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m Essentially exclusively RG topic, with QFT being pretty much implied in that category. |
Citation bot (talk | contribs) Add: s2cid, issue. | Use this bot. Report bugs. | Suggested by Whoop whoop pull up | #UCB_webform 875/1196 |
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| title=Reliable Perturbative Results for Strong Interactions?
| journal=Phys. Rev. Lett.
| volume=30 | issue=26
| pages=1346–1349 | doi=10.1103/PhysRevLett.30.1346
| url=http://inspirehep.net/record/81351?ln=en|bibcode = 1973PhRvL..30.1346P | doi-access=free
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| title=Asymptotically Free Gauge Theories. 1
| journal=Phys. Rev. D
| volume=8 | issue=10
| pages=3633–3652 | doi=10.1103/PhysRevD.8.3633
| url=http://inspirehep.net/record/81404 |bibcode = 1973PhRvD...8.3633G | doi-access=free
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| title= When was Asymptotic Freedom discovered?
| journal=Nucl. Phys. B Proc. Suppl.
| volume=74 | issue=1
| pages=413–425 | doi=10.1016/S0920-5632(99)00207-8
|arxiv = hep-th/9808154 |bibcode = 1999NuPhS..74..413T | s2cid=17360560
}}</ref> ===Standard Model Higgs–Yukawa Couplings===
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The Yukawa couplings of the up, down, charm, strange and bottom quarks, are small at the extremely high energy scale of [[Grand Unified Theory|grand unification]], <math> \mu \approx 10^{15} </math> GeV. Therefore, the <math>y^2</math> term can be neglected in the above equation. Solving, we then find that <math>y</math> is increased slightly at the low energy scales at which the quark masses are generated by the Higgs, <math> \mu \approx 100 </math> GeV.
On the other hand, solutions to this equation for large initial values <math>y</math> cause the ''rhs'' to quickly approach smaller values as we descend in energy scale. The above equation then locks <math>y</math> to the QCD coupling <math>g_3</math>. This is known as the (infrared) quasi-fixed point of the renormalization group equation for the Yukawa coupling.<ref>{{cite journal|last1=Pendleton|first1=B.|last2=Ross|first2=G.G.|title=Mass and Mixing Angle Predictions from Infrared Fixed points|journal=Phys. Lett.|date=1981|volume=B98|issue=4 |page=291|doi=10.1016/0370-2693(81)90017-4|bibcode = 1981PhLB...98..291P }}</ref><ref>{{cite journal|last1=Hill|first1=C.T.|title=Quark and Lepton masses from Renormalization group fixed points|journal=Phys. Rev.|date=1981|volume=D24|issue=3 |page=691|doi=10.1103/PhysRevD.24.691|bibcode = 1981PhRvD..24..691H }}</ref> No matter what the initial starting value of the coupling is, if it is sufficiently large it will reach this quasi-fixed point value, and the corresponding quark mass is predicted.
The value of the quasi-fixed point is fairly precisely determined in the Standard Model, leading to a predicted [[top quark]] mass of 230 GeV.{{Citation needed|date=November 2021}} The observed top quark mass of 174 GeV is slightly lower than the standard model prediction by about 30% which suggests there may be more Higgs doublets beyond the single standard model Higgs boson.
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