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I have the following equation for the renormalised mass of some scalar particle (i.e. Higgs boson)

[tex]m_{r}^{2}=m_{0}^{2}+\frac{\lambda}{32\pi^{2}}( \Lambda ^{2}-m_{0}^{2}ln(1+\frac{\Lambda^{2}}{\mu^{2}}))[/tex]

Where I have the first order correction to the mass of the loop in a two point function as

[tex]\delta m^{2}=\frac{\lambda}{32\pi^{2}}(\Lambda^{2}-m^{2}ln(1+\frac{\Lambda^{2}}{m^{2}}))[/tex]

Now I'm a bit confused with all these different terms and wanted to know what μ means in the top equation as I'd of thought it was just our mass squared in the second equation?

I suppose, more importantly, what I want to ask is the 'Renormalised Mass' the mass we measure (so for the Higgs Boson 125GeV) and the capital Lambda is our UV-limit (on planck scale 10^(19)GeV). If this is so then our bare mass is negative??

Also is it safe to assume the self-coupling constant of a Higgs boson is 1/8?

I'm sure we measure the mass to be about 125GeV however quantum corrections due to the 'divergences' (from virtual particles) want to push this mass up by about an order of 10^(17) which is not observed... so there 'must' be something else going on...

Is this correct?

Thanks,

SK

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# Renormalised Mass and the Higgs Boson

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