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It has been suggested that scattering cross sections at very high energies for producing large numbers of Higgs particles may exhibit factorial growth, and that curing this growth might be relevant to other questions in the Standard Model. We point out, first, that the question is inherently non-perturbative; low orders in the formal perturbative expansion do not give a good approximation to the scattering amplitude for sufficiently large N for any fixed, small value of the coupling. Focusing on $lambda phi^{4}$ theory, we argue that there may be a systematic approximation scheme for processes where N particles near threshold scatter to produce N particles, and discuss the leading contributions to the scattering amplitude and cross sections in this limit. Scattering amplitudes do not grow as rapidly as in perturbation theory. Additionally, partial and total cross sections do not show factorial growth. In the case of cross sections for $2 to N$ particles, there is no systematic large N approximation available. That said, we provide evidence that non-perturbatively, there is no factorial growth in partial or total cross sections.
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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.
We demonstrate how to efficiently expand cross sections for color-singlet production at hadron colliders around the kinematic limit of all final state radiation being collinear to one of the incoming hadrons. This expansion is systematically improvable and applicable to a large class of physical observables. We demonstrate the viability of this technique by obtaining the first two terms in the collinear expansion of the rapidity distribution of the gluon fusion Higgs boson production cross section at next-to-next-to leading order (NNLO) in QCD perturbation theory. Furthermore, we illustrate how this technique is used to extract universal building blocks of scattering cross section like the N-jettiness and transverse momentum beam function at NNLO.
Neutrino oscillations physics is entered in the precision era. In this context accelerator-based neutrino experiments need a reduction of systematic errors to the level of a few percent. Today one of the most important sources of systematic errors are neutrino-nucleus cross sections which in the hundreds-MeV to few-GeV energy region are known with a precision not exceeding 20%. In this article we review the present experimental and theoretical knowledge of the neutrino-nucleus interaction physics. After introducing neutrino oscillation physics and accelerator-based neutrino experiments, we overview general aspects of the neutrino-nucleus cross sections, both theoretical and experimental views. Then we focus on these quantities in different reaction channels. We start with the quasielastic and quasielastic-like cross section, putting a special emphasis on multinucleon emission channel which attracted a lot of attention in the last few years. We review the main aspects of the different microscopic models for this channel by discussing analogies and differences among them.The discussion is always driven by a comparison with the experimental data. We then consider the one pion production channel where data-theory agreement remains very unsatisfactory. We describe how to interpret pion data, then we analyze in particular the puzzle related to the impossibility of theoretical models and Monte Carlo to simultaneously describe MiniBooNE and MINERvA experimental results. Inclusive cross sections are also discussed, as well as the comparison between the $ u_mu$ and $ u_e$ cross sections, relevant for the CP violation experiments. The impact of the nuclear effects on the reconstruction of neutrino energy and on the determination of the neutrino oscillation parameters is reviewed. A window to the future is finally opened by discussing projects and efforts in future detectors, beams, and analysis.
Neutrino oscillations physics entered in the precision era. In this context accelerator-based neutrino experiments need a reduction of systematic errors to the level of a few percent. Today one of the most important sources of systematic errors are the neutrino-nucleus cross sections. The status of our knowledge of these cross sections in the different open channels in the few-GeV region, i.e. the quasielastic, the pion production and the multinucleon emission, is reviewed. Special emphasis is devoted to the multinucleon emission channel, which attracted a lot of attention in the last few years. It is crucial to properly reconstruct the neutrino energy which enters the expression of the oscillation probability. This channel was not included in the generators used for the analyses of the neutrino cross sections and oscillations experiments.
We show that for a rather generic set of regular spectral curves, the Topological-Recursion invariants F_g grow at most like $O((beta g)! r^{-g}) $ with some $r>0$ and $betaleq 5$.
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