Lepton Pair Research Articles

Phenomenology of TMD parton distributions in Drell-Yan and Z0 boson production in a hadron structure oriented approach

We present a first practical implementation of a recently proposed hadron structure oriented (HSO) approach to transverse momentum dependent (TMD) phenomenology applied to Drell-Yan-like processes, including lepton pair production at moderate Q2 and Z0 boson production. We compare and contrast general features of our methodology with other common practices and emphasize aspects that we view as improvements. Separately, we discuss the importance of treatments that preserve various theoretical properties of the nonperturbative parts of TMD parametrizations for future applications that have the extraction of hadron structure as a primary goal. These include the HSO’s preservation of a basic TMD parton-model-like framework even while accounting for full TMD factorization and evolution, explicit preservation of the integral relationship between TMD and collinear parton density functions, and the ability to meaningfully compare different theoretical models of nonperturbative TMD parton distributions. In our examples, we show that there is significant sensitivity at moderate Q2 to both the form of the nonperturbative transverse momentum dependence and the parametrization of collinear parton densities. However, we also find that evolving to Q2=MZ2, without fitting, results in a satisfactory postdiction of existing data for Z0 production, nearly independently of the modeling of nonperturbative transverse momentum behavior. We argue that this demonstrates that moderate Q measurements should be given greater weight than high Q measurements in extractions of nonperturbative transverse momentum dependence. We also obtain new extractions of the nonperturbative Collins-Soper kernel within the HSO approach. We discuss its features and compare with some earlier extractions. Published by the American Physical Society 2024

Hunting for Bileptons at Hadron Colliders.

I review possible signals at hadron colliders of bileptons, namely doubly charged vectors or scalars with lepton number L=±2, as predicted by a 331 model, based on a SU(3)c×SU(3)L×U(1)X symmetry. In particular, I account for a version of the 331 model wherein the embedding of the hypercharge is obtained with the addition of three exotic quarks and vector bileptons. Furthermore, a sextet of SU(3)L, necessary to provide masses to leptons, yields an extra scalar sector, including a doubly charged Higgs, i.e., scalar bileptons. As bileptons are mostly produced in pairs at hadron colliders, their main signal is provided by two same-sign lepton pairs at high invariant mass. Nevertheless, they can also decay according to non-leptonic modes, such as a TeV-scale heavy quark, charged 4/3 or 5/3, plus a Standard Model quark. I explore both leptonic and non-leptonic decays and the sensitivity to the processes of the present and future hadron colliders.

Study of intrinsic-kT in the Parton Branching Method

The work presented here focuses on the production of Drell-Yan lepton pairs in hadron-hadron collisions with very low transverse momentum which is sensitive to the contribution from the non-perturbative transverse motion of partons inside hadrons as well as to the multiple soft gluon emissions which have to be resumed. To study the two contributions, we use Parton Branching Method which describes the evolution of transverse momentum dependent parton distributions and provides very precise predictions for inclusive observables such as the Drell–Yan cross section as a function of transverse momentum. In this study, we tune a parameter that describes the internal transverse motion of partons within hadron (intrinsic-kT) depending on the soft gluon contribution which is varied applying a lower limit to the transverse momentum of the emitted parton in branching up to 2 GeV. It will be shown that the parameter presented by the width of the Gaussian distribution increases with the minimal transverse momentum. This means that by reducing the contribution of soft gluons, more intense internal transverse motion is required (larger intrinsic-kT) to describe experimental data. Moreover, it was observed that the value of the intrinsic-kT increases with the collision energy and such a trend is more pronounced when the minimum transverse momentum of the parton at the branching is higher.

Search for bottom-type vectorlike quark pair production in dileptonic and fully hadronic final states in proton-proton collisions at s=13 TeV

A search is described for the production of a pair of bottom-type vectorlike quarks (B VLQs) with mass greater than 1000 GeV. Each B VLQ decays into a b quark and a Higgs boson, a b quark and a Z boson, or a t quark and a W boson. This analysis considers both fully hadronic final states and those containing a charged lepton pair from a Z boson decay. The products of the H→bb boson decay and of the hadronic Z or W boson decays can be resolved as two distinct jets or merged into a single jet, so the final states are classified by the number of reconstructed jets. The analysis uses data corresponding to an integrated luminosity of 138 fb−1 collected in proton-proton collisions at s=13 TeV with the CMS detector at the LHC from 2016 to 2018. No excess over the expected background is observed. Lower limits are set on the B VLQ mass at the 95% confidence level. These depend on the B VLQ branching fractions and are 1570 and 1540 GeV for 100% B→bH and 100% B→bZ, respectively. In most cases, the mass limits obtained exceed previous limits by at least 100 GeV. © 2024 CERN, for the CMS Collaboration 2024 CERN

CLFV leptophilic Z′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z^\\prime $$\\end{document} as a dark matter portal: prospects for colliders

Extensions of the Standard Model featuring light vector bosons have been explored with the goal of resolving certain tensions between theory and experiment, among them the discrepancy in the anomalous magnetic moment of the muon, Δaμ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta a_{\\mu }$$\\end{document}. In particular, this is the case of a minimal construction including a leptophilic, strictly flavour violating, vector boson Z′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z^\\prime $$\\end{document}. These new vector bosons are also well-motivated dark matter portals, with non-trivial couplings to stable, weakly interacting states which can account for the correct dark matter density. Here we study the prospects of a Standard Model extension (via a vector boson and a fermionic dark matter candidate) concerning signatures at the LHC, and at future lepton and hadron colliders. We discuss the cross-sections of several processes leading to same- and opposite-sign muon-tau lepton pairs in the final state, as well as final states with missing energy (in the form of neutrinos and/or dark matter). Our findings suggest that a future muon collider offers the best prospects to probe this model (together with searches for dilepton pairs and missing energy signatures at the FCC-ee running at the Z-pole); moreover, the complementarity of the different future high-energy colliders is also paramount to probing distinct Z′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z^\\prime $$\\end{document} mass regimes.

Improving probes of hAA coupling in the Type-X two Higgs doublet model scenario: The crucial role of τ-jet charge identification

The exotic decay modes of the already discovered 125-GeV scalar into a pair of light pseudoscalars are a good probe of those new physics scenarios where such pseudoscalars exist. Searches in the mass region where the pseudoscalar (A) is lighter than 62.5 GeV have yielded null findings so far. No search has yet examined mA>62.5 GeV where the cross section is suppressed by the off-shell pseudoscalar. We point out a possible enhancement of the sensitivity of probing hAA coupling in the context of a Type-X two Higgs doublet model. We focus on h→AA(⁎)→4τ, and select events with two same-sign τ-jets along with a pair of same-sign leptons. This enables much more effective background elimination than in the erstwhile proposed channels. Taking two values of the ττA coupling into account, we obtain limits on the hAA coupling that can be probed at 2σ and 3σ significance, for mA ranging up to 85 GeV. For mA<62.5 GeV, too, we find the probe through our suggested channel exhibits considerable improvement upon the usual 2μ2τ-based searches conducted at the LHC. Within this region, achieving the reach of λhAA coupling at 3000 fb−1 luminosity using our strategy would require approximately ∼3.6×105 fb−1 luminosity using conventional 2μ2τ-based searches.

Probing the effect of background fields on coupling constants in ultraperipheral heavy ion collisions

In this paper, we propose to measure the effect of the background field on the coupling constant through the process of photon annihilation into lepton pairs and a real photon in ultraperipheral collisions of relativistic heavy ion. In our study, the coupling constant after being corrected by background field has a significant impact on cross-section compared to the uncorrected one.

Search for a scalar or pseudoscalar dilepton resonance produced in association with a massive vector boson or top quark-antiquark pair in multilepton events at s=13 TeV

A search for beyond the standard model spin-0 bosons, ϕ, that decay into pairs of electrons, muons, or tau leptons is presented. The search targets the associated production of such bosons with a W or Z gauge boson, or a top quark-antiquark pair, and uses events with three or four charged leptons, including hadronically decaying tau leptons. The proton-proton collision data set used in the analysis was collected at the LHC from 2016 to 2018 at a center-of-mass energy of 13 TeV, and corresponds to an integrated luminosity of 138 fb−1. The observations are consistent with the predictions from standard model processes. Upper limits are placed on the product of cross sections and branching fractions of such new particles over the mass range of 15 to 350 GeV with scalar, pseudoscalar, or Higgs-boson-like couplings, as well as on the product of coupling parameters and branching fractions. Several model-dependent exclusion limits are also presented. For a Higgs-boson-like ϕ model, limits are set on the mixing angle of the Higgs boson with the ϕ boson. For the associated production of a ϕ boson with a top quark-antiquark pair, limits are set on the coupling to top quarks. Finally, limits are set for the first time on a fermiophilic dilaton-like model with scalar couplings and a fermiophilic axion-like model with pseudoscalar couplings. © 2024 CERN, for the CMS Collaboration 2024 CERN

Testing Bell inequality through at CEPC* *Tong Li is Supported by the National Natural Science Foundation of China (12375096, 12035008, 11975129), and "the Fundamental Research Funds for the Central Universities", Nankai University (63196013). Kai Ma was supported by the Natural Science Basic Research Program of Shaanxi Province, China (2023-JC-YB-041) and the Innovation Capability Support Program of Shaanxi Province, China (2021KJXX-47)

The decay of Higgs boson into two spin-1/2 particles provides an ideal system to reveal quantum entanglement and Bell-nonlocality. Future colliders can improve the measurement accuracy of the spin correlation of tau lepton pairs from Higgs boson decay. We show the testability of Bell inequality through at Circular Electron Positron Collider (CEPC). Two realistic methods of testing Bell inequality are investigated, i.e., Törnqvist's method and Clauser-Home-Shimony-Holt (CHSH) inequality. In the simulation, we consider the detector effects of CEPC including uncertainties for tracks and jets from Z boson in the production of . Necessary reconstruction approaches are described to measure quantum entanglement between and . Finally, we show the sensitivity of CEPC to Bell inequality violation for the two methods.

One-Loop Contributions for A0 → ℓℓ̄V with ℓ ≡ e, μ and V ≡ γ , Z in Higgs Extensions of the Standard Model

Abstract We present one-loop formulas for the decay of the CP-odd Higgs $A^0 \rightarrow \ell \bar{\ell } V$ with $\ell \equiv e, \mu$ and $V\equiv \gamma , Z$ in Higgs extensions of the Standard Model, considering a two Higgs doublet model with an extra complex (and real) scalar, a two Higgs doublet model as well as a triplet Higgs model. Analytic results for one-loop amplitudes are expressed in terms of the basic Passarino–Veltman functions following the standard notations of LoopTools. As a result, physical results can be generated numerically by using the package. In the phenomenological results, the total decay widths and the differential decay rates with respect to the invariant mass of a lepton pair are analyzed for two typical models such as the two Higgs doublet model and the triplet Higgs model.

Test of lepton flavor universality in B±→K±μ+μ− and B±→K±e+e− decays in proton-proton collisions at s=13TeV

A test of lepton flavor universality in B±→K±μ+μ− and B±→K±e+e− decays, as well as a measurement of differential and integrated branching fractions of a nonresonant B±→K±μ+μ− decay are presented. The analysis is made possible by a dedicated data set of proton-proton collisions at s=13TeV recorded in 2018, by the CMS experiment at the LHC, using a special high-rate data stream designed for collecting about 10 billion unbiased b hadron decays. The ratio of the branching fractions B(B±→K±μ+μ−) to B(B±→K±e+e−) is determined from the measured double ratio R(K) of these decays to the respective branching fractions of the B±→J/ψK± with J/ψ→μ+μ− and e+e− decays, which allow for significant cancellation of systematic uncertainties. The ratio R(K) is measured in the range 1.1<q2<6.0GeV2 , where q is the invariant mass of the lepton pair, and is found to be R(K)=0.78−0.23+0.47 , in agreement with the standard model expectation R(K)≈1 . This measurement is limited by the statistical precision of the electron channel. The integrated branching fraction in the same q 2 range, B(B±→K±μ+μ−)=(12.42±0.68)×10−8 , is consistent with the present world-average value and has a comparable precision.

Lepton pair photoproduction in hadronic heavy-ion collisions with nuclear overlap

Lepton pair photoproduction in hadronic heavy-ion collisions with nuclear overlap

Dilepton Polarization as a Signature of Plasma Anisotropy.

We propose the angular distribution of lepton pairs produced in ultrarelativistic heavy-ion collisions as a probe of thermalization of the quark-gluon plasma. We focus on dileptons with invariant masses large enough that they are produced through quark-antiquark annihilation in the early stages of the collision. The angular distribution of the lepton in the rest frame of the pair then reflects the angular distribution of quark momenta. At early times, the transverse pressure of the quark-gluon plasma is larger than its longitudinal pressure as a result of the fast longitudinal expansion, which results in an oblate lepton distribution. By contrast, direct (Drell-Yan) production by quarks and antiquarks from incoming nuclei, whose momenta are essentially longitudinal, results in a prolate distribution. As the invariant mass increases, Drell-Yan gradually becomes the dominant source of dilepton production, and the lepton distribution evolves from oblate to prolate. The invariant mass at which the transition occurs is highly sensitive to the equilibration time of the quark-gluon plasma or, equivalently, the shear viscosity over entropy ratio η/s in the early stages of the collision.

Di-electron production at the LHC: unravelling virtual-photon and heavy-flavour contributions

The production of virtual photons is a very sensitive probe of the properties of the quark-gluon plasma. As they are experimentally detected by lepton pairs, they suffer from a large background arising from hadron decays. Light-flavour hadrons dominate at low invariant masses below mee ~ 0.5 GeV and heavy flavours above. These contributions must therefore also be taken into account in experimental analyses at the LHC. In this paper, we calculate the direct contribution from virtual photons produced in the Drell-Yan process with an additional jet in POWHEG and find that it is significant at low invariant masses. We also simulate the background contributions from cc¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ c\\overline{c} $$\\end{document} and bb¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ b\\overline{b} $$\\end{document} production with POWHEG and quantify the theoretical uncertainties due to variations of the perturbative scales and parton distribution functions. We find larger relative and absolute uncertainties for the lighter c quarks than for heavier b quarks.

Lepton pair production in muon-nucleus scattering

The MUonE experiment aims at providing a novel determination of the leading hadronic contribution to the muon anomalous magnetic moment through the study of elastic muon-electron scattering. Since the initial-state electrons are bound in a low-Z atomic target, the interaction between the incoming muons and the nuclei is expected to be the main source of experimental background. In this article, we study the production of a real lepton pair from the muon-nucleus scattering, discussing its numerical impact in the MUonE kinematic configuration. The process is described as a scattering of a muon in an external Coulomb field with the addition of a form factor to describe the nuclear charge distribution. The calculation is implemented in the fully differential Monte Carlo event generator Mesmer, without introducing any approximation on the angular variables.

Probing dark photons from a light scalar at Belle II

In the minimal U(1) extension of the Standard Model (SM), a new gauge boson referred to as “dark photon” is predicted. The dark-photon mass can be generated from an additional Higgs mechanism associated with a dark scalar boson. At B-factories such as Belle II, large numbers of B-mesons are produced and can decay to a kaon plus the dark scalar via the latter’s mixing with the SM Higgs boson. We evaluate the sensitivity of Belle II for the case in which the dark scalar decays exclusively into a pair of dark photons via the new U(1) gauge coupling, and the dark photons are long lived owing to a small kinetic mixing ϵ. We study the experimental signature in which each dark photon decays into a pair of charged leptons, pions, or kaons, resulting in a pair of displaced vertices, and argue that the search is essentially background-free. We perform detailed Monte-Carlo simulations to determine the expected number of signal events at Belle II with an integrated luminosity of 50 ab−1, taking into account the efficiencies for both final-state-particle identification and displaced tracking. We find that for experimentally allowed values of the scalar mixing angle and kinematically allowed dark-photon and dark-scalar masses, the proposed search is uniquely sensitive to the medium-ϵ regime, which is currently mostly unexcluded by experiments.

New physics couplings from angular coefficient functions of B¯→D*(Dπ)ℓν¯ℓ

The Belle Collaboration has recently measured the complete set of angular coefficient functions for the exclusive decays B¯→D*(Dπ)ℓν¯ℓ, with ℓ=e, μ, in four bins of the parameter w=mB2+mD*2−q22mBmD*, with q the lepton pair momentum [M. T. Prim (Belle Collaboration), ]. Under the assumption that physics beyond the Standard Model does not contribute to such modes, the measurements are useful to determine the hadronic form factors describing the B→D* matrix elements of the Standard Model weak current, and to improve the determination of |Vcb|. On the other hand, they can be used to assess the impact of possible new physics contributions. In a bottom-up approach, we extend the Standard Model effective Hamiltonian governing this mode with the inclusion of the full set of Lorentz invariant d=6 operators compatible with the gauge symmetry of the theory. The measured angular coefficient functions can tightly constrain the couplings in the generalized Hamiltonian. We present the first results of this analysis, discussing how improvements can be achieved when more complete data on the angular coefficient functions will be available. Published by the American Physical Society 2024

Extracting transition generalized parton distributions from hard exclusive pion-nucleon scattering

We study the extraction of transition generalized parton distributions (GPDs) from production of two back-to-back high transverse momentum photons (γγ) and a massive pair of leptons (ℓ+ℓ−) in hard exclusive pion-nucleon scattering. We argue that the exclusive scattering amplitude of both processes could be factorized into nonperturbative pion distribution amplitude and nucleon transition GPDs that are convoluted with perturbatively calculable short-distance matching coefficients. We demonstrate that the exclusive diphoton production not only is complementary to the Drell-Yan-type dilepton production for extracting the GPDs but also provides enhanced sensitivities for extracting the parton momentum fraction x dependence of the GPDs. We show that both exclusive observables are physically measurable at the J-PARC and AMBER experiment energies. If the target nucleon can be polarized, corresponding spin asymmetries can offer additional sensitivities for extracting transition GPDs. Published by the American Physical Society 2024

Search for the anomalous ZZZ and ZZγ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ZZ\\gamma $$\\end{document} gauge couplings through the process e+e-→ZZ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e^+e^- \\rightarrow ZZ $$\\end{document} with unpolarized and polarized beams

This work offers the constraints on the anomalous neutral triple gauge couplings for the process e+e-→ZZ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e^+e^- \\rightarrow ZZ $$\\end{document} at the CLIC with s=3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{s}=3$$\\end{document} TeV. The realistic CLIC detector environments and their effects are considered in our analysis. The study is planned for the decays of produced Z bosons to a pair of charged leptons (electrons or muons) and neutrino pairs. The bounds on the anomalous neutral triple gauge couplings defining CP-violating CB~W/Λ4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_{\\widetilde{B}W}/{\\Lambda ^4}$$\\end{document} coupling and three CP-conserving CWW/Λ4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_{WW}/{\\Lambda ^4}$$\\end{document}, CBW/Λ4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_{BW}/{\\Lambda ^4}$$\\end{document}, and CBB/Λ4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_{BB}/{\\Lambda ^4}$$\\end{document} couplings are obtained. Also, the effects and advantages of polarization for incoming electron beams in these calculations are investigated.

QCD corrections to the Golden decay channel of the Higgs boson

Future colliders aim to provide highly precise experimental measurements of the properties of the Higgs boson. In order to benefit from these precision machines, theoretical errors in the Higgs sector observables have to match at least the experimental uncertainties. The theoretical uncertainties in the Higgs sector observables can be reduced by including missing higher-order terms in their perturbative calculations. In this direction, we compute the mixed QCD-electroweak corrections at \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{O}\\left({\\alpha \\alpha }_{s}\\right)$$\\end{document} to the Higgs decay into four charged leptons by considering the golden decay channel, H → e+e−μ+μ−. Due to color conservation, these corrections receive contributions only from the two-loop virtual diagrams. In the complex mass scheme, we find that the mixed QCD-electroweak corrections to the partial decay width, relative to the leading order predictions, are positive and about 0.27% for αs(MZ). Relative to the next-to-leading order electroweak corrections, the mixed QCD-electroweak corrections are found to be approximately 18% for αs(MZ). With respect to the leading order, we observe a flat effect of the mixed QCD-electroweak corrections on the invariant mass distribution of the lepton pairs with fixed QCD coupling. The ϕ distribution, due to the mixed QCD-electroweak corrections, follows a (1 − cos ϕ) dependence.