We study multi-Higgs final states in vector boson fusion (VBF) processes at the LHC and at future proton-proton colliders, focusing on the prospects for measurements at 27 and 100 TeV. We use an effective Lagrangian which includes higher-dimensional operators in the mass eigenstates which are relevant to VBF processes and relate this to specific parametrizations and models for new physics in the Higgs sector. We derive theoretical constraints on the parameter space from the unitarity of $2\to n$ scattering amplitudes and apply the results to $VV\to hh$ and $hhh$ processes, where $V=W$, $Z$. As a result, we present constraints on differential distributions as appropriate to the study of $VV\to hh$ and $hhh$ processes.

The coherent oscillation of ultralight dark matter in the mass regime around ${10}^{-23}\mathrm{eV}$ induces changes in gravitational potential with the frequency in the nanohertz range. This effect is known to produce a monochromatic signal in the pulsar timing residuals. Here we discuss a multifield scenario that produces a wide spectrum of frequencies, such that the ultralight particle oscillation can mimic the pulsar timing signal of stochastic common spectrum process. We discuss how ultralight dark matter with various spins produces such a wide band spectrum on pulsar timing residuals and perform the Bayesian analysis to constrain the parameters. It turns out that the stochastic background detected by NANOGrav can be associated with a wideband ultralight dark matter.

The axion objects such as axion miniclusters and axion clouds around spinning black holes induce parametric resonances of electromagnetic waves through the axion-photon interaction. In particular, it has been known that the resonances from the axion with the mass around ${10}^{-6}\mathrm{eV}$ may explain the observed fast radio bursts (FRBs). Here we argue that similar bursts of high frequency gravitational waves, which we call fast gravitational wave bursts (FGBs), are generated from axion clumps with the presence of gravitational Chern-Simons (CS) coupling. The typical frequency is half of the axion mass, which in general can range from kHz to GHz. We also discuss the secondary gravitational wave production associated with FRB, as well as the possible host objects of the axion clouds, such as primordial black holes with typical masses around ${10}^{-5}{M}_{\odot }$. Future detections of FGBs together with the observed FRBs are expected to provide more evidence for the axion.

Motivated by the recent rare $B$ decays measurements, we study the matching procedure of operators $O_9$, $O_{10}$ in the low energy effective Hamiltonian and operators in the Standard Model effective theory (SMEFT). It is noticed that there are more related operators in the SMEFT whose coefficients cannot be determined only from the low-energy data from $B$ physics. We demonstrate how to determine these coefficients with some new physics models, like the $Z^{\prime }$ model and leptoquark models, and then consider how to probe these operators of SMEFT at high energy by using the process ${\mu }^{+}{\mu }^{-}\to tc$ at future muon colliders, which can provide complementary information except for ${\mu }^{+}{\mu }^{-}\to bs$ on the underlying models which lead to rare $B$ decay processes. We perform a Monte Carlo study (a hadron level analysis) to show how to separate the signal events from the SM background events and estimate the sensitivity to the Wilson coefficients for different models.

We explore the possibility of detecting entangled photon pairs from cosmic microwave background or other cosmological sources coming from two patches of the sky. The measurements use two detectors with different photon polarizer directions. When two photon sources are separated by a large angle relative to the earth, such that each detector has only one photon source in its field of view, a null test of unentangled photons can be performed. The deviation from this unentangled background is, in principle, the signature of photon entanglement. To confirm whether the deviation is consistent with entangled photons, we derive a photon polarization correlation to compare with, similar to that in a Bell inequality measurement. However, since photon coincidence measurement cannot be used to discriminate unentangled cosmic photons, it is unlikely that the correlation expectation value alone can violate Bell inequality to provide the signature for entanglement.

Gravitational waves can generate electromagnetic effects inside a strong electric or magnetic field within the Standard Model and general relativity. Here we propose using a quarterly split cavity and LC (inductor and capacitor) resonance circuit to detect a high-frequency gravitational wave from 0.1 MHz to GHz. We perform a full 3D simulation of the cavity’s signal for sensitivity estimate. Our sensitivity depends on the coherence timescale of the high-frequency gravitational wave sources and the volume size of the split cavity. We discuss the resonant measurement schemes for narrow-band gravitational wave sources and also a nonresonance scheme for broadband signals. For a meter-sized split cavity under a 14 Tesla magnetic field, the LC resonance enhanced sensitivity to the gravitational wave strain is expected to reach $h\sim {10}^{-20}$ around 10 MHz.