[Paper Review] Impact of CP phases on the search for top and bottom squarks

A. Bartl, S. Hesselbach+3 more|ArXiv.org|Sep 29, 2004

Marine and Offshore Engineering Studies3 citations

TL;DR

This paper investigates how complex CP-violating phases in the MSSM—specifically in the trilinear couplings $A_t$, $A_b$, and the Higgsino mass parameter $μ$, along with the U(1) gaugino mass $M_1$—significantly alter the decay branching ratios of top and bottom squarks ($\tilde{t}_{1,2}$, $\tilde{b}_{1,2}$). Using a $\chi^2$ fit to simulated collider observables, the study shows that neglecting these phases leads to large errors in parameter determination, with $A_b$ being particularly poorly constrained unless phases are included, highlighting the critical need to account for CP phases in future SUSY searches and precision physics at colliders.

ABSTRACT

We study the decays of top squarks (~t_{1,2}) and bottom squarks (~b_{1,2}) in the Minimal Supersymmetric Standard Model (MSSM) with complex parameters A_t, A_b, mu and M_1. We show that including the corresponding phases strongly affects the branching ratios of ~t_{1,2} and ~b_{1,2} decays in a large domain of the MSSM parameter space. This could have an important impact on the search for ~t_{1,2} and ~b_{1,2} and the determination of the underlying MSSM parameters at future colliders.

Motivation & Objective

• To investigate the impact of complex CP-violating phases in $A_t$, $A_b$, $\mu$, and $M_1$ on the decay branching ratios of top and bottom squarks in the MSSM.
• To assess how these phases affect the detectability and reconstruction of $\tilde{t}_{1,2}$ and $\tilde{b}_{1,2}$ at future colliders.
• To evaluate the feasibility of accurately determining underlying MSSM parameters, including complex phases, from experimental observables such as masses, cross sections, and branching ratios.
• To demonstrate that assuming real parameters in fits leads to significantly larger $\chi^2$ values, indicating incorrect parameter reconstruction when phases are ignored.

Proposed method

• The study constructs the squark mass matrices in the $(\tilde{q}_L, \tilde{q}_R)$ basis, incorporating complex parameters $A_t$, $A_b$, $\mu$, and $M_1$, and diagonalizes them to obtain mass eigenstates $\tilde{q}_1$, $\tilde{q}_2$ with phase-dependent mixing angles.
• It computes decay branching ratios for $\tilde{t}_{1,2}$ and $\tilde{b}_{1,2}$, including modes such as $t\tilde{g}$, $t\tilde{\chi}^0_i$, $b\tilde{\chi}^+_j$, $\tilde{b}_{1,2}W^+$, and $\tilde{b}_{1,2}H^+$, with phase-dependent widths arising from complex couplings and mixings.
• Two benchmark scenarios are defined: one with small $\tan\beta = 6$ and one with large $\tan\beta = 30$, each with specific values for soft-breaking masses, trilinear couplings, and phases.
• A $\chi^2$ fit is performed on simulated experimental data (masses, cross sections, branching ratios) to reconstruct the underlying MSSM parameters, including complex phases.
• The fit includes expected experimental errors from TESLA, CLIC, and LHC, and the reconstructed parameters are compared to the true input values to assess accuracy.
• The impact of ignoring complex phases is quantified by comparing the $\chi^2$ value of a fit assuming real parameters to the true fit with complex parameters.

Experimental results

Research questions

• RQ1 How do complex phases in $A_t$, $A_b$, $\mu$, and $M_1$ affect the branching ratios of top and bottom squark decays in the MSSM?
• RQ2 To what extent can the underlying MSSM parameters, including complex phases, be reconstructed from collider observables such as masses, cross sections, and branching ratios?
• RQ3 What is the impact on parameter determination if complex phases are incorrectly assumed to be zero in a $\chi^2$ fit?
• RQ4 How does the sensitivity of branching ratios to phases vary with $\tan\beta$?
• RQ5 Why is the parameter $A_b$ particularly difficult to determine accurately when phases are neglected?

Key findings

• The inclusion of complex CP phases in $A_t$, $A_b$, $\mu$, and $M_1$ significantly alters the branching ratios of $\tilde{t}_{1,2}$ and $\tilde{b}_{1,2}$ decays across a large domain of the MSSM parameter space.
• For $\tan\beta = 6$, the $\tilde{t}_1$ decay branching ratios are fairly sensitive to the phase $\varphi_1$ of $M_1$, indicating non-trivial CP effects in the U(1) gaugino sector.
• $\tan\beta$ can be determined with a relative error of about 3% in both small and large $\tan\beta$ scenarios, demonstrating good sensitivity to this parameter.
• The real and imaginary parts of $A_t$ can be measured with errors of 2–3% independently of $\tan\beta$, showing high precision for $A_t$ determination.
• The determination of $A_b$ is significantly less precise: in the small $\tan\beta$ case, only an order-of-magnitude estimate is possible, due to weak dependence of mixing and couplings on $A_b$.
• A $\chi^2$ fit assuming real parameters yields a drastically larger $\chi^2$ value: $\Delta\chi^2 = 286.6$ (DOF=61) for $\tan\beta=6$ and $\Delta\chi^2 = 22.5$ (DOF=61) for $\tan\beta=30$, proving that neglecting phases leads to severe misidentification of the underlying MSSM model.