International Journal of Modern Physics A

There is a wide class of models which give a dynamical description of the origin of flavor in terms of spontaneous symmetry breaking of an underlying symmetry. Many of these models exhibit sum rules which relate on the one hand mixing angles and the Dirac CP phase with each other and/or on the other hand neutrino masses and Majorana phases with each other. We will briefly sketch how this happens and discuss briefly the impact of renormalization group corrections to the mass sum rules.

The LHC experiments ATLAS and CMS have reported an excess in the diphoton spectrum at $\sim$750 GeV. At the same time the motivation for Supersymmetry (SUSY) remains unbowed. Consequently, we review briefly the proposals to explain this excess in SUSY, focusing on “pure” (N)MSSM solutions. We then review in more detail a proposal to realize this excess within the NMSSM. In this particular scenario a Higgs boson with mass around 750 GeV decays to two light pseudo-scalar Higgs bosons. Via mixing with the pion these pseudo-scalars decay into a pair of highly collimated photons, which are identified as one photon, thus resulting in the observed signal.

In this paper, we construct the generalized parton distribution (GPD) in terms of the kinematical variables $x$, $\xi$, $t$, using the double distribution model. By employing these functions, we could extract some quantities which makes it possible to gain a three-dimensional insight into the nucleon structure function at the parton level. The main objective of GPDs is to combine and generalize the concepts of ordinary parton distributions and form factors. They also provide an exclusive framework to describe the nucleons in terms of quarks and gluons. Here, we first calculate, in the Double Distribution model, the GPD based on the usual parton distributions arising from the GRV and CTEQ phenomenological models. Obtaining quarks and gluons angular momenta from the GPD, we would be able to calculate the scattering observables which are related to spin asymmetries of the produced quarkonium. These quantities are represented by $A_N$ and $A_{LS}$. We also calculate the Pauli and Dirac form factors in deeply virtual Compton scattering. Finally, in order to compare our results with the existing experimental data, we use the difference of the polarized cross-section for an initial longitudinal leptonic beam and unpolarized target particles $(\mathrm{\Delta }{\sigma }_{LU})$. In all cases, our obtained results are in good agreement with the available experimental data.

We scrutinize recent QCD spectral sum rules (QSSR) results to lowest order (LO) predicting the masses of the $BK$ molecule and $(su)(\overline{bd})$ four-quark states. We improve these results by adding NLO and N2LO corrections to the PT contributions giving a more precise meaning on the $b$-quark mass definition used in the analysis. We extract our optimal predictions using Laplace sum rule (LSR) within the standard stability criteria versus the changes of the external free parameters ($\tau$-sum rule variable, $t_c$ continuum threshold and subtraction constant $\mu$). The smallness of the higher order PT corrections justifies (a posteriori) the LO order results ⊕ the uses of the ambiguous heavy quark mass to that order. However, our predicted spectra in the range $(5173\sim 5226)$ MeV, summarized in Table 7, for exotic hadrons built with four different flavors $(buds)$, do not support some previous interpretations of the D0 candidate,¹ $X(5568)$, as a pure molecule or a four-quark state. If experimentally confirmed, it could result from their mixing with an angle: $sin2𝜃\approx 0.15$. One can also scan the region $(2327\sim 2444)$ MeV (where the $D_{s0}^{\ast }(2317)$ might be a good candidate) and the one $(5173\sim 5226)$ MeV for detecting these $(cuds)$ and $(buds)$ unmixed exotic hadrons (if any) via, eventually, their radiative or $\pi$+hadrons decays.

The origin of small mixing among the quarks and a large mixing among the neutrinos has been an open question in particle physics. In order to answer this question, we postulate general relations among the quarks and the leptonic mixing angles at a high scale, which could be the scale of Grand Unified Theories. The central idea of these relations is that the quark and the leptonic mixing angles can be unified at some high scale either due to some quark–lepton symmetry or some other underlying mechanism and as a consequence, the mixing angles of the leptonic sector are proportional to that of the quark sector. We investigate the phenomenology of the possible relations where the leptonic mixing angles are proportional to the quark mixing angles at the unification scale by taking into account the latest experimental constraints from the neutrino sector. These relations are able to explain the pattern of leptonic mixing at the low scale and thereby hint that these relations could be possible signatures of a quark–lepton symmetry or some other underlying quark–lepton mixing unification mechanism at some high scale linked to Grand Unified Theories.

The main motivation to study models in the presence of a minimal length is to obtain a quantum field theory free of the divergences. In this way, in this paper, we have constructed a new framework for quantum electrodynamics embedded in a minimal length scale background. New operators are introduced and the Green function method was used for the solution of the field equations, i.e. the Maxwell, Klein–Gordon and Dirac equations. We have analyzed specifically the scalar field and its one loop propagator. The mass of the scalar field regularized by the minimal length was obtained. The QED Lagrangian containing a minimal length was also constructed and the divergences were analyzed. The electron and photon propagators, and the electron self-energy at one loop as a function of the minimal length was also obtained.

We study the possibility of explaining the recently reported 750 GeV di-photon excess at LHC within the framework of a left–right symmetric model. The 750 GeV neutral scalar in the model is dominantly an admixture of neutral components of scalar bidoublets with a tiny fraction of neutral scalar triplet. Incorporating $SU(2)$ septuplet scalar pairs into the model, we enhance the partial decay width of the 750 GeV neutral scalar into di-photons through charged septuplet components in loop while keeping the neutral septuplet components as subdominant dark matter candidates. The model also predicts the decay width of the 750 GeV scalar to be around 36 GeV to be either confirmed or ruled out by future LHC data. The requirement of producing the correct di-photon signal automatically keeps the septuplet dark matter abundance subdominant in agreement with bounds from direct and indirect detection experiments. We then briefly discuss different possibilities to account for the remaining dark matter component of the Universe in terms of other particle candidates whose stability arises either due to remnant discrete symmetry after spontaneous breaking of $U{(1)}_{B-L}$ or due to high $SU(2)$-dimension forbidding their decay into lighter particles.

We present predictions for the inclusive production of bottom jets in proton–antiproton collisions at 1.96 TeV and proton–proton collisions at 7 TeV. The bottom quark is considered massless. In this scheme, we find that at small transverse momentum $(p_T)$ the ratio of the next-to-leading order to the leading-order cross-section ($K$ factor) is smaller than one. It increases with increasing $p_T$ and approaches one at larger $p_T$ at a value depending essentially on the choice of the renormalization scale. Adding nonperturbative corrections obtained from PYTHIA Monte Carlo calculations leads to reasonable agreement with experimental $b$-jet cross-sections obtained by the CDF and the CMS collaborations.

In the framework of the minimal $U{(1)}_{B-L}$ extension of the Standard Model, we investigate the Higgs boson production processes $e^{+}{e}^{-}\to ZH$, $e^{+}{e}^{-}\to {\nu }_e{\bar{\nu }}_{e}H$, $e^{+}{e}^{-}\to t\bar{t}H$, $e^{+}{e}^{-}\to ZHH$ and $e^{+}{e}^{-}\to {\nu }_e{\bar{\nu }}_{e}HH$ at the International Linear Collider (ILC). We present the production cross-sections, the relative corrections and compare our results with the expected experimental accuracies for Higgs decay channel $H\to b\bar{b}$. In the allowed parameter space, we find that the effects of the three single Higgs boson production processes might approach the observable threshold of the ILC. But the Higgs signal strengths ${\mu }_{b\bar{b}}$ of the two double Higgs boson production processes are all out of the observable threshold so that these effects will be difficult to be observed at the ILC.

With an analytical solutions of DGLAP evolution equations based on the Laplace transform method, we find the fragmentation functions (FFs) of neutral mesons, ${\pi }^0$ and $k^0$ at NLO approximation. We also calculated the total fragmentation functions of these mesons and compared them with experimental data and those from global fits. The results show a good agreement between our solutions and other models and they are compatible with experimental data.