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T. Gehrmann

Publications and source records attributed to T. Gehrmann.

At least 91 records · Page 5Linked to original sources
arXiv2010

Precise determination of the strong coupling constant at NNLO in QCD from the three-jet rate in electron--positron annihilation at LEP

We present the first determination of the strong coupling constant from the three-jet rate in e+e- annihilation at LEP, based on a next-to-next-to-leading order (NNLO) perturbative QCD prediction. More precisely, we extract alpha_s by fitting perturbative QCD predictions at O(alpha_s^3) to data from the ALEPH experiment at LEP. Over a large range of the jet-resolution parameter ycut this observable is characterised by small non-perturbative corrections and an excellent stability under renormalisation scale variation. For the three-jet rate at ln(ycut) = -3.9 we find alpha_s(MZ) = 0.1175 +/- 0.0020(exp) \+/- 0.0015(theo), which is among the most precise determinations from jet observables at LEP.

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arXiv2009

Antenna subtraction at NNLO with hadronic initial states: initial-final configurations

We extend the antenna subtraction method to include initial states containing one hadron at NNLO. We present results for all the necessary subtraction terms, antenna functions, for the master integrals required to integrate them over the relevant phase space and finally for the integrated antennae themselves. Where applicable, our results are cross-checked against the known NNLO coefficient functions for deep inelastic scattering processes.

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arXiv2009

Two-Loop Planar Corrections to Heavy-Quark Pair Production in the Quark-Antiquark Channel

We evaluate the planar two-loop QCD diagrams contributing to the leading color coefficient of the heavy-quark pair production cross section, in the quark-antiquark annihilation channel. We obtain the leading color coefficient in an analytic form, in terms of one- and two-dimensional harmonic polylogarithms of maximal weight 4. The result is valid for arbitrary values of the Mandelstam invariants s and t, and of the heavy-quark mass m. Our findings agree with previous analytic results in the small-mass limit and numerical results for the exact amplitude.

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arXiv2009

Determination of the strong coupling constant using matched NNLO+NLLA predictions for hadronic event shapes in e+e- annihilations

We present a determination of the strong coupling constant from a fit of QCD predictions for six event-shape variables, calculated at next-to-next-to-leading order (NNLO) and matched to resummation in the next-to-leading-logarithmic approximation (NLLA). These event shapes have been measured in e+e- annihilations at LEP, where the data we use have been collected by the ALEPH detector at centre-of-mass energies between 91 and 206 GeV. Compared to purely fixed order NNLO fits, we observe that the central fit values are hardly affected, but the systematic uncertainty is larger because the NLLA part re-introduces relatively large uncertainties from scale variations. By combining the results for six event-shape variables and eight centre-of-mass energies, we find alpha_s(MZ)= 0.1224 +/- 0.0009 (stat) +/- 0.0009 (exp) +/- 0.0012 (had) +/- 0.0035 (theo), which improves previously published measurements at NLO+NLLA. We also carry out a detailed investigation of hadronisation corrections, using a large set of Monte Carlo generator predictions.

hep-ph↗
arXiv2009

Two-Loop QCD Helicity Amplitudes for (2+1)-Jet Production in Deep Inelastic Scattering

We derive the two-loop QCD helicity amplitudes for the processes $l q \to l qg$ ($l \bar q \to l \bar q g$) and $l g \to l q\bar q$, which are the partonic reactions yielding $(2+1)$-jet final states in deep inelastic lepton nucleon scattering. The amplitudes are obtained by analytic continuation of the known helicity amplitudes for $e^+e^- \to q\bar q g$. We separate the infrared divergent and finite parts of the amplitudes using Catani's infrared factorization formula. The analytic results for the finite parts of the amplitudes are expressed in terms of one- and two-dimensional harmonic polylogarithms. To evaluate these functions numerically, we list in detail the non-trivial (and kinematic region dependent) variable transformations one needs to perform.

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arXiv2009

NNLO moments of event shapes in e+e- annihilation

We compute the next-to-next-to-leading order (NNLO) QCD corrections to the first five moments of six event shape variables related to three-particle final states in electron-positron annihilation; the thrust, the heavy jet mass, the C-parameter, the wide and total jet broadenings and the three-to-two-jet transition parameter in the Durham algorithm Y3. The NNLO corrections to the first moment are moderate for all event shapes, while the renormalisation scale dependence of the theoretical prediction is substantially reduced compared to the previously existing NLO results. From a comparison with data from JADE and OPAL, we observe that the energy dependence of the moments of the wide jet broadening and Y3 can be largely explained without any non-perturbative power corrections, while the other observables exhibit a clear need for power-like contributions at low centre-of-mass energy.

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arXiv2009

NNLO corrections to event shapes in $e^+e^-$ annihilation

We compute the next-to-next-to-leading order (NNLO) QCD corrections to the six most important event shape variables related to three-particle final states in electron-positron annihilation. The corrections are sizeable for all variables, however their magnitude is substantially different for different observables. We observe that the NNLO corrections yield a considerably better agreement between theory and experimental data both in shape and normalisation of the event shape distributions. The renormalisation scale dependence of the theoretical prediction is substantially reduced compared to the previously existing NLO results. Our results will allow a precise determination of the strong coupling constant from event shape data collected at LEP.

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arXiv2008

Two-Loop QCD Corrections to the Heavy-to-Light Quark Decay

We present an analytic expression for the two-loop QCD corrections to the decay process b -> u W^*, where b and u are a massive and massless quark, respectively, while W^* is an off-shell charged weak boson. Since the W-boson can subsequently decay in a lepton anti-neutrino pair, the results of this paper are a first step towards a fully analytic computation of differential distributions for the semileptonic decay of a b-quark. The latter partonic process plays a crucial role in the study of inclusive semileptonic charmless decays of B-mesons. The three independent form factors characterizing the b W u vertex are provided in form of a Laurent series in (d-4), where d is the space-time dimension. The coefficients in the series are expressed in terms of Harmonic Polylogarithms of maximal weight 4, and are functions of the invariant mass of the leptonic decay products of the W-boson.

hep-ph↗
arXiv2008

Infrared structure of e+e- --> 3 jets at NNLO

We describe the calculation of the next-to-next-to-leading order (NNLO) QCD corrections to three-jet production and related event shape observables in electron-positron annihilation. Infrared singularities due to double real radiation at tree level and single real radiation at one loop are subtracted from the full QCD matrix elements using antenna functions, which are then integrated analytically and added to the two loop contribution. Using this antenna subtraction method, we obtain numerically finite contributions from five-parton and four-parton processes, and observe an explicit analytic cancellation of infrared poles in the four-parton and three-parton contributions. All contributions are implemented in a flexible parton-level event generator programme, allowing the numerical computation of any infrared-safe observable related to three-jet final states to NNLO accuracy.

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arXiv2008

Matching of Resummed NLLA with Fixed NNLO for Event Shapes

We report work on the matching of the next-to-leading logarithmic approximation (NLLA) onto the fixed next-to-next-to-leading order (NNLO) calculation for event shape variables in electron-positron annihilation. The correction of the combined NLLA+NNLO computation in the three-jet region, relevant for precision phenomenology, is small compared with pure NNLO or NLLA+NLO.

hep-ph↗
arXiv2008

Matching NLLA+NNLO for event shape distributions

We study the matching of the next-to-leading logarithmic approximation (NLLA) onto the fixed next-to-next-to-leading order (NNLO) calculation for event shape distributions in electron-positron annihilation. The resulting theoretical predictions combine all precision QCD knowledge on the distributions, and are theoretically reliable over an extended kinematical range. Compared to previously available matched NLLA+NLO and fixed order NNLO results, we observe that the effects of the combined NLLA+NNLO are small in the three-jet region, relevant for precision physics.

hep-ph↗
arXiv2008

e^+ e^- -> 3 jets and event shapes at NNLO

We report on the calculation of NNLO corrections to the 3-jet cross section and related event shape distributions in electron-positron annihilation. The corrections are sizable for all variables, however the magnitude of the corrections is substantially different for different observables. We observe that inclusion of the NNLO corrections yields a considerably better agreement between theory and experimental data both in shape and normalization of the event shape distributions in the region where the perturbative result is expected to hold. A new extraction of $α_{s}$ using the event shape variables up to NNLO yields a considerably better consistency between the observables indicating a stabilization of the perturbative corrections at this order.

hep-ph↗
arXiv2008

Two-Loop Fermionic Corrections to Heavy-Quark Pair Production: the Quark-Antiquark Channel

We evaluate the fermionic two-loop QCD corrections to the heavy-quark pair production process in the quark-antiquark channel. We obtain analytic results which are valid for any value of the Mandelstam invariants s and t, and of the heavy quark mass m. Our findings confirm previous results for the analytic evaluation in the small-mass limit and numerical results for the exact amplitude. We furthermore provide the expansion of the two-loop amplitude at the production threshold s ~ 4m^2.

hep-ph↗
arXiv2008

Jet rates in electron-positron annihilation at O(α_s^3) in QCD

We compute production rates for two, three, four and five jets in electron-positron annihilation at the third order in the QCD coupling constant. At this order, three-jet production is described to next-to-next-to-leading order (NNLO) in perturbation theory while the two-jet rate is obtained at next-to-next-to-next-to-leading order (N$^3$LO). Our results yield an improved perturbative description of the dependence of jet multiplicity on the jet resolution parameter, $\ycut$, particularly at small values of $\ycut$.

hep-ph↗
arXiv2008

First determination of the strong coupling constant using NNLO predictions for hadronic event shapes in e^+e^- annihilations

We present the first determination of the strong coupling constant from a fit of next-to-next-to-leading order QCD predictions to event-shape variables, measured in $e^+e^-$ annihilations at LEP. The data have been collected by the ALEPH detector at centre-of-mass energies between 91 and 206 GeV. Compared to results of next-to-leading order fits we observe that the central fit values are lower by about 10%, with considerably reduced scatter among the results obtained with different event-shape variables. The dominant systematic uncertainty from renormalization scale variations is reduced by a factor of two. By combining the results for several event-shape variables and centre-of-mass energies, we find α_s(M_Z^2) = 0.1240+-0.0008(stat)+-0.0010(exp)+-0.0011(had)+-0.0029(theo).

hep-ph↗
arXiv2008

Event shapes in $e^+e^-$ annhilation at NNLO

We report first results on the calculation of NNLO corrections to event shape distributions in electron-positron annhilation. The corrections are sizeable for all variables, however their magnitude is substantially different for different observables. We observe that inclusion of the NNLO corrections yields a considerably better agreement between theory and experimental data both in shape and normalisation of the event shape distributions.

hep-ph↗
arXiv2007

Antenna Subtraction at NNLO

The computation of exclusive QCD jet observables at higher orders requires a method for the subtraction of infrared singular configurations arising from multiple radiation of real partons. We present a subtraction scheme relevant for NNLO perturbative calculations in $e^+e^- \to $ jets. The building blocks of the scheme are antenna functions derived from the matrix elements for tree-level $1\to 3$ and $1 \to 4$ and one-loop $1 \to 3$ processes. By construction, these building blocks have the correct infrared behaviour when one or two particles are unresolved. At the same time, their integral over the antenna phase space is straightforward. As an example of how to use the scheme we compute the NNLO contributions to the subleading colour QED-like contribution to $e^+e^- \to 3$ jets. To illustrate the application of NNLO antenna subtraction for different colour structures, we construct the integrated forms of the subtraction terms needed for the five-parton and four-parton contributions to $e^+e^- \to 3$ jets at NNLO in all colour factors, and show that their infrared poles cancel analytically with the infrared poles of the two-loop virtual correction to this observable.

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