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andr Z
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- TL;DR Summary
- In the standard model, the mathematical expression for the Higgs decay width is well known. However, in the extended model known as 2HDM (Two Higgs Doublet Model) ,I study type III, there are 5 new fields: two neutral, one pseudo-scalar and two charged. If I want to calculate the decay width for the higgs h, does the mathematical expression only change at the vertices?
In the Standard model the decay width for Higgs into fermion-antifermion pairs is
$$ \Gamma_{fi}=\frac{\mathrm{N}_{C}}{8\pi}\frac{m_{f}^{2}}{\nu^{2}}m_{\mathcal{H}}\left [ 1-\frac{4m_{f}^{2}}{m_{\mathcal{H}}^{2}} \right ]^{3/2}$$
where the vertex of interaction between the Higgs and the fermions is ##-i\frac{m_{f}}{\nu}##
On the other hand, in the 2HDM the Lagrangian that describes the model for the quark sector is
$$
-\mathcal{L}=\overline{\mathrm{U}}M_{U}^{diag}\mathrm{U}+\overline{\mathrm{D}}M_{D}^{diag}\mathrm{D}+\frac{\mathrm{g}}{2M_{\mathrm{W}}}
\left [ \overline{\mathrm{U}}M_{U}^{diag}\mathrm{U}+\overline{\mathrm{D}}M_{D}^{diag}\mathrm{D} \right ]\left ( H^{0}\cos{\alpha}-h^{0}\sin{\alpha} \right )\nonumber\\+\frac{1}{\sqrt{2}}\left [ \overline{\mathrm{U}}\xi^{U}\mathrm{U}+\overline{\mathrm{D}}\xi^{D}\mathrm{D} \right ]\left ( H^{0}\sin{\alpha}+h^{0}\cos{\alpha} \right )+i\frac{1}{\sqrt{2}}A^{0}\left [ \overline{\mathrm{D}}\xi^{D}\gamma_{5}\mathrm{D}-\overline{\mathrm{U}}\xi^{U}\gamma_{5}\mathrm{U} \right ]\nonumber\\+H^{+}\overline{\mathrm{U}}\left [ V\xi^{D}\gamma_{R}-\xi^{U}V\gamma_{L} \right ]\mathrm{D}+\text{Goldstone's interactions}+h.c.
$$
with: ##h^{0},\,H^{0}## (scalars), ##A^{0}## (pseudo-scalar) and ##H^{\pm}## (charged). ##\xi^{U,D}## are flavor change matrices
If i want to calculate the decay width of the higgs then i must use the vertex of interaction for this higgs with the quarks, but I feel like I'm forgetting something.
Following the paper "Flavor Changing Neutral Scalar Currents at μ+μ− Colliders" by David Atwood, Laura Reina and Amarjit Soni the following expressions are reached for the decay width
and it is these expressions that I cannot demonstrate. Could someone tell me how should I proceed?.
Sorry for my terrible english.
$$ \Gamma_{fi}=\frac{\mathrm{N}_{C}}{8\pi}\frac{m_{f}^{2}}{\nu^{2}}m_{\mathcal{H}}\left [ 1-\frac{4m_{f}^{2}}{m_{\mathcal{H}}^{2}} \right ]^{3/2}$$
where the vertex of interaction between the Higgs and the fermions is ##-i\frac{m_{f}}{\nu}##
On the other hand, in the 2HDM the Lagrangian that describes the model for the quark sector is
$$
-\mathcal{L}=\overline{\mathrm{U}}M_{U}^{diag}\mathrm{U}+\overline{\mathrm{D}}M_{D}^{diag}\mathrm{D}+\frac{\mathrm{g}}{2M_{\mathrm{W}}}
\left [ \overline{\mathrm{U}}M_{U}^{diag}\mathrm{U}+\overline{\mathrm{D}}M_{D}^{diag}\mathrm{D} \right ]\left ( H^{0}\cos{\alpha}-h^{0}\sin{\alpha} \right )\nonumber\\+\frac{1}{\sqrt{2}}\left [ \overline{\mathrm{U}}\xi^{U}\mathrm{U}+\overline{\mathrm{D}}\xi^{D}\mathrm{D} \right ]\left ( H^{0}\sin{\alpha}+h^{0}\cos{\alpha} \right )+i\frac{1}{\sqrt{2}}A^{0}\left [ \overline{\mathrm{D}}\xi^{D}\gamma_{5}\mathrm{D}-\overline{\mathrm{U}}\xi^{U}\gamma_{5}\mathrm{U} \right ]\nonumber\\+H^{+}\overline{\mathrm{U}}\left [ V\xi^{D}\gamma_{R}-\xi^{U}V\gamma_{L} \right ]\mathrm{D}+\text{Goldstone's interactions}+h.c.
$$
with: ##h^{0},\,H^{0}## (scalars), ##A^{0}## (pseudo-scalar) and ##H^{\pm}## (charged). ##\xi^{U,D}## are flavor change matrices
If i want to calculate the decay width of the higgs then i must use the vertex of interaction for this higgs with the quarks, but I feel like I'm forgetting something.
Following the paper "Flavor Changing Neutral Scalar Currents at μ+μ− Colliders" by David Atwood, Laura Reina and Amarjit Soni the following expressions are reached for the decay width
and it is these expressions that I cannot demonstrate. Could someone tell me how should I proceed?.
Sorry for my terrible english.