Problem Set 5 Solutions

References 1 j gasser h leutwyler nucl phys b 250

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: −2 . 2 ￿1/2 ≈ 90.4 M eV (28) 2.) Gasser-Leutwyler operators In order to obtain the higher derivative order terms in the chiral Lagrangian we need to follow the GasserLeutwyler [1] way of obtaining gauge and Lorentz’ invariant terms. It is fairly simple to generalize the leading (two-derivative) order Lagrangian: 2 fπ Tr(∂µ U ∂ µ U † ) 4 U (x) = exp(2 i π a (x)ta /fπ ) L= (29) (30) to include to higher (four-derivative) order terms: ∆L1 ∆L2 ∆L3 ∼ (Tr(∂µ U ∂ µ U † ))2 ∼ Tr(∂µ U ∂ν U † ) Tr(∂ µ U ∂ ν U † ) ∼ Tr(∂µ U ∂ µ U † ∂ν U ∂ ν U † ) Evidently each of the above terms are manifestly Lorentz’ invariant. References [1] J. Gasser, H. Leut...
View Full Document

Ask a homework question - tutors are online