Improved variables for measuring the LambdabLambda_b polarization

We discuss a few possible strategies for measuring the polarization of the $\Lambda_{\mathrm{b}}$ baryons produced in $e^+e^-$-annihilation at the $\mathrm{Z}$ resonance through their inclusive semileptonic decays. After reviewing the existing methods, a new method is proposed, based on the ratio of the averages of the squared electron and neutrino energy, including both perturbative and nonperturbative corrections. This variable minimizes the statistical error on the $\Lambda_{\mathrm{b}}$ polarization, while keeping the systematic theoretical errors at the level of 1-2%. A number of other polarization-sensitive variables are also discussed, such as averages of ratios of the electron and neutrino energy and the distribution in the difference of the electron and neutrino rapidities.Comment: 23 pages, 4 uuencoded figures, REVTe

Analyticity, crossing and the absorptive parts of the one-loop contributions to the quark-quark-gluon gauge boson four-point function

Starting from the known one-loop result for the $e^{+}e^{-}$-annihilation process $e^{+}e^{-}\stackrel{\gamma,Z} {\longrightarrow} q\bar{q}g$ with massless quarks we employ analyticity and crossing to determine the absorptive parts of the corresponding one-loop contributions in Deep Inelastic Scattering (DIS) and in the Drell-Yan process (DY). Whereas the ${\cal O}(\alpha_s^2)$ absorptive parts generate a non-measurable phase factor in the $e^{+}e^{-}$-annihilation channel one obtains measurable phase effects from the one-loop contributions in the deep inelastic and in the Drell-Yan case. We compare our results with the results of previous calculations where the absorptive parts in DIS and in the DY process were calculated directly in the respective channels. We also present some new results on the dispersive and absorptive contributions of the triangle anomaly graph to the DIS process.Comment: 23 pages, 5 figures, typos corrected. Version to appear in Phys. Rev.

Inclusive Semileptonic Decays in QCD Including Lepton Mass Effects

Starting from an Operator Product Expansion in the Heavy Quark Effective Theory up to order 1/m_b^2 we calculate the inclusive semileptonic decays of unpolarized bottom hadrons including lepton mass effects. We calculate the differential decay spectra d\Gamma/(dE_\tau ), and the total decay rate for B meson decays to final states containing a \tau lepton.Comment: 16 pages + 4 figs. appended in uuencoded form, LaTeX, MZ-TH/93-3

Laurent series expansion of a class of massive scalar one-loop integrals up to {\cal O}(\ep^2) in terms of multiple polylogarithms

In a recent paper we have presented results for a set of massive scalar one-loop master integrals needed in the NNLO parton model description of the hadroproduction of heavy flavors. The one--loop integrals were evaluated in n=4-2\ep dimension and the results were presented in terms of a Laurent series expansion up to {\cal O}(\ep^2). We found that some of the \ep^2 coefficients contain a new class of functions which we termed the $L$ functions. The $L$ functions are defined in terms of one--dimensional integrals involving products of logarithm and dilogarithm functions. In this paper we derive a complete set of algebraic relations that allow one to convert the $L$ functions of our previous approach to a sum of classical and multiple polylogarithms. Using these results we are now able to present the \ep^2 coefficients of the one-loop master integrals in terms of classical and multiple polylogarithms.Comment: 32 pages, Latex, references added, matches published versio

Next-to-next-to-leading order O(αs4){\cal O}(\alpha_s^4) results for heavy quark pair production in quark--antiquark collisions: The one-loop squared contributions

We calculate the next-to-next-to-leading order ${\cal O}(\alpha_s^4)$ one-loop squared corrections to the production of heavy quark pairs in quark-antiquark annihilations. These are part of the next-to-next-to-leading order ${\cal O}(\alpha_s^4)$ radiative QCD corrections to this process. Our results, with the full mass dependence retained, are presented in a closed and very compact form, in the dimensional regularization scheme. We have found very intriguing factorization properties for the finite part of the amplitudes.Comment: 12 pages, 2 figures, electronic results file, abbreviation NNLO in Title and Abstract expanded, Summary expanded, reference updated, version to appear in Phys.Rev.

Quark and Pole Models of Nonleptonic Decays of Charmed Baryons

Quark and pole models of nonleptonic decays of charmed baryons are analysed from the point of view of their symmetry properties. The symmetry structure of the parity conserving amplitudes that corresponds to the contribution of the ground-state intermediate baryons is shown to differ from the one hitherto employed in the symmetry approach. It is pointed out that the "subtraction" of sea quark effects in hyperon decays leads to an estimate of $W$-exchange contributions in charmed baryon decays that is significantly smaller than naively expected on the basis of $SU(4)$. An $SU(2)_{W}$ constraint questioning the reliability of the factorization technique is exhibited. Finally, a successful fit to the available data is presented.Comment: 25 pages, LATEX, 1643/PH IFJ Krako

Helicity Analysis of Semileptonic Hyperon Decays Including Lepton Mass Effects

Using the helicity method we derive complete formulas for the joint angular decay distributions occurring in semileptonic hyperon decays including lepton mass and polarization effects. Compared to the traditional covariant calculation the helicity method allows one to organize the calculation of the angular decay distributions in a very compact and efficient way. In the helicity method the angular analysis is of cascade type, i.e. each decay in the decay chain is analyzed in the respective rest system of that particle. Such an approach is ideally suited as input for a Monte Carlo event generation program. As a specific example we take the decay $\Xi^0 \to \Sigma^+ + l^- + \bar{\nu}_l$ ($l^-=e^-, \mu^-$) followed by the nonleptonic decay $\Sigma^+ \to p + \pi^0$ for which we show a few examples of decay distributions which are generated from a Monte Carlo program based on the formulas presented in this paper. All the results of this paper are also applicable to the semileptonic and nonleptonic decays of ground state charm and bottom baryons, and to the decays of the top quark.Comment: Published version. 40 pages, 11 figures included in the text. Typos corrected, comments added, references added and update

Probing the tails of the ground state energy distribution for the directed polymer in a random medium of dimension d=1,2,3d=1,2,3 via a Monte-Carlo procedure in the disorder

In order to probe with high precision the tails of the ground-state energy distribution of disordered spin systems, K\"orner, Katzgraber and Hartmann \cite{Ko_Ka_Ha} have recently proposed an importance-sampling Monte-Carlo Markov chain in the disorder. In this paper, we combine their Monte-Carlo procedure in the disorder with exact transfer matrix calculations in each sample to measure the negative tail of ground state energy distribution $P_d(E_0)$ for the directed polymer in a random medium of dimension $d=1,2,3$. In $d=1$, we check the validity of the algorithm by a direct comparison with the exact result, namely the Tracy-Widom distribution. In dimensions $d=2$ and $d=3$, we measure the negative tail up to ten standard deviations, which correspond to probabilities of order $P_d(E_0) \sim 10^{-22}$. Our results are in agreement with Zhang's argument, stating that the negative tail exponent $\eta(d)$ of the asymptotic behavior $\ln P_d (E_0) \sim - | E_0 |^{\eta(d)}$ as $E_0 \to -\infty$ is directly related to the fluctuation exponent $\theta(d)$ (which governs the fluctuations $\Delta E_0(L) \sim L^{\theta(d)}$ of the ground state energy $E_0$ for polymers of length $L$) via the simple formula $\eta(d)=1/(1-\theta(d))$. Along the paper, we comment on the similarities and differences with spin-glasses.Comment: 13 pages, 16 figure