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The grand unified group $E_6$~is a predictive scheme for physics beyond the standard model (SM). It offers the possibility of extra $Z$ bosons, new vector-like fermions, sterile neutrinos, and neutral scalars in addition to the SM Higgs boson. Some previous discussions of these features are updated and extended. Their relevance to present searches at the CERN Large Hadron Collider and in patterns of neutrino masses is noted. Addition of a small set of scalar bosons at the TeV scale permits gauge unification near a scale of $10^{16}$ GeV, and leads to bounds on masses of particles beyond those in the standard model.
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Heavy-ion collisions at low beam energies explore the high density regime of strongly-interacting matter. The dynamical evolution of these collisions can be successfully described by hadronic transport approaches. In March 2019, the HADES collaboration has taken data for AgAg collisions at $E_{rm Kin}=1.58A$ GeV and in this work, we provide predictions for particle production and spectra within the Simulating Many Accelerated Strongly-interacting Hadrons (SMASH) approach. The multiplicities and spectra of strange and non-strange particles follow the expected trends as a function of system size. In particular, in AuAu collisions, much higher yields of double-strange baryons were observed experimentally than expected from a thermal model. Therefore, we incorporate a previously suggested mechanism to produce $Xi$ baryons via rare decays of high mass $N^*$ resonances and predict the multiplicities. In addition, we predict the invariant mass spectrum for dilepton emission and explore the most important sources of dileptons above 1 GeV, that are expected to indicate the temperature of the medium. Interestingly, the overall dilepton emission is very similar to the one in AuAu collisions at $1.23 A$ GeV, a hint that the smaller system at a higher energy behaves very similar to the larger system at lower beam energy.
We present multi-band results for GRB071010B based on Swift, Suzaku, and ground-based optical observations. This burst is an ideal target to evaluate the robustness of the ${rm E^{src}_{peak}-E_{iso}}$ and ${rm E^{src}_{peak}-E_{gamma}}$ relations, whose studies have been in stagnation due to the lack of the combined estimation of $rm E^{src}_{peak}$ and long term optical monitoring. The joint prompt spectral fitting using Swift/Burst Alert Telescope and Suzaku/Wide-band All sky Monitor data yielded the spectral peak energy as E$^{src}_{peak}$ of $86.5^{+6.4}_{-6.3}$ keV and E$_{iso}$ of $2.25^{+0.19}_{-0.16}times10^{52}$ erg with $z=0.947$. The optical afterglow light curve is well fitted by a simple power law with temporal index $alpha=-0.60pm0.02$. The lower limit of temporal break in the optical light curve is 9.8 days. Our multi-wavelength analysis reveals that GRB071010B follows ${rm E^{src}_{peak}-E_{iso}}$ but violates the ${rm E^{src}_{peak}-E_{gamma}}$ and ${rm E_{iso}-E^{src}_{peak}-t^{src}_{jet}}$ at more than the 3$sigma$ level.
We describe operation of the CESR-TA vertical beam size monitor (xBSM) with $e^pm$ beams with $E_{rm b}$=4 GeV. The xBSM measures vertical beam size by imaging synchrotron radiation x-rays through an optical element onto a detector array of 32 InGaAs photodiodes with 50 $mu$m pitch. The device has previously been successfully used to measure vertical beam sizes of 10-100 $mu$m on a bunch-by-bunch, turn-by-turn basis at $e^pm$ beam energies of $sim$2 GeV and source magnetic fields below 2.8 kG, for which the detector required calibration for incident x-rays of 1-5 keV. At $E_{rm b}=4.0$ GeV and $B$=4.5 kG, however, the incident synchrotron radiation spectrum extends to $sim$20 keV, requiring calibration of detector response in that regime. Such a calibration is described and then used to analyze data taken with several different thicknesses of filters in front of the detector. We obtain a relative precision of better than 4% on beam size measurement from 15-100 $mu$m over several different ranges of x-ray energy, including both 1-12 keV and 6-17 keV. The response of an identical detector, but tilted vertically by 60$^circ$ in order to increase magnfication without a longer beamline, is measured and shown to improve x-ray detection above 4 keV without compromising sensitivity to beam size. We also investigate operation of a coded aperture using gold masking backed by synthetic diamond.
We prove the perfectness of Kirillov-Reshetikhin crystals $B^{r,s}$ for types $E_{6}^{(1)}$ and $E_{7}^{(1)}$ with $r$ being the minuscule node and $sgeq 1$ using the polytope model of KR crystals introduced by Jang.
We analyse a possible connection between CP violations in the quark and lepton sectors, parametrised by the CKM and PMNS phases. If one assumes that CP breaking arises from complex Yukawa couplings, both in the quark and lepton sectors, the above connection is not possible in general, since Yukawa couplings in the two sectors have independent flavour structures. We show that both the CKM and PMNS phases can instead be generated by a vacuum phase in a class of two Higgs doublet models, and in this case a connection may be established. This scenario requires the presence of scalar FCNC at tree level, both in the quark and lepton sectors. The appearance of these FCNC is an obstacle and a blessing. An obstacle since one has to analyse which models are able to conform to the strict experimental limits on FCNC, both in the quark and lepton sectors. A blessing, because this class of models is falsifiable since FCNC arise at a level which can be probed experimentally in the near future, specially in the processes $hto e^pmtau^mp$ and $tto h c$. The connection between CP violations in CKM and PMNS is explicitely illustrated in models with Minimal Flavour Violation.
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