arXiv subjects

Roberto Martinez

Publications and source records attributed to Roberto Martinez.

4 recordsLinked to original sources

arXiv2020

Jacob's Ladder: Prime numbers in 2d

Prime numbers are one of the most intriguing figures in mathematics. Despite centuries of research, many questions remain still unsolved. In recent years, computer simulations are playing a fundamental role in the study of an immense variety of problems. In this work, we present a simple representation of prime numbers in two dimensions that allows us to formulate a number of conjectures that may lead to important avenues in the field of research on prime numbers. In particular, although the zeroes in our representation grow in a somewhat erratic, hardly predictable way, the gaps between them present a remarkable and intriguing property: a clear exponential decay in the frequency of gaps vs gap size. The smaller the gaps, the more frequently they appear. Additionally, the sequence of zeroes, despite being non-consecutive numbers, contains a number of primes approximately equal to n/log(n) , being n the number of terms in the sequence.

math.HO↗

arXiv2018

SM Higgs boson and $t\rightarrow cZ$ decays in the 2HDM type III with CP violation

We compute the contributions to rare top decays $t\rightarrow cZ$ and $t\rightarrow ch_1$ from the scalar sector in the 2HDM type III with CP violation, where $h_1$ is the Standard Model Higgs boson. The branching ratio for $BR(t\rightarrow c Z)$ and $BR(t\rightarrow c h_1)$ are obtained as a function of the model parameters. In particular, the $BR(t\rightarrow c Z)$ can increase its value up to $10^{-3}$ for $\tanβ= 1$ and masses for the additional Higgs bosons of $m_{h_2,h_3,H^\pm}\sim 0.5$ TeV. Meanwhile $BR(t\rightarrow c h_1)$ can reach values of the order of $\sim10^{-2}$. We constrain the model parameters (mixing angles of the neutral scalar fields in the CP violation context and $\tanβ$) using the reported values of the signal strengths $R_{XX}$ and $b \rightarrow s γ$ process.

hep-ph↗

arXiv2017

Top and bottom tensor couplings from a color octet scalar

We compute the one-loop contributions from a color octet scalar to the tensor anomalous couplings of top and bottom quarks to gluons, photons and W bosons. We use known constraints on the parameters of the model to compare the predicted size of these couplings with existing phenomenological constraints.

hep-ph↗

arXiv2016

Rare top decay $t \rightarrow c γ$ with flavor changing neutral scalar interactions in two Higgs doublet model

Models beyond the Standard Model with extra scalars have been highly motivated by the recent discovery of a Higgs boson. The Two Higgs Doublet Model Type III considers the most general case for the scalar potential, allowing mixing between neutral CP-even and CP-odd scalar fields. This work presents the results of the study on the $t\rightarrow cγ$ decay at one loop level if neutral flavor changing is generated by top-charm-Higgs coupling given by the Yukawa matrix. For instance, a value for the branching ratio $Br(t\rightarrow cγ)\sim 10^{-6}$ for $\tanβ=2.5$ and general neutral Higgs mixing parameters, $1.16\leqα_1\leq1.5$, $-0.48\leqα_2\leq-0.1$. The number of events for the $t\rightarrow c γ$ decay with an integrated luminosity of 300 $fb^{-1}$ is estimated as $10\lesssim N_{Eff}\lesssim 100$ for the parameters of the model constrained by experimental data.

hep-ph↗