On the triplet anti-triplet symmetry in 3-3-1 models

We present a detailed discussion of the triplet anti-triplet symmetry in 3-3-1 models. The full set of conditions to realize this symmetry is provided, which includes in particular the requirement that the two vacuum expectation values of the two scalar triplets responsible for making the W and Z bosons massive must be interchanged. We apply this new understanding to the calculation of processes that have a Z-Z' mixing.Comment: 14 page

Freeware As An Advertisement

This paper examines the situation in which a monopolist offers freeware as an advertisement to increase the demand in order to maximize profit even though the existence of such freeware will reduce the power of the monopolist in the market. We prove that the successful application of freeware is dependent on the number of potential consumers and there exists an optimal quality design for freeware in this situation.Freeware; Software; Advertisement

Polarisation at NLO in WZ production at the LHC

The pair production of a $W$ and a $Z$ boson at the LHC is an important process to study the triple-gauge boson couplings as well as to probe new physics that could arise in the gauge sector. In particular the leptonic channel $p p \to W^\pm Z\to 3\ell +\nu + X$ is considered by ATLAS and CMS collaborations. Polarisation observables can help pinning down new physics and give information on the spin of the gauge bosons. Measuring them requires high statistics as well as precise theoretical predictions. We define in this contribution fiducial polarisation observables for the $W$ and $Z$ bosons and we present theoretical predictions in the Standard Model at next-to-leading order (NLO) including QCD as well as NLO electroweak corrections, the latter in the double-pole approximation. We also show that this approximation works remarkably well for $W^\pm Z$ production at the LHC by comparing to the full results.Comment: 6 pages, 2 figures, 2 tables. Contribution to the proceedings of the 54th Rencontres de Moriond, EW interactions and unified theory, March 16-23 2019, La Thuile, Ital

Fiducial polarization observables in hadronic WZ production: A next-to-leading order QCD+EW study

We present a study at next-to-leading-order (NLO) of the process $pp \to W^\pm Z \to \ell \nu_l \ell'^+ \ell'^-$, where $\ell,\ell' =e, \mu$, at the Large Hadron Collider. We include the full NLO QCD corrections and the NLO electroweak (EW) corrections in the double-pole approximation. We define eight fiducial polarization coefficients directly constructed from the polar-azimuthal angular distribution of the decay leptons. These coefficients depend strongly on the kinematical cuts on the transverse momentum or rapidity of the individual leptons. Similarly, fiducial polarization fractions are also defined and they can be directly related to the fiducial coefficients. We perform a detailed analysis of the NLO QCD+EW fiducial polarization observables including theoretical uncertainties stemming from the scale variation and parton distribution function uncertainties, using the fiducial phase space defined by the ATLAS and CMS experiments. We provide results in the helicity coordinate system and in the Collins-Soper coordinate system, at a center-of-mass energy of 13 TeV. The EW corrections are found to be important in two of the angular coefficients related to the $Z$ boson, irrespective of the kinematical cuts or the coordinate system. Meanwhile, those EW corrections are very small for the $W^\pm$ bosons.Comment: Substantial improvement after useful comments from the anonymous referee: Numerical results for the EW corrections to the cross sections and distributions shifted by -5 (-2)% for ATLAS (CMS) cuts after fixing a bug in the momentum assignment in some cut and histogram routines; results for polarization observables marginally affected, hence conclusions for them unchanged; published versio

Euler reflexion formulas for motivic multiple zeta functions

We introduce a new notion of \boxast-product of two integrable series with coefficients in distinct Grothendieck rings of algebraic varieties, preserving the integrability and commuting with the limit of rational series. In the same context, we define a motivic multiple zeta function with respect to an ordered family of regular functions, which is integrable and connects closely to Denef-Loeser's motivic zeta functions. We also show that the \boxast-product is associative in the class of motivic multiple zeta functions. Furthermore, a version of the Euler reflexion formula for motivic zeta functions is nicely formulated to deal with the \boxast-product and motivic multiple zeta functions, and it is proved using the theory of arc spaces. As an application, taking the limit for the motivic Euler reflexion formula we recover the well known motivic Thom-Sebastiani theorem.Comment: To appear in Journal of Algebraic Geometr

The DKAP Project The Country Report of Vietnam

Viet Nam is at the beginning of the Fourth Industrial Revolution. In order to grasp the opportunities that the revolution has brought about, and to successfully build the society of digital citizens, there must be the demand of enhancing the capacity and capability for students to meet international standards in terms of Information and Communications Technology (ICT) skills. Viet Nam was selected as one of the four countries (Viet Nam, Bangladesh, Fiji, and the Republic of Korea) to join UNESCO Bangkok’s “Digital Kids Asia Pacific (DKAP)” project, a comparative cross-national study with the aim to seek the understanding and address children’s ICT practices, attitudes, behaviors, and competency levels within an educational context. Thanks to the project, the Vietnamese research team completely conducted the survey in twenty (20) schools from five (5) provinces in Viet Nam. With the data on the digital citizenship competency levels of 1,061 10th grade students, the research team discovered the valuable findings to draw an initial big picture for Vietnamese policy makers, educators, and teachers about digital citizenship competencies of 15-year-old Vietnamese students