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The usefulness and value of Multi-step Machine Learning (ML), where a task is organized into connected sub-tasks with known intermediate inference goals, as opposed to a single large model learned end-to-end without intermediate sub-tasks, is presented. Pre-optimized ML models are connected and better performance is obtained by re-optimizing the connected one. The selection of an ML model from several small ML model candidates for each sub-task has been performed by using the idea based on Neural Architecture Search (NAS). In this paper, Differentiable Architecture Search (DARTS) and Single Path One-Shot NAS (SPOS-NAS) are tested, where the construction of loss functions is improved to keep all ML models smoothly learning. Using DARTS and SPOS-NAS as an optimization and selection as well as the connections for multi-step machine learning systems, we find that (1) such a system can quickly and successfully select highly performant model combinations, and (2) the selected models are consistent with baseline algorithms, such as grid search, and their outputs are well controlled.

We investigate the baseline range in which the $\theta_{23}$ degeneracy in neutrino oscillation probabilities is absent for fixed values of $\theta_{13}$ and CP violation phase $\delta_{\rm CP}$. We begin by studying sensitivities of neutrino oscillation probabilities to $\theta_{13}$, $\theta_{23}$ and $\delta_{\rm CP}$ for very-long-baseline neutrino oscillations. We show contour graphs of the muon-neutrino survival probability $P(\nu_{\mu}\to \nu_{\mu})$ and the appearance probability $P(\nu_e\to \nu_{\mu})$ on the $\cos 2\theta_{23}-\sin 2\theta_{13}$ plane for baseline lengths $L=1000, 5000, \ 10000$, and 12000 km. For each baseline length, it is found that $P(\nu_{\mu}\to \nu_{\mu})$ is more sensitive to $\sin 2\theta_{13}$ at energies around its local maximum while it is more sensitive to $\cos 2\theta_{23}$ at energies around its local minimum. On the other hand, the appearance probability $P(\nu_e\to \nu_{\mu})$ is sensitive to $\sin2\theta_{13}$ and $\cos2\theta_{23}$ only near its local maximum. We observe that the $\theta_{23}$ degeneracy in $P(\nu_{\mu}\to \nu_{\mu})$ is absent at energies around the local maximum of this probability, provided $\theta_{13}$ is sufficiently large. The $\theta_{23}$ degeneracy is also absent in general near the local maximum of $P(\nu_e\to \nu_{\mu})$. Using analytic approximations for neutrino oscillation probabilities, we demonstrate that the above observations for $L=1000, 5000, 10000, {\rm and} 12000$ km are in fact valid for all distances. The implications of these results on probing the octant of $\theta_{23}$ are discussed in details., Comment: 23 pages, 10 figures, 1 Table, revtex4

We study the matter effects to neutrino oscillations \nu_\mu \to \nu_e and \nu_\mu \to \nu_\mu at very long baselines. It has been observed that, for a very long baseline L~10000 km, the resonance peak for the \nu_\mu \to \nu_e oscillation and the local minimum of the \nu_\mu survival probability occurs at similar energies. With a good knowledge on the absolute value of \Delta m_{31}^2, measurements of the above oscillation probabilities, P_{\mu e} and P_{\mu\mu}, can be performed with the neutrino energy tuned to the resonance peak of the \nu_\mu \to \nu_e oscillations. We show that the variations of CP violating phase and the solar neutrino mixing parameters have negligible effects on P_{\mu e} and P_{\mu\mu} for such a long baseline. Hence P_{\mu e} and P_{\mu\mu} together determine the mixing angles \theta_{13} and \theta_{23}. Around the resonance peak for \nu_\mu \to \nu_e oscillations, the dependencies of P_{\mu e} and P_{\mu\mu} on the above mixing angles are worked out in detail, and the implications of such dependencies are discussed., Comment: 10 pages including 5 figures

We discuss one-loop contributions of supersymmetry (SUSY) particles to the process $e^+e^- \to W^+W^-$ in the minimal supersymmetric standard model. The calculation is tested by using the sum rule among the form factors, which is based on the BRS invariance. The overall normalization factor of the amplitudes is tested by using the decoupling property of the SUSY particles in the large mass limit. The correction due to the one-loop effect of the sfermions can be of a few times $\pm 0.1$ % level, whereas that of the charginos and neutralinos can be order 1%. We also study the CP-violating effects in the chargino and neutralino sector., Comment: Proceedings for the Linear Collider Workshop (LCWS2004) in Paris, France, April 19-23, 2004, Talk given by S. Kanemura, 4 pages, 6 figures

We study one-loop effects of charginos and neutralinos on the helicity amplitudes for the process $e^+e^-\to W^+W^-$ in the MSSM. The calculation is tested by using two methods. First, the sum rules among form factors which result from BRS invariance. Second, the decoupling property in the large mass limit is used to test the overall normalization of the amplitudes. The one-loop contribution to the helicity amplitudes is shown as a function of $\mu$ Higgs parameter and $\sqrt{s}$. We also study the effects of the CP-violating phase., Comment: To appear in the Proceedings of SUSY 2003, held at the University of Arizona, Tucson, AZ, 5-10 June 2003

The semileptonic decays of polarised top quarks are analysed for a general chirality-conserving tbW vertex. We calculate double differential distributions for the charged lepton and the neutrino to order \alpha_s in the QCD coupling. We present these QCD corrections in terms of compact parameterisations that should be useful for the future investigation of the structure of the top decay vertex on the basis of large data samples., Comment: 7 pages, 2 figures, Latex

We study the one-loop effects of charginos and neutralinos on the helicity amplitudes for $\eeww$ in the minimal supersymmetric standard model. The calculation is tested by using two methods. First, the sum rule for the form factors between $\eeww$ and the process where the external $W^\pm$ bosons are replaced by the corresponding Goldstone bosons $\omega^\pm$ is employed to test the analytic expression and the accuracy of the numerical program. Second, the decoupling property in the large mass limit is used to test the overall normalization of the amplitudes. These two tests are most effectively carried out when the amplitudes are expanded in terms of the modified minimal subtraction ($\bar{\rm MS}$) couplings of the standard model. The resulting perturbation expansion is valid at collider energies below and around the threshold of the light supersymmetric particles. We find that the corrections to the cross section of the longitudinally polarized $W$-pair production can be as large as -1.4% at the threshold of the light chargino-pair production for large scattering angles. We also study the effects of the CP-violating phase in the chargino and neutralino sectors on the helicity amplitudes. We find that the resulting CP-violating asymmetries can be at most 0.1%., Comment: 30 pages, 25 figures, Final verision, To appear in Physical Review D, Several sentences are improved

One-loop contributions of super-partner particles to $W$-pair production at $e^+e^-$ collision are discussed in the MSSM. To obtain trustworthy results we test our calculation using three methods: (1) sum rules among form factors which result from the BRS invariance, (2) the decoupling theorem, (3) the high-energy stability. We examine the corrections taking into account constraints from the direct search experiments and the precision data. The results for the sfermion contributions are presented., Comment: Proceedings of ICHEP2000 (July-August 2000, Osaka Japan), Talk given by Shinya Kanemura, 3 pages including 5 figures

We study one-loop effects of sfermions on helicity amplitudes for $\eeww$ in the Minimal Supersymmetric Standard Model. The one-loop contributions are calculated in the $\bar{\rm MS}$ renormalization scheme. In order to verify the validity of the analytic calculation and the numerical program, the following tests are performed. (i) The BRS sum rules hold exactly among the analytic expressions of the form factors of the $\eeww$ amplitude and those of the amplitudes where the external $W^\pm$ bosons are replaced by the corresponding Goldstone bosons $\chi^\pm$, hence they hold within the expected accuracy of the numerical program. (ii) The one-loop sfermion contribution to the amplitudes decouple in the heavy mass limit. This property is used to test the overall normalization of the amplitudes. In order to observe the analytically exact decoupling, the amplitudes are expanded by the $\bar{\rm MS}$ couplings of the Standard Model. (iii) The high-energy analytic formulas of the helicity amplitudes, which are verified by using the equivalence theorem analytically, are used for the numerical test of the high energy behavior of the amplitudes. We then investigate the magnitude of the one-loop effects on each helicity amplitude which may be measured by experiments at future linear colliders. Under the constraint from available precision data, the one-loop corrections to a few helicity amplitudes (for example, the longitudinal-$W$-pair production) can be at most from -0.8% to $+0.6$% in magnitude in the observables. The corrections in the helicity-summed cross sections are smaller, typically a few times $\pm 0.1$% at large scattering angles., Comment: 48 pages including 35 figures, To appear in Physical Review D

The BRS invariance of the electroweak gauge theory leads to relationships between amplitudes with external massive gauge bosons and amplitudes where some of these gauge bosons are replaced with their corresponding Nambu-Goldstone bosons. Unlike the equivalence theorem, these identities are exact at all energies. In this paper we discuss such identities which relate the process $e^+e^- \to W^+W^-$ to $W^\pm\chi^\mp$ and $\chi^+\chi^-$ production. By using a general form-factor decomposition for $e^+e^- \to W^+W^-$, $e^+e^- \to W^\pm \chi^\mp$ and $e^+e^- \to \chi^+\chi^-$ amplitudes, these identities are expressed as sum rules among scalar form factors. Because these sum rules may be applied order by order in perturbation theory, they provide a powerful test of higher order calculations. By using additional Ward-Takahashi identities we find that the various contributions are divided into separately gauge-invariant subsets, the sum rules applying independently to each subset. After a general discussion of the application of the sum rules we consider the one-loop contributions of scalar-fermions in the Minimal Supersymmetric Standard Model as an illustration., Comment: 37 pages, including 16 figures

We study the constraints from updated electroweak data on the three leptophobic Z' models, the ${\eta}$ model with an appropriate $U(1)'-U(1)_Y$ kinetic mixing, a Z' model motivated by the flipped SU(5) \times U(1) unification, and the phenomenological Z' model of Agashe, Graesser, and Hinchliffe. The $Z-Z'$ mixing effects are parametrized in terms of a positive contribution to the $T$ parameter, $T_{new}$, and the effective mass mixing parameter, $\bar{\xi}$. All the theoretical predictions for the $Z$ boson parameters, the $W$ boson mass and the observables in low-energy neutral current experiments are presented together with the standard model radiative corrections. The allowed region in the ($\bar{\xi},T_{new}$) plane is shown for the three models. The 95% CL lower limit on the heavier mass eigenstate $Z_2$ is given as a function of the effective $Z-Z'$ mixing parameter $\zeta$., Comment: LaTeX, 22pages, 2 figures, corrected some typos. Final version to appear in Phys. Rev. D

We study constraints on additional $Z'$ bosons predicted in the supersymmetric (SUSY) $E_6$ models by using the updated results of electroweak experiments -- $Z$-pole experiments, $m_W$ measurements and low-energy neutral current (LENC) experiments. We find that the effects of $Z$-$Z'$ mixing are parametrized by (i) a tree-level contribution to the $T$-parameter, (ii) the effective $Z$-$Z'$ mass mixing angle $\xibar$. In addition, the effect of the direct exchange of the heavier mass eigenstate $Z_2$ in the LENC processes is parametrized by (iii) a contact term $\contact$. We give the theoretical predictions for the observables in the electroweak experiments together with the standard model radiative corrections. Constraints on $T_{\rm new}$ and $\xibar$ from the $Z$-pole and $m_W$ experiments and those on $\contact$ from the LENC experiments are separately shown. Impacts of the kinetic mixing between the ${\rm U(1)}_Y$ and ${\rm U(1)'}$ gauge bosons on the $\chi^2$-analysis are studied. We show the 95% CL lower mass limit of $Z_2$ as a function of the effective $Z$-$Z'$ mixing parameter $\zeta$, a combination of the mass and kinetic mixings. Theoretical prediction on $\zeta$ and $g_E$ is found for the $\chi, \psi, \eta$ and $\nu$ models by assuming the minimal particle content of the SUSY $E_6$ models. In a certain region of the parameter space, the $Z_2$ boson mass in the detectable range of LHC is still allowed., Comment: LaTeX, 36pages, 4 figures. One referece added. Final version to appear in Nucl. Phys. B