Hierarchy problem: Difference between revisions

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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.

Throughout the 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.

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=== 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 its 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>