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Next: 3.4.5 -Parity Violation Up: 3.4 Other Scenarios Previous: 3.4.3 Gauge Mediated Supersymmetry

3.4.4 Anomaly Mediated Supersymmetry Breaking

Anomaly mediation is a special case of gravity mediation where there is no direct tree level coupling that transmits the SUSY breaking in the hidden sector to the observable one. In this case the masses of the gauginos are generated at one-loop, while those of the scalars are generated at two-loop level, because of the superconformal anomaly that breaks scale invariance[6,7]. Since the anomaly is topological in origin, it naturally conserves flavor, thereby inducing no new FCNC amplitudes. AMSB models thus preserve virtues of the gravity-mediated models with the FCNC problem resolved. The scale invariant one-loop gaugino mass expressions are

Mi = $\displaystyle b_i \left( \frac{\alpha_i}{4\pi} \right) m_{3/2}
~~=~~ \left( \frac{b_i}{b_2} \right)
\left( \frac{\alpha_i}{\alpha_2} \right),$  

where bi's are related to the one-loop beta functions through $\beta_i = - b_i g_i^3/(4\pi)^2$ and numerically b1 = 33/5, b2 = 1, b3 = -3. In the minimal AMSB model, however, the sleptons become tachyonic, which necessitated, for instance, introduction of a universal scalar mass parameter m02:
$\displaystyle m_{\tilde{f}}^2$ = $\displaystyle C_{\tilde{f}} \frac{m_{3/2}^2}{(16\pi^2)^2} + m_0^2
~~=~~ \sum 2a_{\tilde{f},i} b_i
\left( \frac{\alpha_i}{\alpha_2} \right)^2 M_2^2
+ m_0^2,$  

where $a_{\tilde{f},i}$'s are related to the RG functions through $\gamma_{\tilde{f}} = - a_{\tilde{f},i} g_i^2/(4\pi)^2$.

As already stressed in Section 3.2, the first and the most important message from the gaugino mass formula above is the hierarchy:

M1 : M2 : M3 = 2.8 : 1 : 8.3

as opposed to M1 : M2 : M3 = 1 : 2 : 7that is expected for the gravity- or gauge-mediated models. This implies that the lightest neutralino ( ${\tilde{\chi}_1^0}$) and the lighter chargino ( $\tilde{\chi}_{1}^{\pm}$) are almost pure winos and consequently mass-degenerate8. This degeneracy is lifted by the tree-level gaugino-higgsino mixing and loop corrections, resulting in a small but finite mass splitting as depicted in Fig. 3.34 for $\tan\beta = 10, 30$, $\mu >0$, and $m_0 = 450~{\rm GeV}$.
  
Figure 3.34: Mass difference $\Delta M \equiv m_{\tilde{\chi}_1^\pm} - m_{\tilde{\chi}_1^0}$as a function of the gravitino mass for $\tan{\beta}= 10$ (upper curve) and $\tan\beta = 30$ (lower curve), $\mu >0$, and $m_0 = 450~{\rm GeV}$.
\epsfxsize=6cm\epsfbox{physsusy/figs/delm.eps}

The lighter chargino thus decays mostly (96-98 %) into the lightest neutralino and a soft $\pi^\pm$, possibly with a visibly displaced vertex. Ref. [43] discusses search strategies for the chargino pair production: $e^+e^- \to \tilde{\chi}_1^+ \tilde{\chi}_1^- (\gamma)$, where the additional photon will be very useful to suppress the huge two-photon $\pi\pi$ background expected for the $\Delta M$ range shown above, or to tag the chargino pair production when the final-state pions are too soft to be detected. When the decay length is comparable or larger than the detector size, the charginos will appear as heavily ionizing particles as in the case of the slepton LSP in the GMSB models. If the daughter pions are too soft to be detected, one may observe abruptly terminating tracks in the central tracker. Fig. 3.35 summarizes the search methods and corresponding discovery limits shown in the $m_{\tilde{\chi}_{1}^{\pm}}$-$\Delta M$ plane.
  
Figure: 3.35 Viable search modes in different regions in the $m_{\tilde{\chi}_{1}^{\pm}}$-$\Delta M$( $\equiv m_{\tilde{\chi}_1^\pm} - m_{\tilde{\chi}_1^0}$) plane. Discovery reach is given for $50~{\rm fb}^{-1}$ and also for $1~{\rm ab}^{-1}$accumulated at $\sqrt{s} = 600~{\rm GeV}$. The vertical band and vertical line (the band for $50~{\rm fb}^{-1}$ and the line for $1~{\rm ab}^{-1}$) is the reach of the $\gamma+\sla{M}$ detection mode, which is relevant only if the $\pi $'s are too soft to detect[43].
\epsfxsize=7cm\epsfbox{physsusy/figs/mvsdm.eps}

The figure tells us that, with all the methods combined, one can cover the parameter space almost to the kinematical limit.

The scalar mass formula also contains a phenomenologically important message that is the near degeneracy of the left- and right-handed sleptons, which means that left- and right-handed sleptons can be produced simultaneously, with relative rates controlled by the beam polarization. Slepton productions are studied[44,45] in the context of the AMSB models assuming $\sqrt{s} = 1~{\rm TeV}$9.

For instance, let us consider the left-handed selectron pair production: $e^+e^- \to \tilde{e}_L^+ \tilde{e}_L^-$followed by the mixed decays: $\tilde{e}_L^\pm \to e^\pm \tilde{\chi}_1^0$and $\tilde{e}_L^\mp \to \mathop{\nu_e}\limits^{\mbox{\scriptsize$(-)$ }}
\tilde{\chi}_1^\mp$with $\tilde{\chi}_1^\mp$ decaying slowly into $\tilde{\chi}_1^\mp \to \tilde{\chi}_1^0 + \pi^\mp$. This results in a final state: $e^\pm \tilde{\chi}_1^0
\mathop{\nu_e}\limits^{\mbox{\scriptsize$(-)$ }} \tilde{\chi}_1^0 \pi^\mp$. The signal is a fast $e^\pm + \sla{E}_T$ and a soft $\pi^\mp$. The soft $\pi $ can give rise to a visibly displaced vertex, if the decay length of the chargino is less than 3cm. If it is longer than 3cm, then one sees a heavily ionizing track of the chargino as discussed above. Fig. 3.36 shows the effective cross sections after cuts to select the signal events as contours in the m3/2-m0 plane.

  
Figure: 3.36 Effective cross section contours in the m3/2-m0 plane expected for the $e^\pm \tilde{\chi}_1^0
\mathop{\nu_e}\limits^{\mbox{\scriptsize$(-)$ }} \tilde{\chi}_1^0 \pi^\mp$ signal from $e^+e^- \to \tilde{e}_L^+ \tilde{e}_L^-$ at $\sqrt{s} = 1~{\rm TeV}$: (a) $\tan\beta=3$, and (b) $\tan\beta = 30$. The shaded regions are ruled out by various constraints[45].
\epsfxsize=13cm\epsfbox{physsusy/figs/nlcfig6.eps}

Note that the effective cross sections include branching fraction as well as the selection efficiency due to the selection cuts. We can see that large regions, allowed by all the current constraints, have large effective cross sections $\sim 10-100$ fb at $\sqrt {s}$ = 1000 GeV.


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Next: 3.4.5 -Parity Violation Up: 3.4 Other Scenarios Previous: 3.4.3 Gauge Mediated Supersymmetry
ACFA Linear Collider Working Group
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