Editing Hierarchy problem (section)

== Technical definition ==
A hierarchy problem<ref>{{cite journal |last1=Arkani–Hamed |first1=Nima |last2=Dimopoulos |first2=Savas |last3=Dvali |first3=Gia |date=1998-06-18 |title=The hierarchy problem and new dimensions at a millimeter |journal=Physics Letters B |volume=429 |issue=3 |pages=263–272 |doi=10.1016/S0370-2693(98)00466-3 |issn=0370-2693|doi-access=free |arxiv=hep-ph/9803315 |bibcode=1998PhLB..429..263A }}</ref> occurs when the fundamental value of some physical parameter, such as a [[coupling constant]] or a mass, in some [[Lagrangian mechanics|Lagrangian]] is vastly different from its effective value, which is the value that gets measured in an experiment. This happens because the effective value is related to the fundamental value by a prescription known as [[renormalization]], which applies corrections to it. 

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 |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.