the relaxion mechanism |journal=Journal of High Energy Physics |volume=2016 |issue=8 |pages=100 |arxiv=1602.03889 |bibcode=2016JHEP...08..100F |doi=10.1007/JHEP08(2016)100 |s2cid=119102534}}</ref><ref>{{cite journal |last=Fowlie |first=Andrew |date=10 July 2014 |title=CMSSM, naturalness and the 'fine-tuning price' of the Very Large Hadron Collider |journal=Physical Review D |volume=90 |issue=1 |pages=015010 |arxiv=1403.3407 |bibcode=2014PhRvD..90a5010F |doi=10.1103/PhysRevD.90.015010 |s2cid=118362634}}</ref><ref>{{cite journal |last=Fowlie |first=Andrew |date=15 October 2014 |title=Is the CNMSSM more credible than the CMSSM? |journal=The European Physical Journal C |volume=74 |issue=10 |page=3105 |arxiv=1407.7534 |doi=10.1140/epjc/s10052-014-3105-y |bibcode=2014EPJC...74.3105F |s2cid=119304794}}</ref><ref>{{cite journal |last1=Cabrera |first1=Maria Eugenia |last2=Casas |first2=Alberto |last3=Austri |first3=Roberto Ruiz de |last4=Marzola |first4=Luca |last5=Raidal |first5=Martti |year=2009 |title=Bayesian approach and naturalness in MSSM analyses for the LHC |journal=Journal of High Energy Physics |volume=2009 |issue=3 |page=075 |arxiv=0812.0536 |bibcode=2009JHEP...03..075C |doi=10.1088/1126-6708/2009/03/075 |s2cid=18276270}}</ref><ref>{{cite journal |last=Fichet |first=S. |date=18 December 2012 |title=Quantified naturalness from Bayesian statistics |journal=Physical Review D |volume=86 |issue=12 |pages=125029 |arxiv=1204.4940 |bibcode=2012PhRvD..86l5029F |doi=10.1103/PhysRevD.86.125029 |s2cid=119282331}}</ref> argued that the hierarchy problem is a specific application of [[Bayesian statistics]].

Studying [[renormalization]] in hierarchy problems is difficult, because such quantum corrections are usually power-law divergent, which means that the shortest-distance physics are most important. Because we do not know the precise details of the [[quantum gravity]], we cannot even address how this delicate cancellation between two large terms occurs. Therefore, researchers are led to postulate new physical phenomena that resolve hierarchy problems without fine-tuning.

== Overview ==

{{refimprove|date=April 2024}}

Suppose a physics model requires four parameters to produce a very high-quality working model capable of generating predictions regarding some aspect of our physical universe. Suppose we find through experiments that the parameters have values: 1.2, 1.31, 0.9 and a value near {{val|4|e=29}}. One might wonder how such figures arise. But in particular, might be especially curious about a theory where three values are close to one, and the fourth is so different; in other words, the huge disproportion we seem to find between the first three parameters and the fourth. We might also wonder if one force is so much weaker than the others that it needs a factor of {{val|4|e=29}} to allow it to be related to them in terms of effects, how did our universe come to be so exactly balanced when its forces emerged? In current [[particle physics]], the differences between some parameters are much larger than this, so the question is even more noteworthy.

One might wonder how such figures arise. But in particular, might be especially curious about a theory where three values are close to one, and the fourth is so different; in other words, the huge disproportion we seem to find between the first three parameters and the fourth. We might also wonder if one force is so much weaker than the others that it needs a factor of {{val|4|e=29}} to allow it to be related to them in terms of effects, how did our universe come to be so exactly balanced when its forces emerged? In current [[particle physics]], the differences between some parameters are much larger than this, so the question is even more noteworthy.

One answer given by philosophers is the [[anthropic principle]]. If the universe came to exist by chance, and perhaps vast numbers of other universes exist or have existed, then life capable of physics experiments only arose in universes that, by chance, had very balanced forces. All of the universes where the forces were not balanced did not develop life capable of asking this question. So if lifeforms like [[human being]]s are aware and capable of asking such a question, humans must have arisen in a universe having balanced forces, however rare that might be.<ref>{{cite web |date=2024-02-08 |title=Anthropic principle {{!}} Cosmology, Physics & Philosophy {{!}} Britannica |url=https://www.britannica.com/science/anthropic-principle |access-date=2024-04-01 |website=www.britannica.com |language=en}}</ref><ref>{{citation |last1=Dimopoulos |first1=Savas |title=The anthropic principle, dark energy and the LHC |date=2007 |work=Universe or Multiverse? |pages=211–218 |publication-date=5 July 2014 |editor-last=Carr |editor-first=Bernard |url=https://www.cambridge.org/core/books/universe-or-multiverse/anthropic-principle-dark-energy-and-the-lhc/1FEAD231F875FB51E8A01EF68541A9D8 |access-date=2024-04-01 |place=Cambridge |publisher=Cambridge University Press |isbn=978-0-521-14069-0 |last2=Thomas |first2=Scott|bibcode=2007unmu.book..211D }}</ref>