We study the kinematic cusps and endpoints of processes with the "antler topology" as a way to measure the masses of the parity-odd missing particle and the intermediate parent at a high energy lepton collider. The fixed center of mass energy at a lepton collider makes many new physics processes suitable for the study of the antler decay topology. It also provides new kinematic observables with cusp structures, optimal for the missing mass determination. We also study realistic effects on these observables, including initial state radiation, beamstrahlung, acceptance cuts, and detector resolution. We find that the new observables, such as the reconstructed invariant mass of invisible particles and the summed energy of the observable final state particles, appear to be more stable than the commonly considered energy endpoints against realistic factors and are very efficient at measuring the missing particle mass. For the sake of illustration, we study smuon pair production and chargino pair production within the framework of the minimal supersymmetric standard model. We adopt the log-likelihood method to optimize the analysis. We find that at the 500 GeV ILC, a precision of approximately 0.5 GeV can be achieved in the case of smuon production with a leptonic final state, and approximately 2 GeV in the case of chargino production with a hadronic final state.
We analyze the tree-level 2 → 2 scattering of massive spin-2 bosons in a theory with only relevant and marginal operators and extract the sum rules on the coupling constants and masses required to achieve tree-level unitarity to very high energy. We do this for four illustrative cases. In the first, we include massive spin-1 and spin-0 bosons in our theory, but do not require gauge invariance. For this case, we find that it is, in fact, possible to construct a theory where all 2 → 2 scattering processes are tree-level unitary to very high energy. In the second case, we consider a theory that only includes massive spin-2 and spin-0 bosons. In the absence of spin-1 bosons, we find that it is impossible to unitarize the spin-2 scattering. In the third and fourth cases, we reintroduce the spin-1 bosons as gauge bosons and demand that all interactions are gauge invariant. We take the spin-2 bosons to transform under the adjoint representation of one or two gauge groups. For both of these cases, we find that unitarization is unachievable.
We present a search for conformal invariance in vorticity isolines of two-dimensional compressible turbulence. The vorticity is measured by tracking the motion of particles that float at the surface of a turbulent tank of water. The three-dimensional turbulence in the tank has a Taylor microscale Re λ ≃ 160. The conformal invariance theory being tested here is related to the behavior of equilibrium systems near a critical point. This theory is associated with the work of Löwner, Schramm and others and is usually referred to as Schramm-Löwner Evolution (SLE). The system was exposed to several tests of SLE. The results of these tests suggest that zero-vorticity isolines exhibit noticeable departures from this type of conformal invariance.
Parents have a crucial role in constructing children's mental health, because children are individuals in the developmental phase from infancy to adolescence. The development processes involve physical, mental, self-concept and imitating patterns in its environment. According to WHO reports, 450 million people across the world suffer mental disorders, with a prevalence of 20% of the incidence occurring in children. There are several factors affecting the mental emotional level of children, namely: the attitude of parents to their children, parenting patterns in the family, the stimulus provided, love and affection. In building a child's mental health, Christian parents must become role models and a systematic formulation of the 5Ps (Guidance, Advisory, Training, Friendship, Listening) so that they are able to build their mentality.
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