Quantum Chromodynamics Corrections Research Articles

Revisiting the top-quark pair production at future e + e − colliders* *Supported in part by the Natural Science Foundation of China (12175025, 12147102, 12265011), by the Projects of Guizhou Provincial Department (YQK[2023]016, ZK[2023]141, [2020]1Y027, GZMUZK[2022]PT01)

In this study, we reanalyze the top-quark pair production at next-to-next-to-leading order (NNLO) in quantum chromodynamics (QCD) at future colliders using the Principle of Maximum Conformality (PMC) method. The PMC renormalization scales in are determined by absorbing the non-conformal β terms by recursively using the Renormalization Group Equation (RGE). Unlike the conventional scale-setting method of fixing the scale at the center-of-mass energy , the determined PMC scale is far smaller than the and increases with the , yielding the correct physical behavior for the top-quark pair production process. Moreover, the convergence of the pQCD series for the top-quark pair production is greatly improved owing to the elimination of the renormalon divergence. For a typical collision energy of GeV, the PMC scale is GeV; the QCD correction factor K for conventional results is , where the first error is caused by varying the scale and the second error is from the top-quark mass GeV. After applying the PMC, the renormalization scale uncertainty is eliminated, and the QCD correction factor K is improved to , where the error is from the top-quark mass GeV. The PMC improved predictions for the top-quark pair production are helpful for detailed studies of the properties of the top-quark at future colliders.

Radiation from a gluon-gluino colour-singlet dipole at N3LO

We compute the quantum chromodynamics (QCD) corrections to the decay of a neutralino to gluinos and partons at next-to-next-to-next-to-leading order (N3LO) in the strong coupling constant αs, integrated separately over the phase-space of two, three, four or five particles in the final state. The resulting matrix elements are related to the quark-gluon antenna functions, completing the set of integrated antenna functions in final-final kinematics required for the extension of the antenna subtraction scheme to N3LO. For a model with massless partons (quarks and gluons) and an arbitrary number of adjoint fermions, we obtained the following new results to Oαs3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left({\\alpha}_s^3\\right) $$\\end{document}: the inclusive cross section for the decay of a neutralino, the renormalization of the effective coupling of a neutralino to a gluino and gluon(s), the gluino collinear anomalous dimension, the gluino contribution to the parton collinear anomalous dimensions and the neutralino-gluino-gluon(s) vertex form factors. A special case of this model is the N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 super Yang-Mills theory, where we can relate some of our findings to known results.

Effects of anisotropic pressure on interacting quark star structure

Perturbative Quantum Chromodynamics (pQCD) corrections and color superconductivity predict that strongly interacting matter can reveal new physical phenomena under extreme conditions. Taking into account these interaction effects, we investigate the role of anisotropic pressure in quark stars composed of interacting quark matter. Adopting two physically well-motivated anisotropy profiles, we numerically solve the stellar structure equations in order to explore the consequences of anisotropic pressure on various macroscopic properties such as radius, gravitational mass, surface redshift, moment of inertia, tidal Love number and oscillation spectrum. Remarkably, for both anisotropy models, negative anisotropies increase the radial stability of interacting quark stars, while the opposite occurs for positive anisotropies. However, for the Bowers-Liang profile, the central density corresponding to the maximum-mass point does not coincide with the central density where the squared oscillation frequency vanishes, indicating that the existence of stable anisotropic interacting quark stars is possible beyond the maximum mass for negative anisotropies. Additionally, we compare our theoretical predictions with several observational mass-radius measurements and tidal deformability constraints, which suggest that both strong interaction effects and anisotropy effects play a crucial role in describing compact stars observed in the Universe.

Planar three-loop QCD helicity amplitudes for V+jet production at hadron colliders

We compute the planar three-loop Quantum Chromodynamics (QCD) corrections to the helicity amplitudes involving a vector boson V=Z,W±,γ⁎, two quarks and a gluon. These amplitudes are relevant to vector-boson-plus-jet production at hadron colliders and other precision QCD observables. The planar corrections encompass the leading colour factors N3, N2Nf, NNf2 and Nf3. We provide the finite remainders of the independent helicity amplitudes in terms of multiple polylogarithms, continued to all kinematic regions and in a form which is compact and lends itself to efficient numerical evaluation. The presented amplitude respects the conjectured symbol-adjacency constraints for amplitudes with three massless and one massive leg.

Two-loop helicity amplitudes for V+jet production including axial vector couplings to higher orders in ϵ

We compute the two-loop Quantum Chromodynamics (QCD) corrections to all partonic channels relevant for the production of an electroweak boson V = Z, W±, γ* and a jet at hadron colliders. We consider the decay of a vector boson V to three partons V → qq¯g\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ q\\overline{q}g $$\\end{document}, V → ggg with a vector and axial vector coupling in both channels, including singlet and non-singlet contributions. For the quark channel, we use a recent tensor decomposition and extend the calculation to O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(ϵ2). For the gluonic channel, we define a new tensor decomposition which allows us to compute the vector and the axial vector amplitudes at once and to perform the computation of the amplitudes to O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(ϵ2). We provide finite remainders of the helicity amplitudes analytically continued to all relevant scattering regions qq¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ q\\overline{q} $$\\end{document} → Vg, qg → Vq and gg → Vg. The axial vector contribution to the gluon-induced channel completes the set of two-loop amplitudes for this process, while the extension to O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(ϵ2) represents the first step in the calculation of next-to-next-to-next-to-leading-order (N3LO) QCD corrections to Z+jet production at hadron colliders.

Predictions of the ratio and asymmetry probes of the invisible Z-boson decay

Higher-order predictions through the combined accuracy including next-to-leading order (NLO) electroweak (EW) and next-to-NLO (NNLO) quantum chromodynamics (QCD) corrections in underlying perturbation theories are presented thoroughly for the invisible decay of the Z boson into neutrino pair relative to its decay into charged-lepton pair (leptonic decay). The combined NNLO QCD+NLO EW predictions are achieved based on the fully-differential calculations of cross sections of both the invisible and leptonic processes in proton-proton (pp) collisions at 13 TeV center-of-mass energy. Differential distributions of cross-section ratios of the invisible process to the leptonic process are presented as a function of the transverse momentum of the Z boson . For the first time, the predictions for differential distributions of cross-section asymmetries between the invisible process and the leptonic process are presented in bins of the . The cross-section ratio and asymmetry distributions, which are referred to as the invisible probes, are considered to be important for controlling the invisible process by the leptonic process of the Z boson and probing deviation from the Standard Model (SM) for new-physics searches. The predictions are extensively presented beyond the Z-boson mass resonance region to assess the potential of the invisible ratio and asymmetry probes for new-phenomena searches in high-invariant mass region of the lepton-pair final states. Various tests with threshold requirements of transverse momenta of neutrino pair and leptons are performed to assess the impact on the combined predictions. The invisible ratio and asymmetry probes are proposed to be important probes for indirect searches of new-physics scenarios.

The parton-level structure of Higgs decays to hadrons at N3LO

We present the quantum chromodynamics (QCD) corrections for Higgs boson decays to hadronic final states at next-to-next-to-next-to-leading order (N3LO) in the strong coupling constant αs. In particular, we consider the Higgs boson decay to massless bottom quarks and the Higgs boson decay to a pair of gluons in the limit of a heavy top quark. The tree-level five-parton, the one-loop four-parton, the two-loop three-parton, and the three-loop two-parton matrix elements are integrated separately over the inclusive phase space and classified by partons appearing in the final state and by colour structure. As a check, we reproduce known results for the inclusive hadronic decay rates at N3LO. We study patterns of infrared singularity cancellation within the colour layers of the integrated expressions and we comment on the similarities between H → boverline{b} and γ∗→ qoverline{q} . We anticipate that our result will be an essential ingredient for the formulation of N3LO subtraction schemes.

Three-loop matching coefficients for heavy flavor-changing currents and the phenomenological applications

Within the framework of non-relativistic QCD (NRQCD) factorization, we compute the matching coefficients between full Quantum Chromodynamics (QCD) and NRQCD for the heavy flavor-changing vector, axial-vector, scalar and pseudo-scalar currents up to next-to-next-to-next-to-leading order (N3LO). We accomplish the analytical expressions for the three-loop renormalization constants and the corresponding anomalous dimensions for all of the four NRQCD currents with two different heavy flavors. The three-loop QCD corrections to the matching coefficients turn out to be significantly larger than lower order corrections. By employing the scale relation, we approximately simulate the N3LO correction to the wave functions at the origin for the vector {B}_c^{ast } meson and the pseudo-scalar Bc meson from the known result for the equal-mass heavy quarkonium in potential NRQCD (pNRQCD). We find large cancellations at the third order between the matching coefficients and the wave functions at the origin, and obtain the convergent decay constants of {B}_c^{ast } and Bc up to N3LO. We present the complete perturbative QCD predictions for the decay constants, leptonic decay widths, and branching ratios of the beauty-charmed mesons.

Three-loop QCD matching of the flavor-changing scalar current involving the heavy charm and bottom quark

We compute the matching coefficient between the quantum chromodynamics (QCD) and the non-relativistic QCD (NRQCD) for the flavor-changing scalar current involving the heavy charm and bottom quark, up to the three-loop order within the NRQCD factorization. For the first time, we obtain the analytical expressions for the three-loop renormalization constant tilde{Z}_s(x,R_f) and the corresponding anomalous dimension tilde{gamma }_s(x,R_f) for the NRQCD scalar current with the two heavy bottom and charm quark. We present the precise numerical results for those relevant coefficients (C_{FF}(x_0), ldots , C_{FBB}(x_0)) with an accuracy of about thirty digits. The three-loop QCD correction turns out to be significantly large. The obtained matching coefficient C_s(mu _f,mu ,m_b,m_c) is helpful to analyze the threshold behaviours when two different heavy quarks are close to each other and form the double heavy B_c meson family.

The parton-level structure of e+e− to 2 jets at N3LO

We investigate the quantum chromodynamics (QCD) corrections to hadronic final states in electron-positron collisions at mathcal{O} ( {alpha}_s^3 ) in the strong coupling constant αs. Namely, we analytically compute the total cross section for this process by separately integrating the tree-level five-parton, the one-loop four-parton, the two-loop three-parton, and the three-loop two-parton matrix elements over the respective phase space. All the contributions to the calculation are treated in a common framework whereby phase space integrals are expressed as physical cuts of the four-loop two-point function. We check the cancellation of infrared poles at all colour levels and we reproduce the known result for the R-ratio at order {alpha}_s^3 .

Next-to-next-to-leading order matching of beauty-charmed meson Bc and Bc* decay constants

We present the next-to-next-to-leading order (NNLO) quantum chromodynamics (QCD) corrections to the decay constants for both the pseudoscalar ${B}_{c}$ meson and the vector ${B}_{c}^{*}$ meson in the nonrelativistic QCD (NRQCD) effective theory. The explicit NNLO calculations prove that the ${B}_{c}$ decay constant from the pseudoscalar current is identical with the ${B}_{c}$ decay constant from the axial-vector current. The NNLO result for the vector decay constant of ${B}_{c}^{*}$ meson is novel. Combining this result with the latest extraction of the NRQCD long-distance matrix elements of ${B}_{c}$ and ${B}_{c}^{*}$ meson, we calculate and show the theoretical predictions for the branching ratios of the leptonic decays ${B}_{c}^{+}/{B}_{c}^{*+}\ensuremath{\rightarrow}{l}^{+}{\ensuremath{\nu}}_{l}$ with ${l}^{+}=({e}^{+},{\ensuremath{\mu}}^{+},{\ensuremath{\tau}}^{+})$. In addition, the novel anomalous dimension for the flavor-changing heavy quark vector current in the NRQCD effective theory is helpful to investigate the threshold behaviors of the two different heavy quarks.

Accurate prediction of the Drell-Yan distribution in wide dilepton mass and rapidity ranges in pp collisions through NNLO+N3LL

This paper presents high-accuracy predictions for the differential cross ss as a function of the key observable of the neutral-current Drell-Yan (DY) dilepton production in proton-proton (pp) collisions. The differential distributions for the are presented by using the state-of-the-art predictions from the combined calculations of fixed-order perturbative quantum chromodynamics (QCD) corrections at next-to-next-to-leading order (NNLO) accuracy and resummation of large logarithmic terms at next-to-next-to-leading logarithmic (NNLL) and next-to-NNLL (N3LL) accuracies, i.e., NNLO+NNLL and NNLO+N3LL, respectively. The predicted distributions are reported for a thorough set of the DY dilepton invariant mass m ll ranges, spanning a wide kinematic region of 50 < m ll < 1000 GeV both near and away from the Z-boson mass peak, and rapidity y ll ranges in the central detector acceptance region of ∣y ll ∣ < 2.4. The differential distributions in the wide m ll and y ll ranges offer stringent tests to assess the reliability of the predictions, where the m ll and y ll are closely correlated with the parton distribution functions (PDFs) of the incoming partons. The matched predictions through NNLO+N3LL are observed to provide good description of the 13 TeV pp collision data for the (including the dilepton transverse momentum as well) distributions in almost the entire m ll and y ll ranges, apart from the intermediate- to high- region in the lowest mass range 50–76 GeV which is assessed to constitute a challenge for the presented predictions. The predictions at NNLO+N3LL are also reported at 14 TeV for the upcoming high-luminosity running era of the Large Hadron Collider (LHC), in which increasing amount of data is expected to require more accurate and precise theoretical description. The most recent PDF models MSHT20 and CT18, in addition to the NNPDF3.1, are tested for the first time for the matched predictions of the distribution. The differential distributions by the combined predictions through NNLO QCD+NLO EW are finally provided to enable assessment of the impact of the EW corrections for the .

Next-to-Next-to-Leading Order Study of Three-Jet Production at the LHC.

Multijet rates at hadron colliders provide a unique possibility for probing quantum chromodynamics (QCD), the theory of strong interactions. By comparing theory predictions with collider data, one can directly test perturbative QCD, extract fundamental parameters like the strong coupling α_{s}, and search for physics beyond the standard model. In this work we calculate, for the first time, the next-to-next-to-leading order (NNLO) QCD corrections to typical three-jet observables and to differential three-to-two jet ratios. The calculation is complete apart from the three-jet double virtual contributions which are included in the leading-color approximation. We demonstrate that the inclusion of the NNLO corrections significantly reduces the dependence of those observables on the factorization and renormalization scales. Besides its phenomenological value, this proof-of-principle computation represents a milestone in perturbative QCD.

Bc meson exclusive decays to a P -wave charmonium and a pion at NLO accuracy

In this paper, we calculate the next-to-leading order (NLO) quantum chromodynamics (QCD) corrections to the exclusive processes $B_c^+\to \chi_{cJ}(h_c)\pi^+$ in the framework of the nonrelativistic QCD (NRQCD) factorization formalism. The results show that NLO QCD corrections markedly enhance the branching ratios with $K$ factors of about 2.5. In combination with the study of $B_c^+\to J/\psi\pi^+$, we find that the NLO NRQCD prediction for the ratio of branching fractions $\frac{\mathcal{B}(B_c^+\to \chi_{c0}\pi^+)}{\mathcal{B}(B_c^+\to J/\psi \pi^+)}$ is then compatible with the experimental measurement.

Calculations of Higher Order Quantum Chromodynamics Corrections

Calculations of Higher Order Quantum Chromodynamics Corrections

Z-boson hadronic decay width up to {{mathcal {O}}}(alpha _s^4)-order QCD corrections using the single-scale approach of the principle of maximum conformality

In the paper, we study the properties of the Z-boson hadronic decay width by using the mathcal {O}(alpha _s^4)-order quantum chromodynamics (QCD) corrections with the help of the principle of maximum conformality (PMC). By using the PMC single-scale approach, we obtain an accurate renormalization scale-and-scheme independent perturbative QCD (pQCD) correction for the Z-boson hadronic decay width, which is independent to any choice of renormalization scale. After applying the PMC, a more convergent pQCD series has been obtained; and the contributions from the unknown mathcal {O}(alpha _s^5)-order terms are highly suppressed, e.g. conservatively, we have Delta Gamma _{mathrm{Z}}^{mathrm{had}}|^{{{mathcal {O}}}(alpha _s^5)}_{mathrm{PMC}}simeq pm 0.004 MeV. In combination with the known electro-weak (EW) corrections, QED corrections, EW–QCD mixed corrections, and QED–QCD mixed corrections, our final prediction of the hadronic Z decay width is Gamma _{mathrm{Z}}^{mathrm{had}}=1744.439^{+1.390}_{-1.433} MeV, which agrees with the PDG global fit of experimental measurements, 1744.4pm 2.0 MeV.

NLO QCD corrections to exclusive quarkonium-pair production in photon\u2013photon collision

We calculate the next-to-leading order (NLO) quantum chromodynamics (QCD) corrections to the exclusive processes gamma +gamma rightarrow {mathcal {Q}}+{mathcal {Q}}, with {mathcal {Q}}=J/psi , eta _c, Upsilon , or eta _b, in the framework of non-relativistic QCD (NRQCD) factorization formalism. The cross sections at the SuperKEKB electron–positron collider, as well as at the future colliders, like the circular electron positron collider (CEPC) and the international linear collider (ILC), are evaluated. Numerical result indicates that the processes for J/psi -pair production and eta _c-pair production are hopefully observable at the Belle II detector within the next decade.

NLO QCD corrections to inclusive charmonium and Bc meson production in W+ decays

We calculate the next-to-leading order (NLO) quantum chromodynamics (QCD) corrections to inclusive processes $W^+\to J/\psi(\eta_c)+c+\bar{s}+X$ and $W^+\to B_c(B_c^{*})+b+\bar{s}+X$ in the framework of nonrelativistic QCD (NRQCD) factorization formalism. Result indicates that the NLO corrections are significant, and the uncertainties in theoretical predictions with NLO corrections are greatly reduced. The charmonium and $B_c$ meson yielding rates at the Large Hadron Collider (LHC) are given.

Polarised amplitudes and soft-virtual cross sections for b overline{b} \u2192 Z H at NNLO in QCD

Production of the Higgs boson, H in association with a massive vector boson, V, i.e., the V H process, plays an important role in the explorations of Higgs physics at the Large Hadron Collider, both for a precise study of Higgs’ Standard Model couplings and for probing New Physics. In this publication we present the two-loop corrections in mass- less quantum chromodynamics (QCD) to the amplitude of the Higgs production associated with a Z boson via the bottom quark-antiquark annihilation channel with a non-vanishing bottom-quark Yukawa coupling, which is a necessary ingredient of the full next-to-next- to-leading-order QCD corrections to the V H process in the five-flavour scheme. The computation is performed by projecting the D-dimensional scattering amplitude directly onto an appropriate set of Lorentz structures related to the linear polarisation states of the Z boson. We provide analytic expressions of the complete set of renormalised polarised amplitudes in terms of polylogarithms of maximum weight four. To give an estimation of the size of contributions from amplitudes considered in this work, we compute numerically the resulting cross sections under the soft-virtual approximation. We also take the opportunity to make a dedicated discussion regarding an interesting subtlety appearing in the conventional form factor decomposition of amplitudes involving axial currents regularised in D dimensions.

NNLO QCD⊕QED corrections to Higgs production in bottom quark annihilation

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 and soft anomalous dimensions. In addition, we derive the QED as well as QCD$\times$QED contributions to soft distribution function as well as to the ultraviolet renormalization constant of the bottom Yukawa coupling up to second order in strong coupling and fine structure constant. Finally, we report our findings on the numerical impact of the NNLO results from QED and QCD$\times$QED at the LHC energies taking into account the dominant NNLO QCD corrections.