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TTP94-32 QCD Corrections to the $e^+e^-$ Cross Section and

TTP94-32 QCD Corrections to the $e^+e^-$ Cross Section and

QCD corrections to the electron positron annihilation cross section into hadrons and to the hadronic $Z$ boson decay rate are reviewed. Formal developments are introduced in a form particularly suited for practical applications. These include the operator product expansion, the heavy mass expansion, the decoupling of heavy quarks and matching conditions. Exact results for the quark mass dependence are presented whenever available, and formulae valid in the limit of small bottom mass ($m_{\rmfont{b}}^2\ll s$) or of large top mass ($m_{\rmfont{t}}^2\gg s$) are presented. The differences between vector and axial vector induced rates as well the classification of singlet and nonsinglet rates are discussed. Handy formulae for all contributions are collected and their numerical relevance is investigated. Prescriptions for the separation of the total rate into partial rates are formulated. The applicability of the results in the low energy region, relevant for measurements around 10 GeV and below, is investigated and numerical predictions are collected for this energy region.

anonymous
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TTP94-31 HQQET: An Effective Theory Approach to Heavy Quarkonia Decays

TTP94-31 HQQET: An Effective Theory Approach to Heavy Quarkonia Decays

We discuss systems containing a heavy quark and a heavy antiquark in the infinite mass limit of QCD. Studying the limit of equal velocities for both heavy particles, we formulate an effective theory approach to heavy quarkonia-like systems. The method is well suited to processes in which the two heavy quarks annihilate, such as electromagnetic and strong decays of charmonium and bottomonium and weak decays of $B_c$.

T. Mannel and G. Schuler
Phys. Lett. B349 181-189 1995
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TTP94-28 Polarization in Top Quark Pair Production near Threshold

TTP94-28 Polarization in Top Quark Pair Production near Threshold

The polarization dependent momentum distributions of top quarks and their decay products are calculated for $t\bar t$ production at future $e^+e^-$ colliders with polarized beams. The Green function formalism is applied to this reaction near energy threshold. The Lippmann–Schwinger equations for the $S$-wave and $P$-wave Green functions are solved numerically for the QCD chromostatic potential given by the two-loop formula at large momentum transfers and Richardson ansatz at intermediate and small ones. It is demonstrated that for the longitudinally polarized electron beam an optimally polarized sample of top quarks can be produced.

R. Harlander, M. Je\.zabek, J.H. K\„uhn and T. Teubner
Phys. Lett. B346 137–142 1995
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TTP94-27 Semileptonic tau decays, structure functions,

TTP94-27 Semileptonic tau decays, structure functions,

The most general angular distribution of two or three meson final states from semileptonic decays

$\tau\rightarrow \pi\pi\nu$, $K\pi\nu$,

$\pi\pi\pi\nu$, $K\pi\pi\nu$, $K\pi\nu$, $KKK\nu$, $\eta\pi\pi\nu,\,\ldots{}$ of polarized $\tau$ leptons can be characterized by 16 structure functions. Predictions for hadronic matrix elements, based on CVC and chiral Lagrangians and their relations to the structure functions are discussed. Most of them can be determined in currently ongoing high statistics experiments. Emphasis of the kinematical analysis is firstly put on $\tau$ decays in $e^{+}e^{-}$ experiments where the neutrino escapes detection and the $\tau$ rest frame cannot be reconstructed. Subsequently it is shown, how the determination of hadron tracks in double semileptonic events allows to fully reconstruct the $\tau$ kinematics. The implications for the spin analysis are indicated.

anonymous
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TTP94-26 Radiative corrections to $b\to c\tau\bar\nu_\tau$

TTP94-26 Radiative corrections to $b\to c\tau\bar\nu_\tau$

Analytical calculation is presented of the QCD radiative corrections to the rate of the process $b\to c\tau\bar\nu_\tau$ and to the $\tau$ lepton longitudinal polarization in $\tau\bar\nu_\tau$ rest frame. The results are given in the form of one dimensional infrared finite integrals over the invariant mass of the leptons. We argue that this form may be optimal for phenomelogical applications due to a possible breakdown of semilocal hadron-parton duality in decays of heavy flavours.

Andrzej Czarnecki, Marek Je\.zabek, and Johann H. K\„uhn.
Phys. Lett. B346 335–341 1995
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TTP94-24 Polarization in Top Pair Production and Decay near Threshold

TTP94-24 Polarization in Top Pair Production and Decay near Threshold

Theoretical results are presented for top quarks produced in annihilation of polarized electrons on positrons. Polarization studies for $t\bar t$ pairs near threshold are free from hadronization ambiguities. This is due to the short lifetime of the top quark. Semileptonic decays are discussed as well as their applications in studying polarization dependent processes involving top quarks. The Green function formalism is applied to $t\bar t$ production at future $e^+e^-$ colliders with polarized beams. Lippmann–Schwinger equation is solved numerically for the QCD chromostatic potential given by the two-loop formula at large momentum transfers and Richardson ansatz at intermediate and small ones. The polarization dependent momentum distributions of top quarks and their decay products are calculated.

R. Harlander, M. Je\.zabek, J.H. K\„uhn and T. Teubner
Proceedings of the Workshop „Spin 94,“ Bloomington, IN, Sept. 1994, pg. 675-680
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TTP94-21 On the new method of computing two-loop massive diagrams

TTP94-21 On the new method of computing two-loop massive diagrams

A recently proposed method of calculating scalar two-loop propagator and vertex functions with massive particles is illustrated with simple examples. A double integral representation is derived with the example of a propagator function. An analogous representation is used to compute the vertex function for space-like external momenta. Ways of dealing with divergent diagrams and of controlling the accuracy of the numerical evaluation of the two-loop functions are also discussed.

Andrzej Czarnecki
Frontiers in Particle Physics. Proceedings of the NATO Advanced Study Institute, 1-13 Aug 1994, Cargese, France. Edited by Maurice Levy, Jean Iliopoulos, Raymond Gastmans, Jean-Marc Gerard. NATO ASI series B, Physics v. 350, Plenum Press, New York, 1995, p. 153-160.
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TTP94-20 Inelastic J/$\Psi$ Photoproduction

TTP94-20 Inelastic J/$\Psi$ Photoproduction

Inelastic photoproduction of $J/\psi$ particles at high energies is one of the processes to determine the gluon distribution in the nucleon. We have calculated the QCD radiative corrections to the color-singlet model of this reaction. They are large at moderate photon energies, but decrease with increasing energies. The cross section and the $J/\psi$ energy spectrum are compared with the available fixed-target photoproduction data and predictions are given for the HERA energy range.

M. Krämer, J. Zunft, J. Steegborn and P. Zerwas
Phys. Lett. B348 657-664 1995
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====== TTP94-19 QCD Corrections to Inclusive Distributions of Leptons in Decays of Polarised Heavy Quarks

TTP94-19 QCD Corrections to Inclusive Distributions of Leptons in Decays of Polarised Heavy Quarks

TTP94-19 QCD Corrections to Inclusive Distributions of Leptons in Decays of Polarised Heavy Quarks

Compact analytic expressions have been obtained for the first order perturbative QCD corrections to the inclusive spectra of the leptons in the semileptonic decays of polarised heavy quarks.<BR> Charmed and beautiful $\Lambda$ baryons from $Z^0$ decays can be viewed as sources of highly polarised charm and bottom quarks. Charged leptons and neutrinos from $\Lambda_b$ and $\Lambda_c$ decays can be used in the polarisation studies for the corresponding heavy quarks. Thus our results are applicable for the b quark polarisation measurements at LEP.<BR> Short lifetime enables polarisation studies for the top quark. The angular-energy spectra of the charged leptons are particularly useful in this respect whereas the distributions of the neutrinos are sensitive to deviations from the V-A structure of the charged weak current in the decay.

Marek Je\.zabek
Proceedings of the 27th International Conference on High Energy Physics (ICHEP), 20-27 Jul 1994, Glasgow, Scotland. Edited by P.J. Bussey and I.G. Knowles. Philadelphia, Pa., Institute of Physics, 1995, p. 1093-1096.
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TTP94-18 Some Properties of a Transient New Coherent Condition of Matter

TTP94-18 Some Properties of a Transient New Coherent Condition of Matter

We investigate the dynamical possibility for the formation of a transient new coherent condition of matter in high-energy hadronic collisions. The coherent bosonic amplitude is characterized by a non-zero momentum and is sustained by $P$-wave interactions of quasi-pions in a dense fermionic medium. We make quantitative estimates of several essential properties: the condensate momentum and the fermionic density, the size of the coherent amplitude and the negative energy density contributed by the condensate, a characteristic proper time for the system to exist prior to breakdown into a few pions, and a characteristic extension of the system over the plane perpendicular to the collision axis. These quantities then allow us to make definite estimates of new signals: a few pions with anomalously small transverse momenta $\leq 50$ MeV/c; and a possible anomalous bremsstrahlung of very soft photons with characteristic transverse momenta as low as about 4 MeV/c.

Saul Barshay and Patrick Heiliger
Z. Phys. C66 459-466 1995
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TTP94-14 O(\alpha\alpha_s\ln m_t^2) non-universal Corrections to the Decay Rate \Gamma(Z\to b\bar b)

TTP94-14 O(\alpha\alpha_s\ln m_t^2) non-universal Corrections to the Decay Rate \Gamma(Z\to b\bar b)

The partial decay rate $\Gamma(Z\to b\bar{b})$ is significantly influenced by the mass of the top quark due to electroweak radiative corrections. The leading $\sim m_t^2$ and the next-to-leading contribution $\sim \ln m_t^2$ are known to be numerically of similar size. In this work we calculate the QCD corrections to the logarithmic correction using the heavy top mass expansion. The ${\cal O} (\alpha\as \ln m_t^2)$ corrections are of the same order as the QCD corrections to the quadratic top mass term, but of different sign.

A. Kwiatkowski and M. Steinhauser
Phys. Lett. B344 359-364 1995
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TTP94-13 Large Tau Decays into Four Pions

TTP94-13 Large Tau Decays into Four Pions

We compute branching ratios and invariant mass distributions of the tau decays into four pions. The hadronic matrix elements are obtained by starting from the structure of the hadronic current in chiral limit and then implementing low-lying resonances in the different channels with slowly varying coupling constants. Reasonable agreement with experiment is obtained both for the $\tau \to \nu_{\tau} + (4 \pi \!) $ decay rates and the $e^+e^- \to (4 \pi \!) $ cross sections. We derive a new prediction for the decay rate of $\tau^-\to\nu_\tau 2\pi^- \pi^+ \pi^0 $ which is significantly lower than a previous one. Furthermore we supply an interface to use our matrix elements within the Tauola Monte-Carlo program.

R. Decker, M. Finkemeier, P. Heiliger and H. H. Jonsson
Z. Phys. C70 247-254 1996
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TTP94-12 $R_{had}$ at the $B$-factory

TTP94-12 $R_{had}$ at the $B$-factory

A systematic theoretical evaluation of the cross section for hadron production in electron-positron collisions in the energy range just below the $B$ meson threshold is presented which includes charm and bottom mass effects and is accurate to order $\as^3$. The corresponding measurement in the energy region several $GeV$ above the threshold is also discussed.

K.G.Chetyrkin and J.H. K\„uhn
Phys. Lett. B342 356-361 1995
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TTP94-11 Radiation of Heavy Quarks,

TTP94-11 Radiation of Heavy Quarks,

The rate for the production of massive fermions radiated off a pair of massless fermions is calculated analytically. Combined with the analytic calculation of the corresponding virtual contribution one obtains the order $\alpha^2$ correction to the cross section which is induced by the real and virtual radiation of a pair of massive fermions by massless fermions. Approximations valid for large and for small masses are derived and shown to agree with earlier calculations.

A.H. Hoang, M. Je\.zabek, J.H. K\„uhn and T. Teubner,
Phys. Lett. B338 330-335 1994
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TTP94-10 Perturbative QCD Corrections to the $Z$ Boson Width and

TTP94-10 Perturbative QCD Corrections to the $Z$ Boson Width and

Radiative QCD corrections

significantly influence the theoretical

predictions for the decay rates of the $Z$ and the Higgs boson. The status of the QCD calculations to the hadronic $Z$ width is reviewed. The role of mass corrections from bottom quark final states is emphasized. An estimate of the theoretical uncertainties is given. New results for quartic mass terms of order ${\cal O}(\alpha_s^2)$ are presented. The impact of secondary radiation of bottom quarks on the determination of $\Gamma(Z\rightarrow b\bar{b})$ is discussed. Second order QCD corrections to the partial decay rate $\Gamma(H\rightarrow b\bar{b})$ are also presented in this talk. A recent result for the flavour singlet contribution to this quantity is presented. It includes quark mass effects and completes the otherwise massless calculations of order $\ordas^2)$.

anonymous
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TTP94-09 Top Quark Physics

TTP94-09 Top Quark Physics

Top quark studies at future $e^+e^-$ colliders are considered.<BR> Two issues are discussed: <OL TYPE=a> <LI>Some results are presented on the decays of top quarks. Energy distributions of charged leptons and neutrinos in $t\to bW\to be^+\nu$ and jets in $t\to bW\to b\bar du$ decays are sensitive to the structure of $tbW$ vertex. Distributions of charged leptons from top decays are particularly useful in polarization studies whereas neutrinos are sensitive to deviations from the Standard Model. <LI>Recent calculations are reviewed on the top quark pair production in $e^+e^-$ annihilation. The differential cross sections in the threshold region can lead to an accurate determination of the top quark mass and the interquark potential. The effects of the top-Higgs Yukawa coupling and some higher order QCD corrections are also under control. </OL>

M. Je\.zabek
Nucl. Phys. Proc. Suppl. 37B 197 1994
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TTP94-08 Quartic Mass Corrections to $R_{had}$

TTP94-08 Quartic Mass Corrections to $R_{had}$

The influence of nonvanishing quark masses on the total cross section in electron positron collisions and on the $Z$ decay rate is calculated. The corrections are expanded in $m^2/s$ and $\as$. Methods similar to those applied for the quadratic mass terms allow to derive the corrections of order $\as m^4/s^2$ and $\as^2m^4/s^2$. Coefficients which depend logarithmically on $m^2/s$ and which cannot be absorbed in a running quark mass arise in order $\as^2$. The implications of these results on electron positron annihilation cross sections at LEP and at lower energies in particular between the charm and the bottom threshold and for energies several GeV above the $b\bar b$ threshold are discussed.

K.G.Chetyrkin and J.H. K\„uhn
Nucl. Phys. B329 317–324 1994
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TTP94-07 Corrections of Order ${\cal O}(G_F\alpha_s m_t^2)$ to the Higgs Decay Rate $\Gamma(H\to b\bar{b})$

TTP94-07 Corrections of Order ${\cal O}(G_F\alpha_s m_t^2)$ to the Higgs Decay Rate $\Gamma(H\to b\bar{b})$

QCD corrections to the electroweak one-loop result for the partial width $\Gamma(H\rightarrow b\bar{b})$ are studied. For the decay channel into bottom quarks the rate is affected by a virtual top quark through electroweak interactions. The calculation of QCD corrections to this quantity is performed for an intermediate range Higgs mass in the heavy top mass limit. The leading correction of order ${\cal O}(G_F\alpha_s m_t^2)$ is estimated. Numerically the contribution is of comparable size as the electroweak correction, but of opposite sign.

A. Kwiatkowski, M. Steinhauser
Phys. Lett. B338 66-70 1994
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TTP94-05 Short and long distance effects in the decay $\tau \to \pi \nu_\tau (\gamma)$

TTP94-05 Short and long distance effects in the decay $\tau \to \pi \nu_\tau (\gamma)$

We calculate the radiative corrections to the decays $\tau\to M \nu_\tau$ and $\pi \to l \nu_\l$, where the meson $M$ is $M=\pi$ or $K$ and the lepton $l$ is $l = e$ or $\mu$. We perform a complete calculation, which includes internal bremsstrahlung and structure dependent radiation in the radiative decays and point meson, hadronic structure dependent and short distance contributions in the virtual corrections. Our result for the radiative correction to the ratio $\Gamma(\tau\to\pi\nu_\tau(\gamma))/ \Gamma(\pi\to\mu\nu_\mu(\gamma))$ is $\delta R_{\tau/\pi} = \left(0.16_{\T - 0.14}^{\T+ 0.09}\right) \%$. For the ratio $\Gamma(\tau\to K\nu_\tau(\gamma))/ \Gamma(K\to\mu\nu_\mu(\gamma))$, we obtain $\delta R_{\tau/K } = \left(0.90_{\T - 0.26}^{\T + 0.17}\right) \%$.<BR> For completeness we have also calculated the ratio of the electronic and muonic decay modes of the pion.

R. Decker and M. Finkemeier
Nucl. Phys. B438 17-53 1995
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TTP94-04 V-A tests through leptons from polarised top quarks

TTP94-04 V-A tests through leptons from polarised top quarks

Angular-energy distributions are studied for charged leptons and neutrinos from the decays of polarised top quarks. A small admixture of V+A interactions is incorporated. The polarisation dependent part of the neutrino distribution which can be measured experimentally through the missing momentum is particularly sensitive towards deviations from the V-A structure. This result remains unaffected by QCD corrections which, however, cannot be neglected in a quantitative analysis.

M. Je\.zabek and J.H. K\„uhn
Phys. Lett. B239 317–324 1994
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TTP94-03 A Transient New Coherent Condition of Matter: The Signal for New Physics in Hadronic Diffractive Scattering

TTP94-03 A Transient New Coherent Condition of Matter: The Signal for New Physics in Hadronic Diffractive Scattering

We demonstrate the existence of an anomalous structure in the data on the diffractive elastic scattering of hadrons at high energies and small momentum transfer. We analyze five sets of experimental data on $p(\overline{p})-p$ scattering from five different experiments with colliding beams, ranging from the first - and second - generation experiments at $\sqrt{s} = 53$ GeV to the most recent experiments at 546 GeV and at 1800 GeV. All of the data sets exhibit a localized anomalous structure in momentum transfer. We represent the anomalous behavior by a phenomenological formula. This is based upon the idea that a transient coherent condition of matter occurs in some of the intermediate inelastic states which give rise, via unitarity, to diffractive elastic scattering. The Fourier-Bessel transform into momentum-transfer space of a spatial oscillatory behavior of matter in the impact-parameter plane results in a small piece of the diffractive amplitude which exhibits a localized anomalous behavior near a definite value of $-t$. We emphasize in addition, possible signals coming directly from such a new condition of matter, that may be present in current experiments on inelastic processes.

Saul Barshay and Patrick Heiliger
Z. Phys. C64 675-682 1994
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