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In this paper, we will give a brief review of some important beam physics in circular and linear electron–positron collider designs, covering beam–beam tune limits, longitudinal and transverse single bunch collective effects, electron cloud and space charge effects, dynamic aperture estimations, etc. The main feature of this review is that the corresponding beam physics treatments are coming from author's previous research works which are scattered in different scientific publications both for circular and linear colliders. With the progresses of future linear colliders, such as ILC, and future circular electron–positron colliders, such as CEPC, it is high time to review the key beam physics issues in the optimization designs of these two kinds of machines.

I summarize our recent works on using differential observables to explore the physics potential of future $e^{+}{e}^{-}$ colliders in the framework of Higgs effective field theory. This proceeding is based upon Refs. 1 and 2. We study angular observables in the $e^{+}{e}^{-}\to ZH{\ell }^{+}{\ell }^{-}b\bar{b}$ channel at future circular $e^{+}{e}^{-}$ colliders such as CEPC and FCC-ee. Taking into account the impact of realistic cut acceptance and detector effects, we forecast the precision of six angular asymmetries at CEPC (FCC-ee) with center-of-mass energy $\sqrt{s}=240$ GeV and 5 (30) ab${}^{-1}$ integrated luminosity. We then determine the projected sensitivity to a range of operators relevant for the Higgsstrahlung process in the dimension-6 Higgs EFT. Our results show that angular observables provide complementary sensitivity to rate measurements when constraining various tensor structures arising from new physics. We further find that angular asymmetries provide a novel means of constraining the “blind spot” in indirect limits on supersymmetric scalar top partners. We also discuss the possibility of using $ZZ$-fusion at $e^{+}{e}^{-}$ machines at different energies to probe new operators.

The nonunitarity of the leptonic mixing matrix is a generic signal of new physics aiming at the generation of the observed neutrino masses. We discuss the Minimal Unitarity Violation (MUV) scheme, an effective field theory framework which represents the class of extensions of the Standard Model (SM) by heavy neutral leptons, and discuss the present bounds on the nonunitarity parameters as well as estimates for the sensitivity of the CEPC, based on the performance parameters from the preCDR.

In scenarios with sterile (right-handed) neutrinos with an approximate “lepton-number-like” symmetry, the heavy neutrinos (the mass eigenstates) can have masses around the electroweak scale and couple to the Higgs boson with, in principle, unsuppressed Yukawa couplings, while the smallness of the light neutrinos’ masses is guaranteed by the approximate symmetry. The on-shell production of the heavy neutrinos at lepton colliders, together with their subsequent decays into a light neutrino and a Higgs boson, constitutes a resonant contribution to the Higgs production mechanism. This resonant mono-Higgs production mechanism can contribute significantly to the mono-Higgs observables at future lepton colliders. A dedicated search for the heavy neutrinos in this channel exhibits sensitivities for the electron neutrino Yukawa coupling as small as $\sim 5\times 10^{-3}$. Furthermore, the sensitivity is enhanced for higher center-of-mass energies, when identical integrated luminosities are considered.

The $WW$ production is the primary channel to directly probe the triple gauge couplings (TGCs). We analyze the $e^{+}{e}^{-}\to W^{+}{W}^{-}$ process at the proposed circular electron–positron collider (CEPC), and find that the anomalous TGCs and relevant dimension six operators can be probed up to the order of $10^{-4}$. We also estimate constraints at the 14 TeV (LHC), with both 300 fb${}^{-1}$ and 3000 fb${}^{-1}$ integrated luminosity from the leading lepton $p_T$ and azimuthal angle difference $\mathrm{\Delta }{\varphi }_{ll}$ in the di-lepton channel. The constrain is somewhat weaker, up to the order of $10^{-3}$. The limits on the TGCs are complementary to those on the electroweak precision observables and Higgs couplings.

After the Higgs discovery, it is believed that a circular $e^{+}{e}^{-}$ collider could serve as a Higgs factory. The high energy physics community in China launched a study of a 50–100 km ring collider. A preliminary conceptual design report (Pre-CDR) has been published in early 2015. This report is based on a 54-km ring design. Some progress on beam–beam effect study after Pre-CDR is shown in the paper. We estimate the beamstrahlung lifetime using a pure strong–strong code as a comparison with the result obtained using a quasi-strong–strong method. The effect of parasitic crossing in the pretzel scheme is also estimated for the very first time. The feasibility of the main parameters for partial double ring scheme are evaluated from the point view of beam–beam interaction.

In order to avoid the pretzel orbit, CEPC is proposed to use partial double ring scheme in CDR. In this paper, a general method of how to make an consistent machine parameter design of CEPC with crab-waist by using analytical expression of maximum beam–beam tune shift and beamstrahlung beam lifetime started from given IP vertical beta, beam power and other technical limitations were developed. FFS with crab sextupoles will be developed and the arc lattice will be redesigned to acheive the lower emittance for crab-waist scheme.

The physics potential of the Circular Electron Positron Collider (CEPC) can be significantly strengthened by two detectors with complementary designs. A promising detector approach based on the Silicon Detector (SiD) designed for the International Linear Collider (ILC) is presented. Several simplifications of this detector for the lower energies expected at the CEPC are proposed. A number of cost optimizations of this detector are illustrated using full detector simulations. We show that the proposed changes will enable one to reach the physics goals at the CEPC.

In this paper we will give an introduction to the Circular Electron Positron Collider (CEPC). The scientific background, physics goal, the collider design requirements and the conceptual design principle of the CEPC are described. On the CEPC accelerator, the optimization of parameter designs for the CEPC with different energies, machine lengths, single ring and crab-waist collision partial double ring, advanced partial double ring and fully partial double ring options, etc. have been discussed systematically, and compared. The CEPC accelerator baseline and alternative designs have been proposed based on the luminosity potential in relation with the design goals. The CEPC sub-systems, such as the collider main ring, booster, electron positron injector, etc. have also been introduced. The detector and the MAchine-Detector Interface (MDI) design have been briefly mentioned. Finally, the optimization design of the Super Proton–Proton Collider (SppC), its energy and luminosity potentials, in the same tunnel of the CEPC are also discussed. The CEPC-SppC Progress Report (2015–2016) has been published.

In this paper, a consistent calculation method for the CEPC parameter choice with a crab waist scheme is reported. A crosscheck of luminosity with beam–beam simulations has been done. With this new scheme, a higher Higgs luminosity (+170%) can be reached while keeping Pre-CDR beam power or the beam power (19 MW) can be reduced while keeping the same Pre-CDR luminosity. CEPC is compatible with W and Z experiment. The luminosity for Z is at the level of $10^{35}{\mathrm{\text{cm}}}^{-2}{\mathrm{\text{s}}}^{-1}$. Requirement for energy acceptance of Higgs has been reduced to 1.5% by enlarging the ring to 100 km. The arc optics and the Final Focus System (FFS) with crab sextupoles have been designed, and also some primary Dynamic Aperture (DA) results were introduced.

We describe the phenomenology of light singlet Higgs bosons in the Next-to-Minimal Supersymmetry Model (NMSSM) which are mostly decoupled from the rest of Supersymmetry. Noting that the Large Hadron Collider has not excluded this scenario, we describe previous searches for light Higgs bosons at the Large Electron Positron collider and evaluate the sensitivity to neutralino production and decay to light singlet Higgs bosons at the proposed $\sqrt{s}=250$ GeV Circular Electron Positron Collider.

One of the interesting portals linking a dark sector and the Standard Model (SM) is the kinetic mixing between the SM $U{(1)}_Y$ field with a new dark photon $A^{\prime }$ from a $U{(1)}_{A^{\prime }}$ gauge interaction. Stringent limits have been obtained for the kinetic mixing parameter $𝜖$ through various processes. In this work, we study the possibility of searching for a dark photon interaction at a circular $e^{+}{e}^{-}$ collider through the process $e^{+}{e}^{-}\to \gamma A^{\prime }\to \gamma {\mu }^{+}{\mu }^{-}$. We find that the constraint on ${𝜖}^2$ for dark photon mass in the few tens of GeV range, assuming that the ${\mu }^{+}{\mu }^{-}$ invariant mass can be measured to an accuracy of 0.5% $m_{A^{\prime }}$, can be better than $3\times 10^{-6}$ for the proposed CEPC with a 10-year running at $3\sigma$ (statistic) level, and better than $2\times 10^{-6}$ for FCC-ee with even just one-year running at $\sqrt{s}=240\mathrm{\text{GeV}}$, better than the LHCb, ATLAS, CMS experiments and other facilities can do in a similar dark photon mass range. For FCC-ee, running at $\sqrt{s}=160\mathrm{\text{GeV}}$, the constraint can be even better.

A future Circular Electron Positron Collider (CEPC) has been proposed by China with the main goal of studying the Higgs boson. Its baseline design, chosen on the basis of its performance, is a double ring scheme; an alternative design is a partial double ring scheme which reduces the budget while maintaining an adequate performance. This paper will present the collider ring lattice design for the double ring scheme. The CEPC will also work as a W and a Z factory. For the W and Z modes, except in the RF region, compatible lattices were obtained by scaling down the magnet strength with energy.

With the discovery of the Higgs boson at around 125 GeV, a circular Higgs factory design with high luminosity $(L\sim 10^{34}{\mathrm{\text{cm}}}^{-2}{\mathrm{\text{s}}}^{-1})$ is becoming more popular in the accelerator world. The CEPC project in China is one of them. Machine Detector Interface (MDI) is the key research area in electron–positron colliders, especially in CEPC; it is one of the criteria to measure the accelerator and detector design performance. Because of the limited space available in the designed tunnel, many equipment including magnets, beam diagnostic instruments, masks, vacuum pumps, and components of the detector must coexist in a very small region. In this paper, some important MDI issues will be reported for the Interaction Region (IR) design, e.g. the final doublet quadrupoles physics design parameters, beam-stay-clear region and beam pipe, synchrotron radiation power and critical energy are also calculated.

The Circular Electron–Positron Collider (CEPC) is a 100-km ring $e^{+}{e}^{-}$ collider for a Higgs factory. The injector of CEPC is composed of Linac and Booster. The Linac is a normal conducting S-band Linac with a frequency of 2860 MHz; it provides electron and positron beams at an energy of up to 10 GeV with 100 Hz repetition frequency of 100 Hz. The Linac design and dynamic simulation results are discussed in detail in this paper, including electron bunching system, positron source, electron bypass transport line, damping ring and main Linacs.

CEPC is a 100-km double-ring circular electron–positron collider operating at 90–240 GeV center-of-mass energy of Z-pole, WW-pair production threshold and Higgs resonance. The conceptual design report (CDR) of CEPC has been published as an important step to move the project forward. The superconducting RF (SRF) system is one of the most important and challenging accelerator systems due to the wide range of beam energy and current. In this paper, the layout, parameters and configuration of the superconducting RF system for the CEPC collider ring will be introduced. Issues of beam cavity interactions including transient beam loading and coupled-bunch instabilities of accelerating mode are discussed.

The interaction region is designed to provide strong focusing at the interaction point. A local correction scheme is adopted to get a large momentum acceptance. The interaction region consists of several modular sections. This paper presents the optics design of each section and its optimization. As an example, the optics design for the CEPC single-ring scheme is presented.

The energy sawtooth will be significant in the future circular Higgs factory with beam energy as high as 120 GeV. For the partial double ring scheme, unlike the double ring scheme, the effects of energy sawtooth cannot be corrected by tapering the magnet strength with beam energy along the beamline. In this paper, the energy sawtooth effects in the partial double ring scheme and its mitigation methods are presented. As an example, the study of the energy sawtooth effects of the CEPC advanced partial double ring scheme is presented.

In this paper, we describe our work on spin polarization in high-energy electron storage rings which we base on the Full Bloch equation (FBE) for the polarization density and which aims towards the $e^{-}-e^{+}$ option of the proposed Future Circular Collider (FCC-ee) and the proposed Circular Electron Positron Collider (CEPC). The FBE takes into account non spin-flip and spin-flip effects due to synchrotron radiation including the spin-diffusion effects and the Sokolov–Ternov effect with its Baier–Katkov generalization as well as the kinetic-polarization effect. This mathematical model is an alternative to the standard mathematical model based on the Derbenev–Kondratenko formulas. For our numerical and analytical studies of the FBE, we develop an approximation to the latter to obtain an effective FBE. This is accomplished by finding a third mathematical model based on a system of stochastic differential equations (SDEs) underlying the FBE and by approximating that system via the method of averaging from perturbative ODE theory. We also give an overview of our algorithm for numerically integrating the effective FBE. This discretizes the phase space using spectral methods and discretizes time via the additive Runge–Kutta (ARK) method which is a high-order semi-implicit method. We also discuss the relevance of the third mathematical model for spin tracking.

We study a possibility of obtaining transversely polarized electron/positron beams in the CEPC collider. Also, original results are presented for another project, the FCCee collider, which allows us to identify some features and differences of these similar machines. Important is the comparison of the data obtained with the expected and measured polarizations at LEP. In estimation of the depolarizing effect of field errors, in addition to the usual nonresonant spin diffusion, an attempt was made to take into account the resonant diffusion, which is due to a large spin tune spread. We consider a possibility to obtain polarization by accelerating polarized particles in the CEPC booster and then injecting them into the main ring. This option can be crucial for obtaining longitudinal polarization. We propose a scheme in which long-term preservation of such polarization is possible.