The extremal algebra on two hermitians with square 1

Let Ea(u,v) be the extremal algebra determined by two hermitians u and v with u2 = v2 = 1. We show that: Ea(u,v) = {f=gu:f,g ε C(T)}, where T is the unit circle; Ea(u,v) is C*-equivelant to C*(G), where G is the infinite dihedral group; most of the hermitian elements k od Ea(u,v) have the property that kn is hermitian for all odd n but for no even n; any two hermitian words in G generate an isometric copy of Ea(u,v) in Ea(u,v)

Some extremal algebras for hermitians

We study three extremal Banach algebras: (a) generated by two hermitian unitaries; (b) generated by an element of norm 1 all of whose odd positive powers are hermitian; (c) generated by an element of norm 1 all of whose even positive powers are hermitian. In all three cases the numerical range is found for various elements. The second algebra is shown to be isometrically isomorphic to a subalgebra of the first. The third algebra is identified with a space of functions

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

Quarkonium Physics at a Fixed-Target Experiment using the LHC Beams

We outline the many quarkonium-physics opportunities offered by a multi-purpose fixed-target experiment using the p and Pb LHC beams extracted by a bent crystal. This provides an integrated luminosity of 0.5 fb-1 per year on a typical 1cm-long target. Such an extraction mode does not alter the performance of the collider experiments at the LHC. With such a high luminosity, one can analyse quarkonium production in great details in pp, pd and pA collisions at sqrt(sNN)~115 GeV and at sqrt(sNN)~72 GeV in PbA collisions. In a typical pp (pA) run, the obtained quarkonium yields per unit of rapidity are 2-3 orders of magnitude larger than those expected at RHIC and about respectively 10 (70) times larger than for ALICE. In PbA, they are comparable. By instrumenting the target-rapidity region, the large negative-xF domain can be accessed for the first time, greatly extending previous measurements by Hera-B and E866. Such analyses should help resolving the quarkonium-production controversies and clear the way for gluon PDF extraction via quarkonium studies. The nuclear target-species versatility provides a unique opportunity to study nuclear matter and the features of the hot and dense matter formed in PbA collisions. A polarised proton target allows the study of transverse-spin asymmetries in J/psi and Upsilon production, providing access to the gluon and charm Sivers functions.Comment: Proceedings of the workshop "30 years of strong interactions", Spa, Belgium, 6-8 April 2011. Version to appear in Few-Body Systems. 14 pages, 2 tables, LaTe

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

Tensor Polarization of the phi meson Photoproduced at High t

As part of a measurement of the cross section of $\phi$ meson photoproduction to high momentum transfer, we measured the polar angular decay distribution of the outgoing $K^+$ in the channel $\phi \to K^+K^-$ in the $\phi$ center-of-mass frame (the helicity frame). We find that s-channel helicity conservation (SCHC) holds in the kinematical range where $t$-channel exchange dominates (up to $-t \sim 2.5$ GeV$^2$ for $E_{\gamma}$=3.6 GeV). Above this momentum, $u$-channel production of a $\phi$ meson dominates and induces a violation of SCHC. The deduced value of the $\phi NN$ coupling constant lies in the upper range of previously reported values.Comment: 6 pages; 5 figure

Beam Spin Asymmetries in DVCS with CLAS at 4 .8 GeV

We report measurements of the beam spin asymmetry in Deeply Virtual Compton Scattering (DVCS) at an electron beam energy of 4.8 GeV using the CLAS detector at the Thomas Jefferson National Accelerator Facility. The DVCS beam spin asymmetry has been measured in a wide range of kinematics, 1(GeV/c)$^2$ $<Q^2<2.8$(GeV/c)$^2$, $0.12<x_B<0.48$, and 0.1 (GeV/c)$^2$ $<-t<0.8$(GeV/c)$^2$, using the reaction \pEpX. The number of H$(e,e^{\prime}\gamma p)$ and H$(e,e^{\prime}\pi^0 p)$ events are separated in each $(Q^2,x_B,t)$ bin by a fit to the line shape of the H$(e,e^{\prime}p)X$ $M_x^2$ distribution. The validity of the method was studied in detail using experimental and simulated data. It was shown, that with the achieved missing mass squared resolution and the available statistics, the separation of DVCS-BH and $\pi^0$ events can reliably be done with less than 5% uncertainty. The $Q^2$- and $t$-dependences of the $\sin\phi$ moments of the asymmetry are extracted and compared with theoretical calculations

Semi-inclusive pi(0) target and beam-target asymmetries from 6 GeV electron scattering with CLAS

We present precision measurements of the target and beam-target spin asymmetries from neutral pion electroproduction in deep-inelastic scattering (DIS) using the CEBAF Large Acceptance Spectrometer (CLAS) at Jefferson Lab. We scattered 6-GeV, longitudinally polarized electrons off longitudinally polarized protons in a cryogenic $^{14}$NH$_3$ target, and extracted double and single target spin asymmetries for $ep\rightarrow e^\prime\pi^0X$ in multidimensional bins in four-momentum transfer ($1.0<Q^2<3.2$ GeV$^2$), Bjorken-$x$ ($0.12<x<0.48$), hadron energy fraction ($0.4<z<0.7$), transverse pion momentum ($0<P_T<1.0$ GeV), and azimuthal angle $\phi_h$ between the lepton scattering and hadron production planes. We extracted asymmetries as a function of both $x$ and $P_T$, which provide access to transverse-momentum distributions of longitudinally polarized quarks. The double spin asymmetries depend weakly on $P_T$. The $\sin 2\phi_h$ moments are zero within uncertainties, which is consistent with the expected suppression of the Collins fragmentation function. The observed $\sin\phi_h$ moments suggest that quark gluon correlations are significant at large $x$.Comment: 18 preprint pages, 3 figure