arXiv subjects

Daniel Hernández

Publications and source records attributed to Daniel Hernández.

23 records · Page 2Linked to original sources

arXiv2016

Correlation and Substitution in SPARQL

In the current SPARQL specification the notion of correlation and substitution are not well defined. This problem triggers several ambiguities in the semantics. In fact, implementations as Fuseki and Virtuoso assume different semantics. In this technical report, we provide a semantics of correlation and substitution following the classic philosophy of substitution and correlation in logic, programming languages and SQL. We think this proposal not only fix the current ambiguities and problems, but helps to set a safe formal base to further extensions of the language. This work is part of an ongoing work of Daniel Hernandez. These anomalies in the W3C Specification of SPARQL 1.1 were detected early and reported no later than 2014, when two erratas were registered (cf. https://www.w3.org/2013/sparql-errata#errata-query-8 and https://www.w3.org/2013/sparql-errata#errata-query-10).

cs.DB↗

arXiv2016

Imperfect Mirrors of the Standard Model

Inspired by the Standard Model of particle physics, we discuss a mechanism for constructing chiral, anomaly-free gauge theories. The gauge symmetries and particle content of such theories are identified using subgroups and complex representations of simple anomaly-free Lie groups, such as $SO(10)$ or $E_6$. We explore, using mostly $SO(10)$ and the $\mathbf{16}$ representation, several of these "imperfect copies" of the Standard Model, including $U(1)^N$ theories, $SU(5)\otimes U(1)$ theories, $SU(4)\otimes U(1)^2$ theories with 4-plets and 6-plets, and chiral $SU(3)\otimes SU(2)\otimes U(1)$. A few general properties of such theories are discussed, as well as how they might shed light on nonzero neutrino masses, the dark matter puzzle, and other phenomenologically relevant questions.

hep-ph↗

arXiv2016

On the behavior of singularities at the $F$-pure threshold

We provide a family of examples where the $F$-pure threshold and the log canonical threshold of a polynomial are different, but where $p$ does not divide the denominator of the $F$-pure threshold (compare with an example of \mustata-Takagi-Watanabe). We then study the $F$-signature function in the case where either the $F$-pure threshold and log canonical threshold coincide or where $p$ does not divide the denominator of the $F$-pure threshold. We show that the $F$-signature function behaves similarly in those two cases. Finally, we include an appendix which shows that the test ideal can still behave in surprising ways even when the $F$-pure threshold and log canonical threshold coincide.

math.AC↗

arXiv2015

Flavorspin

We propose that the flavor structure of the quark sector of the Standard Model is determined by a vectorial SU(2) flavor symmetry, which we dub Flavorspin, under which quarks transform as triplets. The fundamental Yukawa couplings are real and CP violation is not directly linked to the breaking of the flavor symmetry. A CP-conserving scenario is naturally defined with the feature that the Yukawa spurions are completely determined in terms of the masses and mixings. CP violation may be introduced with negligible impact on low-energy observables other than generating a large CP violating phase in the Standard Model mixing matrix. The scale of flavor-symmetry violation must be large in order to prevent sizable Flavor Changing Neutral Currents, which can be partially suppressed if Flavorspin is a residual symmetry of a larger flavor group.

hep-ph↗

arXiv2015

Non-Unitary Neutrino Propagation From Neutrino Decay

Neutrino propagation in space-time is not constrained to be unitary if very light states - lighter than the active neutrinos - exist into which neutrinos may decay. If this is the case, neutrino flavor-change is governed by a handful of extra mixing and "oscillation" parameters, including new sources of CP-invariance violation. We compute the transition probabilities in the two- and three-flavor scenarios and discuss the different phenomenological consequences of the new physics. These are qualitatively different from other sources of unitarity violation discussed in the literature.

hep-ph↗