Theoretical Uncertainties in the QCD Evolution of Structure Functions and their Impact on αs(MZ2)\alpha_s(M_Z^2)

The differences are discussed between various next-to-leading order prescriptions for the QCD evolution of parton densities and structure functions. Their quantitative impact is understood to an accuracy of 0.02\%. The uncertainties due to the freedom to choose the renormalization and factorization scales are studied. The quantitative consequences of the different uncertainties on the extraction of the strong coupling constant $\alpha_s$ from scaling violations in deep--inelastic scattering are estimated for the kinematic regime accessible at HERA.Comment: 10 pages Latex, including 3 eps-figures, and a style file. To appear in: Proc. of the International Workshop: QCD and QED in Higher Orders, Rheinsberg, April, 1996, Nucl. Phys. {\bf B} (Proc. Suppl); The lay-out of the paper has been changed, one figure sent separately before has been bound i

THE VOLUME OPERATOR IN DISCRETIZED QUANTUM GRAVITY

We investigate the spectral properties of the volume operator in quantum gravity in the framework of a previously introduced lattice discretization. The presence of a well-defined scalar product in this approach permits us to make definite statements about the hermiticity of quantum operators. We find that the spectrum of the volume operator is discrete, but that the nature of its eigenstates differs from that found in an earlier continuum treatment.Comment: 15 pages, TeX, 3 figures (postscript, compressed and uu-encoded), May 9

The Singlet Contribution to the Structure Function g1(x,Q2)g_1(x,Q^2) at Small xx

The resummation of $O(\alpha_s^{l+1} \ln^{2l} x)$ terms in the evolution equation of the singlet part of $g_1(x,Q^2)$ is carried out. The corresponding singlet evolution kernels are calculated explicitely. The leading small-$x$ contribution to the three-loop splitting function matrix is determined in the $\overline{\rm MS}$ scheme. Relations are derived for the case of ${\cal N} = 1$ supersymmetric Yang--Mills field theory. Numerical results are presented for the polarized singlet and gluon densities, and the structure functions $g_1^{\, p}(x,Q^2)$ and $g_1^{\, n}(x,Q^2)$. They are compared for different assumptions on the non--perturbative input distributions, and the stability of the results against presently unknown subleading contributions is investigated.Comment: 10 pages Latex, including two eps-figures, all compressed by uufil

The Evolution of Unpolarized and Polarized Structure Functions at Small xx

A survey is given of recent developments on the resummed small-$x$ evolution, in a framework based on the renormalization group equation, of non--singlet and singlet structure functions in both unpolarized and polarized deep--inelastic scattering. The available resummed anomalous dimensions are discussed for all these cases, and the most important analytic and numerical results are compiled. The quantitative effects of these small-$x$ resummations on the evolution of the various parton densities and structure functions are presented, and their present uncertainties are investigated. An application to QED radiative corrections is given.Comment: 18 pages Latex, including 11 eps-figures, and a style file. To appear in: Proc. of the International Workshop: QCD and QED in Higher Orders, Rheinsberg, April, 1996, Nucl. Phys. B (Proc. Suppl

A novel role for Hedgehog in T-cell receptor signaling: implications for development and immunity

The Hedgehog (Hh) signaling pathway is a key regulator of both embryonic development and homeostasis of adult tissues, including thymus and blood. In the thymus, Hh signals for differentiation, survival and proliferation in the early stages of T cell development, before TCR gene rearrangement. Our recent data has shown that Hh signaling also modulates T cell receptor (TCR) signal strength in more mature T lineage cells. We showed that constitutive activation of the Hh pathway in thymocytes (by transgenic expression of the transcriptional activator form of Gli2) decreased TCR signal strength with profound consequences for the thymus--allowing self-reactive T cells to escape deletion and altering T cell CD4/CD8 lineage decisions. In contrast, in the Sonic Hh deficient thymus, TCR signaling was increased, again influencing both TCR repertoire selection and CD4/8 lineage commitment. In peripheral T cells, the transcriptional changes induced by activation of the Hh signaling pathway lead to reduced T cell activation. Hh signaling also attenuated ERK phosphorylation and proliferation in mature T cells on TCR ligation. Modulation of TCR signal strength by Hh pathway activation has importance for immunity as the presence or absence of Hh in the environment in which a T cell is activated would shape the immune response

On parton distributions beyond the leading order

The importance of properly taking into account the factorization scheme dependence of parton distribution functions is emphasized. A serious error in the usual handling of this topic is pointed out and the correct procedure for transforming parton distribution functions from one factorisation scheme to another recalled. It is shown that the conventional $\overline{\rm {MS}}$ and DIS definitions thereof are ill-defined due to the lack of distinction between the factorisation scheme dependence of parton distribution functions and renormalisation scheme dependence of the strong coupling constant $\alpha_s$. A novel definition of parton distribution functions is suggested and its role in the construction of consistent next-to-leading order event generators briefly outlined.Comment: PRA-HEP-93/05, Latex, 10 pages and 2 Postscript figures appended at the end of this fil

The 16th Moment of the Non--Singlet Structure Functions F2(x,Q2)F_2(x,Q^2) and FL(x,Q2)F_L(x,Q^2) to O(αs3)O(\alpha_s^3)

We present the results of an analytic next--to--next--to leading order QCD calculation of the non--singlet anomalous dimension $\gamma_{\rm NS}^+(N)$ and the coefficient functions $C_{2,L}(N)$ associated to the deeply inelastic structure functions $F_2(x,Q^2)$ and $F_L(x,Q^2)$ for the Mellin moment N=16. Comparisons are made with results in the literature.Comment: 11 pages, 1 style file, 1 figur

Universal Higher Order Singlet QED Corrections to Unpolarized Lepton Scattering

We calculate the universal flavor-singlet radiative QED corrections to unpolarized lepton scattering applicable to general differential scattering cross sections, involving charged fermions or photons in initial or final states. The radiators are derived to $O((\alpha \ln(Q^2/m_f^2))^5)$ in analytic form. Numerical illustrations are given.Comment: 31 pages, 3 figures, 1 style fil

Strong Coupling Constant from Scaling Violations in Fragmentation Functions

We present a new determination of the strong coupling constant alpha_s through the scaling violations in the fragmentation functions for charged pions, charged kaons, and protons. In our fit we include the latest e+e- annihilation data from CERN LEP1 and SLAC SLC on the Z-boson resonance and older, yet very precise data from SLAC PEP at center-of-mass energy sqrt(s)=29 GeV. A new world average of alpha_s is given.Comment: 10 pages, 3 eps figue

Light Gluinos and the Parton Structure of the Nucleon

We study the effects of light gluinos with mass below about 1 GeV on the nucleon parton densities and the running of alpha_(S). It is shown that from the available high-statistics DIS data no lower bound on the gluino mass can be derived. Also in the new kinematical region accessible at HERA the influence of such light gluinos on structure f unctions is found to be very small and difficult to detect. For use in more direct searches involving final state signatures we present a radiative estimate of the gluino distribution in the nucleon.Comment: 23 pages, LateX, 8 figures, MPI-PhT/94-22, LMU-3/9