We construct a new kinematical variable that is able to fully reconstruct the absolute value, and partially reconstruct the sign, of the angular distribution in the center of momentum system of a decaying particle in certain cases where the center of momentum system is only known up to a two-fold ambiguity. After making contact with Drell-Yan production at the Large Hadron Collider, we apply this method to the pair-production of dark matter in association with two charged leptons at the International Linear Collider and show that for a small intermediate width, perfect agreement is found with the true angular distribution in the absence of initial state radiation. In the presence of initial state radiation, we find that the modification to the angular distributions is small for most angles and that different spin combination classes should still be distinguishable. This enables us to determine the spin of the mother particle and the dark matter particle in certain cases.The existence of dark matter has been well established through a combination of galactic rotation curves [1][2][3][4], weak and strong gravitational lensing [5,6], Big Bang nucleosynthesis [7], the cosmic microwave background [8] and the bullet cluster [9]. From these observations, we know that dark matter is electrically neutral, nonbaryonic and composes roughly 83% of the matter and 23% of the energy of the universe. However, these observations do not tell us the detailed properties of dark matter such as its mass, spin and how it interacts with visible matter. For that, we need to observe a dark matter particle (DMP) in the laboratory.Because the Standard Model (SM) of particle physics does not contain dark-matter (among other things) it is a low-energy effective theory that fits inside a larger, more complete theory. Two prominent examples of these theories are the minimal supersymmetric extension of the SM (MSSM) and the universal extra-dimension (UED) model. In the present context, one of the most important features of these models is the presence of a new parity symmetry with the consequence that the lightest parity-odd particle (LPP) is stable and (if neutral) a dark-matter candidate [10][11][12][13]. In these theories, the LPP is a weakly interacting massive particle (WIMP) and, so, can be pair produced at particle colliders, such as the Large Hadron Collider (LHC) and the International Linear Collider (ILC).To determine the spin of a DMP at a collider, ideally, we would like to boost into the center of momentum (CM) frame of its parent particle and histogram the angle of its decay with respect to the boost direction (see Figure 1). We will call this the CM angular distribution, where θ LB is the angle of the decay product L with respect to the boost direction in the B CM system. If the width of the parent particle is narrow, this distribution will correspond with linear combinations of squares of the Wigner d challenge for dark-matter particles is that they do not interact with particle detectors and are, thus, not measured. Therefore, ...
We perform a model-independent investigation of spin and chirality correlation effects in the antler-topology processes e + e − → P + P − → ( + D 0 )( −D0 ) at highenergy e + e − colliders with polarized beams. Generally the production process e + e − → P + P − can occur not only through the s-channel exchange of vector bosons, V 0 , including the neutral Standard Model (SM) gauge bosons, γ and Z , but also through the s-and t-channel exchanges of new neutral states, S 0 and T 0 , and the u-channel exchange of new doubly charged states, U −− . The general set of (nonchiral) three-point couplings of the new particles and leptons allowed in a renormalizable quantum field theory is considered. The general spin and chirality analysis is based on the threshold behavior of the excitation curves for P + P − pair production in e + e − collisions with longitudinal-and transverse-polarized beams, the angular distributions in the production process and also the production-decay angular correlations. In the first step, we present the observables in the helicity formalism. Subsequently, we show how a set of observables can be designed for determining the spins and chiral structures of the new particles without any model assumptions. Finally, taking into account a typical set of approximately chiral invariant scenarios, we demonstrate how the spin and chirality effects can be probed experimentally at a high-energy e + e − collider.
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