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Typus
KomplettPlagiat
Bearbeiter
Graf Isolan
Gesichtet
No.png
Untersuchte Arbeit:
Seite: 17, Zeilen: 1ff. (komplett)
Quelle: Niegel 2009
Seite(n): 25-26, Zeilen: 25:29-32 - 26:1-22
Neutralinos and Charginos

Neutralinos and Charginos are the mass eigenstates of the neutral and charged fields, respectively. Their mass eigenstates are mixed states of gauginos and higgsinos:

\chi = \left(\begin{array}{c}\tilde B\\ \tilde W^3\\ \tilde H^0_d\\ \tilde H^0_u\end{array} \right)\quad , \quad \psi =\left(\begin{array}{c}\tilde W^+\\ \tilde H^+\end{array} \right)\quad , \quad\quad (2.35)

where χ and Ψ are the Majorana neutralino and Dirac chargino fields, respectively.

The corresponding neutralino mass matrix can be written as:


\begin{array}{c}
M^{(0)}
\end{array}
=
\left(
\begin{array}{cccc}
M_1 & 0 & -M_Z \cos \beta \sin \theta_W& M_Z \sin \beta \sin \theta_W\\
0 & M_2 &  M_Z \cos \beta \cos \theta_W& -M_Z \sin \beta \cos \theta_W\\
-M_Z \cos \beta \sin \theta_W& M_Z \cos \beta \cos \theta_W  & 0 & -\mu\\
M_Z \sin \beta \sin \theta_W& -M_Z \sin \beta \cos \theta_W & -\mu & 0
\end{array}
\right)
\quad (2.36)

with the gaugino masses M1, M2, the weak mixing angle θW and tan β, the ratio of two Higgs vacuum expectation values. The physical masses of the neutralinos are given by the eigenvalues of this matrix. The neutralino mass eigenstates are denoted as \begin{array}{c}\chi^0_1\end{array}, \begin{array}{c}\chi^0_2\end{array}, \begin{array}{c}\chi^0_3\end{array}, \begin{array}{c}\chi^0_4\end{array} with \begin{array}{c}m_{\chi_1^0}\end{array}\le \begin{array}{c}m_{\chi_2^0}\end{array}\le \begin{array}{c}m_{\chi_3^0}\le \begin{array}{c}m_{\chi_4^0}.\end{array}\end{array}

The mass matrix for the charginos is given by:


\begin{array}{c}
M^{(c)}
\end{array}
=
\left(
\begin{array}{cc}
M_2 & \sqrt{2} M_W \sin \beta \\
\sqrt{2} M_W \cos \beta & \mu
\end{array}
\right ),
\quad (2.37)

which leads to two chargino eigenstates \begin{array}{c}m_{\chi^\pm_{1,2}}\end{array} with the mass eigenvalues


\begin{array}{rl}
m_{\chi^\pm_{1,2}}^2 = & \frac{1}{2} M_2^2 + \frac{1}{2} \mu^2 + \frac{1}{2} M_W^2 \\
& \mp \frac{1}{2} \sqrt{(M_2^2 - \mu^2)^2 + 4 M_W^4 \cos^2 2\beta + 4 M_W^2 (M_2^2 + \mu^2 + 2 M_2 \mu \sin 2\beta)}
\end{array}. \quad (2.38)

The gluino is the only color octet fermion. Since SU(3) is unbroken, the gluino does not mix with other MSSM particles. The mass of the physical particle is defined by the gaugino mass parameter 
\begin{array}{c}
m_{\tilde g} \equiv M_3.
\end{array}

Approximately, the gaugino mass parameters at the electroweak scale are:


\begin{array}{lcll}
M_3 & \simeq & 2.7 m_{1/2} & \quad\quad (2.39) \\
M_2 & \simeq & 0.8 m_{1/2} & \quad\quad (2.40) \\
M_1 & \simeq & 0.4 m_{1/2} & \quad\quad (2.41) 
\end{array}

The physical masses of the neutralinos are obtained by diagonalizing the mass matrix Eq. 2.36. In the mSUGRA model, the lightest neutralino is dominantly bino-like [and the next-to-lightest neutralino is mostly wino-like, with masses close to M1 and M2, respectively.]

[Seite 25]

Neutralinos and Charginos

Neutralinos and Charginos are the mass eigenstates of the neutral and charged fields, respectively. Their mass eigenstates are mixed states of gauginos and higgsinos:

\chi = \left(\begin{array}{c}\tilde B\\ \tilde W^3\\ \tilde H^0_1\\ \tilde H^0_2\end{array} \right)\quad , \psi =\left(\begin{array}{c}\tilde W^+\\ \tilde H^+\end{array} \right)\quad , \quad\quad (2.64)

[Seite 26]

where χ and Ψ are the Majorana neutralino and Dirac chargino fields, respectively.

The corresponding neutralino mass matrix reads as:


\begin{array}{c}
M^{(0)}
\end{array}
=
\left(
\begin{array}{cccc}
M_1 & 0 & -M_Z \cos \beta \sin \theta_W& M_Z \sin \beta \sin \theta_W\\
0 & M_2 &  M_Z \cos \beta \cos \theta_W& -M_Z \sin \beta \cos \theta_W\\
-M_Z \cos \beta \sin \theta_W& M_Z \cos \beta \cos \theta_W  & 0 & -\mu\\
M_Z \sin \beta \sin \theta_W& -M_Z \sin \beta \cos \theta_W & -\mu & 0
\end{array}
\right)
\quad (2.65)

with the gaugino masses M1, M2, the weak mixing angle θW and tan β, the ratio of two Higgs vacuum expectation values. The physical masses of the neutralinos are given by the eigenvalues of this matrix. The neutralino mass eigenstates are denoted as \begin{array}{c}\chi^0_1\end{array}, \begin{array}{c}\chi^0_2\end{array}, \begin{array}{c}\chi^0_3\end{array}, \begin{array}{c}\chi^0_4\end{array} with \begin{array}{c}m_{\chi_1^0}\end{array}\le \begin{array}{c}m_{\chi_2^0}\end{array}\le \begin{array}{c}m_{\chi_3^0}\le \begin{array}{c}m_{\chi_4^0}.\end{array}\end{array}

The mass matrix for the charginos given by:


\begin{array}{c}
M^{(c)}
\end{array}
=
\left(
\begin{array}{cc}
M_2 & \sqrt{2} M_W \sin \beta \\
\sqrt{2} M_W \cos \beta & \mu
\end{array}
\right )
\quad (2.66)

leads to two chargino eigenstates \begin{array}{c}m_{\chi^\pm_{1,2}}\end{array} with the mass eigenvalues


\begin{array}{rl}
m_{\chi^\pm_{1,2}}^2 = & \frac{1}{2} M_2^2 + \frac{1}{2} \mu^2 + \frac{1}{2} M_W^2 \\
& \mp \frac{1}{2} \sqrt{(M_2^2 - \mu^2)^2 + 4 M_W^4 \cos^2 2\beta + 4 M_W^2 (M_2^2 + \mu^2 + 2 M_2 \mu \sin 2\beta)}
\end{array}. \quad (2.67)

The gluino is the only color octet fermion. Since the SU(3) is unbroken, the gluino does not mix with other MSSM particles. The mass of the physical particle is defined by the gaugino mass parameter 
\begin{array}{c}
m_{\tilde g} \equiv M_3.
\end{array}

Approximately, the gaugino mass parameters at the electroweak scale are:


\begin{array}{lcll}
M_3 & \simeq & 2.7 m_{1/2} & \quad\quad (2.68) \\
M_2 & \simeq & 0.8 m_{1/2} & \quad\quad (2.69) \\
M_1 & \simeq & 0.4 m_{1/2} & \quad\quad (2.70) 
\end{array}

The physical masses of the neutralinos are obtained by diagonalizing the mass matrix Eq. 2.65. In the mSUGRA model, the lightest neutralino is dominantly bino-like and the next-to-lightest neutralino is mostly wino-like, with masses close to M1 and M2, respectively.

Anmerkungen

Identisch; ohne Hinweis auf eine Übernahme.

Sichter
(Graf Isolan)

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