Changes between Version 17 and Version 18 of ComplexMassScheme

Timestamp:

Aug 13, 2015, 3:17:58 AM (9 years ago)

Author:

Valentin Hirschi

Comment:

--

ComplexMassScheme

@@ -11 +11 @@
  * The logarithms appearing in the UV wavefunction renormalization must be evaluated in the correct Riemann sheet.
 
-The details of these issues will be discussed in a forthcoming publication;  This wiki page is mainly to describe the various options to the command '{{{check cms}}}' which automatically tests the consistency of the CMS implementation. The core idea of the test is to compare amplitudes in the CMS scheme ($\mathcal{A}_{\text{CMS}}$) and in the case of widths set to zero ($\mathcal{A}_{\Gamma=0}$) for a given kinematic configuration where all resonances are far off-shell.
-The difference between these two amplitudes must be higher order. More formally, this means $\mathcal{A}^{\text{Born}}_{\text{CMS}}\sim \mathcal{A}^{\text{Born}}_{\Gamma=0} \sim \mathcal{O}(\alpha^a)$. 
+The details of these issues will be discussed in a forthcoming publication;  this wiki page is mainly to describe the various options to the command '{{{check cms}}}' which automatically tests the consistency of the CMS implementation. The core idea of the test is to compare amplitudes in the CMS scheme ($\mathcal{A}_{\text{CMS}}$) and in the case of widths set to zero ($\mathcal{A}_{\Gamma=0}$) for a given kinematic configuration where all resonances are far off-shell.
+The difference between these two amplitudes must be higher order. More formally, this means that if we have $\mathcal{A}^{\text{Born}}_{\text{CMS}}\sim \mathcal{A}^{\text{Born}}_{\Gamma=0} \sim \mathcal{O}(\alpha^a)$, then we can write the following:
 
 At LO, we can write $(\mathcal{A}^{\text{Born}}_{\text{CMS}}-\mathcal{A}^{\text{Born}}_{\Gamma=0})/\alpha^a \equiv \Delta^{\text{LO}} = \kappa^{\text{LO}}_0 + \kappa^{\text{LO}}_1\alpha + \mathcal{O}(\alpha^2) $. The statement that the difference is higher order is then equivalent to state that $\kappa^{\text{LO}}_0=0$.