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Summary of determinations of αs from hadronic τ -decays (a), from lattice calculations (b), from DIS structure functions (c) and from e + e − annihilation (d). The shaded bands indicate the pre-average values explained in the text, to be included in the determination of the nal world average of αs. In a), full circles are results obtained using CIPT, and open circles using FOPT expansions, see text.

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This is a preliminary update of the measurements of αs and the determination of the world average value of αs (M2Z) presented in the 2013/2014 edition of the Review of Particle Properties [1].

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... The results are shown in Fig. 8. The one-loop perturbative expression (32), evaluated at α ¼ 0.3 ≈ α MS ð2 GeVÞ [61,62] and m q ¼ 17 MeV and with μ ¼ 2 GeV, is also plotted. We have used the subtracted bare quark mass rather than the renormalized mass in this calculation, but this makes little difference as varying m q even by a factor 2 has a negligible effect for the range of momenta we are considering here. ...
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We study the quark-gluon vertex in the limit of vanishing gluon momentum using lattice QCD with two flavors of O(a) improved Wilson fermions, for several lattice spacings and quark masses. We find that all three form factors in this kinematics have a significant infrared strength and that both the leading form factor λ1, multiplying the tree-level vertex structure, and the scalar, chiral symmetry breaking form factor λ3 are significantly enhanced in the infrared compared to the quenched (Nf=0) case. These enhancements are orders of magnitude larger than predicted by one-loop perturbation theory. We find only a weak dependence on the lattice spacing and quark mass.
... where β 0 > 0 for α S and β 0 < 0 for α. The α (S) are running couplings, depending on the physical scale Q 2 and on µ R , with a much stronger dependence in QCD [59] than in QED [60]. A few couplings used in practice are α(m Z ) = 1/128 and α S (m Z ) = 0.118, or values from ...
Thesis
In dieser Dissertation wird die Suche nach schweren neutralen pseudoskalaren A und skalaren H Higgs-Bosonen vorgestellt, die in gg-Fusionen erzeugt werden, und in ein Top-Antitop-Quark-Paar zerfallen. Gesucht wurde im vollständigen Datensatz von Proton–Proton-Kollisionen bei einer Schwerpunktsenergie von 8 TeV die vom ATLAS-Detektor am Large Hadron Collider aufgezeichnet wurde und einer integrierten Luminosität von 20.3 fb−1 entspricht. Der Signalprozess und der Haupthintergrund aus der Top-Quark-Paar-Produktion über starke gg-Fusionen-Prozesse, interferieren heftig, was zu einer Verzerrung des reinen Breit-Wigner-Resonanzpeak in eine Peak-Dip-Struktur führt. Diese Analyse ist die erste am LHC, die die Interferenz zwischen Signal und Hintergrundprozessen vollständig berücksichtigt. Die Suche stützt sich auf die statistische Analyse des invarianten Top-Quark-Paar-Massenspektrum, welches aus Ereignissen mit einem Elektron oder Myon mit hohem Transversalimpuls, einer hohen fehlenden Transversalenergie von dem nicht detektierten Neutrino und mindestens vier Jets rekonstruiert wird. In den Daten wird keine signifikante Abweichung vom erwarteten Standardmodell-Hintergrund beobachtet. Die Ausschließungsgrenzen wurden abgeleitet im Kontext des Typ II Two-Higgs-Doublet Model, für Higgs-Bosonen mit einer Masse von 500 und 750 GeV und mit niedrigerem tan(\beta)-Parameter, bei der tan(\beta) das Verhältnis der Vakuumerwartungswerte der beiden Higgs-Dublett-Felder ist. Diese Parameterregionen sind weitgehend unerforscht in Untersuchungen von beliebigen Endzuständen.
... In the GE potential we use the vector coupling constant, which does not contain fitting parameters and takes into account the asymptotic freedom behavior [33], so that the effective coupling of the ground state α V (eff.) = 0.39 is relatively small, while α V = 0.54 is larger for excited states with n r ≥ 2. Details can be found in Ref. [22], where the vector coupling α v (n f = 3) is shown to be defined via the QCD vector constant Λ V (n f = 3) = 0.455 GeV, which corresponds to the QCD constant Λ M S (n f = 3) = 330 MeV from Ref. [34]. ...
Article
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The spectrum of the $$s\bar{s}$$ mesons is studied performing a phenomenological analysis of the Regge trajectories defined for the excitation energies. For the $$\phi (3\,^3S_1)$$ state the mass $$M(\phi (3S))=2100(20)$$ MeV and the leptonic width $$\varGamma _{ee}(\phi (3S))=0.27(2)$$ keV are obtained, while the mass of the $$2\,^3D_1$$ state, $$M(\phi (2\,^3D_1))=2180(5)$$ MeV, appears to be in agreement with the mass of the $$\phi (2170)$$ resonance, and its leptonic width, $$\varGamma _{ee}(2\,^3D_1)=0.20\pm 0.10$$ keV, has a large theoretical uncertainty, depending on the parameters of the flattened confining potential.
... This property, known as asymptotic freedom, implies that quantum chromodynamics (QCD) is well-defined at arbitrarily short distances. Despite this, the running of g 3 has only been measured up to the TeV scale [80] and the addition of new coloured particles could lead to the loss of this property. However, the possibility arises in which the strong gauge coupling reaches an interacting ultraviolet fixed point, as proposed in [81]. ...
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A bstract We consider the requirements that all coupling constants remain perturbative and the electroweak vacuum metastable up to the Planck scale in high-scale thermal leptogenesis, in the context of a type-I seesaw mechanism. We find a large region of the model parameter space that satisfies these conditions in combination with producing the baryon asymmetry of the Universe. We demonstrate these conditions require Tr[ Y N † Y N ] ≲ 0.66 on the neutrino Yukawa matrix. We also investigate this scenario in the presence of a large number N F of coloured Majorana octet fermions in order to make quantum chromodynamics asymptotically safe in the ultraviolet.
... For the CKM matrix we assume the unit matrix, which for the most relevant element of our computation V tb is consistent with the measured value (1.021 ± 0.032 [102]). Furthermore, we set the initial value for the strong (running) coupling constant to [103] α s µ = m Z = 0.118 , (3.14) ...
Article
A bstract We present an approach to predict exclusive $${W}^{+}b{W}^{-}\overline{b}$$ W + b W − b ¯ production at lepton colliders that correctly describes the top-anti-top threshold as well as the continuum region. We incorporate $$t\overline{t}$$ t t ¯ form factors for the NLL threshold resummation derived in NRQCD into a factorized relativistic cross section using an extended double-pole approximation, which accounts for fixed-order QCD corrections to the top decays at NLO. This is combined with the full fixed-order QCD result at NLO for $${W}^{+}b{W}^{-}\overline{b}$$ W + b W − b ¯ production to obtain predictions that are not only valid at threshold but smoothly transition to the continuum region. Our implementation is based on the Monte Carlo event generator Whizard and the code Toppik and allows to compute fully-differential threshold-resummed cross sections including the interference with non-resonant background processes. For the first time it is now possible to systematically study general differential observables at future lepton colliders involving the decay products of the top quarks at energies close to the pair production threshold and beyond.
... This asymmetry causes, via multiple collisions, an anisotropic momentum distribution as shown in Figure 1. 6. ...
... This model [44] also factorizes the charmonium production cross section into perturbative and non-perturbative steps, but unlike the CSM, it does not assume that the charm quarks are produced in their final color state. The J/ψ production cross section under this model is given by [45]: This model has been successful in describing many charmonium observables including the J/ψ production cross sections at different LHC energies measured by ALICE as will be discussed in section 2. 6 ...
... As Figure 4.7: Invariant mass distributions of opposite-charge muon pairs from semileptonic decay of bb pairs at s NN = 5.02 TeV using PYTHIA. 6. The different distributions correspond to the applying of different kinematic cuts. ...
Thesis
Ultra relativistic heavy-ion collisions are considered as a unique tool to produce, in the laboratory, thehot and dense strongly-interacting medium, the Quark-Gluon Plasma (QGP). This thesis is dedicated to the studyof two powerful probes, the J/ψ and Z-boson, that can help reaching a better understanding of the properties of theQGP.An important observable to study the QGP formation in heavy-ion collisions is the measurement of the J/ψproduction. The sizes of the different effects that can enhance or suppress this production vary with the collisionenergy. In this thesis, the J/ψ production is measured in Pb-Pb collisions at √sNN = 5.02 TeV using mainly themuon spectrometer of the ALICE detector. The J/ψ nuclear modification factor is presented as a function ofcollision centrality, rapidity and transverse momentum (pT). In addition, results on the J/ψ average pT and squaredaverage pT are also obtained. The comparison between the results and various theoretical calculations suggests thatthe J/ψ production is affected in the medium by an interplay between dissociation and regeneration mechanisms.In heavy-ion collisions, the initial state of the collision can affect the results even in the absence of the QGP.Understanding and quantifying such effects is crucial in order to separate them from the ones caused by thepresence of the QGP. One of these effects is the nuclear modification of the parton distribution functions (PDFs).The measurement of Z-boson production in heavy-ion collisions is a powerful tool to study the nuclearmodification of PDFs since it is not affected by the presence of the strongly-interacting medium. The second partof this thesis is devoted to measure the Z-boson production, for the first time with ALICE, in p-Pb and Pb-Pbcollisions at √sNN = 5.02 TeV. In Pb-Pb collisions where the precision of the measurement is higher, the agreementbetween data and theoretical calculations is better when the latter take into account the nuclear modification of thePDFs.
... For the experimental values M t ≈ 173.34 ± 0.76 GeV [65], M H ≈ 125.09 ± 0.24 GeV[66] and α s (M Z ) = 0.1184 ± 0.0007 [67] we get the couplings in the MS-scheme at the scale of the top mass using two-loop matching relations [15] ...
Article
We present analytical results for the leading top-Yukawa and QCD contribution to the $\beta$-function for the Higgs self-coupling $\lambda$ of the Standard Model at four-loop level, namely the part $\propto y_t^4 g_s^6$. We also give the contribution $\propto y_t^2 g_s^6$ of the anomalous dimension of the Higgs field as well as the terms $\propto y_t g_s^8$ to the top-Yukawa $\beta$-function which can also be derived from the anomalous dimension of the top quark mass. Together with the recently computed top-Yukawa and QCD contributions to $\beta_{g_s}$ these constitute the leading four-loop contributions to the evolution of the Higgs self-coupling. A numerical estimate of these terms at the scale of the top-quark mass is presented as well as an analysis of the impact on the evolution of $\lambda$ up to the Planck scale and the vacuum stability problem.
... Furthermore, there are other precise determinations with lower central values and in disagreement with the world average from event-shapes64656667 and DIS [68]. A review on recent α s determinations can be found in Refs.697071 . Therefore , in analogy with Ref. [6], we perform our analyses for several values of α s (m Z ) between 0.113 and 0.119, and provide the central values and perturbative errors as (approximate) linear functions of α s (m Z ). ...
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We present new determinations of the $$\overline{\mathrm{MS}}$$ charm quark mass using relativistic QCD sum rules at $$\mathcal{O}\left({\alpha}_s^3\right)$$ from the moments of the vector and the pseudoscalar current correlators. We use available experimental measurements from e +e − collisions and lattice simulation results, respectively. Our analysis of the theoretical uncertainties is based on different implementations of the perturbative series and on independent variations of the renormalization scales for the mass and the strong coupling. Taking into account the resulting set of series to estimate perturbative uncertainties is crucial, since some ways to treat the perturbative expansion can exhibit extraordinarily small scale dependence when the two scales are set equal. As an additional refinement, we address the issue that double scale variation could overestimate the perturbative uncertainties. We supplement the analysis with a test that quantifies the convergence rate of each perturbative series by a single number. We find that this convergence test allows to determine an overall and average convergence rate that is characteristic for the series expansions of each moment, and to discard those series for which the convergence rate is significantly worse. We obtain $$\overline{m_c}\left(\overline{m_c}\right)=1.288\pm 0.020$$ GeV from the vector correlator. The method is also applied to the extraction of the $$\overline{\mathrm{MS}}$$ bottom quark mass from the vector correlator. We compute the experimental moments including a modeling uncertainty associated to the continuum region where no data is available. We obtain $$\overline{m_b}\left(\overline{m_b}\right)=4.176\pm 0.023$$ GeV.
... Whether this fact is due to missing higher-order contributions in our calculations or to other effects is not yet clear at this point. Apart from the kurtosis, the QCD coupling value extracted from all the other moments has values around α s (m 2 Z ) = 0.118, in striking agreement with the current world-average obtained by other methods [57, 58]. ) at NLO (MS scheme, n f = 5 quark flavours) obtained from the fits of the √ s-dependence of the moments of the charged hadron distribution of jets in e + e − collisions obtained from their NMLLA+NLO * evolution. The last column provides the weighted-average of the individual measurements with its total propagated uncertainty. ...
... ) uncertainties have been enlarged by a common factor such that their final weighted average has a χ 2 /ndf close to unity. Such a " χ 2 averaging " method [58] ) = 0.1195 ± 0.0022 which is in excellent agreement with the current world-average of the strong coupling at the Z mass [57, 58]. Our extraction of the QCD strong coupling has an uncertainty (±2%) that is commensurate with that from other e + e − observables such as jet-shapes (±1%) and 3-jets rates (±2%) [57, 58]. ...
... Such a " χ 2 averaging " method [58] ) = 0.1195 ± 0.0022 which is in excellent agreement with the current world-average of the strong coupling at the Z mass [57, 58]. Our extraction of the QCD strong coupling has an uncertainty (±2%) that is commensurate with that from other e + e − observables such as jet-shapes (±1%) and 3-jets rates (±2%) [57, 58]. In a forthcoming work, we will extend the extraction of the strong coupling via the NMLLA+NLO * evolution of the moments of the hadron distribution in jet world-data measured not only in e + e − but also including deep-inelastic e ± p collisions [59]. ...
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The moments of the single inclusive momentum distribution of hadrons in QCD jets, are studied in the next-to-modified-leading-log approximation (NMLLA) including next-to-leading-order (NLO) corrections to the αs strong coupling. The evolution equations are solved using a distorted Gaussian parametrisation, which successfully reproduces the spectrum of charged hadrons of jets measured in e + e − collisions. The energy dependencies of the maximum peak, multiplicity, width, kurtosis and skewness of the jet hadron distribution are computed analytically. Comparisons of all the existing jet data measured in e + e − collisions in the range $$\sqrt{\mathrm{s}}\approx 2-200$$ GeV to the NMLLA + NLO* predictions allow one to extract a value of the QCD parameter ΛQCD , and associated two-loop coupling constant at the Z resonance α s(m Z 2 ) = 0.1195 ± 0.0022, in excellent numerical agreement with the current world average obtained using other methods.
... The recent measurements of m h by the ATLAS [12] and CMS [14] According to ref. [29, 30], the world average of α s (M 2 Z ) from the fit to various data, excluding the EW precision measurements, is given by α s (M 2 Z ) = 0.1184 ± 0.0006. For the hadronic contribution to the running of the electromagnetic coupling, we adopt the recent evaluation ∆α ...
Article
We perform the fit of electroweak precision observables within the Standard Model with a 126 GeV Higgs boson, compare the results with the theoretical predictions and discuss the impact of recent experimental and theoretical improvements. We introduce New Physics contributions in a model-independent way and fit for the S, T and U parameters, for the $\epsilon_{1,2,3,b}$ ones, for modified $Zb\bar{b}$ couplings and for a modified Higgs coupling to vector bosons. We point out that composite Higgs models are very strongly constrained. Finally, we compute the bounds on dimension-six operators relevant for the electroweak fit.