Hierarchy problem: Difference between revisions

Revision as of 12:36, 11 February 2023

Revision as of 16:49, 11 February 2023

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====Supersymmetry====

Some physicists believe that one may solve the hierarchy problem via [[supersymmetry]]. Supersymmetry can explain how a tiny Higgs mass can be protected from quantum corrections. Supersymmetry removes the power-law divergences of the radiative corrections to the Higgs mass and solves the hierarchy problem as long as the supersymmetric particles are light enough to satisfy the [[Riccardo Barbieri|Barbieri]]–[[Gian Francesco Giudice|Giudice]] criterion.<ref>{{Cite journal |last1=Barbieri |first1=R. |last2=Giudice |first2=G. F. |year=1988 |title=Upper Bounds on Supersymmetric Particle Masses |url=http://cds.cern.ch/record/180560 |journal=Nucl. Phys. B |volume=306 |issue=1 |page=63 |bibcode=1988NuPhB.306...63B |doi=10.1016/0550-3213(88)90171-X}}</ref> This still leaves open the [[mu problem]], however. Currently, theThe tenets of supersymmetry are being tested at the [[Large Hadron Collider|LHC]], although no evidence has been found so far for supersymmetry.

Each particle that couples to the Higgs field has an associated [[Yukawa coupling]] λ_f. The coupling with the Higgs field for fermions gives an interaction term <math>\mathcal{L}_{\mathrm{Yukawa}}=-\lambda_f\bar{\psi}H\psi</math>, with <math>\psi</math> being the [[Dirac field]] and <math>H</math> the [[Higgs field]]. Also, the mass of a fermion is proportional to its Yukawa coupling, meaning that the Higgs boson will couple most to the most massive particle. This means that the most significant corrections to the Higgs mass will originate from the heaviest particles, most prominently the top quark. By applying the [[Feynman diagram#Feynman rules|Feynman rules]], one gets the quantum corrections to the Higgs mass squared from a fermion to be:

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====Extra dimensions====

Currently, noNo experimental or observational evidence of [[extra dimensions]] has been officially reported. Analyses of results from the [[Large Hadron Collider]] severely constrain theories with [[large extra dimensions]].<ref name="ATLAS_blackholes">{{Cite journal |last1=Aad |first1=G. |last2=Abajyan |first2=T. |last3=Abbott |first3=B. |last4=Abdallah |first4=J. |last5=Abdel Khalek |first5=S. |last6=Abdinov |first6=O. |last7=Aben |first7=R. |last8=Abi |first8=B. |last9=Abolins |first9=M. |last10=Abouzeid |first10=O. S. |last11=Abramowicz |first11=H. |display-authors=29 |year=2014 |title=Search for Quantum Black-Hole Production in High-Invariant-Mass Lepton+Jet Final States Using Proton-Proton Collisions at {{sqrt|s}} = 8 TeV and the ATLAS Detector |journal=Physical Review Letters |volume=112 |issue=9 |pages=091804 |arxiv=1311.2006 |bibcode=2014PhRvL.112i1804A |doi=10.1103/PhysRevLett.112.091804 |pmid=24655244 |last12=Abreu |first12=H. |last13=Abulaiti |first13=Y. |last14=Acharya |first14=B. S. |last15=Adamczyk |first15=L. |last16=Adams |first16=D. L. |last17=Addy |first17=T. N. |last18=Adelman |first18=J. |last19=Adomeit |first19=S. |last20=Adye |first20=T. |last21=Aefsky |first21=S. |last22=Agatonovic-Jovin |first22=T. |last23=Aguilar-Saavedra |first23=J. A. |last24=Agustoni |first24=M. |last25=Ahlen |first25=S. P. |last26=Ahmad |first26=A. |last27=Ahmadov |first27=F. |last28=Aielli |first28=G. |last29=Åkesson |first29=T. P. A. |last30=Akimoto |first30=G.|s2cid=204934578 }}</ref> However, extra dimensions could explain why the gravity force is so weak, and why the expansion of the universe is faster than expected.<ref>{{Cite web |date=20 January 2012 |title=Extra dimensions, gravitons, and tiny black holes |url=http://home.web.cern.ch/about/physics/extra-dimensions-gravitons-and-tiny-black-holes |access-date=13 December 2015 |website=Home.web.cern.ch}}</ref>

If we live in a 3+1 dimensional world, then we calculate the gravitational force via [[Gauss's law for gravity]]: