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Register a new userTwo-Loop Threshold Singularities, Unstable Particles and Complex Masses
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The effect of threshold singularities induced by unstable particles on two-loop observables is investigated and it is shown how to cure them working in the complex-mass scheme. The impact on radiative corrections around thresholds is thoroughly analyzed and shown to be relevant for two selected LHC and ILC applications: Higgs production via gluon fusion and decay into two photons at two loops in the Standard Model. Concerning Higgs production, it is essential to understand possible sources of large corrections in addition to the well-known QCD effects. It is shown that NLO electroweak corrections can incongruently reach a 10 % level around the WW vector-boson threshold without a complete implementation of the complex-mass scheme in the two-loop calculation.
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We study the survival probability of moving relativistic unstable particles with definite momentum $vec{p} eq 0$. The amplitude of the survival probability of these particles is calculated using its integral representation. We found decay curves of such particles for the quantum mechanical models considered. These model studies show that late time deviations of the survival probability of these particles from the exponential form of the decay law, that is the transition times region between exponential and non-expo-nen-tial form of the survival probability, should occur much earlier than it follows from the classical standard approach resolving itself into replacing time $t$ by $t/gamma$ (where $gamma$ is the relativistic Lorentz factor) in the formula for the survival probability and that the survival probabilities should tend to zero as $trightarrow infty$ much slower than one would expect using classical time dilation relation. Here we show also that for some physically admissible models of unstable states the computed decay curves of the moving particles have fluctuating form at relatively short times including times of order of the lifetime.
Three-loop vacuum integrals are an important building block for the calculation of a wide range of three-loop corrections. Until now, only results for integrals with one and two independent mass scales are known, but in the electroweak Standard Model and many extensions thereof, one often encounters more mass scales of comparable magnitude. For this reason, a numerical approach for the evaluation of three-loop vacuum integrals with arbitrary mass pattern is proposed here. Concretely, one can identify a basic set of three master integral topologies. With the help of dispersion relations, each of these can be transformed into one-dimensional or, for the most complicated case, two-dimensional integrals in terms of elementary functions, which are suitable for efficient numerical integration.
The spectrum of hadrons is the manifestation of color confinement of quantum chromodynamics. Hadronic resonances correspond to poles of the S-matrix. Since 2003, lots of new hadron resonant structures were discovered in the mass regions from light mesons to hadrons containing a pair of a heavy quark and an antiquark. Many of them are candidates of exotic hadrons, and they are usually observed as peaks in invariant mass distributions. However, the S-matrix also has kinematical singularities due to the on-shellness of intermediate particles for a process, such as two-body thresholds and triangle singularities, and they can produce peaks as well. On the one hand, such singularities may be misidentified as resonances; on the other hand, they can be used as tools for precision measurements. In this paper, we review the threshold cusps and various triangle singularities in hadronic reactions, paying attention to their manifestations in phenomena related to exotic hadron candidates.
We present a composite scotogenic model for neutrino masses, which are generated via loops of $mathbb{Z}_2$-odd composite scalars. We consider three different approaches to the couplings of the neutrinos (including three right-handed singlets) and the composite sector: ETC-like four-fermion interactions, fundamental partial compositeness and fermion partial compositeness. In all cases, the model can feature sizeable couplings and remain viable with respect to various experimental constraints if the three $ mathbb{Z}_2 $-odd right-handed neutrinos have masses between the TeV and the Planck scales. Additionally, the lightest $mathbb{Z}_2$-odd composite scalar may play the role of Dark Matter, either via thermal freeze-out or as an asymmetric relic. This mechanism can be featured in a variety of models based on vacuum misalignment. For concreteness, we demonstrate it in a composite two-Higgs scheme based on the coset SU(6)/Sp(6).
We present a program for the numerical evaluation of scalar integrals and tensor form factors entering the calculation of one-loop amplitudes which supports the use of complex masses in the loop integrals. The program is built on an earlier version of the golem95 library, which performs the reduction to a certain set of basis integrals using a formalism where inverse Gram determinants can be avoided. It can be used to calculate one-loop amplitudes with arbitrary masses in an algebraic approach as well as in the context of a unitarity-inspired numerical reconstruction of the integrand.
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