A class that performs renormalization group evolution in the context of the SMEFT.
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| RGESolver () |
| The default constructor.
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| ~RGESolver () |
| The default destructor.
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double | epsrel () |
| Getter for the relative error used in the numerical integration.
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double | epsabs () |
| Getter for the absolute error used in the numerical integration.
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void | Setepsrel (double epsrel) |
| Setter for the relative error used in the numerical integration (default value = 0.005)
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void | Setepsabs (double epsabs) |
| Setter for the absolute error used in the numerical integration (default value = e-13)
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void | Evolve (std::string method, double muI, double muF) |
| Performs the RGE evolution.
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void | EvolveToBasis (std::string method, double muI, double muF, std::string basis) |
| Performs the RGE evolution and the back rotation on the coefficients with flavour indices.
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void | GenerateSMInitialConditions (double mu, std::string basis, std::string method) |
| Generates the initial conditions for Standard Model's parameters (gauge couplings, Yukawa coupling, quartic coupling and Higgs' boson mass) at the scale mu (in GeV), using one-loop pure SM beta functions. Default low-energy input is used.
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void | GenerateSMInitialConditions (double muIn, double muFin, std::string basis, std::string method, double g1in, double g2in, double g3in, double lambdain, double mh2in, double Muin[3], double Mdin[3], double Mein[3], double s12in, double s13in, double s23in, double deltain) |
| Generates the initial conditions for Standard Model's parameters (gauge couplings, Yukawa coupling, quartic coupling and Higgs' boson mass) at the scale mu (in GeV), using one-loop pure SM beta functions. User-defined low energy input is used.
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void | EvolveSMOnly (std::string method, double muI, double muF) |
| Same as Evolve, but only for the SM parameters. The user should use this method instead of Evolve when interested in pure SM running. Using this function is the same of using Evolve with all the SMEFT coefficients set to 0, but it is faster since it does compute only the evolution for the SM parameters.
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double | GetCKMAngle (std::string name) |
| Getter function for the CKM matrix angles \(\theta_{12},\theta_{13},\theta_{23}\).
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double | GetCKMRealPart (int i, int j) |
| Getter function for the CKM matrix (real part)
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double | GetCKMImagPart (int i, int j) |
| Getter function for the CKM matrix (imaginary part)
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double | GetCKMPhase () |
| Getter function for the CKM matrix phase \(\delta\).
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void | SetCoefficient (std::string name, double val) |
| Setter function for scalar/0F parameters (no flavour indices).
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void | SetCoefficient (std::string name, double val, int i, int j) |
| Setter function for 2F parameters (2 flavour indices).
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void | SetCoefficient (std::string name, double val, int i, int j, int k, int l) |
| Setter function for 4F parameters (4 flavour indices).
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double | GetCoefficient (std::string name) |
| Getter function for scalar/0F parameters (no flavour indices).
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double | GetCoefficient (std::string name, int i, int j) |
| Getter function for 2F parameters (2 flavour indices).
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double | GetCoefficient (std::string name, int i, int j, int k, int l) |
| Getter function for 4F parameters (4 flavour indices). one of the inserted indices is outside the [0:2] range, an error message is printed and the value 0 is returned.
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void | Reset () |
| Resets all the SMEFT coefficients to 0 and the SM parameters to their default value. \(\epsilon_{\textrm{abs}}\) and \(\epsilon_{\textrm{rel}}\) are reset to their default value (in the UP basis).
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void | SaveOutputFile (std::string filename, std::string format) |
| Saves the current values of parameters in a file.
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A class that performs renormalization group evolution in the context of the SMEFT.
The class solves the Renormalization Group Equations (RGEs) numerically. A faster, approximate solution that neglects the scale dependence of the anomalous dimension matrix is also available. Only operators up to dimension six that preserve lepton and baryon numbers are considered. The operator basis is the Warsaw basis, defined in https://arxiv.org/abs/1008.4884. RGESolver
splits real and imaginary part of each complex parameter.
The numerical integration is performed with an adaptive step-size routine (the explicit embedded Runge-Kutta-Fehlberg method), using the tools in the GNU Scientific Library. See https://www.gnu.org/software/gsl/doc/html/ode-initval.html for all the details.
The accuracy level of the numerical integration can be tuned selecting the parameters \(\epsilon_{rel}\) and \(\epsilon_{abs}\) using the dedicated setter functions.
All the SMEFT coefficients are set using the SetCoefficient methods and accessed with the GetCoefficient methods. There exist three different signatures for each method, depending on the number of flavour indices of the parameter (0,2,4).
These two routines must be used also for the SM parameters \(g_1,g_2,g_3,\lambda,m_h^2,\) \(\mathrm{Re}(\mathcal{Y}_u),\mathrm{Im}(\mathcal{Y}_u),\) \(\mathrm{Re}(\mathcal{Y}_d),\mathrm{Im}(\mathcal{Y}_d),\) \(\mathrm{Re}(\mathcal{Y}_e),\mathrm{Im}(\mathcal{Y}_e)\) (we follow https://arxiv.org/abs/1308.2627 for what concerns the conventions in the Higgs' sector).
The routines GetCKMAngle, GetCKMPhase, GetCKMRealPart, GetCKMImagPart should be used when interested in the CKM parameters or elements. The usage of this method is recommended after methods such GenerateSMInitialConditions or EvolveToBasis that choose a specific flavour basis ("UP" or "DOWN"), in which cases the CKM matrix is updated. A complete list of the keys that must be used to correctly invoke setter/getter methods are given in tables SM, 0F, 2F and 4F.
A summary of the operators symmetry classes is given in table Sym.
We follow http://www.utfit.org/UTfit/Formalism for what concerns the conventions for the CKM matrix.
- Author
- S. Di Noi, L. Silvestrini.
- Copyright
- GNU General Public License
Standard Model parameters. The labels in the left column must be used with the GetCoefficient/SetCoefficient methods, the ones in the right column must be used with GetCKMAngle methods.
Parameter | Name
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\(g_1\) | g1 |
\(g_2\) | g2 |
\(g_3\) | g3
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\(\lambda\) | lambda
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\(m_h^2\) \([\mathrm{GeV}^2]\) | mh2
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\(\mathrm{Re}(\mathcal{Y}_u)\) | YuR
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\(\mathrm{Im}(\mathcal{Y}_u)\) | YuI
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\(\mathrm{Re}(\mathcal{Y}_d)\) | YdR
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\(\mathrm{Im}(\mathcal{Y}_d)\) | YdI
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\(\mathrm{Re}(\mathcal{Y}_e)\) | YeR
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\(\mathrm{Im}(\mathcal{Y}_e)\) | YeI |
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Parameter | Name
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\( \sin(\theta_{12})\) | s12
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\( \sin(\theta_{13})\) | s13
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\( \sin(\theta_{23})\) | s23
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Scalar (and real) SMEFT operators.
Classes 1-3 |
Coefficient | Name
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\(C_{G}\) | CG
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\(C_{\tilde{G}}\) | CGtilde |
\(C_{W}\) | CW
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\(C_{\tilde{W}}\) | CWtilde |
\(C_H\) | CH
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\(C_{H \Box} \) | CHbox
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\(C_{HD}\) | CHD
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Class 4
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Coefficient | Name
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\(C_{HG}\) | CHG
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\(C_{H\tilde{G}}\) | CHGtilde |
\(C_{HW}\) | CHW
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\(C_{H\tilde{W}}\) | CHWtilde |
\(C_{HB}\) | CHB
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\(C_{H\tilde{B}}\) | CHBtilde |
\(C_{HWB}\) | CHWB
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\(C_{H\tilde{W}B}\) | CHWtildeB |
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2F SMEFT operators.
Class 5
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Coefficient | Name | Symmetry
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\(\mathrm{Re}(C_{eH})\) | CeHR | WC1
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\(\mathrm{Im}(C_{eH})\) | CeHI | WC1 |
\(\mathrm{Re}(C_{uH})\) | CuHR | WC1 |
\(\mathrm{Im}(C_{uH})\) | CuHI | WC1 |
\(\mathrm{Re}(C_{dH})\) | CdHR | WC1 |
\(\mathrm{Im}(C_{dH})\) | CdHI | WC1 |
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Class 6
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Coefficient | Name | Symmetry
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\(\mathrm{Re}(C_{eW})\) | CeWR | WC1
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\(\mathrm{Im}(C_{eW})\) | CeWI | WC1 |
\(\mathrm{Re}(C_{eB})\) | CeBR | WC1 |
\(\mathrm{Im}(C_{eB})\) | CeBI | WC1 |
\(\mathrm{Re}(C_{uG})\) | CuGR | WC1 |
\(\mathrm{Im}(C_{uG})\) | CuGI | WC1 |
\(\mathrm{Re}(C_{uW})\) | CuWR | WC1 |
\(\mathrm{Im}(C_{uW})\) | CuWI | WC1 |
\(\mathrm{Re}(C_{uB})\) | CuBR | WC1 |
\(\mathrm{Im}(C_{uB})\) | CuBI | WC1 |
\(\mathrm{Re}(C_{dG})\) | CdGR | WC1 |
\(\mathrm{Im}(C_{dG})\) | CdGI | WC1 |
\(\mathrm{Re}(C_{dW})\) | CdWR | WC1 |
\(\mathrm{Im}(C_{dW})\) | CdWI | WC1 |
\(\mathrm{Re}(C_{dB})\) | CdBR | WC1 |
\(\mathrm{Im}(C_{dB})\) | CdBI | WC1 |
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Class 7
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Coefficient | Name | Symmetry
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\(\mathrm{Re}(C_{Hl1})\) | CHl1R | WC2R
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\(\mathrm{Im}(C_{Hl1})\) | CHl1I | WC2I |
\(\mathrm{Re}(C_{Hl3})\) | CHl3R | WC2R |
\(\mathrm{Im}(C_{Hl3})\) | CHl3I | WC2I |
\(\mathrm{Re}(C_{He})\) | CHeR | WC2R |
\(\mathrm{Im}(C_{He})\) | CHeI | WC2I |
\(\mathrm{Re}(C_{Hq1})\) | CHq1R | WC2R |
\(\mathrm{Im}(C_{Hq1})\) | CHq1I | WC2I |
\(\mathrm{Re}(C_{Hq3})\) | CHq3R | WC2R
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\(\mathrm{Im}(C_{Hq3})\) | CHq3I | WC2I |
\(\mathrm{Re}(C_{Hu})\) | CHuR | WC2R |
\(\mathrm{Im}(C_{Hu})\) | CHuI | WC2I |
\(\mathrm{Re}(C_{Hd})\) | CHdR | WC2R |
\(\mathrm{Im}(C_{Hd})\) | CHdI | WC2I |
\(\mathrm{Re}(C_{Hud})\) | CHudR | WC1 |
\(\mathrm{Im}(C_{Hud})\) | CHudI | WC1
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4F SMEFT Operators.
Class 8 \((\bar{L}L)(\bar{L}L)\)
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Coefficient | Name | Symmetry
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\(\mathrm{Re}(C_{ll})\) | CllR | WC6R |
\(\mathrm{Im}(C_{ll})\) | CllI | WC6I
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\(\mathrm{Re}(C_{qq1})\) | Cqq1R | WC6R |
\(\mathrm{Im}(C_{qq1})\) | Cqq1I | WC6I
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\(\mathrm{Re}(C_{qq3})\) | Cqq3R | WC6R |
\(\mathrm{Im}(C_{qq3})\) | Cqq3I | WC6I |
\(\mathrm{Re}(C_{lq1})\) | Clq1R | WC7R |
\(\mathrm{Im}(C_{lq1})\) | Clq1I | WC7I |
\(\mathrm{Re}(C_{lq3})\) | Clq3R | WC7R |
\(\mathrm{Im}(C_{lq3})\) | Clq3I | WC7I
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Class 8 \((\bar{L}R)(\bar{L}R)\)
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Coefficient | Name | Symmetry
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\(\mathrm{Re}(C_{quqd1})\) | Cquqd1R | WC5 |
\(\mathrm{Im}(C_{quqd1})\) | Cquqd1I | WC5 |
\(\mathrm{Re}(C_{quqd8})\) | Cquqd8R | WC5 |
\(\mathrm{Im}(C_{quqd8})\) | Cquqs8I | WC5 |
\(\mathrm{Re}(C_{lequ1})\) | Clequ1R | WC5 |
\(\mathrm{Im}(C_{lequ1})\) | Clequ1I | WC5
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\(\mathrm{Re}(C_{lequ3})\) | Clequ3R | WC5 |
\(\mathrm{Im}(C_{lequ3})\) | Clequ3I | WC5
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Class 8 \((\bar{R}R)(\bar{R}R)\)
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Coefficient | Name | Symmetry
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\(\mathrm{Re}(C_{ee})\) | CeeR | WC8R |
\(\mathrm{Im}(C_{ee})\) | CeeI | WC8I |
\(\mathrm{Re}(C_{uu})\) | CuuR | WC6R |
\(\mathrm{Im}(C_{uu})\) | CuuI | WC6I |
\(\mathrm{Re}(C_{dd})\) | CddR | WC6R |
\(\mathrm{Im}(C_{dd})\) | CddI | WC6I
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\(\mathrm{Re}(C_{eu})\) | CeuR | WC7R |
\(\mathrm{Im}(C_{eu})\) | CeuI | WC7I |
\(\mathrm{Re}(C_{ed})\) | CedR | WC7R |
\(\mathrm{Im}(C_{ed})\) | CedI | WC7I |
\(\mathrm{Re}(C_{ud1})\) | Cud1R | WC7R |
\(\mathrm{Im}(C_{ud1})\) | Cud1I | WC7I |
\(\mathrm{Re}(C_{ud8})\) | Cud8R | WC7R |
\(\mathrm{Im}(C_{ud8})\) | Cud8I | WC7I
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Class 8 \((\bar{L}R)(\bar{R}L)\)
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Coefficient | Name | Symmetry
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\(\mathrm{Re}(C_{ledq})\) | CledqR | WC5 |
\(\mathrm{Im}(C_{ledq})\) | CledqI | WC5 |
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Class 8 \((\bar{L}L)(\bar{R}R)\)
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Coefficient | Name | Symmetry
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\(\mathrm{Re}(C_{le})\) | CleR | WC7R |
\(\mathrm{Im}(C_{le})\) | CleI | WC7I |
\(\mathrm{Re}(C_{lu})\) | CluR | WC7R |
\(\mathrm{Im}(C_{lu})\) | CluI | WC7I |
\(\mathrm{Re}(C_{ld})\) | CldR | WC7R |
\(\mathrm{Im}(C_{ld})\) | CldI | WC7I |
\(\mathrm{Re}(C_{qe})\) | CqeR | WC7R |
\(\mathrm{Im}(C_{qe})\) | CqeI | WC7I |
\(\mathrm{Re}(C_{qu1})\) | Cqu1R | WC7R |
\(\mathrm{Im}(C_{qu1})\) | Cqu1I | WC7I |
\(\mathrm{Re}(C_{qu8})\) | Cqu8R | WC7R |
\(\mathrm{Im}(C_{qu8})\) | Cqu8I | WC7I |
\(\mathrm{Re}(C_{qd1})\) | Cqd1R | WC7R |
\(\mathrm{Im}(C_{qd1})\) | Cqd1I | WC7I |
\(\mathrm{Re}(C_{qd8})\) | Cqd8R | WC7R |
\(\mathrm{Im}(C_{qd8})\) | Cqd8I | WC7I
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Symmetry categories for operators in the SMEFT. nF indicates the number of flavour indices for each category.
Parameter | Name
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0 | 0F scalar object |
WC1 | 2F generic real matrix |
WC2R | 2F Hermitian matrix (real part)
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WC2I | 2F Hermitian matrix (imaginary part)
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WC5 | 4F generic real object |
WC6R | 4F two identical \( \bar{\psi} \psi \) currents (real part)
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WC6I | 4F two identical \( \bar{\psi} \psi \) currents (imaginary part)
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WC7R | 4F two independent \( \bar{\psi} \psi \) currents (real part)
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WC7I | 4F two independent \( \bar{\psi} \psi \) currents (imaginary part)
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WC8R | \( \mathcal{C}_{ee}\) (real part)
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WC8I | \( \mathcal{C}_{ee}\) (imaginary part)
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SM parameters used by default to generate SM initial conditions at an arbitrary scale. The scale at which these parameters are given is \( \mu = 173.65\) GeV. We follow http://www.utfit.org/UTfit/Formalism for what concerns the conventions for the CKM matrix.
Parameter | Value
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\(g_1\) | 0.3573 |
\(g_2\) | 0.6511 |
\(g_3\) | 1.161
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\(\lambda\) | 0.1297
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\(m_h^2\) \([\mathrm{GeV}^2]\) | 15650
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\(\sin(\theta_{12})\) | 0.225
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\(\sin(\theta_{13})\) | 0.042
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\(\sin(\theta_{23})\) | 0.003675
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\(\delta\) [rad] | 1.1676
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Parameter | Value [GeV]
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\(m_u\) | 0.0012
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\(m_c\) | 0.640
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\(m_t\) | 162.0
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\(m_d\) | 0.0027
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\(m_s\) | 0.052
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\(m_b\) | 2.75
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\(m_{e}\) | 0.000511
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\(m_{\mu}\) | 0.1057
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\(m_{\tau}\) | 1.776
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