Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userGeometric Properties of function $az^{2}J_{ u }^{prime prime }(z)+bzJ_{ u }^{prime}(z)+cJ_{ u }(z)$
104
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In this paper our aim is to find the radii of starlikeness and convexity for three different kind of normalization of the $N_ u(z)=az^{2}J_{ u }^{prime prime }(z)+bzJ_{ u }^{prime}(z)+cJ_{ u }(z)$ function, where $J_ u(z)$ is called the Bessel function of the first kind of order $ u.$ The key tools in the proof of our main results are the Mittag-Leffler expansion for $N_ u(z)$ function and properties of real zeros of it. In addition, by using the Euler-Rayleigh inequalities we obtain some tight lower and upper bounds for the radii of starlikeness and convexity of order zero for the normalized $N_ u(z)$ function. Finally, we evaluate certain multiple sums of the zeros for $N_ u(z)$ function.
rate research
Read More
We study $Z$ phenomenology at hadron colliders in an $U(1)$ extended MSSM. We choose a $U(1)$ model with a secluded sector, where the tension between the electroweak scale and developing a large enough mass for $Z$ is resolved by incorporating three additional singlet superfields into the model. We perform a detailed analysis of the production, followed by decays, including into supersymmetric particles, of a $Z$ boson with mass between 4 and 5.2 TeV, with particular emphasis on its possible discovery. We select three different scenarios consistent with the latest available experimental data and relic density constraints, and concentrate on final signals with two leptons, four leptons and six leptons. Including the SM background from processes with two, three or four vector bosons, we show the likelihood of observing a $Z^prime$ boson is not promising for the HL-LHC at 14 TeV. While at 27 and 100 TeV, the situation is more optimistic, and we devise specific benchmark scenarios which could be observed.
We analyse supersymmetric models augmented by an extra $U(1)$ gauge group. To avoid anomalies in these models without introducing exotics, we allow for family-dependent $U(1)^prime$ charges, and choose a simple form for these, dependent on one $U(1)^prime$ charge parameter only. With this choice, $Z^prime$ decays into di-taus but not di-leptons, weakening considerably the constraints on its mass. In the supersymmetric sector, the effect is to lower the singlino mass, allowing it to be the dark matter candidate. We investigate the dark matter constraints and collider implications of such models, with mostly singlino, or mostly higgsinos, or a mixture of the two as lightest supersymmetric particles. In these scenarios, $Z^prime$ decays significantly into chargino or neutralino pairs, and thus indirectly into final state leptons. We devise benchmarks which, with adequate cuts, can yield signals visible at the high-luminosity LHC.
The flavorful $Z^prime$ model with its couplings restricted to the left-handed second generation leptons and third generation quarks can potentially resolve the observed anomalies in $R_K$ and $R_{K^*}$. After examining the current limits on this model from various low-energy processes, we probe this scenario at 14 TeV high-luminosity run of the LHC using two complementary channels: one governed by the coupling of $Z$ to $b$-quarks and the other to muons. We also discuss the implications of the latest LHC high mass resonance searches in the dimuon channel on the model parameter space of our interest.
We consider a neutrinophilic $U(1)$ extension of the standard model (SM) which couples only to SM isosinglet neutral fermions, charged under the new group. The neutral fermions couple to the SM matter fields through Yukawa interactions. The neutrinos in the model get their masses from a standard inverse-seesaw mechanism while an added scalar sector is responsible for the breaking of the gauged $U(1)$ leading to a light neutral gauge boson ($Z$) which has minimal interaction with the SM sector. We study the phenomenology of having such a light $Z$ in the context of neutrinophilic interactions as well as the role of allowing kinetic mixing between the new $U(1)$ group with the SM hypercharge group. We show that current experimental searches allow for a very light $Z$ if it does not couple to SM fields directly and highlight the search strategies at the LHC. We observe that multi-lepton final states in the form of $(4ell + mET)$ and $(3ell + 2j + mET)$ could be crucial in discovering such a neutrinophilic gauge boson lying in a mass range of $200$--$500$ GeV.
Recently the RBC-UKQCD lattice collaboration presented new results for the hadronic matrix elements relevant for the ratio $varepsilon/varepsilon$ in the Standard Model (SM). With the present knowledge of the Wilson coefficients and isospin breaking effects there is still much room for new physics (NP) contributions to $varepsilon/varepsilon$ which could both enhance or suppress this ratio to agree with the data. The new SM value for the $K^0-bar K^0$ mass difference $Delta M_K$ from RBC-UKQCD is on the other hand by $2sigma$ above the data hinting for NP required to suppress $Delta M_K$. Simultaneously the most recent results for $K^+rightarrowpi^+ ubar u$ from NA62 and for $K_{L}rightarrowpi^0 ubar u$ from KOTO still allow for significant NP contributions. We point out that the suppression of $Delta M_K$ by NP requires the presence of new CP-violating phases with interesting implications for $Ktopi ubar u$, $K_Stomu^+mu^-$ and $K_Ltopi^0ell^+ell^-$ decays. Considering a $Z^prime$-scenario within the SMEFT we analyze the dependence of all these observables on the size of NP still allowed by the data on $varepsilon/varepsilon$. The NP QCD penguin scenario for $varepsilon/varepsilon$ is excluded by SMEFT renormalization group effects in $varepsilon_K$ so that NP effects in $varepsilon/varepsilon$ are governed by electroweak penguins. We also investigate for the first time whether the presence of a heavy $Z^prime$ with flavour violating couplings could generate through top Yukawa renormalization group effects FCNCs mediated by the SM $Z$-boson. The outcome turns out to be very interesting.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
