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---
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title: Already defined Operators in FlavorKit
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permalink: /Already_defined_Operators_in_FlavorKit/
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---
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# Already defined Operators in FlavorKit
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[Category:FlavorKit](/Category:FlavorKit "wikilink")
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Lagrangian
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==========
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... | ... | @@ -12,81 +9,64 @@ In this section we present our notation and conventions for the operators (and t |
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The interaction Lagrangian relevant for flavor violating processes can be written as
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$\\label{eq:L-total}
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{\\cal L}_{\\text{FV}} = {\\cal L}_{\\text{LFV}} + {\\cal L}_{\\text{QFV}} \\, .$
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$` {\mathcal L}_{\text{FV}} = {\mathcal L}_{\text{LFV}} + {\mathcal L}_{\text{QFV}} \, .`$
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The first piece contains the operators that can trigger lepton flavor violation whereas the second piece contains the operators responsible for quark flavor violation.
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The general Lagrangian relevant for lepton flavor violation can be written as
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$\\label{eq:L-LFV}
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{\\cal L}_{\\text{LFV}} = {\\cal L}_{\\ell \\ell \\gamma} + {\\cal L}_{\\ell \\ell Z}
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+ {\\cal L}_{\\ell \\ell h} + {\\cal L}_{4 \\ell} + {\\cal L}_{2 \\ell 2q} \\, .$
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$` {\mathcal L}_{\text{LFV}} = {\mathcal L}_{\ell \ell \gamma} + {\mathcal L}_{\ell \ell Z} + {\mathcal L}_{\ell \ell h} + {\mathcal L}_{4 \ell} + {\mathcal L}_{2 \ell 2q} \, .`$
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The first term contains theℓ − ℓ − *γ* interaction, given by
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$\\label{eq:L-llg}
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{\\cal L}_{\\ell \\ell \\gamma} = e \\, \\bar \\ell_\\beta \\left\[ \\gamma^\\mu \\left(K_1^L P_L + K_1^R P_R \\right) + i m_{\\ell_\\alpha} \\sigma^{\\mu \\nu} q_\\nu \\left(K_2^L P_L + K_2^R P_R \\right) \\right\] \\ell_\\alpha A_\\mu + h.c.$
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$` {\mathcal L}_{\ell \ell \gamma} = e \, \bar \ell_\beta \left[ \gamma^\mu \left(K_1^L P_L + K_1^R P_R \right) + i m_{\ell_\alpha} \sigma^{\mu \nu} q_\nu \left(K_2^L P_L + K_2^R P_R \right) \right] \ell_\alpha A_\mu + h.c.`$
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Here*e* is the electric charge,*q* the photon momentum,$P_{L,R} =
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\\frac{1}{2} (1 \\mp \\gamma_5)$ are the usual chirality projectors andℓ<sub>*α*, *β*</sub> denote the lepton flavors. For practical reasons, we will always consider the photonic contributions independently, and we will not include them in other vector operators. On the contrary, the*Z*- and Higgs boson contributions will be included whenever possible. Therefore, theℓ − ℓ − *Z* andℓ − ℓ − *h* interaction Lagrangians will only be used for observables involving real*Z*- and Higgs bosons. These two Lagrangians can be written as
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\frac{1}{2} (1 \mp \gamma_5)$ are the usual chirality projectors andℓ<sub>*α*, *β*</sub> denote the lepton flavors. For practical reasons, we will always consider the photonic contributions independently, and we will not include them in other vector operators. On the contrary, the*Z*- and Higgs boson contributions will be included whenever possible. Therefore, theℓ − ℓ − *Z* andℓ − ℓ − *h* interaction Lagrangians will only be used for observables involving real*Z*- and Higgs bosons. These two Lagrangians can be written as
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$\\label{eq:L-llZ}
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{\\cal L}_{\\ell \\ell Z} = \\bar \\ell_\\beta \\left\[ \\gamma^\\mu \\left(R_1^L P_L + R_1^R P_R \\right) + p^\\mu \\left(R_2^L P_L + R_2^R P_R \\right) \\right\] \\ell_\\alpha Z_\\mu \\, ,$
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$` {\mathcal L}_{\ell \ell Z} = \bar \ell_\beta \left[ \gamma^\mu \left(R_1^L P_L + R_1^R P_R \right) + p^\mu \left(R_2^L P_L + R_2^R P_R \right) \right] \ell_\alpha Z_\mu \, ,`$
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where*p* is theℓ<sub>*β*</sub> 4-momentum, and
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$\\label{eq:L-llh}
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{\\cal L}_{\\ell \\ell h} = \\bar \\ell_\\beta \\left(S_L P_L + S_R P_R \\right) \\ell_\\alpha h \\, .$
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$` {\mathcal L}_{\ell \ell h} = \bar \ell_\beta \left(S_L P_L + S_R P_R \right) \ell_\alpha h \, .`$
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The general4ℓ 4-fermion interaction Lagrangian can be written as
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${\\cal L}_{4 \\ell} = \\sum_{\\substack{I=S,V,T\\\\X,Y=L,R}} A_{XY}^I \\bar \\ell_\\beta \\Gamma_I P_X \\ell_\\alpha \\bar \\ell_\\delta \\Gamma_I P_Y \\ell_\\gamma + h.c. \\, , \\label{eq:L-4L}$
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$`{\mathcal L}_{4 \ell} = \sum_{\substack{I=S,V,T\\X,Y=L,R}} A_{XY}^I \bar \ell_\beta \Gamma_I P_X \ell_\alpha \bar \ell_\delta \Gamma_I P_Y \ell_\gamma + h.c. \, , `$
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whereℓ<sub>*α*, *β*, *γ*, *δ*</sub> denote the lepton flavors and*Γ*<sub>*S*</sub> = 1,*Γ*<sub>*V*</sub> = *γ*<sub>*μ*</sub> and*Γ*<sub>*T*</sub> = *σ*<sub>*μ**ν*</sub>. We omit flavor indices in the Wilson coefficients for the sake of clarity. This Lagrangian contains the most general form compatible with Lorentz invariance. The Wilson coefficients*A*<sub>*L**R*</sub><sup>*S*</sup> and*A*<sub>*R**L*</sub><sup>*S*</sup> were included in , but absent in . As previously stated, the coefficients in Eq. do not include photonic contributions, but they include Z-boson and scalar ones. Finally, the general2ℓ2*q* four fermion interaction Lagrangian at the quark level is given by
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${\\cal L}_{2 \\ell 2q} = {\\cal L}_{2 \\ell 2d} + {\\cal L}_{2 \\ell 2u} \\label{eq:L-2L2Q}$
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$`{\mathcal L}_{2 \ell 2q} = {\mathcal L}_{2 \ell 2d} + {\mathcal L}_{2 \ell 2u} `$
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where
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$\\begin{aligned}
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{\\cal L}_{2 \\ell 2d} =
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&& \\sum_{\\substack{I=S,V,T\\\\X,Y=L,R}} B_{XY}^I \\bar \\ell_\\beta \\Gamma_I P_X \\ell_\\alpha \\bar d_\\gamma \\Gamma_I P_Y d_\\gamma + h.c. \\label{eq:L-2L2D} \\\\
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{\\cal L}_{2 \\ell 2u} = && \\left. {\\cal L}_{2 \\ell 2d} \\right|_{d \\to u, \\, B \\to C} \\label{eq:L-2L2U} \\, .\\end{aligned}$
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$` {\mathcal L}_{2 \ell 2d} = \sum_{\substack{I=S,V,T\\X,Y=L,R}} B_{XY}^I \bar \ell_\beta \Gamma_I P_X \ell_\alpha \bar d_\gamma \Gamma_I P_Y d_\gamma + h.c. \\ {\mathcal L}_{2 \ell 2u} = \left. {\mathcal L}_{2 \ell 2d} \right|_{d \to u, \, B \to C} \, .`$
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Here*d*<sub>*γ*</sub> denotes the d-quark flavor.
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Let us now consider the Lagrangian relevant for quark flavor violation. This can be written as
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$\\label{eq:L-QFV}
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{\\cal L}_{\\text{QFV}} = {\\cal L}_{q q \\gamma} + {\\cal L}_{q q g} + {\\cal L}_{4 d} +
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{\\cal L}_{2d2l} + {\\cal L}_{2d2\\nu} + {\\cal L}_{du\\ell\\nu} + {\\cal L}_{d d H} \\, .$
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$` {\mathcal L}_{\text{QFV}} = {\mathcal L}_{q q \gamma} + {\mathcal L}_{q q g} + {\mathcal L}_{4 d} + {\mathcal L}_{2d2l} + {\mathcal L}_{2d2\nu} + {\mathcal L}_{du\ell\nu} + {\mathcal L}_{d d H} \, .`$
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The first two terms correspond to operators that couple quark bilinears to massless gauge bosons. These are
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$\\begin{aligned}
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{\\cal L}_{q q \\gamma} = && e \\left\[ \\bar d_\\beta \\sigma_{\\mu \\nu} \\left( m_{d_\\beta} Q_1^L P_L + m_{d_\\alpha} Q_1^R P_R \\right) d_\\alpha \\right\] F^{\\mu \\nu} \\label{eq:L-qqgamma} \\\\
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{\\cal L}_{q q g} = && g_s \\left\[ \\bar d_\\beta \\sigma_{\\mu \\nu} \\left( m_{d_\\beta} Q_2^L P_L + m_{d_\\alpha} Q_2^R P_R \\right) T^a d_\\alpha \\right\] G_a^{\\mu \\nu} \\label{eq:L-qqgluon} \\, .\\end{aligned}$
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$` {\mathcal L}_{q q \gamma} = e \left[ \bar d_\beta \sigma_{\mu \nu} \left( m_{d_\beta} Q_1^L P_L + m_{d_\alpha} Q_1^R P_R \right) d_\alpha \right] F^{\mu \nu} \\ {\mathcal L}_{q q g} = g_s \left[ \bar d_\beta \sigma_{\mu \nu} \left( m_{d_\beta} Q_2^L P_L + m_{d_\alpha} Q_2^R P_R \right) T^a d_\alpha \right] G_a^{\mu \nu} \, .`$
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Here*T*<sup>*a*</sup> are*S**U*(3) matrices. The Wilson coefficients*Q*<sub>1, 2</sub><sup>*L*, *R*</sup> can be easily related to the usual*C*<sub>7, 8</sub><sup>(′)</sup> coefficients, sometimes normalized with an additional$\\frac{1}{16 \\pi^2}$ factor. The4*d* four fermion interaction Lagrangian can be written as
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Here*T*<sup>*a*</sup> are*S**U*(3) matrices. The Wilson coefficients*Q*<sub>1, 2</sub><sup>*L*, *R*</sup> can be easily related to the usual*C*<sub>7, 8</sub><sup>(′)</sup> coefficients, sometimes normalized with an additional$`\frac{1}{16 \pi^2}`$ factor. The4*d* four fermion interaction Lagrangian can be written as
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${\\cal L}_{4 d} = \\sum_{\\substack{I=S,V,T\\\\X,Y=L,R}} D_{XY}^I \\bar d_\\beta \\Gamma_I P_X d_\\alpha \\bar d_\\delta \\Gamma_I P_Y d_\\gamma + h.c. \\, , \\label{eq:L-4D}$
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$`{\mathcal L}_{4 d} = \sum_{\substack{I=S,V,T\\X,Y=L,R}} D_{XY}^I \bar d_\beta \Gamma_I P_X d_\alpha \bar d_\delta \Gamma_I P_Y d_\gamma + h.c. \, , `$
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where*d*<sub>*α*, *β*, *γ*, *δ*</sub> denote the lepton flavors. Again, we omit flavor indices in the Wilson coefficients for the sake of clarity. The2*d*2ℓ four fermion interaction Lagrangian is given by
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${\\cal L}_{2d 2 \\ell} = \\sum_{\\substack{I=S,V,T\\\\X,Y=L,R}} E_{XY}^I \\bar d_\\beta \\Gamma_I P_X d_\\alpha \\bar \\ell_\\gamma \\, \\Gamma_I P_Y \\ell_\\gamma + hc \\label{eq:L-2D2L} \\, .$
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$`{\mathcal L}_{2d 2 \ell} = \sum_{\substack{I=S,V,T\\X,Y=L,R}} E_{XY}^I \bar d_\beta \Gamma_I P_X d_\alpha \bar \ell_\gamma \, \Gamma_I P_Y \ell_\gamma + hc \, .`$
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Hereℓ<sub>*γ*</sub> denotes the lepton flavor.${\\cal L}_{2d 2 \\ell}$ should not be confused with${\\cal L}_{2 \\ell 2d}$. In the former case one has QFV operators, whereas in the latter one has LFV operators. This distinction has been made for practical reasons. The2*d*2*ν* and*d**u*ℓ*ν* terms of the QFV Lagrangian are
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Hereℓ<sub>*γ*</sub> denotes the lepton flavor.$`{\mathcal L}_{2d 2 \ell}`$ should not be confused with$`{\mathcal L}_{2 \ell 2d}`$. In the former case one has QFV operators, whereas in the latter one has LFV operators. This distinction has been made for practical reasons. The2*d*2*ν* and*d**u*ℓ*ν* terms of the QFV Lagrangian are
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$\\begin{aligned}
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{\\cal L}_{2d 2 \\nu} &=& \\sum_{X,Y=L,R} F_{XY}^V \\bar d_\\beta \\gamma_\\mu P_X d_\\alpha \\bar \\nu_\\gamma \\gamma^\\mu P_Y \\nu_\\gamma + hc \\label{eq:L-2D2V} \\\\
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{\\cal L}_{du\\ell\\nu} &=& \\sum_{\\substack{I=S,V\\\\X,Y=L,R}} G_{XY}^I \\bar d_\\beta \\Gamma_I P_X u_\\alpha \\bar \\ell_\\gamma \\, \\Gamma_I P_Y \\nu_\\gamma + hc \\label{eq:L-DULV} \\, .\\end{aligned}$
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$` {\mathcal L}_{2d 2 \nu} = \sum_{X,Y=L,R} F_{XY}^V \bar d_\beta \gamma_\mu P_X d_\alpha \bar \nu_\gamma \gamma^\mu P_Y \nu_\gamma + hc \\ {\mathcal L}_{du\ell\nu} = \sum_{\substack{I=S,V\\X,Y=L,R}} G_{XY}^I \bar d_\beta \Gamma_I P_X u_\alpha \bar \ell_\gamma \, \Gamma_I P_Y \nu_\gamma + hc \, .`$
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Note that we have not introduced scalar or tensor2*d*2*ν* operators, nor tensor*d**u*ℓ*ν* ones, and that lepton flavor (denoted by the index*γ*) is conserved in these operators. Finally, we have also included a term in the Lagrangian accounting for operators of the type(*d̄**Γ**d*)*S* and(*d̄**Γ**d*)*P*, where*S* (</math>P</math>) is a virtual [1] scalar (pseudoscalar) state. This piece can be written as
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$\\label{eq:L-ddSP}
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{\\cal L}_{d d H} = \\bar d_\\beta \\left(H_L^S P_L + H_R^S P_R \\right) d_\\alpha S
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+ \\bar d_\\beta \\left(H_L^P P_L + H_R^P P_R \\right) d_\\alpha P \\, .$
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$` {\mathcal L}_{d d H} = \bar d_\beta \left(H_L^S P_L + H_R^S P_R \right) d_\alpha S + \bar d_\beta \left(H_L^P P_L + H_R^P P_R \right) d_\alpha P \, .`$
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Operators available by default in the SPheno output of SARAH
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============================================================
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... | ... | @@ -195,14 +175,14 @@ The normalization is changed to match the standard definitions by |
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};
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$\\bar \\ell_\\beta \\left( q^2 \\gamma^\\mu + i m_{\\ell_\\alpha} \\sigma^{\\mu \\nu} q_\\nu \\right) \\ell_\\alpha A_\\mu$
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$`\bar \ell_\beta \left( q^2 \gamma^\mu + i m_{\ell_\alpha} \sigma^{\mu \nu} q_\nu \right) \ell_\alpha A_\mu`$
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| Variable | Operator | Name |
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|----------|-------------------------------------------------------------------------------------------------------|-------------------------------|
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| K2L | $e m_{\\ell_\\alpha} (\\bar \\ell_\\beta \\sigma_{\\mu\\nu} P_L \\ell_\\alpha) q^{\\nu} A^\\mu$ | *K*<sub>2</sub><sup>*L*</sup> |
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| K1L | $q^2 (\\bar \\ell_\\beta \\gamma_\\mu P_L \\ell_\\alpha) A^\\mu$ | *K*<sub>1</sub><sup>*L*</sup> |
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| K2R | $e m_{\\ell_\\alpha} (\\bar \\ell_\\beta \\sigma_{\\mu\\nu} P_R \\ell_\\alpha) q^{\\nu} A^\\mu$ | *K*<sub>2</sub><sup>*L*</sup> |
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| K1R | $q^2 (\\bar \\ell_\\beta \\gamma_\\nu P_R \\ell_\\alpha) A^\\mu$ | *K*<sub>1</sub><sup>*R*</sup> |
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| K2L | $`e m_{\ell_\alpha} (\bar \ell_\beta \sigma_{\mu\nu} P_L \ell_\alpha) q^{\nu} A^\mu`$ | *K*<sub>2</sub><sup>*L*</sup> |
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| K1L | $`q^2 (\bar \ell_\beta \gamma_\mu P_L \ell_\alpha) A^\mu`$ | *K*<sub>1</sub><sup>*L*</sup> |
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| K2R | $`e m_{\ell_\alpha} (\bar \ell_\beta \sigma_{\mu\nu} P_R \ell_\alpha) q^{\nu} A^\mu`$ | *K*<sub>2</sub><sup>*L*</sup> |
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| K1R | $`q^2 (\bar \ell_\beta \gamma_\nu P_R \ell_\alpha) A^\mu`$ | *K*<sub>1</sub><sup>*R*</sup> |
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These operators are derived by PreSARAH with the following input files
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... | ... | @@ -249,14 +229,14 @@ The normalization is changed to match the standard definitions by |
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"K2R(3,:) = -0.5_dp*K2R(3,:)/sqrt(Alpha_MZ*4*Pi)/MFe(3)"
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};
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$(\\bar \\ell \\Gamma \\ell) Z$
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$`(\bar \ell \Gamma \ell) Z`$
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| Variable | Operator | Name |
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|----------|------------------------------------------------------|-------------------------------|
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| OZ2lVL | $(\\bar{\\ell} \\, \\gamma^\\mu P_L \\ell) Z_\\mu$ | *R*<sub>1</sub><sup>*L*</sup> |
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| OZ2lSL | $(\\bar{\\ell} p^\\mu P_L \\ell) Z_\\mu$ | *R*<sub>2</sub><sup>*L*</sup> |
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| OZ2lVR | $(\\bar{\\ell} \\, \\gamma^\\mu P_R \\ell) Z_\\mu$ | *R*<sub>1</sub><sup>*R*</sup> |
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| OZ2lSR | $(\\bar{\\ell} p^\\mu P_R \\ell) Z_\\mu$ | *R*<sub>2</sub><sup>*R*</sup> |
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| OZ2lVL | $`(\bar{\ell} \, \gamma^\mu P_L \ell) Z_\mu`$ | *R*<sub>1</sub><sup>*L*</sup> |
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| OZ2lSL | $`(\bar{\ell} p^\mu P_L \ell) Z_\mu`$ | *R*<sub>2</sub><sup>*L*</sup> |
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| OZ2lVR | $`(\bar{\ell} \, \gamma^\mu P_R \ell) Z_\mu`$ | *R*<sub>1</sub><sup>*R*</sup> |
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| OZ2lSR | $`(\bar{\ell} p^\mu P_R \ell) Z_\mu`$ | *R*<sub>2</sub><sup>*R*</sup> |
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In the following we omit flavor indices for the sake of simplicity. These operators are derived by PreSARAH with the following input files
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... | ... | @@ -280,12 +260,12 @@ In the following we omit flavor indices for the sake of simplicity. These operat |
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Filters = {};
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$(\\bar{\\ell} \\Gamma \\ell) h$
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$`(\bar{\ell} \Gamma \ell) h`$
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| Variable | Operator | Name |
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|----------|---------------------------------|-------------------|
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| OH2lSL | $\\bar{\\ell} P_L \\ell \\, h$ | *S*<sub>*L*</sub> |
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| OH2lSR | $\\bar{\\ell} P_R \\ell \\, h$ | *S*<sub>*R*</sub> |
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| OH2lSL | $`\bar{\ell} P_L \ell \, h`$ | *S*<sub>*L*</sub> |
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| OH2lSR | $`\bar{\ell} P_R \ell \, h`$ | *S*<sub>*R*</sub> |
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These operators are derived by PreSARAH with the following input files
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... | ... | @@ -380,26 +360,26 @@ We will denote the 4-fermion operators involving two leptons and two down-type q |
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ℓℓ*d**d*
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for LFV and*d**d*ℓℓ for QFV.
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$(\\bar{d} \\Gamma d) (\\bar{\\ell} \\Gamma^\\prime \\ell)$ and(*d̄**Γ**d*)(*ν̄**Γ*<sup>′</sup>*ν*)
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$`(\bar{d} \Gamma d) (\bar{\ell} \Gamma^\prime \ell)`$ and(*d̄**Γ**d*)(*ν̄**Γ*<sup>′</sup>*ν*)
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| Variable | Operator | Name |
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|----------|--------------------------------------------------------------------------------------|------------------------------------|
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| OddllSLL | $(\\bar{d} P_L d) (\\bar{\\ell} P_L \\ell)$ | *E*<sub>*L**L*</sub><sup>*S*</sup> |
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| OddllSRR | $(\\bar{d} P_R d) (\\bar{\\ell} P_R \\ell)$ | *E*<sub>*R**R*</sub><sup>*S*</sup> |
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| OddllSLR | $(\\bar{d} P_L d) (\\bar{\\ell} P_R \\ell)$ | *E*<sub>*L**R*</sub><sup>*S*</sup> |
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| OddllSRL | $(\\bar{d} P_R d) (\\bar{\\ell} P_L \\ell)$ | *E*<sub>*R**L*</sub><sup>*S*</sup> |
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| OddllVLL | $(\\bar{d} \\gamma_\\mu P_L d) (\\bar{\\ell} \\gamma^\\mu P_L \\ell)$ | *E*<sub>*L**L*</sub><sup>*V*</sup> |
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| OddllSLL | $`(\bar{d} P_L d) (\bar{\ell} P_L \ell)`$ | *E*<sub>*L**L*</sub><sup>*S*</sup> |
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| OddllSRR | $`(\bar{d} P_R d) (\bar{\ell} P_R \ell)`$ | *E*<sub>*R**R*</sub><sup>*S*</sup> |
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| OddllSLR | $`(\bar{d} P_L d) (\bar{\ell} P_R \ell)`$ | *E*<sub>*L**R*</sub><sup>*S*</sup> |
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| OddllSRL | $`(\bar{d} P_R d) (\bar{\ell} P_L \ell)`$ | *E*<sub>*R**L*</sub><sup>*S*</sup> |
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| OddllVLL | $`(\bar{d} \gamma_\mu P_L d) (\bar{\ell} \gamma^\mu P_L \ell)`$ | *E*<sub>*L**L*</sub><sup>*V*</sup> |
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| OddvvVLL | (*d̄**γ*<sub>*μ*</sub>*P*<sub>*L*</sub>*d*)(*ν̄**γ*<sup>*μ*</sup>*P*<sub>*R*</sub>*ν*) | *F*<sub>*L**L*</sub><sup>*V*</sup> |
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| OddllVRR | $(\\bar{d} \\gamma_\\mu P_R d) (\\bar{\\ell} \\gamma^\\mu P_R \\ell)$ | *E*<sub>*R**R*</sub><sup>*V*</sup> |
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| OddllVRR | $`(\bar{d} \gamma_\mu P_R d) (\bar{\ell} \gamma^\mu P_R \ell)`$ | *E*<sub>*R**R*</sub><sup>*V*</sup> |
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| OddvvVRR | (*d̄**γ*<sub>*μ*</sub>*P*<sub>*R*</sub>*d*)(*ν̄**γ*<sup>*μ*</sup>*P*<sub>*R*</sub>*ν*) | *F*<sub>*R**R*</sub><sup>*V*</sup> |
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| OddllVLR | $(\\bar{d} \\gamma_\\mu P_L d) (\\bar{\\ell} \\gamma^\\mu P_R \\ell)$ | *E*<sub>*L**R*</sub><sup>*V*</sup> |
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| OddllVLR | $`(\bar{d} \gamma_\mu P_L d) (\bar{\ell} \gamma^\mu P_R \ell)`$ | *E*<sub>*L**R*</sub><sup>*V*</sup> |
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| OddvvVLR | (*d̄**γ*<sub>*μ*</sub>*P*<sub>*L*</sub>*d*)(*ν̄**γ*<sup>*μ*</sup>*P*<sub>*R*</sub>*ν*) | *F*<sub>*L**R*</sub><sup>*V*</sup> |
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| OddllVRL | $(\\bar{d} \\gamma_\\mu P_R d) (\\bar{\\ell} \\gamma^\\mu P_L \\ell)$ | *E*<sub>*R**L*</sub><sup>*V*</sup> |
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| OddllVRL | $`(\bar{d} \gamma_\mu P_R d) (\bar{\ell} \gamma^\mu P_L \ell)`$ | *E*<sub>*R**L*</sub><sup>*V*</sup> |
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| OddvvVRL | (*d̄**γ*<sub>*μ*</sub>*P*<sub>*R*</sub>*d*)(*ν̄**γ*<sup>*μ*</sup>*P*<sub>*L*</sub>*ν*) | *F*<sub>*R**L*</sub><sup>*V*</sup> |
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| OddllTLL | $(\\bar{d} \\sigma_{\\mu\\nu} P_L d) (\\bar{\\ell} \\sigma^{\\mu\\nu} P_L \\ell)$ | *E*<sub>*L**L*</sub><sup>*T*</sup> |
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| OddllTRR | $(\\bar{d} \\sigma_{\\mu\\nu} P_R d) (\\bar{\\ell} \\sigma^{\\mu\\nu} P_R \\ell)$ | *E*<sub>*R**R*</sub><sup>*T*</sup> |
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| OddllTLR | $(\\bar{d} \\sigma_{\\mu\\nu} P_L d) (\\bar{\\ell} \\sigma^{\\mu\\nu} P_R \\ell)$ | *E*<sub>*L**R*</sub><sup>*T*</sup> |
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| OddllTRL | $(\\bar{d} \\sigma_{\\mu\\nu} P_R d) (\\bar{\\ell} \\sigma^{\\mu\\nu} P_L \\ell)$ | *E*<sub>*R**L*</sub><sup>*T*</sup> |
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| OddllTLL | $`(\bar{d} \sigma_{\mu\nu} P_L d) (\bar{\ell} \sigma^{\mu\nu} P_L \ell)`$ | *E*<sub>*L**L*</sub><sup>*T*</sup> |
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| OddllTRR | $`(\bar{d} \sigma_{\mu\nu} P_R d) (\bar{\ell} \sigma^{\mu\nu} P_R \ell)`$ | *E*<sub>*R**R*</sub><sup>*T*</sup> |
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| OddllTLR | $`(\bar{d} \sigma_{\mu\nu} P_L d) (\bar{\ell} \sigma^{\mu\nu} P_R \ell)`$ | *E*<sub>*L**R*</sub><sup>*T*</sup> |
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| OddllTRL | $`(\bar{d} \sigma_{\mu\nu} P_R d) (\bar{\ell} \sigma^{\mu\nu} P_L \ell)`$ | *E*<sub>*R**L*</sub><sup>*T*</sup> |
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These operators are derived by PreSARAH with the following input files
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... | ... | @@ -451,34 +431,34 @@ These operators are derived by PreSARAH with the following input files |
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{OddvvVLR,Op[6,Lor[1]].Op[7,Lor[1]]}
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};
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$(\\bar{\\ell} \\Gamma \\ell) (\\bar{d} \\Gamma^\\prime d)$ and$(\\bar{\\ell} \\Gamma \\ell) (\\bar{u} \\Gamma^\\prime u)$
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$`(\bar{\ell} \Gamma \ell) (\bar{d} \Gamma^\prime d)`$ and$`(\bar{\ell} \Gamma \ell) (\bar{u} \Gamma^\prime u)`$
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| Variable | Operator | Name |
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|----------|--------------------------------------------------------------------------------------|------------------------------------|
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| OllddSLL | $(\\bar{\\ell} P_L \\ell) (\\bar{d} P_L d)$ | *B*<sub>*L**L*</sub><sup>*S*</sup> |
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| OlluuSLL | $(\\bar{\\ell} P_L \\ell) (\\bar{u} P_L u)$ | *C*<sub>*L**L*</sub><sup>*S*</sup> |
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| OllddSRR | $(\\bar{\\ell} P_R \\ell) (\\bar{d} P_R d)$ | *B*<sub>*R**R*</sub><sup>*S*</sup> |
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| OlluuSRR | $(\\bar{\\ell} P_R \\ell) (\\bar{u} P_R u)$ | *C*<sub>*R**R*</sub><sup>*S*</sup> |
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| OllddSRL | $(\\bar{\\ell} P_R \\ell) (\\bar{d} P_L d)$ | *B*<sub>*R**L*</sub><sup>*S*</sup> |
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| OlluuSRL | $(\\bar{\\ell} P_R \\ell) (\\bar{u} P_L u)$ | *C*<sub>*R**L*</sub><sup>*S*</sup> |
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| OllddSLR | $(\\bar{\\ell} P_L \\ell) (\\bar{d} P_R d)$ | *B*<sub>*L**R*</sub><sup>*S*</sup> |
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| OlluuSLR | $(\\bar{\\ell} P_L \\ell) (\\bar{u} P_R u)$ | *C*<sub>*L**R*</sub><sup>*S*</sup> |
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| OllddVLL | $(\\bar{\\ell} \\gamma_\\mu P_L \\ell) (\\bar{d} \\gamma^\\mu P_L d)$ | *B*<sub>*L**L*</sub><sup>*V*</sup> |
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| OlluuVLL | $(\\bar{\\ell} \\gamma_\\mu P_L \\ell) (\\bar{u} \\gamma^\\mu P_L u)$ | *C*<sub>*L**L*</sub><sup>*V*</sup> |
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| OllddVRR | $(\\bar{\\ell} \\gamma_\\mu P_R \\ell) (\\bar{d} \\gamma^\\mu P_R d)$ | *B*<sub>*R**R*</sub><sup>*V*</sup> |
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| OlluuVRR | $(\\bar{\\ell} \\gamma_\\mu P_R \\ell) (\\bar{u} \\gamma^\\mu P_R u)$ | *C*<sub>*R**R*</sub><sup>*V*</sup> |
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| OllddVLR | $(\\bar{\\ell} \\gamma_\\mu P_L \\ell) (\\bar{d} \\gamma^\\mu P_R d)$ | *B*<sub>*L**R*</sub><sup>*V*</sup> |
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| OlluuVLR | $(\\bar{\\ell} \\gamma_\\mu P_L \\ell) (\\bar{u} \\gamma^\\mu P_R u)$ | *C*<sub>*L**R*</sub><sup>*V*</sup> |
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| OllddVRL | $(\\bar{\\ell} \\gamma_\\mu P_R \\ell) (\\bar{d} \\gamma^\\mu P_L d)$ | *B*<sub>*R**L*</sub><sup>*V*</sup> |
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| OlluuVRL | $(\\bar{\\ell} \\gamma_\\mu P_R \\ell) (\\bar{u} \\gamma^\\mu P_L u)$ | *C*<sub>*R**L*</sub><sup>*V*</sup> |
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| OllddTLL | $(\\bar{\\ell} \\sigma_{\\mu\\nu} P_L \\ell) (\\bar{d} \\sigma^{\\mu\\nu} P_L d)$ | *B*<sub>*L**L*</sub><sup>*T*</sup> |
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| OlluuTLL | $(\\bar{\\ell} \\sigma_{\\mu\\nu} P_L \\ell) (\\bar{u} \\sigma^{\\mu\\nu} P_L u)$ | *C*<sub>*L**L*</sub><sup>*T*</sup> |
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| OllddTRR | $(\\bar{\\ell} \\sigma_{\\mu\\nu} P_R \\ell) (\\bar{d} \\sigma^{\\mu\\nu} P_R d)$ | *B*<sub>*R**R*</sub><sup>*T*</sup> |
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| OlluuTRR | $(\\bar{\\ell} \\sigma_{\\mu\\nu} P_R \\ell) (\\bar{u} \\sigma^{\\mu\\nu} P_R u)$ | *C*<sub>*R**R*</sub><sup>*T*</sup> |
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| OllddTLR | $(\\bar{\\ell} \\sigma_{\\mu\\nu} P_L \\ell) (\\bar{d} \\sigma^{\\mu\\nu} P_R d)$ | *B*<sub>*L**R*</sub><sup>*T*</sup> |
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| OlluuTLR | $(\\bar{\\ell} \\sigma_{\\mu\\nu} P_L \\ell) (\\bar{u} \\sigma^{\\mu\\nu} P_R u)$ | *C*<sub>*L**R*</sub><sup>*T*</sup> |
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| OllddTRL | $(\\bar{\\ell} \\sigma_{\\mu\\nu} P_R \\ell) (\\bar{d} \\sigma^{\\mu\\nu} P_L d)$ | *B*<sub>*R**L*</sub><sup>*T*</sup> |
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| OlluuTRL | $(\\bar{\\ell} \\sigma_{\\mu\\nu} P_R \\ell) (\\bar{u} \\sigma^{\\mu\\nu} P_L u)$ | *C*<sub>*R**L*</sub><sup>*T*</sup> |
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| OllddSLL | $`(\bar{\ell} P_L \ell) (\bar{d} P_L d)`$ | *B*<sub>*L**L*</sub><sup>*S*</sup> |
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| OlluuSLL | $`(\bar{\ell} P_L \ell) (\bar{u} P_L u)`$ | *C*<sub>*L**L*</sub><sup>*S*</sup> |
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| OllddSRR | $`(\bar{\ell} P_R \ell) (\bar{d} P_R d)`$ | *B*<sub>*R**R*</sub><sup>*S*</sup> |
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| OlluuSRR | $`(\bar{\ell} P_R \ell) (\bar{u} P_R u)`$ | *C*<sub>*R**R*</sub><sup>*S*</sup> |
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| OllddSRL | $`(\bar{\ell} P_R \ell) (\bar{d} P_L d)`$ | *B*<sub>*R**L*</sub><sup>*S*</sup> |
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| OlluuSRL | $`(\bar{\ell} P_R \ell) (\bar{u} P_L u)`$ | *C*<sub>*R**L*</sub><sup>*S*</sup> |
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| OllddSLR | $`(\bar{\ell} P_L \ell) (\bar{d} P_R d)`$ | *B*<sub>*L**R*</sub><sup>*S*</sup> |
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| OlluuSLR | $`(\bar{\ell} P_L \ell) (\bar{u} P_R u)`$ | *C*<sub>*L**R*</sub><sup>*S*</sup> |
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| OllddVLL | $`(\bar{\ell} \gamma_\mu P_L \ell) (\bar{d} \gamma^\mu P_L d)`$ | *B*<sub>*L**L*</sub><sup>*V*</sup> |
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| OlluuVLL | $`(\bar{\ell} \gamma_\mu P_L \ell) (\bar{u} \gamma^\mu P_L u)`$ | *C*<sub>*L**L*</sub><sup>*V*</sup> |
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| OllddVRR | $`(\bar{\ell} \gamma_\mu P_R \ell) (\bar{d} \gamma^\mu P_R d)`$ | *B*<sub>*R**R*</sub><sup>*V*</sup> |
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| OlluuVRR | $`(\bar{\ell} \gamma_\mu P_R \ell) (\bar{u} \gamma^\mu P_R u)`$ | *C*<sub>*R**R*</sub><sup>*V*</sup> |
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| OllddVLR | $`(\bar{\ell} \gamma_\mu P_L \ell) (\bar{d} \gamma^\mu P_R d)`$ | *B*<sub>*L**R*</sub><sup>*V*</sup> |
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| OlluuVLR | $`(\bar{\ell} \gamma_\mu P_L \ell) (\bar{u} \gamma^\mu P_R u)`$ | *C*<sub>*L**R*</sub><sup>*V*</sup> |
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| OllddVRL | $`(\bar{\ell} \gamma_\mu P_R \ell) (\bar{d} \gamma^\mu P_L d)`$ | *B*<sub>*R**L*</sub><sup>*V*</sup> |
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| OlluuVRL | $`(\bar{\ell} \gamma_\mu P_R \ell) (\bar{u} \gamma^\mu P_L u)`$ | *C*<sub>*R**L*</sub><sup>*V*</sup> |
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| OllddTLL | $`(\bar{\ell} \sigma_{\mu\nu} P_L \ell) (\bar{d} \sigma^{\mu\nu} P_L d)`$ | *B*<sub>*L**L*</sub><sup>*T*</sup> |
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| OlluuTLL | $`(\bar{\ell} \sigma_{\mu\nu} P_L \ell) (\bar{u} \sigma^{\mu\nu} P_L u)`$ | *C*<sub>*L**L*</sub><sup>*T*</sup> |
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| OllddTRR | $`(\bar{\ell} \sigma_{\mu\nu} P_R \ell) (\bar{d} \sigma^{\mu\nu} P_R d)`$ | *B*<sub>*R**R*</sub><sup>*T*</sup> |
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| OlluuTRR | $`(\bar{\ell} \sigma_{\mu\nu} P_R \ell) (\bar{u} \sigma^{\mu\nu} P_R u)`$ | *C*<sub>*R**R*</sub><sup>*T*</sup> |
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| OllddTLR | $`(\bar{\ell} \sigma_{\mu\nu} P_L \ell) (\bar{d} \sigma^{\mu\nu} P_R d)`$ | *B*<sub>*L**R*</sub><sup>*T*</sup> |
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| OlluuTLR | $`(\bar{\ell} \sigma_{\mu\nu} P_L \ell) (\bar{u} \sigma^{\mu\nu} P_R u)`$ | *C*<sub>*L**R*</sub><sup>*T*</sup> |
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| OllddTRL | $`(\bar{\ell} \sigma_{\mu\nu} P_R \ell) (\bar{d} \sigma^{\mu\nu} P_L d)`$ | *B*<sub>*R**L*</sub><sup>*T*</sup> |
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| OlluuTRL | $`(\bar{\ell} \sigma_{\mu\nu} P_R \ell) (\bar{u} \sigma^{\mu\nu} P_L u)`$ | *C*<sub>*R**L*</sub><sup>*T*</sup> |
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NameProcess="2L2d";
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... | ... | @@ -536,34 +516,34 @@ $(\\bar{\\ell} \\Gamma \\ell) (\\bar{d} \\Gamma^\\prime d)$ and$(\\bar{\\ell} \\ |
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{OlluuTRR,Op[-6,Lor[1],Lor[2]].Op[-6,Lor[1],Lor[2]]}
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};
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(*d̄**Γ**d*)(*d̄**Γ*<sup>′</sup>*d*) and$(\\bar{\\ell} \\Gamma \\ell) (\\bar{\\ell} \\Gamma^\\prime \\ell)$
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(*d̄**Γ**d*)(*d̄**Γ*<sup>′</sup>*d*) and$`(\bar{\ell} \Gamma \ell) (\bar{\ell} \Gamma^\prime \ell)`$
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| Variable | Operator | Name |
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|----------|----------------------------------------------------------------------------------------------|------------------------------------|
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| O4dSLL | (*d̄**P*<sub>*L*</sub>*d*)(*d̄**P*<sub>*L*</sub>*d*) | *D*<sub>*L**L*</sub><sup>*S*</sup> |
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| O4lSLL | $(\\bar{\\ell} P_L \\ell) (\\bar{\\ell} P_L \\ell)$ | *A*<sub>*L**L*</sub><sup>*S*</sup> |
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| O4lSLL | $`(\bar{\ell} P_L \ell) (\bar{\ell} P_L \ell)`$ | *A*<sub>*L**L*</sub><sup>*S*</sup> |
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| O4dSRR | (*d̄**P*<sub>*R*</sub>*d*)(*d̄**P*<sub>*R*</sub>*d*) | *D*<sub>*R**R*</sub><sup>*S*</sup> |
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| O4lSRR | $(\\bar{\\ell} P_R \\ell) (\\bar{\\ell} P_R \\ell)$ | *A*<sub>*R**R*</sub><sup>*S*</sup> |
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| O4lSRR | $`(\bar{\ell} P_R \ell) (\bar{\ell} P_R \ell)`$ | *A*<sub>*R**R*</sub><sup>*S*</sup> |
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| O4dSLR | (*d̄**P*<sub>*L*</sub>*d*)(*d̄**P*<sub>*R*</sub>*d*) | *D*<sub>*L**R*</sub><sup>*S*</sup> |
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| O4lSLR | $(\\bar{\\ell} P_L \\ell) (\\bar{\\ell} P_R \\ell)$ | *A*<sub>*L**R*</sub><sup>*S*</sup> |
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| O4lSLR | $`(\bar{\ell} P_L \ell) (\bar{\ell} P_R \ell)`$ | *A*<sub>*L**R*</sub><sup>*S*</sup> |
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| O4dSRL | (*d̄**P*<sub>*R*</sub>*d*)(*d̄**P*<sub>*L*</sub>*d*) | *D*<sub>*R**L*</sub><sup>*S*</sup> |
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| O4lSRL | $(\\bar{\\ell} P_R \\ell) (\\bar{\\ell} P_L \\ell)$ | *A*<sub>*R**L*</sub><sup>*S*</sup> |
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| O4lSRL | $`(\bar{\ell} P_R \ell) (\bar{\ell} P_L \ell)`$ | *A*<sub>*R**L*</sub><sup>*S*</sup> |
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| O4dVLL | (*d̄**γ*<sub>*μ*</sub>*P*<sub>*L*</sub>*d*)(*d̄**γ*<sup>*μ*</sup>*P*<sub>*L*</sub>*d*) | *D*<sub>*L**L*</sub><sup>*V*</sup> |
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| O4lVLL | $(\\bar{\\ell} \\gamma_\\mu P_L \\ell) (\\bar{\\ell} \\gamma^\\mu P_L \\ell)$ | *A*<sub>*L**L*</sub><sup>*V*</sup> |
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| O4lVLL | $`(\bar{\ell} \gamma_\mu P_L \ell) (\bar{\ell} \gamma^\mu P_L \ell)`$ | *A*<sub>*L**L*</sub><sup>*V*</sup> |
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| O4dVRR | (*d̄**γ*<sub>*μ*</sub>*P*<sub>*R*</sub>*d*)(*d̄**γ*<sup>*μ*</sup>*P*<sub>*R*</sub>*d*) | *D*<sub>*R**R*</sub><sup>*V*</sup> |
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| O4lVRR | $(\\bar{\\ell} \\gamma_\\mu P_R \\ell) (\\bar{\\ell} \\gamma^\\mu P_R \\ell)$ | *A*<sub>*R**R*</sub><sup>*V*</sup> |
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| O4lVRR | $`(\bar{\ell} \gamma_\mu P_R \ell) (\bar{\ell} \gamma^\mu P_R \ell)`$ | *A*<sub>*R**R*</sub><sup>*V*</sup> |
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| O4dVLR | (*d̄**γ*<sub>*μ*</sub>*P*<sub>*L*</sub>*d*)(*d̄**γ*<sup>*μ*</sup>*P*<sub>*R*</sub>*d*) | *D*<sub>*L**R*</sub><sup>*V*</sup> |
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| O4lVLR | $(\\bar{\\ell} \\gamma_\\mu P_L \\ell) (\\bar{\\ell} \\gamma^\\mu P_R \\ell)$ | *A*<sub>*L**R*</sub><sup>*V*</sup> |
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| O4lVLR | $`(\bar{\ell} \gamma_\mu P_L \ell) (\bar{\ell} \gamma^\mu P_R \ell)`$ | *A*<sub>*L**R*</sub><sup>*V*</sup> |
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| O4dVRL | (*d̄**γ*<sub>*μ*</sub>*P*<sub>*R*</sub>*d*)(*d̄**γ*<sup>*μ*</sup>*P*<sub>*L*</sub>*d*) | *D*<sub>*R**L*</sub><sup>*V*</sup> |
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| O4lVRL | $(\\bar{\\ell} \\gamma_\\mu P_R \\ell) (\\bar{\\ell} \\gamma^\\mu P_L \\ell)$ | *A*<sub>*R**L*</sub><sup>*V*</sup> |
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| O4lVRL | $`(\bar{\ell} \gamma_\mu P_R \ell) (\bar{\ell} \gamma^\mu P_L \ell)`$ | *A*<sub>*R**L*</sub><sup>*V*</sup> |
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| O4dTLL | (*d̄**σ*<sub>*μ**ν*</sub>*P*<sub>*L*</sub>*d*)(*d̄**σ*<sup>*μ**ν*</sup>*P*<sub>*L*</sub>*d*) | *D*<sub>*L**L*</sub><sup>*T*</sup> |
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| O4lTLL | $(\\bar{\\ell} \\sigma_{\\mu\\nu} P_L \\ell) (\\bar{\\ell} \\sigma^{\\mu\\nu} P_L \\ell)$ | *A*<sub>*L**L*</sub><sup>*T*</sup> |
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| O4lTLL | $`(\bar{\ell} \sigma_{\mu\nu} P_L \ell) (\bar{\ell} \sigma^{\mu\nu} P_L \ell)`$ | *A*<sub>*L**L*</sub><sup>*T*</sup> |
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| O4dTRR | (*d̄**σ*<sub>*μ**ν*</sub>*P*<sub>*R*</sub>*d*)(*d̄**σ*<sup>*μ**ν*</sup>*P*<sub>*R*</sub>*d*) | *D*<sub>*R**R*</sub><sup>*T*</sup> |
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| O4lTRR | $(\\bar{\\ell} \\sigma_{\\mu\\nu} P_R \\ell) (\\bar{\\ell} \\sigma^{\\mu\\nu} P_R \\ell)$ | *A*<sub>*R**R*</sub><sup>*T*</sup> |
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| O4lTRR | $`(\bar{\ell} \sigma_{\mu\nu} P_R \ell) (\bar{\ell} \sigma^{\mu\nu} P_R \ell)`$ | *A*<sub>*R**R*</sub><sup>*T*</sup> |
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| O4dTLR | (*d̄**σ*<sub>*μ**ν*</sub>*P*<sub>*L*</sub>*d*)(*d̄**σ*<sup>*μ**ν*</sup>*P*<sub>*R*</sub>*d*) | *D*<sub>*L**R*</sub><sup>*T*</sup> |
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| O4lTLR | $(\\bar{\\ell} \\sigma_{\\mu\\nu} P_L \\ell) (\\bar{\\ell} \\sigma^{\\mu\\nu} P_R \\ell)$ | *A*<sub>*L**R*</sub><sup>*T*</sup> |
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| O4lTLR | $`(\bar{\ell} \sigma_{\mu\nu} P_L \ell) (\bar{\ell} \sigma^{\mu\nu} P_R \ell)`$ | *A*<sub>*L**R*</sub><sup>*T*</sup> |
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| O4dTRL | (*d̄**σ*<sub>*μ**ν*</sub>*P*<sub>*R*</sub>*d*)(*d̄**σ*<sup>*μ**ν*</sup>*P*<sub>*L*</sub>*d*) | *D*<sub>*R**L*</sub><sup>*T*</sup> |
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| O4lTRL | $(\\bar{\\ell} \\sigma_{\\mu\\nu} P_R \\ell) (\\bar{\\ell} \\sigma^{\\mu\\nu} P_L \\ell)$ | *A*<sub>*R**L*</sub><sup>*T*</sup> |
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| O4lTRL | $`(\bar{\ell} \sigma_{\mu\nu} P_R \ell) (\bar{\ell} \sigma^{\mu\nu} P_L \ell)`$ | *A*<sub>*R**L*</sub><sup>*T*</sup> |
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NameProcess="4d";
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... | ... | @@ -625,18 +605,18 @@ $(\\bar{\\ell} \\Gamma \\ell) (\\bar{d} \\Gamma^\\prime d)$ and$(\\bar{\\ell} \\ |
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Filters = {NoCrossedDiagrams};
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$(\\bar{d} \\Gamma u) (\\bar{\\ell} \\Gamma^\\prime \\nu)$
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$`(\bar{d} \Gamma u) (\bar{\ell} \Gamma^\prime \nu)`$
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| Variable | Operator | Name |
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|----------|-------------------------------------------------------------------------|------------------------------------|
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| OdulvVLL | $(\\bar{d} \\gamma_\\mu P_L u) (\\bar{\\ell} \\gamma^\\mu P_L \\nu)$ | *G*<sub>*L**L*</sub><sup>*V*</sup> |
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| OdulvSLL | $(\\bar{d} P_L u) (\\bar{\\ell} P_L \\nu)$ | *G*<sub>*L**L*</sub><sup>*S*</sup> |
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| OdulvVRR | $(\\bar{d} \\gamma_\\mu P_R u) (\\bar{\\ell} \\gamma^\\mu P_R \\nu)$ | *G*<sub>*R**R*</sub><sup>*V*</sup> |
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| OdulvSRR | $(\\bar{d} P_R u) (\\bar{\\ell} P_R \\nu)$ | *G*<sub>*R**R*</sub><sup>*S*</sup> |
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| OdulvVLR | $(\\bar{d} \\gamma_\\mu P_L u) (\\bar{\\ell} \\gamma^\\mu P_R \\nu)$ | *G*<sub>*L**R*</sub><sup>*V*</sup> |
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| OdulvSLR | $(\\bar{d} P_L u) (\\bar{\\ell} P_R \\nu)$ | *G*<sub>*L**R*</sub><sup>*S*</sup> |
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| OdulvVRL | $(\\bar{d} \\gamma_\\mu P_R u) (\\bar{\\ell} \\gamma^\\mu P_L \\nu)$ | *G*<sub>*R**L*</sub><sup>*V*</sup> |
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| OdulvSRL | $(\\bar{d} P_R u) (\\bar{\\ell} P_L \\nu)$ | *G*<sub>*R**L*</sub><sup>*S*</sup> |
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| OdulvVLL | $`(\bar{d} \gamma_\mu P_L u) (\bar{\ell} \gamma^\mu P_L \nu)`$ | *G*<sub>*L**L*</sub><sup>*V*</sup> |
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| OdulvSLL | $`(\bar{d} P_L u) (\bar{\ell} P_L \nu)`$ | *G*<sub>*L**L*</sub><sup>*S*</sup> |
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| OdulvVRR | $`(\bar{d} \gamma_\mu P_R u) (\bar{\ell} \gamma^\mu P_R \nu)`$ | *G*<sub>*R**R*</sub><sup>*V*</sup> |
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| OdulvSRR | $`(\bar{d} P_R u) (\bar{\ell} P_R \nu)`$ | *G*<sub>*R**R*</sub><sup>*S*</sup> |
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| OdulvVLR | $`(\bar{d} \gamma_\mu P_L u) (\bar{\ell} \gamma^\mu P_R \nu)`$ | *G*<sub>*L**R*</sub><sup>*V*</sup> |
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| OdulvSLR | $`(\bar{d} P_L u) (\bar{\ell} P_R \nu)`$ | *G*<sub>*L**R*</sub><sup>*S*</sup> |
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| OdulvVRL | $`(\bar{d} \gamma_\mu P_R u) (\bar{\ell} \gamma^\mu P_L \nu)`$ | *G*<sub>*R**L*</sub><sup>*V*</sup> |
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| OdulvSRL | $`(\bar{d} P_R u) (\bar{\ell} P_L \nu)`$ | *G*<sub>*R**L*</sub><sup>*S*</sup> |
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NameProcess="dulv";
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... | ... | |