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Register a new userHolder Inequalities and Bounds on the Masses of Light Quarks
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QCD Laplace sum-rules must satisfy a fundamental (Holder) inequality if they are to consistently represent an integrated hadronic cross-section. After subtraction of the pion-pole, the Laplace sum-rule of pion currents is shown to violate this fundamental inequality unless the up and down quark masses are sufficiently large, placing a lower bound on the 1.0 GeV MS-bar running masses.
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We study bounds on a neutral component of weak doublet scalar lepton. A typical example of such particle is sneutrinos in supersymmetric models. Using constraints from invisible Higgs decays we place a lower bound of approximately $m_h/2$. We recast a mono-$W/Z$ search, with hadronic vector boson tag in order to bound parameter space in the sneutrino--charged slepton mass plane. We find a lower bound on sneutrinos in the range of 55-100 GeV in the 36 $text{fb}^{-1}$ data set depending on the mass of charged component. We propose a sensitivity search in the hadronic mono-$W/Z$ channel for HL-LHC and discuss both the discovery potential in case an excess is seen and exclusion limit assuming no excess is seen.
The Holder-Brascamp-Lieb inequalities are a collection of multilinear inequalities generalizing a convolution inequality of Young and the Loomis-Whitney inequalities. The full range of exponents was classified in Bennett et al. (2008). In a setting similar to that of Ivanisvili and Volberg (2015), we introduce a notion of size for these inequalities which generalizes $L^p$ norms. Under this new setup, we then determine necessary and sufficient conditions for a generalized Holder-Brascamp-Lieb type inequality to hold and establish sufficient conditions for extremizers to exist when the underlying linear maps match those of the convolution inequality of Young.
Bell-type inequalities and violations thereof reveal the fundamental differences between standard probability theory and its quantum counterpart. In the course of previous investigations ultimate bounds on quantum mechanical violations have been found. For example, Tsirelsons bound constitutes a global upper limit for quantum violations of the Clauser-Horne-Shimony-Holt (CHSH) and the Clauser-Horne (CH) inequalities. Here we investigate a method for calculating the precise quantum bounds on arbitrary Bell-type inequalities by solving the eigenvalue problem for the operator associated with each Bell-type inequality. Thereby, we use the min-max principle to calculate the norm of these self-adjoint operators from the maximal eigenvalue yielding the upper bound for a particular set of measurement parameters. The eigenvectors corresponding to the maximal eigenvalues provide the quantum state for which a Bell-type inequality is maximally violated.
From the Dirac sea concept, we infer that a body center cubic quark lattice exists in the vacuum. Adapting the electron Dirac equation, we get a special quark Dirac equation. Using its low-energy approximation, we deduced the rest masses of the quarks: m(u)=930 Mev, m(d)=930 Mev, m(s)=1110 Mev, m(c)=2270 Mev and m(b)=5530 Mev. We predict new excited quarks d$_S$(1390), u$_C$(6490) and d$_b$(9950).
We study an upper bound on masses of additional scalar bosons from the electroweak precision data and theoretical constraints such as perturbative unitarity and vacuum stability in the two Higgs doublet model taking account of recent Higgs boson search results. If the mass of the Standard-Model-like Higgs boson is rather heavy and is outside the allowed region by the electroweak precision data, such a discrepancy should be compensated by contributions from the additional scalar bosons. We show the upper bound on masses of the additional scalar bosons to be about 2 $(1)$ TeV for the mass of the Standard-Model-like Higgs boson to be 240 $(500)$ GeV.
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