Local lower norm estimates for dyadic maximal operators and related Bellman functions

We provide lower $L^q$ and weak $L^p$-bounds for the localized dyadic maximal operator on $R^n$, when the local $L^1$ and the local $L^p$ norm of the function are given. We actually do that in the more general context of homo- geneous tree-like families in probability spaces.Comment: 9 page

Dyadic weights on RnR^n and reverse Holder inequalities

We prove that for any weight $\phi$ defined on $[0,1]^n$ that satisfies a reverse Holder inequality with exponent p > 1 and constant $c\ge1$ upon all dyadic subcubes of $[0,1]^n$, it's non increasing rearrangement satisfies a reverse Holder inequality with the same exponent and constant not more than $2^nc-2^n + 1$, upon all subintervals of $[0; 1]$ of the form $[0; t]$. This gives as a consequence, according to the results in [8], an interval $[p; p_0(p; c)) = I{p,c}$, such that for any $q \in I{p,c}$, we have that $\phi$ is in $L^q$.Comment: 10 page

Sharp Lorentz estimates for dyadic-like maximal operators and related Bellman functions

We precisely evaluate Bellman type functions for the dyadic maximal opeator on $R^n$ and of maximal operators on martingales related to local Lorentz type estimates. Using a type of symmetrization principle, introduced for the dyadic maximal operator in earlier works of the authors we precisely evaluate the supremum of the Lorentz quasinorm of the maximal operator on a function $\phi$ when the integral of $\phi$ is fixed and also the same Lorentz quasinorm of $\phi$ is fixed. Also we find the corresponding supremum when the integral of $\phi$ is fixed and several weak type conditions are given.Comment: 11 page

Estimates for Bellman functions related to dyadic-like maximal operators on weighted spaces

We provide some new estimates for Bellman type functions for the dyadic maximal opeator on $R^n$ and of maximal operators on martingales related to weighted spaces. Using a type of symmetrization principle, introduced for the dyadic maximal operator in earlier works of the authors we introduce certain conditions on the weight that imply estimate for the maximal operator on the corresponding weighted space. Also using a well known estimate for the maximal operator by a double maximal operators on different m easures related to the weight we give new estimates for the above Bellman type functions.Comment: 10 pages. arXiv admin note: text overlap with arXiv:1511.0611

On weak type inequalities for dyadic maximal functions

AbstractWe obtain sharp estimates for the localized distribution function of the dyadic maximal function Mϕd, given the local L1 norms of ϕ and of G○ϕ where G is a convex increasing function such that G(x)/x→+∞ as x→+∞. Using this we obtain sharp refined weak type estimates for the dyadic maximal operator

Minimal Flavour Violation for Leptoquarks

Scalar leptoquarks, with baryon and lepton number conserving interactions, could have TeV scale masses, and be produced at colliders or contribute to a wide variety of rare decays. In pursuit of some insight as to the most sensitive search channels, We assume that the leptoquark-lepton-quark coupling can be constructed from the known mass matrices. We estimate the rates for selected rare processes in three cases: leptoquarks carrying lepton and quark flavour, leptoquarks with quark flavour only, and unflavoured leptoquarks. We find that leptoquark decay to top quarks is an interesting search channel.Comment: 17 pages, 2 figures, minor changes and references adde

LHC Coverage of RPV MSSM with Light Stops

We examine the sensitivity of recent LHC searches to signatures of supersymmetry with R-parity violation (RPV). Motivated by naturalness of the Higgs potential, which would favor light third-generation squarks, and the stringent LHC bounds on spectra in which the gluino or first and second generation squarks are light, we focus on scenarios dominated by the pair production of light stops. We consider the various possible direct and cascade decays of the stop that involve the trilinear RPV operators. We find that in many cases, the existing searches exclude stops in the natural mass range and beyond. However, typically there is little or no sensitivity to cases dominated by UDD operators or LQD operators involving taus. We propose several ideas for searches which could address the existing gaps in experimental coverage of these signals.Comment: 41 pages, 12 figures; v2: included new searches (see footnote 10), minor corrections and improvement

A Stealth Supersymmetry Sampler

The LHC has strongly constrained models of supersymmetry with traditional missing energy signatures. We present a variety of models that realize the concept of Stealth Supersymmetry, i.e. models with R-parity in which one or more nearly-supersymmetric particles (a "stealth sector") lead to collider signatures with only a small amount of missing energy. The simplest realization involves low-scale supersymmetry breaking, with an R-odd particle decaying to its superpartner and a soft gravitino. We clarify the stealth mechanism and its differences from compressed supersymmetry and explain the requirements for stealth models with high-scale supersymmetry breaking, in which the soft invisible particle is not a gravitino. We also discuss new and distinctive classes of stealth models that couple through a baryon portal or Z' gauge interactions. Finally, we present updated limits on stealth supersymmetry in light of current LHC searches.Comment: 45 pages, 16 figure

Dark Matter from Minimal Flavor Violation

We consider theories of flavored dark matter, in which the dark matter particle is part of a multiplet transforming nontrivially under the flavor group of the Standard Model in a manner consistent with the principle of Minimal Flavor Violation (MFV). MFV automatically leads to the stability of the lightest state for a large number of flavor multiplets. If neutral, this particle is an excellent dark matter candidate. Furthermore, MFV implies specific patterns of mass splittings among the flavors of dark matter and governs the structure of the couplings between dark matter and ordinary particles, leading to a rich and predictive cosmology and phenomenology. We present an illustrative phenomenological study of an effective theory of a flavor SU(3)_Q triplet, gauge singlet scalar.Comment: 10 pages, 2 figures; v2: references added, minor changes to collider analysis, conclusions unchange