Quantum Chromodynamics Corrections Research Articles

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.

Resummed prediction for Higgs boson production through b overline{mathrm{b}} annihilation at N3LL

We present an accurate theoretical prediction for the production of Higgs bo- son through bottom quark annihilation at the LHC up to next-to-next-to-next-to leading order (N3LO) plus next-to-next-to-next-to-leading logarithmic (N3LL) accuracy. We de- termine the third order perturbative Quantum Chromodynamics (QCD) correction to the process dependent constant in the resummed expression using the three loop bottom quark form factor and third order quark soft distribution function. Thanks to the recent compu- tation of N3LO corrections to this production cross-section from all the partonic channels, an accurate matching can be obtained for a consistent predictions at N3LO+N3LL accu- racy in QCD. We have studied in detail the impact of resummed threshold contributions to inclusive cross-sections at various centre-of-mass energies and also discussed their sensi- tivity to renormalization and factorization scales at next-to-next-to leading order (NNLO) matched with next-to-next-to leading logarithm (NNLL). At N3LO+N3LL, we predict the cross-section for different centre-of-mass energies using the recently available results in [1] as well as study the renormalization scale dependence at the same order.

Iterated elliptic and hypergeometric integrals for Feynman diagrams

We calculate 3-loop master integrals for heavy quark correlators and the 3-loop quantum chromodynamics corrections to the ρ-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be factorized in Mellin-N space either. The solution of the homogeneous equations is possible in terms of 2F1 Gauß hypergeometric functions at rational argument. In some cases, integrals of this type can be mapped to complete elliptic integrals at rational argument. This class of functions appears to be the next one arising in the calculation of more complicated Feynman integrals following the harmonic polylogarithms, generalized polylogarithms, cyclotomic harmonic polylogarithms, square-root valued iterated integrals, and combinations thereof, which appear in simpler cases. The inhomogeneous solution of the corresponding differential equations can be given in terms of iterative integrals, where the new innermost letter itself is not an iterative integral. A new class of iterative integrals is introduced containing letters in which (multiple) definite integrals appear as factors. For the elliptic case, we also derive the solution in terms of integrals over modular functions and also modular forms, using q-product and series representations implied by Jacobi’s ϑi functions and Dedekind’s η-function. The corresponding representations can be traced back to polynomials out of Lambert–Eisenstein series, having representations also as elliptic polylogarithms, a q-factorial 1/ηk(τ), logarithms, and polylogarithms of q and their q-integrals. Due to the specific form of the physical variable x(q) for different processes, different representations do usually appear. Numerical results are also presented.

The QCD corrections of the process h → ηbZ

We investigate the 125 GeV Higgs boson decay to a pseudoscalar quarkonium [Formula: see text] and [Formula: see text] boson. We calculate the quantum chromodynamics (QCD) one-loop corrections to the branching ratio of the process, [Formula: see text], both in the Standard Model (SM) and in the two Higgs double models (THDM). Adding the QCD one-loop corrections, the branching ratio of [Formula: see text] in the SM is [Formula: see text]. The relative correction of that QCD one-loop level relative to the tree level of [Formula: see text] is around 76% in the SM. Similarly, the relative correction in the THDM also can be around 75%. The key parameter, [Formula: see text], can affect the relative correction in the THDM.

Two loop QCD corrections for the process pseudo-scalar Higgs \u2192 3 partons

We present virtual contributions up to two loop level in perturbative Quantum Chromodynamic (QCD) to the decay of pseudo-scalar Higgs boson (A) to three gluons (g) and also to quark (q), anti-quark ( overline{q} ) and a gluon. With appropriate crossing, they are well suited for predicting the differential distribution of A in association with a jet in hadron colliders up to next-to-next-to-leading order (NNLO) in strong coupling constant and also for the subsequent decay of A to hadrons. We use effective field theory approach to integrate out the top quarks in the heavy top limit. The resulting theory involves two pseudo-scalar composite operators describing the interaction of A with gluons as well as with quark and anti-quark. We perform our computation in dimensional regularisation and use minimal subtraction ( overline{MS} ) scheme to renormalise strong coupling constant as well as the composite operators. The ultraviolet (UV) finite amplitudes contain infrared (IR) divergences that are found to be in agreement with the predictions by Catani. For both the amplitudes namely A → ggg and Ato qoverline{q}g , the leading transcendental terms at one and two loops are found to be identical to those in a three point form factor (FF) of the half-BPS operator in mathcal{N}=4 Supersymmetric Yang Mills (SYM) theory when the QCD color factors are adjusted in a specific way. We present our results in terms of harmonic polylogs well suited for further numerical study.

Precision studies of observables in p p rightarrow W rightarrow lnu _l and pp rightarrow gamma ,Z rightarrow l^+ l^- processes at the LHC

This report was prepared in the context of the LPCC Electroweak Precision Measurements at the LHC WG (https://lpcc.web.cern.ch/lpcc/index.php?page=electroweak_wg) and summarizes the activity of a subgroup dedicated to the systematic comparison of public Monte Carlo codes, which describe the Drell–Yan processes at hadron colliders, in particular at the CERN Large Hadron Collider (LHC). This work represents an important step towards the definition of an accurate simulation framework necessary for very high-precision measurements of electroweak (EW) observables such as the W boson mass and the weak mixing angle. All the codes considered in this report share at least next-to-leading-order (NLO) accuracy in the prediction of the total cross sections in an expansion either in the strong or in the EW coupling constant. The NLO fixed-order predictions have been scrutinized at the technical level, using exactly the same inputs, setup and perturbative accuracy, in order to quantify the level of agreement of different implementations of the same calculation. A dedicated comparison, again at the technical level, of three codes that reach next-to-next-to-leading-order (NNLO) accuracy in quantum chromodynamics (QCD) for the total cross section has also been performed. These fixed-order results are a well-defined reference that allows a classification of the impact of higher-order sets of radiative corrections. Several examples of higher-order effects due to the strong or the EW interaction are discussed in this common framework. Also the combination of QCD and EW corrections is discussed, together with the ambiguities that affect the final result, due to the choice of a specific combination recipe. All the codes considered in this report have been run by the respective authors, and the results presented here constitute a benchmark that should be always checked/reproduced before any high-precision analysis is conducted based on these codes. In order to simplify these benchmarking procedures, the codes used in this report, together with the relevant input files and running instructions, can be found in a repository at https://twiki.cern.ch/twiki/bin/view/Main/DrellYanComparison.

NNLO QCD corrections to the Drell\u2013Yan cross section in models of TeV-scale gravity

The first results on the complete next-to-next-to-leading order (NNLO) Quantum Chromodynamic (QCD) corrections to the production of di-leptons at hadron colliders in large extra dimension models with spin-2 particles are reported in this article. In particular, we have computed these corrections to the invariant mass distribution of the di-leptons taking into account all the partonic sub-processes that contribute at NNLO. In these models, spin-2 particles couple through the energy-momentum tensor of the Standard Model with the universal coupling strength. The tensorial nature of the interaction and the presence of both quark annihilation and gluon fusion channels at the Born level make it challenging computationally and interesting phenomenologically. We have demonstrated numerically the importance of our results at Large Hadron Collider energies. The two-loop corrections contribute an additional 10% to the total cross section. We find that the QCD corrections are not only large but also important to make the predictions stable under renormalisation and factorisation scale variations, providing an opportunity to stringently constrain the parameters of the models with a spin-2 particle.

Study of Υ(nS) → Bcρ and BcK∗ decays within the QCD factorization

Motivated by the heavy-flavor experiments at running Large Hadron Collider (LHC) and upgrading SuperKEKB, which provide abundant [Formula: see text] data samples, the tree-dominated [Formula: see text] and [Formula: see text] (n =1, 2, 3) weak decays are studied within the framework of quantum chromodynamics (QCD) factorization. The QCD corrections to the longitudinal and transverse amplitudes are evaluated at next-to-leading order, and the branching fractions and polarization fractions are predicted. Numerically, the [Formula: see text] decays have relatively large branching fractions at the order of [Formula: see text] and are in the scope of the LHC and SuperKEKB/Belle-II experiments.

Measurement of dijet azimuthal decorrelation in ppcollisions at [Formula: see text

A measurement of the decorrelation of azimuthal angles between the two jets with the largest transverse momenta is presented for seven regions of leading jet transverse momentum up to 2.2,mathrm{TeV}. The analysis is based on the proton-proton collision data collected with the CMS experiment at a centre-of-mass energy of 8,mathrm{TeV} corresponding to an integrated luminosity of 19.7,text {fb}^{-1}. The dijet azimuthal decorrelation is caused by the radiation of additional jets and probes the dynamics of multijet production. The results are compared to fixed-order predictions of perturbative quantum chromodynamics (QCD), and to simulations using Monte Carlo event generators that include parton showers, hadronization, and multiparton interactions. Event generators with only two outgoing high transverse momentum partons fail to describe the measurement, even when supplemented with next-to-leading-order QCD corrections and parton showers. Much better agreement is achieved when at least three outgoing partons are complemented through either next-to-leading-order predictions or parton showers. This observation emphasizes the need to improve predictions for multijet production.

NLO QCD corrections to ηc+hc(1P)/ψ1,2(1D) production at B-factories**Supported by Ministry of Science and Technology of the People's Republic of China (2015CB856703) and National Natural Science Foundation of China (11175249, 11375200)

We calculate the next-to-leading order (NLO) quantum chromodynamics (QCD) corrections to double charmonium production processes e+e− → γ* → ηc+hc(1P)/ψ1,2(1D) within the non-relativistic QCD (NRQCD) factorization framework. We find that the corrections to ηc+hc(1P) production are positive, while those to ηc+ψ1,2(1D) are negative. Unlike the J/ψ+ηc case, all the corrections here are not large. Uncertainties in the renormalization scale, quark mass and running energy of center-of-mass are discussed, and the scale dependence of these processes is found to be greatly reduced with the NLO QCD corrections.

NLO QCD corrections forχcJinclusive production atBfactories

The next-to-leading-order quantum chromodynamics (QCD) corrections for ${\ensuremath{\chi}}_{cJ}({^{3}P}_{J}^{[1]},{^{3}S}_{1}^{[8]})$ $P$-wave charmonium-inclusive production at $B$ factories are calculated utilizing the nonrelativistic QCD factorization formalism. Large next-to-leading-order corrections are found, especially for the ${^{3}P}_{0}^{[1]}$ and ${^{3}S}_{1}^{[8]}$ configurations. Numerical evaluation indicates that the total cross sections of ${\ensuremath{\chi}}_{cJ}$-inclusive production processes are of the order of 10 fb, which is accessible in the BELLE II (super-B) experiment.

HZγ production at 14 TeV LHC in next-to-leading order QCD

We investigate the process at the Large Hadron Collider (LHC) up to the quantum chromodynamics (QCD) next-to-leading order (NLO), and discuss the kinematic distributions of the final products after on-shell Higgs and Z-boson decays by adopting the narrow width approximation. The dependence of the leading order (LO) and the QCD NLO corrected integrated cross-sections on the factorization/renormalization scale is studied. Our results show that the LO integrated cross-section and kinematic distributions are significantly enhanced by the NLO QCD corrections, and the NLO QCD K-factor strongly depends on the observables and phase space. We conclude that in precision experimental data analysis for probing the coupling, we should consider the NLO QCD corrections and put proper constraints on the lepton-pair invariant mass to reduce the background.

QCD NLO corrections to inclusiveBc*production inZ0decays

We calculate the next-to-leading order(NLO) quantum chromodynamics(QCD) corrections to the inclusive process of $Z_0 \rightarrow B^*_c+\bar{c}+b$ under the non-relativistic QCD(NRQCD) factorization scheme. Technical details about contributions from vector and axial-vector currents in dimensional regularization scheme are discussed. Numerical calculation shows that the NLO correction enhances the leading-order decay width by about 50%, and the dependence on renormalization scale $\mu$ is reduced. The uncertainties induced by quark masses and the renormalization scale $\mu$ are also analyzed.

The NLO Calculations of Heavy Quarkonium Production at B Factories

We calculated the next to leading order quantum chromodynamics corrections of J/ψ production at B factories. The next to leading order corrections are very important for heavy quarkonium production at B factories. The next to leading order cross sections can be compared with the B factories data. Some detail of the next to leading order calculations within the non-relativistic quantum chromodynamics factorization framework are given here.

Next-to-next-to-leading order calculation of the strong coupling constant α s by using moments of event-shape variables

The next-to-next-to-leading order (NN’LO) quantum chromodynamics (QCD) correction to the first three moments of the four event-shape variables in electron–positron annihilation, the thrust, heavy jet mass, wide, and total jet broadening, is computed. It is observed that the NNLO correction gives a better agreement between the theory and the experimental data. Also, by using the above observables, the strong coupling constant (α s) is determined and how much its value is affected by the NNLO correction is demonstrated. By combining the results for all variables at different centre-of-mass energies \(\alpha_{\rm s} ({M_{Z^0}})=0.1248\pm 0.0009\left( {\exp\!.} \right)_{-0.0144}^{+0.0283} \left({\mbox{theo}.} \right)\) is obtained.

Quantum chromodynamics effects in electroweak and Higgs physics

Several examples of the often intricate effects of higher-order quantum chromodynamics (QCD) corrections on predictions for hadron-collider observables, are discussed, using the production of electroweak gauge boson and the Standard Model Higgs boson as examples. Particular attention is given to the interplay of QCD effects and experimental cuts, and to the use of scale variations as estimates of theoretical uncertainties.

Shear modulus of the hadron-quark mixed phase

Robust arguments predict that a hadron-quark mixed phase may exist in the cores of some "neutron" stars. Such a phase forms a crystalline lattice with a shear modulus higher than that of the crust due to the high density and charge separation, even allowing for the effects of charge screening. This may lead to strong continuous gravitational-wave emission from rapidly rotating neutron stars and gravitational-wave bursts associated with magnetar flares and pulsar glitches. We present the first detailed calculation of the shear modulus of the mixed phase. We describe the quark phase using the bag model plus first-order quantum chromodynamics corrections and the hadronic phase using relativistic mean-field models with parameters allowed by the most massive pulsar. Most of the calculation involves treating the "pasta phases" of the lattice via dimensional continuation, and we give a general method for computing dimensionally continued lattice sums including the Debye model of charge screening. We compute all the shear components of the elastic modulus tensor and angle average them to obtain the effective (scalar) shear modulus for the case where the mixed phase is a polycrystal. We include the contributions from changing the cell size, which are necessary for the stability of the lower-dimensional portions of the lattice. Stability also requires a minimum surface tension, generally tens of MeV/fm^2 depending on the equation of state. We find that the shear modulus can be a few times 10^33 erg/cm^3, two orders of magnitude higher than the first estimate, over a significant fraction of the maximum mass stable star for certain parameter choices.

NLO QCD corrections to B c -to-charmonium form factors

The $B_c(^1S_0)$ meson to S-wave Charmonia transition form factors are calculated in next-to-leading order(NLO) accuracy of Quantum Chromodynamics(QCD). Our results indicate that the higher order corrections to these form factors are remarkable, and hence are important to the phenomenological study of the corresponding processes. For the convenience of comparison and use, the relevant expressions in asymptotic form at the limit of $m_c\rightarrow0$ for the radiative corrections are presented.