This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: updated Tuesday 8 th February, 2011 11:54 2. the muon anomalous magnetic moment and large logs (a) muon anomalous magnetic moment (b) vacuum polarization corrections to g (c) dimensional regularization and MS (d) large logs in g µ electron g − 2 — one of the most spectacular predictions in science — if we ignore everything in the universe except electrons and photons — calculate the leading quantum correction to the Dirac value from the diagram g e = 2 + α π + 2 A (4) 1 ( α π ) 2 + ··· A (4) 1 = 197 144 + π 2 12 − π 2 2 log(2) + 3 4 ζ (3) independent determination of fine structure constant arXiv:0812.3139 α = . 00729735254 gives g e = 2 . 002319274 + ··· while experiment gives g e = 2 . 0023193043622 difference is what you would expect from ( α/π ) 3 terms — we don’t need to think about other particles because other charged particles are heavy — in fact, the theory has been done beyond ( α/π ) 4 — at this level you cannot ignore other charged stuff — in particular the muon in the effective low energy theory with only electrons and photons, what would we expect for the contribution of muons (or other heavier charged particles) to g − 2 without doing detailed diagrams??? the relevant operator looks like (where ψ is the electron field) e ¯ ψσ µν ψ F µν where σ µν = 1 2 i [ γ µ , γ ν ] dimension 5 so a very naive guess would be ξ e m µ ¯ ψσ µν ψ F µν with ξ = O (1) — this would give a δg e ≈ m e /m µ which is clearly not there chirality  L = ¯ ψ ( i ̸ ∂ − e ̸ A − m e ) ψ − 1 4 F µν F µν invariant under — “spurion analysis” ψ → γ 5 ψ m e → − m e ⇒ ξ em e m 2 µ ¯ ψσ µν ψ F µν in the effective low energy theory with only electrons and photons, what would we expect for the contribution of muons (or other heavier charged particles) to g − 2 without doing detailed diagrams??? chirality  L = ¯ ψ ( i ̸ ∂ − e ̸ A − m e ) ψ − 1 4 F µν F µν invariant under — “spurion analysis” ψ → γ 5 ψ m e → − m e ⇒ ξ em e m 2 µ ¯ ψσ µν ψ F µν muon charge  must be ∝ e 2 µ e 2 e — other charged particles can affect the electron only through diagrams involving at least two virtual photons → ξ ( α π ) 2 em e m 2 µ ¯ ψσ µν ψ F µν this is really little! — it doesn’t affect anything to this order — it is important if you want to calculate to 4th order in α — but let’s not do that!!! so now what about g µ ? — experimentally g µ = 2 . 0023318414 not quite the same as g e = 2 . 0023193043622 to calculate this, we (obviously) have to include the µ in our effective theory — let’s do this and ignore everything else — now effects of both e and µ show up g e = 2 + α π + ( 2 A (4) 1 + 2 A (4) 2 ( m e /m µ ) )( α π ) 2 + ··· g µ = 2 + α π + ( 2 A (4) 1 + 2 A (4) 2 ( m µ /m e ) )( α π ) 2 + ··· A (4) 1 = 197 144 + π 2 12 − π 2 2 log(2) + 3 4 ζ (3) A (4) 2 (1 /x ) = −...
View
Full Document
 Spring '10
 GEORGI
 Quantum Field Theory, Polarization, µ

Click to edit the document details