Higher homotopy groups of complements of complex hyperplane arrangements

We generalize results of Hattori on the topology of complements of hyperplane arrangements, from the class of generic arrangements, to the much broader class of hypersolvable arrangements. We show that the higher homotopy groups of the complement vanish in a certain combinatorially determined range, and we give an explicit Z\pi_1-module presentation of \pi_p, the first non-vanishing higher homotopy group. We also give a combinatorial formula for the \pi_1-coinvariants of \pi_p. For affine line arrangements whose cones are hypersolvable, we provide a minimal resolution of \pi_2, and study some of the properties of this module. For graphic arrangements associated to graphs with no 3-cycles, we obtain information on \pi_2, directly from the graph. The \pi_1-coinvariants of \pi_2 may distinguish the homotopy 2-types of arrangement complements with the same \pi_1, and the same Betti numbers in low degrees.Comment: 24 pages, 3 figure

The Mass Definition in Hqet and a New Determination of Vcb_{\text{cb}}

Positive powers of the mass parameter in a physical quantity calculated with the help of heavy quark effective theory originate from a Wilson coefficient in the matching of QCD and HQET Green function. We show that this mass parameter enters the calculation as a well--defined running current mass. We further argue that the recently found ill--definition of the pole mass, which is the natural expansion parameter of HQET, does not affect a phenomenological analysis which uses truncated perturbative series. We reanalyse inclusive semileptonic decays of heavy mesons and obtain the $c$ quark mass $m_c^{\overline{\text{MS}}}(m_c) = (1.35\pm 0.20)\,\text{GeV}$ where the error is almost entirely due to scale--uncertainties. We also obtain $m_b^{\overline{\text{MS}}}(m_b) = (4.6\pm 0.3)\,\text{GeV}$ and $|V_{cb}|(\tau_B/1.49\,\text{ps})^{1/2} = 0.036\pm 0.005$ where the errors come from the uncertainty in the kinetic energy of the heavy quark inside the meson, in the experimental branching ratios, in QCD input parameters, and scale--uncertainties.Comment: 21 p., 5 figs, all style files incl., TUM-T31-56/R (Sec. 2 revised, phenomenological results unchanged

The diverse origins of neutron-capture elements in the metal-poor star HD 94028 : possible detection of products of i-process nucleosynthesis

We present a detailed analysis of the composition and nucleosynthetic origins of the heavy elements in the metal-poor ([Fe/H] = −1.62 ± 0.09) star HD 94028. Previous studies revealed that this star is mildly enhanced in elements produced by the slow neutron-capture process (s process; e.g., [Pb/Fe] = +0.79 ± 0.32) and rapid neutron-capture process (r process; e.g., [Eu/Fe] = +0.22 ± 0.12), including unusually large molybdenum ([Mo/Fe] = +0.97 ± 0.16) and ruthenium ([Ru/Fe] = +0.69 ± 0.17) enhancements. However, this star is not enhanced in carbon ([C/Fe] = −0.06 ± 0.19). We analyze an archival near-ultraviolet spectrum of HD 94028, collected using the Space Telescope Imaging Spectrograph on board the Hubble Space Telescope, and other archival optical spectra collected from ground-based telescopes. We report abundances or upper limits derived from 64 species of 56 elements. We compare these observations with s-process yields from low-metallicity AGB evolution and nucleosynthesis models. No combination of s- and r-process patterns can adequately reproduce the observed abundances, including the super-solar [As/Ge] ratio (+0.99 ± 0.23) and the enhanced [Mo/Fe] and [Ru/Fe] ratios. We can fit these features when including an additional contribution from the intermediate neutron-capture process (i process), which perhaps operated through the ingestion of H in He-burning convective regions in massive stars, super-AGB stars, or low-mass AGB stars. Currently, only the i process appears capable of consistently producing the super-solar [As/Ge] ratios and ratios among neighboring heavy elements found in HD 94028. Other metal-poor stars also show enhanced [As/Ge] ratios, hinting that operation of the i process may have been common in the early Galaxy

Critical points and resonance of hyperplane arrangements

If F is a master function corresponding to a hyperplane arrangement A and a collection of weights y, we investigate the relationship between the critical set of F, the variety defined by the vanishing of the one-form w = d log F, and the resonance of y. For arrangements satisfying certain conditions, we show that if y is resonant in dimension p, then the critical set of F has codimension at most p. These include all free arrangements and all rank 3 arrangements.Comment: revised version, Canadian Journal of Mathematics, to appea

Hadronic Spectral Moments in Semileptonic B Decays With a Lepton Energy Cut

We compute the first two moments of the final hadronic invariant mass in inclusive semileptonic B decay, in the presence of a cut on the charged lepton energy. These moments may be measured directly by experiments at the Upsilon(4S) using the neutrino reconstruction technique, which requires such a cut. Measurement of these moments will place constraints on the nonperturbative parameters \bar\Lambda and \lambda_1, which are relevant for extracting the quark masses m_b and m_c, as well as the CKM angle V_cb. We include terms of order \alpha_s^2\beta_0 and 1/m_b^3 in the operator product expansion, and use the latter to estimate the theoretical uncertainty in the extraction of \bar\Lambda and \lambda_1.Comment: 13 pages, 5 figures, REVTe