Physics Impact of GigaZ

TL;DR

The paper analyzes how the GigaZ mode of a future e+e- linear collider enables ultra-precise electroweak measurements that probe the Higgs sector and potential new physics. It demonstrates that loop corrections in the SM allow indirect determination of the Higgs mass with a few percent precision, while MSSM effects can be constrained indirectly, including heavy Higgs states and stops, even when direct observation is difficult. The authors quantify expected improvements in sin^2θ_eff and M_W, and show that GigaZ data can bound MSSM parameters such as M_A and m̃_t2, highlighting the role of virtual effects in exploring otherwise inaccessible energy scales. Overall, GigaZ offers powerful consistency tests of the SM and MSSM, extending sensitivity to new physics scales well beyond direct collider reach.

Abstract

By running the prospective high-energy e^+ e^- collider TESLA in the GigaZ mode on the Z resonance, experiments can be performed on the basis of more than 10^9 Z events. They will allow the measurement of the effective electroweak mixing angle to an accuracy of approximately +- 10^-5. Likewise the W boson mass is expected to be measurable with an error of about 6 MeV near the W^+ W^- threshold. In this note, we study the accuracy with which the Higgs boson mass can be determined from loop corrections to these observables in the Standard Model. The comparison with a directly observed Higgs boson may be used to constrain new physics scales affecting the virtual loops. We also study constraints on the heavy Higgs particles predicted in the Minimal Supersymmetric Standard Model, which are very difficult to observe directly for large masses. Similarly, it is possible to constrain the mass of the heavy scalar top particle.

Figures (4)

• Figure 1: $1\sigma$ allowed regions in the $m_{t}$-$M_H$ plane taking into account the anticipated GigaZ precisions for $\sin^2\theta_{\mathrm{eff}}, M_W, \Gamma_Z, R_l, R_q$ and $m_{t}$ (see text). The presently allowed region (full curve labeled 'now') is shown for comparison.
• Figure 2: The theoretical prediction for the relation between $\sin^2\theta_{\mathrm{eff}}$ and $M_W$ in the SM for Higgs boson masses in the intermediate range is compared to the experimental accuracies at LEP 2/Tevatron (Run IIA), LHC/LC and GigaZ (see Tab. \ref{['tab:precallcoll']}). For the theoretical prediction an uncertainty of $\delta\Delta\alpha = \pm 7 \times 10^{-5}$ and $\delta m_{t} = \pm 200 \,\, \mathrm{MeV}$ is taken into account.
• Figure 3: The region in the $M_A-m_{\tilde{t}_2}$ plane, allowed by $1\,\sigma$ errors obtained from the GigaZ measurements of $M_W$ and $\sin^2\theta_{\mathrm{eff}}$: $M_W = 80.40 \,\, \mathrm{GeV}$, $\sin^2\theta_{\mathrm{eff}} = 0.23140$, and from the LC measurement of $M_h$: $M_h = 115 \,\, \mathrm{GeV}$. The experimental errors for the SM parameters are given in Tab. \ref{['tab:precallcoll']}. $\tan \beta$ is assumed to be experimentally constrained by $2.5 < \tan \beta < 3.5$ or $\tan \beta > 10$. The other parameters including their uncertainties are given by $m_{\tilde{t}_1} = 500 \pm 2 \,\, \mathrm{GeV}$, $\sin\theta_{\tilde{t}} = -0.69 \pm 0.014$, $A_b = A_t \pm 10\%$, $\mu = -200 \pm 1 \,\, \mathrm{GeV}$, $M_2 = 400 \pm 2 \,\, \mathrm{GeV}$ and $m_{\tilde{g}} = 500 \pm 10 \,\, \mathrm{GeV}$. For the uncertainties of the theoretical predictions we use Eq. (\ref{['eq:futureunc']}).
• Figure 4: The region in the $M_A-\tan \beta$ plane, allowed by $1\,\sigma$ errors by the GigaZ measurements of $M_W$ and $\sin^2\theta_{\mathrm{eff}}$: $M_W = 80.40 \,\, \mathrm{GeV}$, $\sin^2\theta_{\mathrm{eff}} = 0.23138$, and by the LC measurement of $M_h$: $M_h = 110 \,\, \mathrm{GeV}$. The experimental errors for the SM parameters are given in Tab. \ref{['tab:precallcoll']}. The other parameters including their uncertainties are given by $m_{\tilde{t}_1} = 340 \pm 1 \,\, \mathrm{GeV}$, $m_{\tilde{t}_2} = 640 \pm 10 \,\, \mathrm{GeV}$ or $m_{\tilde{t}_2} = 520 \pm 1 \,\, \mathrm{GeV}$, $\sin\theta_{\tilde{t}} = -0.69 \pm 0.014$, $A_b = -640 \pm 60 \,\, \mathrm{GeV}$, $\mu = 316 \pm 1 \,\, \mathrm{GeV}$, $M_2 = 152 \pm 2 \,\, \mathrm{GeV}$ and $m_{\tilde{g}} = 496 \pm 10 \,\, \mathrm{GeV}$. For the uncertainties of the theoretical predictions we use Eq. (\ref{['eq:futureunc']}).