Hierarchy problem: Difference between revisions

Revision as of 06:19, 1 February 2025

Latest revision as of 14:59, 2 August 2025

(4 intermediate revisions by 3 users not shown)

Line 2:

{{for|the supersymmetric anomaly|Little hierarchy problem}}

{{Use dmy dates|date=December 2024}}

{{MOS|article|date=July 2025| [[MOS:FORMULA]] - avoid mixing {{tag|math}} and {{tl|math}} in the same expression}}

{{Beyond the Standard Model|expanded=Evidence}}

Line 11 ⟶ 12:

Typically the renormalized value of parameters are close to their fundamental values, but in some cases, it appears that there has been a delicate cancellation between the fundamental quantity and the quantum corrections. Hierarchy problems are related to [[Fine-tuning (physics)|fine-tuning problem]]s and problems of naturalness.

OverThroughout the past decade{{timeframe|date=December 2024}}2010s, 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 |pagesarticle-number=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 |pagearticle-number=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 |pagesarticle-number=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.

Line 18 ⟶ 19:

{{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 inIn particular, one might be especially curious about a theory where three values are close to one, and the fourth is so different; in other wordsi.e., the huge disproportion we seem to find between the first three parameters and the fourth. We might also wonder ifIf 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 themthe others in terms of effects, howwe didmight also wonder how our universe come to be so exactly balanced when its forces emerged?. In current [[particle physics]], the differences between some actual parameters are much larger than this, so the question is even more noteworthy.

One answerexplanation 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 lifelifeforms capable of performing 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>

A second possible answer is that there is a deeper understanding of physics that we currently do not possess. There mightmay be parameters thatfrom which we can derive physical constants from that have lessfewer unbalanced values, or there mightmay be a model with fewer parameters.{{Citation needed|reason=Reliable source needed for the whole sentence|date=April 2024}}

== Examples in particle physics ==

Line 108 ⟶ 109:

=== Cosmological constant ===

{{main article|Cosmological constant problem}}

In [[physical cosmology]], current observations in favor of an [[accelerating universe]] imply the existence of a tiny, but nonzero [[cosmological constant]]. This problem, called the '''cosmological constant problem''', is a hierarchy problem very similar to that of the Higgs boson mass problem, since the cosmological constant is also very sensitive to quantum corrections, but itits calculation is complicated by the necessary involvement of [[general relativity]] in the problem. Proposed solutions to the cosmological constant problem include modifying and/or extending gravity,<ref name="dark universe">Bull, Philip, Yashar Akrami, Julian Adamek, Tessa Baker, Emilio Bellini, Jose Beltrán Jiménez, Eloisa Bentivegna et al. "Beyond ΛCDM: Problems, solutions, and the road ahead." Physics of the Dark Universe 12 (2016): 56-99.</ref><ref>{{cite journal|last=Ellis |first=George F. R. |authorlink=George F. R. Ellis |title=The trace-free Einstein equations and inflation |journal=[[General Relativity and Gravitation]] |year=2014 |volume=46 |issue=1 |pagesarticle-number=1619 |doi=10.1007/s10714-013-1619-5 |arxiv=1306.3021|bibcode=2014GReGr..46.1619E |s2cid=119000135 }}</ref><ref>{{cite journal|last=Percacci |first=R. |title=Unimodular quantum gravity and the cosmological constant |doi=10.1007/s10701-018-0189-5 |arxiv=1712.09903 |year=2018 |journal=[[Foundations of Physics]] |volume=48 |number=10 |pages=1364–1379|bibcode=2018FoPh...48.1364P |s2cid=118934871 }}</ref> adding matter with unvanishing pressure,<ref name="Luongo Muccino pp. 2-3">{{cite journal |last1=Luongo |first1=Orlando |last2=Muccino |first2=Marco |title=Speeding up the Universe using dust with pressure |journal=Physical Review D |volume=98 |issue=10 |date=2018-11-21 |issn=2470-0010 |doi=10.1103/physrevd.98.103520 |pages=2–3|arxiv=1807.00180 |bibcode=2018PhRvD..98j3520L |s2cid=119346601 }}</ref> and UV/IR mixing in the Standard Model and gravity.<ref>{{cite journal|title=Effective Field Theory, Black Holes, and the Cosmological Constant|last1=Cohen|first1=Andrew|last2=Kaplan|first2=David B.|last3=Nelson|first3=Ann|journal=Physical Review Letters|volume=82|issue=25|date=21 June 1999|pages=4971–4974|doi=10.1103/PhysRevLett.82.4971|arxiv=hep-th/9803132|bibcode=1999PhRvL..82.4971C|s2cid=17203575}}</ref><ref>{{cite arXiv|title=Densities of States and the CKN Bound|author1=Nikita Blinov|author2=Patrick Draper|eprint=2107.03530|date=7 July 2021|class=hep-ph}}</ref>

Some physicists have resorted to [[anthropic reasoning]] to solve the cosmological constant problem,<ref>{{cite journal|last1=Martel|first1=Hugo|author2-link=Paul R. Shapiro|last2=Shapiro|first2=Paul R.|last3=Weinberg|first3=Steven|title=Likely Values of the Cosmological Constant|journal=The Astrophysical Journal|date=January 1998|volume=492|issue=1|pages=29–40|doi=10.1086/305016|arxiv=astro-ph/9701099|bibcode=1998ApJ...492...29M|s2cid=119064782}}</ref> but it is disputed whether such anthropic reasoning is scientific.<ref>{{cite book | author = Penrose, R. |author-link = Roger Penrose | title = The Emperor's New Mind | url = https://archive.org/details/emperorsnewmindc00penr | url-access = registration | publisher = Oxford University Press | isbn = 978-0-19-851973-7 | date =1989}} Chapter 10.</ref><ref>{{cite journal | author = Starkman, G. D. | author2 = Trotta, R. | title = Why Anthropic Reasoning Cannot Predict Λ | journal = Physical Review Letters | volume = 97 |page = 201301 | date = 2006 | doi = 10.1103/PhysRevLett.97.201301 | pmid = 17155671 | issue = 20 | bibcode=2006PhRvL..97t1301S|arxiv = astro-ph/0607227 | s2cid = 27409290 }} See also this [http://www.physorg.com/news83924839.html news story.]</ref>

== See also ==