# Tree Masses

(Weitergeleitet von Masses)

## General calculation

SARAH uses the definition of the rotations defined in the model file to calculate the mass matrices for particles which mix. In general, all field rotations as listed in 'Supported particle mixing' are possible. The mass matrices for scalars are calculated by

$M^S_{ij} = \frac{-\partial^2 \mathfrak{L}}{\partial {\phi}_i \partial {\phi}_j^*}$

where $\phi$ can be either real or complex, i.e. the resulting $M^S$ corresponds to $M_C$ or $M_R$ as as define here. In the mass matrices of states which include Goldstone bosons also the $R_\xi$ dependent terms are included.

The mass matrices for fermions are calculated as

$M^F_{ij} = \frac{-\partial^2 \mathfrak{L}}{\partial {\psi}^x_i {\psi}^y_j}$

with $x=y=0$ for Majorana fermions, and $x=1$, $y=2$ for Dirac fermions.

SARAH calculates for all states which are rotated to mass eigenstates the mass matrices during the evaluation of a model. In addition, it checks if there are also particles where gauge and mass eigenstates are identical. In that case, it calculates also the expressions for the masses of these states.

## Mass Matrices

SARAH calculates automatically the mass matrices before rotating the fields to the new eigenstates and saves the information in arrays. The mass matrix for a particular field is shown via

MassMatrix[Field]

In addition, one can use the commands

MassMatrices[$EIGENSTATES] and MassMatricesFull[$EIGENSTATES]

to print all masses for a given set of eigenstates. The difference between this two arrays is that in the first one, the different generations are written as indices, while in the second on the generation indices are explicitly inserted. This means, in the first case the basis for the mass matrix in the down squark sector is just

(SdL[{gn,cn}],SdL[{gm,cm}])

while in the second case the basis vector is

(SdL[{1,cn1}],SdL[{2,cn2}],SdL[{3,cn3}],SdL[{1,cm1}],SdL[{2,cm2}],SdL[{3,cm2}])

The order of the mass matrices returned by MassMatrices and MassMatricesFull corresponds to the definition of the mixing as safed in

MixBasis[\$EIGENSTATES]
##### Example
1. The mass matrix for down-squark is returned by
MassMatrix[Su]


or by using either

MassMatricesFull[EWSB][[1]]

or

MassMatrices[EWSB][[1]]

for the short notation

2. To see the mass matrix for neutral gauge bosons one can either use
MassMatrix[VZ]

or

MassMatrix[VP]

## Tree level masses

One can also use the command

TreeMass[Field,Eigenstates]


to get the mass of a given field for a given set of eigenstates. This is in particular useful for states which don't mix, i.e. for which no mass matrix exist, or for gauge bosons.

#### Examples

1. The gluon mass is given via
TreeMass[Glu, EWSB]

2. The mass of the Z boson is caculated by
TreeMass[VZ,EWSB]


## Output

The tree-level masses and mass matrices can be exported

• They are used in the Vevacious output to enable the calculation of the one-loop effective potential
• The mass matrices can also be exported to the CalcHep model files if the user wants to calculate the masses internally with CalcHep instead of using them as input.