Changes between Version 19 and Version 20 of ComplexMassScheme

Timestamp:

Aug 13, 2015, 3:22:20 AM (9 years ago)

Author:

Valentin Hirschi

Comment:

--

ComplexMassScheme

@@ -9 +9 @@
 The CMS implementation is rather straightforward at leading-order (LO) but it becomes more involved at next-to-leading-order (NLO) because of mainly two points
  * The widths must be LO accurate at least in the offshell region and NLO accurate in the onshell region.
- * The logarithms appearing in the UV wavefunction renormalization must be evaluated in the correct Riemann sheet.
+ * Because of the modified onshell renormalization condition in the CMS, 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 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:
+The difference between these two amplitudes must be of 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, $(\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 $\kappa^{\text{LO}}_0=0$. 
+At LO, $(\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 of higher order is then equivalent to state that $\kappa^{\text{LO}}_0=0$. 
 
 At NLO, this relation becomes