index_8.html

•The pion

(2 (32 π^2 (6 (L _ 4^( ) + L _ 5^( )) - λ) - log((m _ π^(ó ))^2/μ^2)) (m _ π^(ó ))^2 + (32 π^2 (24 L _ 4^( ) - λ) - log((m _ K^(ó ))^2/μ^2)) (m _ K^(ó ))^2)/(48 π^2 (f _ ϕ^(ó ))^2) + 1

(i p _ 1^μ _ 1 (2 (32 π^2 λ + log((m _ π^(ó ))^2/μ^2)) (m _ π^(ó ))^2 + (32 π^2 λ + log((m _ K^(ó ))^2/μ^2)) (m _ K^(ó ))^2))/(24 π^2 f _ ϕ^(ó ))

The first order tree amplitude is multiplied with ~~ :

-1/2 i f _ ϕ^(ó ) p _ 1^μ _ 1 (2 - (2 (32 π^2 (6 (L _ 4^( ) + L _ 5^( )) - λ) - log((m _ π^(ó ))^2/μ^2)) (m _ π^(ó ))^2 + (32 π^2 (24 L _ 4^( ) - λ) - log((m _ K^(ó ))^2/μ^2)) (m _ K^(ó ))^2)/(48 π^2 (f _ ϕ^(ó ))^2))

-1/(32 π^2 f _ ϕ^(ó )) (i p _ 1^μ _ 1 (32 π^2 (f _ ϕ^(ó ))^2 + 128 π^2 L _ 5^( ) (m _ π^(ó ))^2 - 64 π^2 λ (m _ π^(ó ))^2 - 2 log((m _ π^(ó ))^2/μ^2) (m _ π^(ó ))^2 - 32 π^2 λ (m _ K^(ó ))^2 - log((m _ K^(ó ))^2/μ^2) (m _ K^(ó ))^2 + 128 π^2 L _ 4^( ) ((m _ π^(ó ))^2 + 2 (m _ K^(ó ))^2)))

-(i p _ 1^μ _ 1 (32 π^2 (f _ ϕ^(ó ))^2 + 128 π^2 L _ 5^(r ) (m _ π^(ó ))^2 - 2 log((m _ π^(ó ))^2/μ^2) (m _ π^(ó ))^2 - log((m _ K^(ó ))^2/μ^2) (m _ K^(ó ))^2 + 128 π^2 L _ 4^(r ) ((m _ π^(ó ))^2 + 2 (m _ K^(ó ))^2)))/(32 π^2 f _ ϕ^(ó ))

The coefficient c of f is then the renormalization factor relating the unrenormalized to the renormalized = c :

(128 π^2 L _ 5^(r ) (m _ π^(ó ))^2 - 2 log((m _ π^(ó ))^2/μ^2) (m _ π^(ó ))^2 - log((m _ K^(ó ))^2/μ^2) (m _ K^(ó ))^2 + 128 π^2 L _ 4^(r ) ((m _ π^(ó ))^2 + 2 (m _ K^(ó ))^2))/(32 π^2 (f _ ϕ^(ó ))^2) + 1

$Using file name D:\\Program Files\\Wolfram Research\\Mathematica\\4.1\\AddOns\\Applications\\HighEnergyPhysics\\Phi\\Factors\\ChPT3A00P20o2.Fac$

Converted by Mathematica (July 10, 2003)