Abstract: We consider the possibility of grand unification of the SU(3)(c) circle times SU(3)(L) circle times U(1)(X) model in an SU(6) gauge unification group. Two possibilities arise. Unlike other conventional grand unified theories, in SU(6) one can embed the 331 model as a subgroup such that different multiplets appear with different multiplicities. Such a scenario may emerge from the flux breaking of the unified group in an E(6) F-theory GUT. This provides new ways of achieving gauge coupling unification in 331 models while providing the radiative origin of neutrino masses. Alternatively, a sequential variant of the SU(3)(c) circle times SU(3)(L) circle times U(1)(X) model can fit within a minimal SU(6) grand unification, which in turn can be a natural E(6) subgroup. This minimal SU(6) embedding does not require any bulk exotics to account for the chiral families while allowing for a TeV scale SU(3)(c) circle times SU(3)(L) circle times U(1)(X) model with seesaw-type neutrino masses.

Abstract: We study the decoupling process of neutrinos in the early universe in the presence of three-flavour oscillations. The evolution of the neutrino spectra is found by solving the corresponding momentum-dependent kinetic equations for the neutrino density matrix, including for the first time the proper collision integrals for both diagonal and off-diagonal elements. This improved calculation modifies the evolution of the off-diagonal elements of the neutrino density matrix and changes the deviation from equilibrium of the frozen neutrino spectra. However, it does not vary the contribution of neutrinos to the cosmological energy density in the form of radiation, usually expressed in terms of the effective number of neutrinos, N-eff. We find a value of N-eff = 3.045, in agreement with previous theoretical calculations and consistent with the latest analysis of Planck data. This result does not depend on the ordering of neutrino masses. We also consider the effect of non-standard neutrino-electron interactions (NSI), predicted in many theoretical models where neutrinos acquire mass. For two sets of NSI parameters allowed by present data, we find that Neff can be reduced down to 3.040 or enhanced up to 3.059.

Abstract: A diphoton excess with an invariant mass of about 750 GeV has been recently reported by both ATLAS and CMS experiments at LHC. While the simplest interpretation requires the resonant production of a 750 GeV (pseudo) scalar, here we consider an alternative setup, with an additional heavy parent particle which decays into a pair of 750 GeV resonances. This configuration improves the agreement between the 8 and 13 TeV data. Moreover, we include a dark matter candidate in the form of a Majorana fermion which interacts through the 750 GeV portal. The invisible decays of the light resonance help to suppress additional decay channels into Standard Model particles in association with the diphoton signal. We realise our hierarchical framework in the context of an effective theory, and we analyse the diphoton signal as well as the consistency with other LHC searches. We finally address the interplay of the LHC results with the dark matter phenomenology, namely the compatibility with the relic density abundance and the indirect detection bounds.

Abstract: We compute the two-loop QED corrections to the Altarelli-Parisi (AP) splitting functions by using a deconstructive algorithmic Abelianization of the well-known NLO QCD corrections. We present explicit results for the full set of splitting kernels in a basis that includes the leptonic distribution functions that, starting from this order in the QED coupling, couple to the partonic densities. Finally, we perform a phenomenological analysis of the impact of these corrections in the splitting functions.

Abstract: The decays B-c(+) -> J/psi D-s(+) and B-c(+) -> J/psi D-s*(+) are studied with the ATLAS detector at the LHC using a dataset corresponding to integrated luminosities of 4.9 and 20.6 fb(-1) of pp collisions collected at centre-of-mass energies root s = 7 TeV and 8 TeV, respectively. Signal candidates are identified through J/psi -> mu(+)mu(-) and D-s(()*()+) -> phi pi(+)(gamma/pi(0)) decays. With a two-dimensional likelihood fit involving the B-c(+) reconstructed invariant mass and an angle between the mu(+) and D-s(+) candidate momenta in the muon pair rest frame, the yields of B-c(+) -> J/psi D-s(+) and B-c(+) -> J/psi D-s*(+), and the transverse polarisation fraction in B-c(+) -> J/psi D-s*(+) decay are measured. The transverse polarisation fraction is determined to be Gamma +/-+/-(B-c(+) -> J/psi D-s*(+))/Gamma(B-c(+) -> J/psi D-s*(+)) = 0.38 +/- 0.23 +/- 0.07, and the derived ratio of the branching fractions of the two modes is B-Bc+ -> J/psi D-s*+/B-Bc+ -> J/psi D-s(+) = 2.8(-0.8)(+1.2) +/- 0.3, where the first error is statistical and the second is systematic. Finally, a sample of B-c(+) -> J/psi pi(+) decays is used to derive the ratios of branching fractions B-Bc+ -> J/psi D-s*+/B-Bc+ -> J/psi pi(+) = 3.8 +/- 1.1 +/- 0.4 +/- 0.2 and B-Bc+ -> J/psi D-s*+/B-Bc+ -> J/psi pi(+) = 10.4 +/- 3.1 +/- 1.5 +/- 0.6, where the third error corresponds to the uncertainty of the branching fraction of D-s(+) -> phi(K+ K-)pi(+) decay. The available theoretical predictions are generally consistent with the measurement.