Regularity of the Hardy-Littlewood maximal operator on block decreasing functions

We study the Hardy-Littlewood maximal operator defined via an unconditional norm, acting on block decreasing functions. We show that the uncentered maximal operator maps block decreasing functions of special bounded variation to functions with integrable distributional derivatives, thus improving their regularity. In the special case of the maximal operator defined by the l_infty-norm, that is, by averaging over cubes, the result extends to block decreasing functions of bounded variation, not necessarily special.Comment: 26 page

Vector triplets at the LHC

Several popular extensions of the Standard Model predict extra vector fields that transform as triplets under the gauge group SU(2)_L. These multiplets contain Z' and W' bosons, with masses and couplings related by gauge invariance. We review some model-independent results about these new vector bosons, with emphasis on di-lepton and lepton-plus-missing-energy signals at the LHC.Comment: LaTex 5 pages. Talk by M. Perez-Victoria at LHCP 2013, Barcelona, Spain, May 13-18, 2013. New reference adde

Constraining decaying dark matter with neutron stars

The amount of decaying dark matter, accumulated in the central regions in neutron stars together with the energy deposition rate from decays, may set a limit on the neutron star survival rate against transitions to more compact objects provided nuclear matter is not the ultimate stable state of matter and that dark matter indeed is unstable. More generally, this limit sets constraints on the dark matter particle decay time, $\tau_{\chi}$. We find that in the range of uncertainties intrinsic to such a scenario, masses $(m_{\chi}/ \rm TeV) \gtrsim 9 \times 10^{-4}$ or $(m_{\chi}/ \rm TeV) \gtrsim 5 \times 10^{-2}$ and lifetimes ${\tau_{\chi}}\lesssim 10^{55}$ s and ${\tau_{\chi}}\lesssim 10^{53}$ s can be excluded in the bosonic or fermionic decay cases, respectively, in an optimistic estimate, while more conservatively, it decreases $\tau_{\chi}$ by a factor $\gtrsim10^{20}$. We discuss the validity under which these results may improve with other current constraints.Comment: 6 pages, 1 figure, matches published versio

Revising the Solution of the Neutrino Oscillation Parameter Degeneracies at Neutrino Factories

In the context of neutrino factories, we review the solution of the degeneracies in the neutrino oscillation parameters. In particular, we have set limits to $\sin^2 2\theta_{13}$ in order to accomplish the unambiguous determination of $\theta_{23}$ and $\delta$. We have performed two different analysis. In the first, at a baseline of 3000 km, we simulate a measurement of the channels $\nu_e\to\nu_\mu$, $\nu_e\to\nu_\tau$ and $\bar{\nu}_\mu\to\bar{\nu}_\mu$, combined with their respective conjugate ones, with a muon energy of 50 GeV and a running time of five years. In the second, we merge the simulated data obtained at L=3000 km with the measurement of $\nu_e\to\nu_\mu$ channel at 7250 km, the so called 'magic baseline'. In both cases, we have studied the impact of varying the $\nu_\tau$ detector efficiency-mass product, $(\epsilon_{\nu_\tau}\times M_\tau)$, at 3000 km, keeping unchanged the $\nu_\mu$ detector mass and its efficiency. At L=3000 km, we found the existance of degenerate zones, that corresponds to values of $\theta_{13}$, which are equal or almost equal to the true ones. These zones are extremely difficult to discard, even when we increase the number of events. However, in the second scenario, this difficulty is overcomed, demostrating the relevance of the 'magic baseline'. From this scenario, the best limits of $\sin^2 2\theta_{13}$, reached at $3\sigma$, for $\sin^2 2\theta_{23}=0.95$, 0.975 and 0.99 are: 0.008, 0.015 and 0.045, respectively, obtained at $\delta=0$, and considering $(\epsilon_{\nu_\tau}\times M_\tau) \approx 125$, which is five times the initial efficiency-mass combination.Comment: 40 pages, 18 figures; added references, corrected typos, updated Eq (15c