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title: Advanced usage of FlavorKit to calculate new Wilson coefficients
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permalink: /Advanced_usage_of_FlavorKit_to_calculate_new_Wilson_coefficients/
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---
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# Advanced usage of FlavorKit to calculate new Wilson coefficients
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[Category:FlavorKit](/Category:FlavorKit "wikilink") The user can also implement new operators and obtain analytical expressions for their Wilson coefficients. In this case, he will need to use PreSARAH which, with the help of FeynArts and FormCalc, provides generic expressions for the coefficients, later to be adapted to specific models with SARAH.
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The user can also implement new operators and obtain analytical expressions for their Wilson coefficients. In this case, he will need to use PreSARAH which, with the help of FeynArts and FormCalc, provides generic expressions for the coefficients, later to be adapted to specific models with SARAH.
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Introduction
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------------
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... | ... | @@ -37,7 +34,7 @@ In order to derive the results for the Wilson coefficients, PreSARAH needs an in |
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q_\alpha)(\bar{q}^\beta \Gamma' q_\beta)`$.
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- `AllOperators` : a list with the definition of the operators. This is a two dimensional list, where the first entry defines the name of the operator and the second one the Lorentz structure. The operators are expressed in the chiral basis and the syntax for Dirac chains in FormCalc is used:
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- `6` for$`P_L = \frac{1}{2}(1-\gamma_5)`$, `7` for$`P_R = \frac{1}{2}(1-\gamma_5)`$
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- `Lor[1]`, `Lor[2]` for $`\gamma_\mu`$, $`\gamma_\nu`$.
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- `Lor[1]`, `Lor[2]` for $`\gamma_\mu`$`, `$`\gamma_\nu`$.
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- `ec[3]` for the helicity of an external gauge boson.
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- `k[N]` for the momentum of the external particle `N` (`N` is an integer).
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- `Pair[A,B]` is used to contract Lorentz indices. For instance, `Pair[k[1],ec[3]]` stands for *k*<sub>*μ*</sub><sup>1</sup>*ϵ*<sup>*μ*, \*</sup>
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... | ... | @@ -98,9 +95,9 @@ For instance, the PreSARAH input to calculate the coefficient of the$`(\bar{\ell |
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Here, we neglect all external masses in the operators (`NeglectMasses={1,2,3,4}` ), and the different coefficients of the scalar operators $`(\bar{\ell}P_X \ell)(\bar{d} P_Y d)`$ are called `OllddSXY`, the ones for the vector operators $`(\bar{\ell} P_X
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\gamma_\mu \ell)(\bar{d} P_Y \gamma^\mu d)`$ are called `OllddVYX` and the ones for the tensor operators$`(\bar{\ell} P_X \sigma_{\mu
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\nu} \ell)(\bar{d} \sigma^{\mu \nu} P_Y d)`$ `OllddTYX`, with X,Y=L,R. Notice that FormCalc returns the results in form of*P*<sub>*X*</sub>*γ*<sub>*μ*</sub> while in the literature the order*γ*<sub>*μ*</sub>*P*<sub>*X*</sub> is often used. Finally, SPheno will not calculate all possible combinations of external states, but only some specific cases
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$`\mu e d d`$, $`\tau e d d`$, $`\tau \mu d d`$, $`\mu e s s`$, $`\tau e s s`$, $`\tau \mu s s`$ [1]. Here we used $`d`$ for the first generation of down-type quarks while in the rest of this manual it is used to summarize all three families. [2]
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$`\mu e d d`$`, `$`\tau e d d`$`, `$`\tau \mu d d`$`, `$`\mu e s s`$`, `$`\tau e s s`$`, `$`\tau \mu s s`$` [1]. Here we used `$`d`$ for the first generation of down-type quarks while in the rest of this manual it is used to summarize all three families. [2]
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The input file to calculate the coefficients of the ℓ − ℓ − *Z* operators $`(\bar{\ell} \gamma_\mu P_{L,R} \ell) Z^\mu`$ and $`(\bar{\ell} p_\mu P_{L,R} \gamma_\mu \ell) Z^\mu`$ is
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The input file to calculate the coefficients of the ℓ − ℓ − *Z* operators $`(\bar{\ell} \gamma_\mu P_{L,R} \ell) Z^\mu`$` and `$`(\bar{\ell} p_\mu P_{L,R} \gamma_\mu \ell) Z^\mu`$ is
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NameProcess="Z2l";
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... | ... | @@ -197,4 +194,4 @@ Notes |
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[1] Here we used*d* for the first generation of down-type quarks while in the rest of this manual it is used to summarize all three families.
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[2] We note that the coefficients for the operators defined above ($`\bar{f} \gamma_\mu f \, V^\mu`$) are by a factor of 2 (4) larger than the coefficients of the standard definition for the dipole operators *f̄**σ*<sub>*μ**ν*</sub>*P*<sub>*L*</sub>*f**q*<sup>*ν*</sup>*V*<sup>*μ*</sup> ($`\bar{f} \sigma_{\mu\nu}P_L f F^{\mu\nu}`$). |
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\ No newline at end of file |
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[2] We note that the coefficients for the operators defined above ($`\bar{f} \gamma_\mu f \, V^\mu`$`) are by a factor of 2 (4) larger than the coefficients of the standard definition for the dipole operators *f̄**σ*<sub>*μ**ν*</sub>*P*<sub>*L*</sub>*f**q*<sup>*ν*</sup>*V*<sup>*μ*</sup> (`$`\bar{f} \sigma_{\mu\nu}P_L f F^{\mu\nu}`$). |
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\ No newline at end of file |