arXiv subjects

S. Groote

Publications and source records attributed to S. Groote.

70 records · Page 4Linked to original sources

arXiv1999

Local and global duality and the determination of α(M_Z)

This talk presents work concepts and results for the determination of the fine structure constant $α$ at the $Z_0$ mass resonance. The problem consisting of the break-down of global duality for singular integral weights is circumvented by using a polynomial fit which mimics this weight function. This method is conservative in the sense that it is mostly independent of special assumptions. In this context the difference between local and global duality is explained.

hep-ph↗

arXiv1999

Transcendental numbers and the topology of three-loop bubbles

We present a proof that all transcendental numbers that are needed for the calculation of the master integrals for three-loop vacuum Feynman diagrams can be obtained by calculating diagrams with an even simpler topology, the topology of spectacles.

hep-ph↗

arXiv1999

Polarized top decay into polarized W: t(up)->W(up) + b at O(alpha_s)

We consider the decay of a polarized top quark into a polarized W-boson plus a bottom quark, followed by the decay of the W-boson into a pair of leptons or quarks. The polar angle distribution of the top spin relative to the W-momentum and the polar angle distribution of the lepton (or quark) in the W-rest frame is governed by three polarized and three unpolarized rate functions which are related to the double density matrix elements of the decay $t \to W^+ + b$. We obtain analytical expressions for the $O(α_s)$ radiative corrections to the three polarized and three unpolarized rate functions. We also provide a comprehensive discussion of the dependence of the longitudinal, transverse and normal polarization of the top quarks produced at $e^+e^-$-colliders on beam polarization parameters.

hep-ph↗

arXiv1998

Gluon Polarization in e^+e^- -> t \bar t G: Polar Angle Dependence and Beam Polarization Effects

We calculate the linear and circular polarization of gluons produced in conjunction with massive quarks in the annihilation process $e^+e^-\to q \bar q G$. The linear polarization is calculated in the hadron event plane as well as in the gluon-beam plane. Beam polarization and polar orientation effects are included in our discussion. For typical top pair production energies at the Next-Linear-Collider (NLC) the degree of linear polarization in the hadron event plane remains close to its soft gluon value of 100% over most of the energy spectrum of the gluon. The linear polarization in the gluon-beam plane is generally smaller but peaks toward the hard end of the gluon spectrum. The dependence of the linear polarization on beam polarization and on the polar orientation of the gluon is small. The circular polarization is largest for maximal gluon energies and shows a strong dependence on the longitudinal beam polarization. The longitudinal polarization of the beam may therefore be used to tune the circular polarization of the gluon. The massive quark results are compared with the corresponding results for the massless quark case.

hep-ph↗

arXiv1998

On the rigidity of back-to-back top quark pairs in e^+e^- annihilation

We consider the effect of gluon radiation on the energy of top/antitop quarks and on the anticollinearity of top-antitop quark pairs produced in $e^+e^-$ annihilation. Our results are presented in terms of the $E_q$-dependence of the $t\bar tg$ cross section and the dependence on the cosine of the opening angle $θ_{12}$ between top and antitop for a center of mass energy of $\sqrt{q^2}=500 GeV$. We then go on to determine mean values for the top quark's energy as well as its longitudinal and transverse projections, and for the deviation of $\sinθ_{12}$ and $\cosθ_{12}$ from the anticollinearity limits $\sinθ_{12}=0$ and $\cosθ_{12}=-1$. For a center of mass energy of $500 GeV$ we obtain $ =248.22 GeV$, $ =247.24 GeV$ and $ =4.70 GeV$. Thus, at this energy gluon radiation causes a total average energy loss of 0.71% of the top quark's energy. The average energy loss in the longitudinal direction is 1.06% and the average energy gain in the transverse direction is 1.88%. These percentage figures go up to 3.77%, 5.19% and 6.06%, respectively, at $1000\GeV$. For the mean of the acollinearity angle $\barθ_{12}=180^0-θ_{12}$ we obtain $<\barθ_{12}>=1.25^0$ at $500 GeV$, the value of which goes up to $4.62^0$ at $1000 GeV$. From an analysis of the transverse momentum of the top we find that the mean transverse momentum of the top stays close to the mean total momentum of the gluon in the energy range from threshold to $1000 GeV$ showing that the gluon momentum has a large mean transverse component in this energy range.

hep-ph↗

arXiv1997

O(α_s) Corrections to Longitudinal Spin-Spin Correlations in e+e- -> q qbar

We calculate the $O(α_s)$ corrections to longitudinal spin-spin correlations in $e^+e^-\to q\bar q$. For top quark pair production the $O(α_s)$ corrections to the longitudinal spin-spin asymmetry amount to less than 1% in the $q^2$-range from above $t\bar t$-treshold up to $\sqrt{q^2}= 1000 GeV$. In the $e^+e^-\to b\bar b$ case the $O(α_s)$ corrections reduce the asymmetry value from its $m=0$ value of -1 to approximately -0.96 for $q^2$-values around the Z-peak. This reduction can be traced to finite anomalous contributions from residual mass effects which survive the $m\to 0$ limit. We discuss the role of the anomalous contributions and the pattern of how they contribute to spin-flip and no-flip terms.

hep-ph↗

arXiv1997

Gluon Polarization in $e^+e^-\to t\bar tG$

We calculate the linear polarization of gluons radiated off top quarks produced in e^+e^- annihilations. For typical top pair production energies at the Next-Linear-Collider (NLC) the degree of linear polarization remains close to its soft gluon value of 100% over almost the whole energy spectrum of the gluon. The massive quark results are compared with the corresponding results for the massless quark case.

hep-ph↗

arXiv1997

Resummation analysis of the $τ$ decay width using the four-loop $β$-function

We extract the strong coupling constant $α_s(m_τ^2)$ from the semileptonic $τ$ decay width taking into account resummation effects from the running of the strong coupling constant. In the $\overline{\rm MS}$ scheme the result reads $α_s=0.375\pm 0.007$ to third order and $α_s=0.378\pm 0.007$ to fourth order in the $β$-function, respectively, where we use the recently computed four-loop coefficient $β_3$. These values for the coupling constant have to be compared with the value $α_s=0.354\pm 0.005$ derived from a third order analysis of $τ$ decays. We determine the exact value of the convergence radius of the perturbation series by analyzing the singularity structure of the complex coupling constant plane.

hep-ph↗

arXiv1997

An Analysis of Diagonal and Non-diagonal QCD Sum Rules for Heavy Baryons at Next-to-Leading Order in α_S

We consider diagonal and non-diagonal QCD sum rules for the ground state heavy baryons to leading order in $1/m_Q$ and at next-to-leading order in $α_S$. In the non-diagonal case we evaluate the eight different two-loop diagrams which determine the perturbative $α_S$-corrections to the Wilson coefficient of the quark condensate in the Operator Product Expansion. The QCD corrections to the non-diagonal sum rules are moderate compared to the QCD corrections in the diagonal case. We also consider constituent type sum rules using constituent type interpolating currents. The obtained results are in reasonable agreement with the corresponding results obtained in the diagonal case. As central values for the bound state energies we find $m(Λ_Q)-m_Q = 760 MeV$ and $m(Σ_Q)-m_Q = 940 MeV$. The central values for the residues are given by $F(Λ_Q) = 0.030 GeV^3$ and $F(Σ_Q) = 0.038 GeV^3$.

hep-ph↗

arXiv1997

Perturbative relations between $e^+e^-$ annihilation and $τ$ decay observables including resummation effects

By exploiting the analyticity properties of the two-point current-current correlator we obtain numerical predictions for the $e^+e^-$ moments in terms of the $τ$ decay rate. We perform a partial resummation of the pertinent perturbative series expansion by solving the renormalization group equation for Adler's function. Our predictions are renormalization scheme independent but depend on the order of the perturbative $β$-function expansion. The analysis involves the unknown five-loop coefficient $k_3$ for which we give some new estimates.

hep-ph↗

arXiv1997

New high order relations between physical observables in perturbative QCD

We exploit the fact that within massless perturbative QCD the same Green's function determines the hadronic contribution to the $τ$ decay width and the moments of the $e^+e^-$ cross section. This allows one to obtain relations between physical observables in the two processes up to an unprecedented high order of perturbative QCD. A precision measurement of the $τ$ decay width allows one then to predict the first few moments of the spectral density in $e^+e^-$ annihilations integrated up to $s\sim m_τ^2$ with high accuracy. The proposed tests are in reach of present experimental capabilities.

hep-ph↗

arXiv1996

Transverse Polarization of Top Quarks Produced in e+e- Annihilation at O(alpha_s)

We present the results of an O(alpha_s) calculation of the transverse polarization of top quarks produced in e+e- annihilation. In a first step we determine the transverse polarization of the top with regard to the hadron plane spanned by the (q,bar q,g) system. We then rotate the transverse components of the polarization to the lepton plane spanned by the (q,e+,e-) system. After azimuthal averaging we determine the three remaining inclusive transversely polarized structure functions. Together with the one-loop and Born term contributions they determine the sin(theta) and sin(2*theta) beam-quark polar angle dependence of the transverse polarization. We present analytic and numerical results for the polarized structure functions and the polar angle dependence of the transverse polarization. We briefly comment on the transverse polarization of bottom quarks produced in e+e- annihilation.

hep-ph↗

arXiv1996

QCD Sum Rules for Heavy Baryons at Next-to-Leading Order in alpha_s

We derive QCD sum rules for heavy baryons at leading order in $1/m_Q$ and at next-to-leading order in $α_s$. The calculation involves the evaluation of four different perturbative three-loop diagrams which determine the $α_s$-corrections to the Wilson coefficients of the leading term in the Operator Product Expansion (OPE). From the sum rules we obtain estimates for the masses and the residues of the heavy baryons $Λ_Q$ and $Σ_Q$. The perturbative $O(α_s)$ corrections to the leading order spectral function amount to about $100%$, and they shift the calculated values for the baryon masses slightly upward. The residues are shifted upward by about $20-50%$. For the bound state energy $\barΛ$ given by the difference of the heavy baryon mass and the pole mass of the heavy quark $m_Q$ we obtain $m_{Λ_Q}-m_Q=780 MeV$ and $m_{Σ_Q}-m_Q=950 MeV$. For the residues we find $|F_Λ|=0.028 GeV^3$ and $|F_Σ|=0.039 GeV^3$.

hep-ph↗

arXiv1996

Two-loop Anomalous Dimensions of Heavy Baryon Currents in Heavy Quark Effective Theory

We present results on the two-loop anomalous dimensions of the heavy baryon HQET currents $J=(q^TCΓτq)Γ'Q$ with arbitrary Dirac matrices $Γ$ and $Γ'$. From our general result we obtain the two-loop anomalous dimensions for currents with quantum numbers of the ground state heavy baryons $Λ_Q$, $Σ_Q$ and $Σ_Q^*$. As a by-product of our calculation and as an additional check we rederive the known two-loop anomalous dimensions of mesonic scalar, pseudoscalar, vector, axial vector and tensor currents $(J=\bar qΓq)$ in massless QCD as well as in HQET.

hep-ph↗

arXiv1996

Polar Angle Dependence of the Alignment Polarization of Quarks Produced in e^+e^- Annihilation

We calculate one-loop radiative QCD corrections to the three polarized and unpolarized structure functions that determine the beam-quark polar angle dependence of the alignment (or longitudinal) polarization of light and heavy quarks produced in e^+e^- annihilations. We present analytical and numerical results for the alignment polarization and its polar angle dependence. We discuss in some detail the zero-mass limit of our results and the role of the anomalous spin-flip contributions to the polarization observables in the zero-mass limit. Our discussion includes transverse and longitudinal beam polarization effects.

hep-ph↗

arXiv1995

Longitudinal Contribution to the Alignment Polarization of Quarks Produced in e+ e- Annihilation: An O(alpha_s) Effect

We calculate the longitudinal contribution to the alignment polarization $\Pl$ of quarks produced in $e^+e^-$ annihilation. In the Standard Model, the longitudinal alignment polarization vanishes at the Born term level and thus receives its first non-zero contribution from the $O(\as)$ tree graph process. We provide analytical and numerical results for the longitudinal alignment polarization of massless and massive quarks, in particular for the recently discovered top quark.

hep-ph↗