Skip to content

GitLab

  • Projects
  • Groups
  • Snippets
  • Help
    • Loading...
  • Help
    • Help
    • Support
    • Community forum
    • Submit feedback
    • Contribute to GitLab
  • Sign in / Register
SARAH SARAH
  • Project overview
    • Project overview
    • Details
    • Activity
  • Packages & Registries
    • Packages & Registries
    • Container Registry
  • Analytics
    • Analytics
    • Repository
    • Value Stream
  • Wiki
    • Wiki
  • Members
    • Members
  • Activity
Collapse sidebar
  • GOODSELL Mark
  • SARAHSARAH
  • Wiki
  • Rotations_in_matter_sector

Last edited by Martin Gabelmann Jun 28, 2019
Page history

Rotations_in_matter_sector

Rotations in matter sector

General

The field rotations in the matter sector are defined via the list

DEFINITION[$EIGENSTATES][MatterSector] = { List of Rotations }

for each set of eigenstates. All possibilities to mix matter fields in the Lagrangian are briefly discussed here. One can see that there are in general two cases:

  • The mass matrix is hermitian or symmetric. That's the case for scalars and Majorana fermions
  • The mass matrix is not hermitian. That's the case for Dirac fermions

For both cases the entries in List of Rotations look slightly different.

Hermitian or symmetric mass matrix

In this case one basis vector of the old eigenstates has to be defined which gets transformed to new mass eigenstates. Therefore, the general syntax is

{{List of Old Eigenstates},{Name of New Eigenstates, Name of Mixing Matrix}}

with

  1. A list of the names of old eigenstates
  2. The name of the new eigenstates
  3. The name of the mixing matrix

Note, while the list of the old eigenstates can be arbitrary long, just one name is defined for the new eigenstates. This eigenstates will appear automatically with the correct number of generations.

Examples

  1. Down-Squarks in the MSSM: the mixing of the three generations of d̃L (SdL) and d̃R (SdR) to six generations of d̃ (Sd) via the rotation matrix ZD (ZD) is defined by {{SdL, SdR}, {Sd, ZD}}

    This definition is interpreted as $\left(\begin{array}{c} \tilde{d}_L^i \\ \tilde{d}_R^i \end{array}\right)k = Z^{D,\dagger}{kj} \tilde{d}_j$

  2. CP-even Higgs bosons in the MSSM: the mixing of ϕd (phid) and ϕu (phi_u) to two generations of h (hh) via the rotation matrix ZH (ZH) is defined by {{phid, phiu}, {hh, ZH}}

    This definition is interpreted as $\left(\begin{array}{c} \phi_d \\ \phi_u \end{array}\right)k = Z^{H,T}{kj} h_j$ Since phid and phiu are real, SARAH automatically defines hh as real as well. In addition, it is also possible to introduce a parametrisation for ZH via parameters.m.

  3. Charged Higgs bosons in the MSSM: the mixing of Hd− (SHdm) and Hu+ (SHup) to two generations of H± (Hpm) via the rotation matrix ZP (ZP) is defined by {{SHdm,conj[SHup]}, {Hpm, ZP}}

    This definition is interpreted as $\left(\begin{array}{c} H_d^- \\ (H_u^+)^* \end{array}\right)k = Z^{P,T}{kj} H^\pm_j$ Note the usage of conj in the above definition.

  4. Neutralinos in the MSSM: the mixing of B̃ (fB), W̃0 (fW0), H̃d0 (FHd0) and H̃u0 (FHu0) to four generations of λ0 (L0) via the rotation matrix ZN (ZN) is defined by {{fB, fW0, FHd0, FHu0}, {L0, ZN}}

    This definition is interpreted as $\left(\begin{array}{c} \tilde B \\ \tilde W^0 \\ \tilde H_d^0 \\ \tilde H_u^0 \end{array}\right)k = Z^{N,\dagger}{kj} \lambda^0_j$ One can form a Majorana spinor from the Weyl spinorsλ0 via

    DEFINITION[EWSB][DiracSpinors]={
    ...
    Chi ->{ L0, conj[L0]}

Non-hermitian mass matrix

In that case two sets of old eigenstates (O1,O2) are rotated to two new sets of mass eigenstates (N1, N2) via two rotation matrices (M1, M2). The general definition in SARAH is therefore

{{{First Basis},{Second Basis}},{{First States,First Matrix},{Second States,Second Matrix}}}

This is interpreted as O_1 = M_1 N_1 \\ O_2 = M_2 N_2 \\

Examples

  1. Up Quarks in the SM or MSSM: the definition {{{FuL},{conj[FuR]}},{{FUL,ZUL},{FUR,ZUR}}}

    is equivalent to $U_{L,i} = Z^{U_L}{ij} u{L,j} \hspace{1cm} U^*{R,i} = Z^{U_R}{ij} u_{R,j}$ where the gauge eigenstates are uL (FuL) and uR (FuR).

  2. Charginos in the MSSM: the definition {{{fWm, FHdm}, {fWp, FHup}}, {{Lm,Um}, {Lp,Up}}}

    is interpreted as

    $\left( \begin{array}{c} \tilde{W}^- \\ \tilde{H}_d^- \end{array} \right)i = U^{-,\dagger}{ij} \lambda^-_j, \hspace{1cm} \left( \begin{array}{c} \tilde{W}^+ \\ \tilde{H}u^+ \end{array} \right)= U^{+,\dagger}{ij} \lambda^+_j$

Rotation without flavour violation

With the above definitions, SARAH assumes always the most case that the new eigenstates can be a general mixture of all old eigenstates. However, when adding the keyword NoFlavorMixing only a mixing between the same generations is considered. Thus, in the definition

{{O1,O2},{N, M},NoFlavorMixing}

it is assumed that the i-th generation of O1 can only mix with the i-th generation of O2. As consequence, the mass eigenstates carry an additional index 'flavour'.

Example

If one uses the flag in the MSSM for the up-squark mixing

{{SuL, SuR}, {Su, ZU},NoFlavorMixing}

the mixing is taken to be \left(\begin{array}{c} \tilde{d}_L^1 \\ \tilde{d}_R^1 \end{array}\right)_k = Z^{D_1,\dagger}_{kj} \tilde{d}_{1j} \\ \left(\begin{array}{c} \tilde{d}_L^2 \\ \tilde{d}_R^2 \end{array}\right)_k = Z^{D_2,\dagger}_{kj} \tilde{d}_{2j} \\ \left(\begin{array}{c} \tilde{d}_L^3 \\ \tilde{d}_R^3 \end{array}\right)_k = Z^{D_3,\dagger}_{kj} \tilde{d}_{3j} or more compact \left(\begin{array}{c} \tilde{d}_L^f \\ \tilde{d}_R^f \end{array}\right)_k = Z^{D_f,\dagger}_{kj} \tilde{d}_{fj} \\ The consequences are

  1. There are three 2 × 2 rotation matrices which get labelled by a flavour index
  2. There are three flavours of fields d̃ which come with two genetations each.

The parameter and particle definitions read therefore

{ZU, {generation, flavor, flavor}, {3, 2, 2}}
{Su, 1, 3, S, {{generation, 3}, {flavor, 2}, {color, 3}}, 2}

While the usage of flavour indices is supported in the FeynArts, CalcHep/CompHep, UFO and WHIZARD output, it is not possible to generate a SPheno version for such a model.

See also

Clone repository

Home

Index

  • Additional terms in Lagrangian
  • Advanced usage of FlavorKit
  • Advanced usage of FlavorKit to calculate new Wilson coefficients
  • Advanced usage of FlavorKit to define new observables
  • Already defined Operators in FlavorKit
  • Already defined observables in FlavorKit
  • Auto-generated templates for particles.m and parameters.m
  • Automatic index contraction
  • Basic definitions for a non-supersymmetric model
  • Basic definitions for a supersymmetric model
  • Basic usage of FlavorKit
  • Boundary conditions in SPheno
  • CalcHep CompHep
  • Calculation of flavour and precision observables with SPheno
  • Checking the particles and parameters within Mathematica
  • Checks of implemented models
  • Conventions
  • Decay calculation with SPheno
  • Defined FlavorKit parameters
  • Definition of the properties of different eigenstates
  • Delete Particles
  • Different sets of eigenstates
  • Diphoton and digluon vertices with SPheno
  • Dirac Spinors
  • FeynArts
  • Fine-Tuning calculations with SPheno
  • Flags for SPheno Output
  • Flags in SPheno LesHouches file
  • FlavorKit
  • FlavorKit Download and Installation
  • Flavour Decomposition
  • GUT scale condition in SPheno
  • Gauge Symmetries SUSY
  • Gauge Symmetries non-SUSY
  • Gauge fixing
  • Gauge group constants
  • General information about Field Properties
  • General information about model implementations
  • Generating files with particle properties
  • Generic RGE calculation
  • Global Symmetries SUSY
  • Global Symmetries non-SUSY
  • Handling of Tadpoles with SPheno
  • Handling of non-fundamental representations
  • HiggsBounds
  • Higher dimensionsal terms in superpotential
  • Input parameters of SPheno
  • Installation
  • Installing Vevacious
  • LHCP
  • LHPC
  • LaTeX
  • Lagrangian
  • Loop Masses
  • Loop calculations
  • Loop functions
  • Low or High scale SPheno version
  • Main Commands
  • Main Model File
  • Matching to the SM in SPheno
  • MicrOmegas
  • ModelOutput
  • Model files for Monte-Carlo tools
  • Model files for other tools
  • Models with Thresholds in SPheno
  • Models with another gauge group at the SUSY scale
  • Models with several generations of Higgs doublets
  • More precise mass spectrum calculation
  • No SPheno output possible
  • Nomenclature for fields in non-supersymmetric models
  • Nomenclature for fields in supersymmetric models
  • One-Loop Self-Energies and Tadpoles
  • One-Loop Threshold Corrections in Scalar Sectors
  • Options SUSY Models
  • Options non-SUSY Models
  • Parameters.m
  • Particle Content SUSY
  • Particle Content non-SUSY
  • Particles.m
  • Phases
  • Potential
  • Presence of super-heavy particles
  • RGE Running with Mathematica
  • RGEs
  • Renormalisation procedure of SPheno
  • Rotations angles in SPheno
  • Rotations in gauge sector
  • Rotations in matter sector
  • SARAH in a Nutshell
  • SARAH wiki
  • SLHA input for Vevacious
  • SPheno
  • SPheno Higgs production
  • SPheno Output
  • SPheno and Monte-Carlo tools
  • SPheno files
  • SPheno mass calculation
  • SPheno threshold corrections
  • Setting up SPheno.m
  • Setting up Vevacious
  • Setting up the SPheno properties
  • Special fields and parameters in SARAH
  • Superpotential
  • Support of Dirac Gauginos
  • Supported Models
  • Supported gauge sectors
  • Supported global symmetries
  • Supported matter sector
  • Supported options for symmetry breaking
  • Supported particle mixing
  • Tadpole Equations
  • The renormalisation scale in SPheno
  • Tree-level calculations
  • Tree Masses
  • Two-Loop Self-Energies and Tadpoles
  • UFO
  • Usage of tadpoles equations
  • Using SPheno for two-loop masses
  • Using auxiliary parameters in SPheno
  • VEVs
  • Vertices
  • Vevacious
  • WHIZARD