# Checks of implemented models

## Inhaltsverzeichnis

- 1 Running the check for a newly implemented model
- 2 Performed Checks
- 2.1 Causes the particle content gauge anomalies?
- 2.2 Leads the particle content to the Witten anomaly?
- 2.3 Are all terms in the (super)potential in agreement with global and local symmetries?
- 2.4 Are there other terms allowed in the (super)potential by global and local symmetries?
- 2.5 Are all unbroken gauge groups respected?
- 2.6 Are there terms in the Lagrangian of the mass eigenstates which can cause additional mixing between fields?
- 2.7 Are all mass matrices irreducible?
- 2.8 Are the properties of all particles and parameters defined correctly?

- 3 See also

## Running the check for a newly implemented model

After the initialization of a model via Start[“MODEL”] it can be checked for (self-) consistency using the command

CheckModel;

## Performed Checks

#### Causes the particle content gauge anomalies?

Gauge anomalies are caused by triangle diagrams with three external gauge bosons and internal fermions . The corresponding conditions for all [math]SU(N)_A[/math] groups to be anomaly free are

[math]\begin{aligned} \sum_i \mbox{Tr}\left[T_{Ar}^a(\psi_i) T_{Ar}^a(\psi_i) T_{Ar}^a(\psi_i)\right] = 0 \end{aligned}[/math]

Again,[math]T_{Ar}^a(\psi_i)[/math] are the generators for a fermion [math]\psi_i[/math] transforming as irreducible representation[math]r[/math] under the gauge group /math>SU(N)_A</math>. The sum is taken over all chiral superfields. In the Abelian sector several conditions have to be fulfilled depending on the number of[math]U(1)[/math] gauge groups

[math]\begin{aligned} U(1)_A^3 &:& \sum_i (Q^A_{\psi_i})^3 = 0 \\ U(1)_A\times U(1)_B^2 &:& \thinspace \sum_i Q^A_{\psi_i} (Q^B_{\psi_i})^2 = 0 \\ U(1)_A\times U(1)_B\times U(1)_C &:& \thinspace \sum_i Q^A_{\psi_i} Q^B_{\psi_i} Q^C_{\psi_i}= 0\end{aligned}[/math]

The mixed condition involving Abelian and non-Abelian groups is

[math]U(1)_A\times SU(N)^2_B : \sum_i Q^A_{\psi_i}\, \mbox{Tr}\left[T_{Br}^a(\psi_i) T_{Br}^a(\psi_i)\right] = 0[/math]

Finally, conditions involving gravity[math]\mathfrak{G}[/math] are

[math]\begin{aligned} \mathfrak{G} \times U(1)_A^2 &:& \sum_i (Q^A_{\psi_i})^2 = 0 \\ \mathfrak{G} \times U(1)_A\times U(1)_B &:& \thinspace \sum_i Q^A_{\psi_i} Q^B_{\psi_i} = 0 \\ \mathfrak{G}^2 \times U(1)_A &:& \sum_i Q^A_{\psi_i} = 0 \end{aligned}[/math]

If one if these conditions is not-fulfilled a warning is printed by SARAH. If some [math]U(1)[/math] charges were defined as variable, the conditions on these variables for anomaly cancellation are printed.

#### Leads the particle content to the Witten anomaly?

SARAH checks that there is an even number of [math]SU(2)[/math] doublets. This is the necessary for a model in order to be free of the Witten anomaly

#### Are all terms in the (super)potential in agreement with global and local symmetries?

As mentioned above, SARAH doesn’t forbid to include terms in the superpotential which violate global or gauge symmetries. However, it prints a warning if this happens.

#### Are there other terms allowed in the (super)potential by global and local symmetries?

SARAH will print a list of renormalizable terms which are allowed by all symmetries but which haven’t been included in the model file.

#### Are all unbroken gauge groups respected?

SARAH checks what gauge symmetries remain unbroken and if the definition of all rotations in the matter sector and of the Dirac spinors are consistent with that.

#### Are there terms in the Lagrangian of the mass eigenstates which can cause additional mixing between fields?

If in the final Lagrangian bilinear terms between different matter eigenstates are present this means that not the entire mixing of states has been taken into account. SARAH checks if those terms are present and returns a warning showing the involved fields and the non-vanishing coefficients.

#### Are all mass matrices irreducible?

If mass matrices are block diagonal, a mixing has been assumed which is actually not there. In that case SARAH will point this out.

#### Are the properties of all particles and parameters defined correctly?

These are formal checks about the implementation of a model. It is checked for instance, if the number of PDGs fits to the number of generations for each particle class, if LaTeX names are defined for all particles and parameters, if the position in a Les Houches spectrum file are defined for all parameters, etc. Not all of these warnings have to be addressed by the user. Especially, if he/she is not interested in the output which would fail because of missing definitions.