Glimpses of the Octonions and Quaternions History and Todays Applications in Quantum Physics

Before we dive into the accessibility stream of nowadays indicatory applications of octonions to computer and other sciences and to quantum physics let us focus for a while on the crucially relevant events for todays revival on interest to nonassociativity. Our reflections keep wandering back to the $Brahmagupta$ $Fibonacc$ two square identity and then via the $Euler$ four square identity up to the $Degen$ $Ggraves$ $Cayley$ eight square identity. These glimpses of history incline and invite us to retell the story on how about one month after quaternions have been carved on the $Broughamian$ bridge octonions were discovered by $John$ $Thomas$ $Ggraves$, jurist and mathematician, a friend of $William$ $Rowan$ $Hamilton$. As for today we just mention en passant quaternionic and octonionic quantum mechanics, generalization of $Cauchy$ $Riemann$ equations for octonions and triality principle and $G_2$ group in spinor language in a descriptive way in order not to daunt non specialists. Relation to finite geometries is recalled and the links to the 7stones of seven sphere, seven imaginary octonions units in out of the $Plato$ cave reality applications are appointed . This way we are welcomed back to primary ideas of $Heisenberg$, $Wheeler$ and other distinguished fathers of quantum mechanics and quantum gravity foundations.Comment: 26 pages, 7 figure

Differential cross section and recoil polarization measurements for the gamma p to K+ Lambda reaction using CLAS at Jefferson Lab

We present measurements of the differential cross section and Lambda recoil polarization for the gamma p to K+ Lambda reaction made using the CLAS detector at Jefferson Lab. These measurements cover the center-of-mass energy range from 1.62 to 2.84 GeV and a wide range of center-of-mass K+ production angles. Independent analyses were performed using the K+ p pi- and K+ p (missing pi -) final-state topologies; results from these analyses were found to exhibit good agreement. These differential cross section measurements show excellent agreement with previous CLAS and LEPS results and offer increased precision and a 300 MeV increase in energy coverage. The recoil polarization data agree well with previous results and offer a large increase in precision and a 500 MeV extension in energy range. The increased center-of-mass energy range that these data represent will allow for independent study of non-resonant K+ Lambda photoproduction mechanisms at all production angles.Comment: 22 pages, 16 figure

Tensor Correlations Measured in 3He(e,e'pp)n

We have measured the 3He(e,e'pp)n reaction at an incident energy of 4.7 GeV over a wide kinematic range. We identified spectator correlated pp and pn nucleon pairs using kinematic cuts and measured their relative and total momentum distributions. This is the first measurement of the ratio of pp to pn pairs as a function of pair total momentum, $p_{tot}$. For pair relative momenta between 0.3 and 0.5 GeV/c, the ratio is very small at low $p_{tot}$ and rises to approximately 0.5 at large $p_{tot}$. This shows the dominance of tensor over central correlations at this relative momentum.Comment: 4 pages, 4 figures, submitted to PR

Coherent Photoproduction of pi^+ from 3^He

We have measured the differential cross section for the $\gamma$$^3$He$\rightarrow \pi^+ t$ reaction. This reaction was studied using the CEBAF Large Acceptance Spectrometer (CLAS) at Jefferson Lab. Real photons produced with the Hall-B bremsstrahlung tagging system in the energy range from 0.50 to 1.55 GeV were incident on a cryogenic liquid $^3$He target. The differential cross sections for the $\gamma$$^3$He$\rightarrow \pi^+ t$ reaction were measured as a function of photon-beam energy and pion-scattering angle. Theoretical predictions to date cannot explain the large cross sections except at backward angles, showing that additional components must be added to the model.Comment: 11 pages, 16 figure

A Bayesian analysis of pentaquark signals from CLAS data

We examine the results of two measurements by the CLAS collaboration, one of which claimed evidence for a $\Theta^{+}$ pentaquark, whilst the other found no such evidence. The unique feature of these two experiments was that they were performed with the same experimental setup. Using a Bayesian analysis we find that the results of the two experiments are in fact compatible with each other, but that the first measurement did not contain sufficient information to determine unambiguously the existence of a $\Theta^{+}$. Further, we suggest a means by which the existence of a new candidate particle can be tested in a rigorous manner.Comment: 5 pages, 3 figure

First measurement of direct f0(980)f_0(980) photoproduction on the proton

We report on the results of the first measurement of exclusive $f_0(980)$ meson photoproduction on protons for $E_\gamma=3.0 - 3.8$ GeV and $-t = 0.4-1.0$ GeV$^2$. Data were collected with the CLAS detector at the Thomas Jefferson National Accelerator Facility. The resonance was detected via its decay in the $\pi^+ \pi^-$ channel by performing a partial wave analysis of the reaction $\gamma p \to p \pi^+ \pi^-$. Clear evidence of the $f_0(980)$ meson was found in the interference between $P$ and $S$ waves at $M_{\pi^+ \pi^-}\sim 1$ GeV. The $S$-wave differential cross section integrated in the mass range of the $f_0(980)$ was found to be a factor of 50 smaller than the cross section for the $\rho$ meson. This is the first time the $f_0(980)$ meson has been measured in a photoproduction experiment

A cellular chemical probe targeting the chromodomains of Polycomb repressive complex 1

We report the design and characterization of UNC3866, a potent antagonist of the methyllysine (Kme) reading function of the Polycomb CBX and CDY families of chromodomains. Polycomb CBX proteins regulate gene expression by targeting Polycomb repressive complex 1 (PRC1) to sites of H3K27me3 via their chromodomains. UNC3866 binds the chromodomains of CBX4 and CBX7 most potently, with a K d of â ∼1/4100 nM for each, and is 6-to 18-fold selective as compared to seven other CBX and CDY chromodomains while being highly selective over >250 other protein targets. X-ray crystallography revealed that UNC3866's interactions with the CBX chromodomains closely mimic those of the methylated H3 tail. UNC4195, a biotinylated derivative of UNC3866, was used to demonstrate that UNC3866 engages intact PRC1 and that EED incorporation into PRC1 is isoform dependent in PC3 prostate cancer cells. Finally, UNC3866 inhibits PC3 cell proliferation, consistent with the known ability of CBX7 overexpression to confer a growth advantage, whereas UNC4219, a methylated negative control compound, has negligible effects

Erratum: Addendum: A cellular chemical probe targeting the chromodomains of Polycomb repressive complex 1 (Nature chemical biology (2016) 12 3 (180-187))

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Partial wave analysis of the reaction gamma p -> p omega$ and the search for nucleon resonances

An event-based partial wave analysis (PWA) of the reaction gamma p -> p omega has been performed on a high-statistics dataset obtained using the CLAS at Jefferson Lab for center-of-mass energies from threshold up to 2.4 GeV. This analysis benefits from access to the world's first high precision spin density matrix element measurements, available to the event-based PWA through the decay distribution of omega-> pi+ pi - pi0. The data confirm the dominance of the t-channel pi0 exchange amplitude in the forward direction. The dominant resonance contributions are consistent with the previously identified states F[15](1680) and D[13](1700) near threshold, as well as the G[17](2190) at higher energies. Suggestive evidence for the presence of a J(P)=5/2(+) state around 2 GeV, a "missing" state, has also been found. Evidence for other states is inconclusive

Deeply Virtual Compton Scattering Beam-Spin Asymmetries

The beam spin asymmetries in the hard exclusive electroproduction of photons on the proton (ep -> epg) were measured over a wide kinematic range and with high statistical accuracy. These asymmetries result from the interference of the Bethe-Heitler process and of deeply virtual Compton scattering. Over the whole kinematic range (x_B from 0.11 to 0.58, Q^2 from 1 to 4.8 GeV^2, -t from 0.09 to 1.8 GeV^2), the azimuthal dependence of the asymmetries is compatible with expectations from leading-twist dominance, A = a*sin(phi)/[1+c*cos(phi)]. This extensive set of data can thus be used to constrain significantly the generalized parton distributions of the nucleon in the valence quark sector.Comment: 1 tex file (6 pages), 4 (eps) figure