We study how effects of the CP violation can be observed indirectly by precision measurements of Higgs boson couplings at a future Higgs factory such as the international linear collider. We consider two Higgs doublet models with the softly broken discrete symmetry. We find that by measuring the Higgs boson couplings very precisely we are able to distinguish the two Higgs doublet model with CP violation from the CP conserving one.
We discuss how one can identify CP violation (and conservation) in multi-Higgs-doublet potentials. After a brief review of CP violation in the 2HDM, we refer to the fact that for NHDM with $N geq 3$ the well known methods useful in the case $N = 2$ have not been generalized in order to provide a set of well defined necessary and sufficient conditions for CP conservation. We then present a simple method, proposed by the authors, to be used in such cases. Two non-trivial examples based on an $S_3$-symmetric three-doublet model are analyzed by means of this new method.
We compute the full vacuum polarization tensor in the minimal QED extension. We find that its low-energy limit is dominated by the radiatively induced Chern-Simons-like term and the high-energy limit is dominated by the c-type coefficients. We investigate the implications of the high-energy limit for the QED and QCD running couplings. In particular, the QCD running offers the possibility to study Lorentz-violating effects on the parton distribution functions and observables such as the hadronic R ratio.
We consider the most general set of $SU(2) times U(1)$ invariant CP-violating operators of dimension six, which contribute to $VVh$ interactions ($V = W, Z, gamma$). Our aim is to constrain any CP-violating new physics above the electroweak scale via the effective couplings that arise when such physics is integrated out. For this purpose, we use, in turn, electroweak precision data, global fits of Higgs data at the Large Hadron Collider and the electric dipole moments of the neutron and the electron. We thus impose constraints mainly on two-parameter and three-parameter spaces. We find that the constraints from the electroweak precision data are the weakest. Among the existing Higgs search channels, considerable constraints come from the diphoton signal strength. We note that potential contribution to $h rightarrow gamma Z$ may in principle be a useful constraining factor, but it can be utilized only in the high energy run. The contributions to electric dipole moments mostly lead to the strongest constraints, though somewhat fine-tuned combinations of more than one parameter with large magnitudes are allowed. We also discuss constraints on gauge boson trilinear couplings which depend on the parameters of the CP-violating operators .
The prospects for a muon collider operated as a Higgs factory are reviewed. The large muon mass means that the s-channel Higgs production mechanism is available, and simultaneously suppresses bremsstrahlung so that the beam energy spread can be kept to the MeV level required to exploit this. Thus this is the only machine which can make a direct scan over the Higgs resonance, and make an extraordinary mass measurement. Further possibilities such as a scan of the H and A of supersymmetry and CP violation are also mentioned.
The diphoton invariant mass distribution of interference between $ggto H to gammagamma$ and $ggto gammagamma$ is almost antisymmetric around the Higgs mass $M_H$. We propose a new observable $A_{text{int}}$ to quantify this effect, which is a ratio of a sign-reversed integral around $M_H$ ( e.g. $int^{M_H}_{M_H-5~mbox{GeV}} -int_{M_H}^{M_H+5~mbox{GeV}}$) and the cross section of the Higgs signal. We study $A_{text{int}}$ both in Standard Model (SM) and new physics with various $CP$-violating $Hgammagamma$ couplings. The $A_{text{int}}$ in SM could reach a value of $10%$, while for $CP$-violating $Hgammagamma$ couplings $A_{text{int}}$ could range from $10%$ to $-10%$, which is probable to be detected in HL-LHC experiment. The $A_{text{int}}$ with both $CP$-violating $Hgammagamma$ and $Hgg$ couplings are also studied and its value range is further extended.