Stefan Weinzierl
I report on a numerical program, which can be used to calculate any infrared safe three-jet observable in electron-positron annihilation to next-to-next-to-leading order in the strong coupling constant alpha_s. The results are compared to a recent calculation by another group. Numerical differences in three colour factors are discussed and explained.
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This article gives the perturbative NNLO results for the moments of the most commonly used event shape variables associated to three-jet events in electron-positron annihilation: Thrust, heavy jet mass, wide jet broadening, total jet broadening, C parameter and the Durham three-to-two jet transition variable.
This article gives the perturbative NNLO results for the most commonly used event shape variables associated to three-jet events in electron-positron annihilation: Thrust, heavy jet mass, wide jet broadening, total jet broadening, C parameter and the Durham three-to-two jet transition variable. In addition the NNLO results for the jet rates corresponding to the Durham, Geneva, Jade-E0 and Cambridge jet algorithms are presented.
The strong coupling constant is a fundamental parameter of nature. It can be extracted from experiments measuring three-jet events in electron-positron annihilation. For this extraction precise theoretical calculations for jet rates and event shapes are needed. In this talk I will discuss the NNLO calculation for these observables.
Precision studies of QCD at electron-positron colliders are based on measurements of event shapes and jet rates. To match the high experimental accuracy, theoretical predictions to next-to-next-to-leading order (NNLO) in QCD are needed for a reliable interpretation of the data. We report the first calculation of NNLO corrections O(alpha_s^3) to three-jet production and related event shapes, and discuss their phenomenological impact.
I report on a numerical program, which can be used to calculate any infra-red safe two-jet observable in electron-positron annihilation to next-to-next-to-leading order in the strong coupling constant alpha_s. The calculation is based on the subtraction method. The result for the two-jet cross section is compared to the literature.
We present a new implementation of the NNLO QCD corrections to three-jet final states and related event-shape observables in electron--positron annihilation. Our implementation is based on the antenna subtraction method, and is performed in the NNLOJET framework. The calculation improves upon earlier results by taking into account the full kinematical information on the initial state momenta, thereby allowing the event orientation to be computed to NNLO accuracy. We find the event-orientation distributions at LEP and SLC to be very robust under higher order QCD corrections.
Analytic NNLO QCD corrections to top quark pair production in electron-positron collisions
本文利用光学定理和正则微分方程计算三圈主积分，给出电子-正电子湮灭产生顶夸克对总截面的解析 NNLO QCD 修正及未来轻子对撞机数值结果。
The resummed transverse-momentum distribution for Higgs bosons produced via bottom-quark annihilation at the LHC is presented. Our results are obtained in the five-flavor scheme to NNLO+NNLL accuracy. We present a theoretical prediction which consistently matches the cross section at small and large transverse momenta. Theoretical uncertainties are derived from a variation of the unphysical scales entering the calculation. Their size is significantly reduced with respect to lower orders.
NNLO+PS predictions for Higgs production via bottom annihilation
本研究在POWHEG框架中用MiNNLOPS方法实现底夸克湮灭产生希格斯粒子的新型NNLO+PS事例生成器，在5FS下完成计算并与多阶预言对比，还在4FS下初步研究以提升有质量方案的精度。
NNLO QCD predictions for jet observables in ZH production at electron-positron colliders
该研究在NNLO QCD精度下预言了电子-正电子对撞机ZH产生中的喷注观测量，分别考虑希格斯玻色子衰变为底/粲夸克对和胶子，并比较了不同Durham喷注分辨率参数下的结果。
Based on the NRQCD factorization formalism, we calculate the next-to-next-to-leading order QCD corrections to the heavy quarkonium $η_c (η_b)$ production associated with a photon at electron-positron colliders. By matching the amplitudes calculated in full QCD theory to a series of operators in NRQCD, the short-distance coefficients up to NNLO QCD radiative corrections are determined. It turns out that the full set of master integrals that we obtained could be analytically expressed in terms of Goncharov Polylogarithms, Chen's iterated integrals, and elliptic functions, which mostly do not exi…
NNLO+PS predictions for Higgs production through bottom-quark annihilation with MINNLO$_{\text{PS}}$
本文计算了强子对撞机上底夸克湮灭产生希格斯玻色子的 NNLO+PS 修正，改进了 MINNLO$_{\text{PS}}$ 方法以处理汤川耦合的标度依赖，并与 NNLO 固定阶及 NNLL 重求和预测进行了比较。
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 th…
We present the computation of energy-energy correlation in $e^+e^-$ collisions in the back-to-back region at next-to-next-to-leading logarithmic accuracy matched with the next-to-next-to-leading order perturbative prediction. We study the effect of the fixed higher order corrections in a comparison of our results to LEP and SLC data. The next-to-next-to-leading order correction has a sizable impact on the extracted value of $α_{\mathrm S}(M_Z)$, hence its inclusion is mandatory for a precise measurement of the strong coupling using energy-energy correlation.
We report on a calculation of the vector current contributions to the electroweak production of top quark pairs in $e^+e^-$ annihilation at next-to-next-to-leading order in Quantum Chromodynamics. Our setup is fully differential and can be used to calculate any infrared-safe observable. The real emission contributions are handled by a next-to-next-to-leading order generalization of the phase-space slicing method. We demonstrate the power of our technique by considering its application to various inclusive and exclusive observables.
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.…
We present next-to-next-to leading order (NNLO) quantum electrodynamics (QED) corrections to the production of the Higgs boson in bottom quark annihilation at the Large Hadron Collider (LHC) in the five flavor scheme. We have systematically included the NNLO corrections resulting from the interference of quantum chromodynamics (QCD) and QED interactions. We have investigated the infrared (IR) structure of the bottom quark form factor up to two loop level in QED and in QCD$\times$QED using K+G equation. We find that the IR poles in the form factor are controlled by the universal cusp, collinear…
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…
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 pa…
We present the CoLoRFulNNLO method to compute higher order radiative corrections to jet cross sections in perturbative QCD. We apply our method to the computation of event shape observables in electron-positron collisions at NNLO accuracy and validate our code by comparing our predictions to previous results in the literature. We also calculate for the first time jet cone energy fraction at NNLO.
We introduce a subtraction method for jet cross sections at next-to-next-to-leading order (NNLO) accuracy in the strong coupling and use it to compute event shapes in three-jet production in electron-positron collisions. We validate our method on two event shapes, thrust and C-parameter, which are already known in the literature at NNLO accuracy and compute for the first time oblateness and the energy-energy correlation at the same accuracy.
We present the inclusive transverse momentum distribution for Higgs bosons produced in bottom quark annihilation at the LHC. The results are obtained in the five-flavor scheme. The soft and collinear terms at small $p_T$ are resummed through NNLL accuracy and matched to the NNLO transverse momentum distribution at large $p_T$. We find that the theoretical uncertainty, derived from a variation of the unphysical scales entering the calculation, is significantly reduced with respect to lower orders.
In the current work, We investigated the production of neutral Higgs boson and two charged Charginos owing to electron-positron annihilation via different propagators
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.
We present a subtraction scheme for computing jet cross sections in electron-positron annihilation at next-to-next-to-leading order accuracy in perturbative QCD. In this second part we deal with the regularization of the real-virtual contribution to the NNLO correction.
In this paper initial state radiation corrections to double production of charmonium mesons on one-photon electron-positron annihilation at center of mass energy $\sqrt{s}=10.6\GeV$ are studied. It is shown, that these corrections have noticeable effect and must be taken into consideration.
A fresh look at the nested soft-collinear subtraction scheme: NNLO QCD corrections to $N$-gluon final states in $q\bar{q}$ annihilation
本文利用嵌套软共线减除方案计算$q\bar{q}$湮灭中任意数目胶子喷注产生的NNLO QCD修正，将红外减除项组织为递归结构，并验证全微分截面奇点相消。
In this talk we report work on the matching of the next-to-leading logarithmic approximation (NLLA) onto the fixed next-to-next-to-leading order (NNLO) calculations for event shape distributions in electron-positron annihilation. Furthermore we present preliminary results on the determination of the strong coupling constant obtained using NLLA+NNLO predictions and ALEPH data.
We report on a recent work proposing measurements of the deeply virtual Compton amplitude (DVCS) $γ^* \to h \bar h γ$ in the timelike kinematic domain which is accessible at electron-positron colliders via the radiative annihilation process $e^+ e^- \to h \bar h γ$.
We present a subtraction scheme for computing jet cross sections in electron-positron annihilation at next-to-next-to-leading order accuracy in perturbative QCD. In this first part we deal with the regularization of the doubly-real contribution to the NNLO correction.
The possibility is examined for the inclusive $Λ$ in unpolarized electron-positron annihilation to be transversely polarized. Due to final-state interactions, there exists a novel structure function $\hat F(z,Q^2)$ for the inclusive $Λ$ hyperon (or any other baryons) production from the unpolarized time-like photon fragmentation, which makes contribution to the transverse $Λ$ polarization in the unpolarized electron-positron annihilation.
This paper has been withdrawn due to disagreement of suggested results and methods between authors.
Expressions for Sudakov form factors for heavy quarks are presented. They are used to construct resummed jet rates in electron-positron annihilation. Predictions are given for production of bottom quarks at LEP and top quarks at the Linear Collider.
We have calculated all contributions to the energy levels of parapositronium at order $m α^7$ coming from vacuum polarization corrections to processes involving virtual annihilation to two photons. This work is motivated by ongoing efforts to improve the experimental determination of the positronium ground-state hyperfine splitting.
Heavy Flavoured Meson Fragmentation Functions in $e^+e^-$ annihilation up to NNLO + NNLL
本研究在 Mellin 空间计算 $e^+e^-$ 湮灭中重夸克碎裂至 NNLO + NNLL，提取 $B$、$D^*$ 非微扰碎裂函数，并揭示粲介子实验数据与标准 DGLAP 演化的冲突。
Radiative corrections due to pair production in process of electron-positron annihilation are considered. The main attention is paid to the corrections of the third order. Simultaneous emission of photons and pairs is taken into account. The leading log approximation and convolution procedure are used. Exponentiation is discussed. Theoretical uncertainty in description of higher order secondary pairs is estimated.
In the paper, we present QCD predictions for $η_{c} + γ$ production at an electron-position collider up to next-to-next-to-leading order (NNLO) accuracy without renormalization scale ambiguities. The NNLO total cross-section for $e^{+}+e^{-}\toγ+η_{c}$ using the conventional scale-setting approach has large renormalization scale ambiguities, usually estimated by choosing the renormalization scale to be the $e^+ e^-$ center-of-mass collision energy $\sqrt{s}$. The Principle of Maximum Conformality (PMC) provides a systematic way to eliminate such renormalization scale ambiguities by summing the…
Rates of the two-, three-, four- and five-photon annihilations of the electron-positron pairs are determined numerically for the three-body positronium ion Ps$^-$ ($e^- e^+ e^-$) and four-body bi-positronium `molecule' Ps$_2$ ($e^- e^+ e^- e^+$). The values obtained in our computations are $Γ_{2 γ}($Ps$^-) \approx$ 2.08048530525$\cdot 10^{9}$ $sec^{-1}$, $Γ_{3 γ}($Ps$^-) \approx$ 5.6364151550$\cdot 10^{6}$ $sec^{-1}$, $Γ_{4 γ}($Ps$^-) \approx$ 3.075$\cdot 10^{3}$ $sec^{-1}$, $Γ_{5 γ}($Ps$^-) \approx 5.383$ $sec^{-1}$ and $Γ_{2 γ}($Ps$_2) \approx$ 4.4385952$\cdot 10^{9}$ $sec^{-1}$, $Γ_{3 γ}($P…
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.
Process of muon (pion) pair production with small invariant mass in the electron-positron high-energy annihilation, accompanied by emission of hard photon at large angles, is considered. We find that the Dell-Yan picture for differential cross section is valid in the charge-even experimental set-up. Radiative corrections both for electron block and for final state block are taken into account.
Events with tagged photons in the process of electron-positron annihilation into hadrons are considered. The initial state radiation is suggested to scan the hadronic cross section with the energy. QED radiative corrections are taken into account. The results for the total and exclusive cross sections are given in an analytic form. Some numerical estimates are presented.
We present the contributions from all types of one-loop corrections to the scattering amplitude for the pair production of polarized charginos or neutralinos from polarized electron-positron annihilation. The contributions are classified in terms of ``prototypes'' distinguished by the number of particles inside the loops and their spins. The results are quoted in terms of the Veltman-Passarino functions in terms of general couplings and internal masses. The results can therefore be applied to any supersymmetric extension of the Standard Model or indeed to any polarized fermion pair production …
We study the decays into six quarks of off-shell pairs of W bosons produced in electron-positron annihilations, through the O(as^2) order in the strong coupling constant. We give explicit helicity amplitude formulae. We present numerical results in the context of phenomenological analyses of relevance at LEP2 and future Linear Colliders: such as MW determinations, New Physics and Higgs searches.
Positronium spectroscopy (n=1 hyperfine splitting, n=2 fine structure, and the 1S-2S interval) has reached a precision of order 1 MHz. Vigorous ongoing efforts to improve the experimental results motivate the calculation of the positronium energy levels at order $m α^7$. In this work we present the result for a complete class of such contributions--those involving virtual annihilation of positronium to three photons in an intermediate state. We find an energy shift of $2.6216(11) m α^7/(n π)^3$ for the spin-triplet S state with principal quantum number n.
We study the structures in cross sections and R ratios concerning electron-positron annihilation reactions, for open-strangeness, open-charm and open-beauty hadron-pair production, from the perspective of a recently developed production formalism. Special attention is paid to non-resonant contributions. Known, tentative, and yet unknown resonances are spotted, with estimates for their masses and widths.
In previous articles we outlined a subtraction scheme for regularizing doubly-real emission and real-virtual emission in next-to-next-to-leading order (NNLO) calculations of jet cross sections in electron-positron annihilation. In order to find the NNLO correction these subtraction terms have to be integrated over the factorized unresolved phase space and combined with the two-loop corrections. In this paper we perform the integration of all one-parton unresolved subtraction terms.
The recent data from PAMELA and Fermi-LAT can be interpreted as evidence of new astrophysical sources of high energy positrons. In that case, such astrophysical positrons constitute an additional background against the positrons from dark matter annihilation. In this paper, we study the effect of that background on the prospects for the detection of a positron dark matter signal in future experiments. In particular, we determine the new regions in the (mass, $\sigmav$) plane that are detectable by the AMS-02 experiment for several dark matter scenarios and different propagation models. We find…
Processes of electron-positron annihilation into a pair of fermions were considered. Forward-backward and left-right asymmetries were studied, taking into account polarization of initial and final particles. Complete 1-loop electroweak radiative corrections were included. A wide energy range including the $Z$ boson peak and higher energies relevant for future $e^+e^-$ colliders was covered. Sensitivity of observable asymmetries to the electroweak mixing angle and fermion weak coupling was discussed.
The program EERAD3 computes the parton-level QCD contributions to event shapes and jet rates in electron-positron annihilation through to order $α_s^3$. For three-jet production and related observables, this corresponds to next-to-next-to-leading order corrections, and allows for precision QCD studies. We describe the program and its usage in detail.
We present next-to-leading order corrections in the leading colour approximation for jet rates in electron-positron annihilation up to seven jets. The results for the two-, three-, and four-jet rates agree with known results. The NLO jet rates have been known previously only up to five jets. The results for the six- and seven-jet rate are new. The results are obtained by a new and efficient method based on subtraction and numerical integration.
This article gives results on several jet algorithms in electron-positron annihilation: Considered are the exclusive sequential recombination algorithms Durham, Geneva, Jade-E0 and Cambridge, which are typically used in electron-positron annihilation. In addition also inclusive jet algorithms are studied. Results are provided for the inclusive sequential recombination algorithms Durham, Aachen and anti-kt, as well as the infrared-safe cone algorithm SISCone. The results are obtained in perturbative QCD and are NNNLO for the two-jet rates, NNLO for the three-jet rates, NLO for the four-jet rate…
The non-radiative scattering amplitudes for electron-positron annihilation into quark and lepton pairs in the TeV energy range are calculated in the double-logarithmic approximation. The expressions for the amplitudes are obtained using infrared evolution equations with different cut-offs for virtual photons and for W and Z bosons, and compared with previous results obtained with an universal cut-off.
Ongoing improvements in the measurement of positronium transition intervals motivate the calculation of the $O(m α^7)$ corrections to these intervals. In this work we focus on corrections to the spin-singlet parapositronium energies involving virtual annihilation to two photons in an intermediate state. We have evaluated all contributions to the positronium S-state energy levels that can be written as the product of a one-loop correction on one side of the annihilation event and another one-loop correction on the other side. These effects contribute $ΔE = -0.561971(25) m α^7/π^3$ to the parapo…
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.
Theory results on precision measurements in electron-positron annihilation at low and high energies are collected. These cover pure QCD calculations as well as mixed electroweak and QCD results, involving light and heavy quarks. The impact of QCD corrections on the $W$-boson mass is discussed and, last not least, the status and the perspectives for the Higgs boson decay rate into $b\bar b$, $c\bar c$ and into two gluons.
We report on a complete calculation of electroweak production of top quark pairs in $e^+e^-$ annihilation at next-to-next-to-leading order in Quantum Chromodynamics. Our setup is fully differential and can be used to calculate any infrared-safe observable. Especially we calculated the next-to-next-to-leading order corrections to top-quark forward-backward asymmetry and found sizable effects. Our results show a large reduction of the theoretical uncertainties in predictions of the forward-backward asymmetry, and allow a precision determination of the top quark electroweak couplings at future $e…
We discuss techniques for obtaining a numerically-stable evaluation of the fully differential cross section for the virtual photon correction to single hard photon bremsstrahlung in two different computational schemes. We also compare the role of finite mass corrections in these schemes.
In a companion publication, we have explored how to examine the summation of large logarithms in a parton shower. Here, we apply this general program to the thrust distribution in electron-positron annihilation, using several shower algorithms. The method is to work with an appropriate integral transform of the distribution for the observable of interest. Then, we reformulate the parton shower calculation so as to obtain the transformed distribution as an exponential for which we can compute the terms in the perturbative expansion of the exponent.
The Monte Carlo event generator PHOKHARA, which simulates hadron and muon production at electron-positron colliders through radiative return, has been extended to final states with three pions. A model for the form factor based on generalized vector dominance has been employed, which is consistent with presently available experimental observations.
The calculational precision of $\ee\to\tautau$ and $\ee\to\mumu$ production cross-sections in electron-positron annihilations at \roots = 10.58 \gev are studied for the \kk Monte Carlo simulation program. We determine $σ(\ee\to\tautau) = (0.919 \pm 0.003) \nb$ and $σ(\ee\to\mumu) = (1.147 \pm 0.005) \nb$, where the error represents the precision of the calculation.
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