NLO Approximation Research Articles

Production cross section of heavy quarks in e−p interaction at the NLO approximation

We present the production cross section of heavy quarks σcc¯, σbb¯ and σtt¯ at the next-to-leading order in the electron-proton interaction by using the quarks and gluon distribution functions at the initial scale Q02. To do this, we use a fitted form of the heavy quark coefficient functions for deep-inelastic lepton-hadron scattering to obtain the structure functions of heavy quarks. Then, we calculate the reduced cross section of heavy quarks by using the structure functions and subsequently present the single differential and the integrated cross section of heavy quarks at the center-of-mass energies of s=319GeV, 1.3TeV and 3.5TeV in the electron-proton collision. The obtained numerical results of the cross section of the charm and beauty quarks are compared with the HERA data, which is a combination from the results of the H1 and ZEUS detectors. Furthermore, we present the production cross section of top quark as a direct prediction from our calculations.

Higher order approximations to the longitudinal structure function FL from the parametrization of F2 based on the Laplace transformation

We describe the determination of the longitudinal structure function $F_{L}$ at NLO and NNLO approximations, using Laplace transform techniques, into the parametrization of $F_{2}(x,Q^{2})$ and its derivative with respect to $\ln{Q^{2}}$ at low values of the Bjorken variable $x$. The obtained results are comparable with others by considering the effect of the charm quark mass to the longitudinal structure function, which leads to rescaling variable for $n_{f}=4$. Numerical calculations and comparison with H1 data demonstrate that the suggested method provides reliable $F_{L}(x,Q^{2})$ at small $x$ in a wide range of $Q^{2}$ values and can be applied as well in analyses of ultra-high energy processes with cosmic neutrinos. The obtained longitudinal structure functions with and without the LHeC simulated uncertainties [CERN-ACC-Note-2020-0002, LHeC Collaboration and FCC-he Study Group, P. Agostini et al., J. Phys. G: Nucl. Part. Phys. {\bf48}, 110501(2021).] are compared with the H1 Collaboration data [Eur.Phys.J.C{\bf74}, 2814(2014) and Eur.Phys.J.C{\bf71}, 1579 (2011)] and with the results from CT18 [Phys.Rev.D{\bf103}, 014013(2021)] parametrization model at NLO and NNLO approximations.

DECAY WIDTH MODELING OF HIGGS BOSON WITHIN THDM MODEL

As part of the search for new physics beyond the Standard Model, we chose the determination of the Higgs boson decay width as one of the least experimentally determined values. The decay widths into the four fermions of the lightest and heaviest CP-even Higgs bosons of the THDM model were calculated, taking into account QCD and electroweak corrections in the NLO approximation. To achieve this goal, the program Monte Carlo Prophecy 4f with special scenarios of parameters, 7B1 and 5B1 were used. It was found that the decay width of the heavier CPeven Higgs boson H differs from HSM by 1227.93 times and changes to a negative value when deviating from the standard scenarios. Scale factors kZ2 and kW2 showed the predominance of the associated with Z boson production cross section of CP-even Higgs boson over the associated with W production cross section.

Non-linear equation in the re-summed next-to-leading order of perturbative QCD: the leading twist approximation

In this paper, we use the re-summation procedure, suggested in Ducloué et al. (JHEP 1904:081, 2019), Salam (JHEP 9807:019 1998), Ciafaloni et al. (Phys Rev D 60:1140361999) and Ciafaloni et al. (Phys Rev D 68:114003, 2003), to fix the BFKL kernel in the NLO. However, we suggest a different way to introduce the non-linear corrections in the saturation region, which is based on the leading twist non-linear equation. In the kinematic region: tau ,equiv ,r^2 Q^2_s(Y),le ,1, where r denotes the size of the dipole, Y its rapidity and Q_s the saturation scale, we found that the re-summation contributes mostly to the leading twist of the BFKL equation. Assuming that the scattering amplitude is small, we suggest using the linear evolution equation in this region. For tau ,>,1 we are dealing with the re-summation of (bar{alpha }_S,ln tau )^n and other corrections in NLO approximation for the leading twist. We find the BFKL kernel in this kinematic region and write the non-linear equation, which we solve analytically. We believe the new equation could be a basis for a consistent phenomenology based on the CGC approach.

QCD analysis of structure functions in deep inelastic neutrino-nucleon scattering without using the orthogonal polynomials approach

A nonsinglet QCD analysis of neutrino-nucleon structure function is performed based on all the data for charged current neutrino-nucleon deep inelastic scattering (DIS) corresponds to NLO and NNLO approximations, with taking into account the nuclear and higher twist corrections. In this analysis, we extract $xu_v(x,Q^2)$ and $xd_v(x,Q^2)$ valence parton distribution functions (PDFs) in a wide range of $x$ and $Q^2$, and determine their parametrization with the correlated errors using the xFitter framework. Our results regarding valence-quark densities with their uncertainties are compared to the prediction extracted using other PDF sets from different groups. We determine $\alpha_{s}(M_Z^2)$= 0.1199 $\pm$ 0.0031 and 0.1185 $\pm$ 0.0023 with considering the nuclear and higher twist corrections at the NLO and NNLO, respectively, and perform a comparison with other reported results. The extracted results regarding valence-quark distributions and the value of $\alpha_{s}(M_Z^2)$ are in good agreement with available theoretical models.

Analytical solutions of the QCD⊗QED DGLAP evolution equations based on the Mellin transform technique in NLO approximation

In this paper we present a new and efficient analytical solutions for evolving the QCD⊗QED DGLAP evolution equations in Mellin space and obtain the parton distribution functions (PDFs) in perturbative QCD including the QED corrections. The validity of our analytical solutions, which have done in the next to leading order QCD and the leading order QED approximations, are checked with the initial parton distributions from newly released CT14QED global analysis code (Schmidt et al., 2016 [9]). The evolved parton distribution functions are in good agreement with CT14QED PDFs set and also with those from APFEL (Bertone et al., 2014 [7]) program. Finally, we derived the impact of the NLO QED corrections to the QCD⊗QED DGLAP evolution equations.

Effective action for reggeized gluons, classical gluon field of relativistic color charge and color glass condensate approach

We discuss application of formalism of small-x effective action for reggeized gluons (Gribov, Sov. Phys. JETP 26:414, 1968; Lipatov, Nucl. Phys. B 452:369, 1995; Lipatov, Phys. Rep. 286:131, 1997; Lipatov, Subnucl. Ser. 49:131, 2013; Lipatov, Int. J. Mod. Phys. Conf. Ser. 39:1560082, 2015; Lipatov, Int. J. Mod. Phys. A 31(28/29):1645011, 2016; Lipatov, EPJ Web Conf. 125:01010, 2016; Lipatov, Sov. J. Nucl. Phys. 23:338, 1976; Kuraev et al., Sov. Phys. JETP 45:199, 1977; Kuraev et al., Zh Eksp, Teor. Fiz. 72:377, 1977; Balitsky and Lipatov, Sov. J. Nucl. Phys. 28:822, 1978; Balitsky and Lipatov, Yad. Fiz. 28:1597 1978), for the calculation of classical gluon field of relativistic color charge, similarly to that done in CGC approach of McLerran and Venugopalan, Phys. Rev. D 49:2233 (1994), Jalilian-Marian et al., Phys. Rev. D 55:5414 (1997), Jalilian-Marian et al., Nucl. Phys. B 504:415 (1997), Jalilian-Marian et al., Phys. Rev. D 59:014014 (1998), Jalilian-Marian et al., Phys. Rev. D 59:014015 (1998), Iancu et al., Nucl. Phys. A 692:583 (2001), Iancu et al., Phys. Lett. B 510:133 (2001), Ferreiro et al., Nucl. Phys. A 703:489 (2002). The equations of motion with the reggeon fields are solved in LO and NLO approximations and new solutions are found. The results are compared to the calculations performed in the CGC framework and it is demonstrated that the LO CGC results for the classical field are reproduced in our calculations. Possible applications of the NLO solution in the effective action and CGC frameworks are discussed as well.

DIS structure functions in the NLO approximation of the Parton Reggeization Approach

The main ideas of the NLO calculations in Parton Reggeization Approach are illustrated on the example of the simplest NLO subprocess, which contributes to DIS: $\gamma^\star+R\to q + \bar{q}$. The double counting with the LO contribution $\gamma^\star + Q \to q$ is resolved. The problem of matching of the NLO results for single-scale observables in the Parton Reggeization Approach on the corresponding NLO results in the Collinear Parton Model is considered. In the developed framework, the usual NLO PDFs in the $\overline{MS}$-scheme can be consistently used as the collinear input for the NLO calculation in the Parton Reggeization Approach.

Numerical solution of DGLAP equations using Laguerre polynomials expansion and Monte Carlo method.

We investigate the numerical solutions of the DGLAP evolution equations at the LO and NLO approximations, using the Laguerre polynomials expansion. The theoretical framework is based on Furmanski et al.’s articles. What makes the content of this paper different from other works, is that all calculations in the whole stages to extract the evolved parton distributions, are done numerically. The employed techniques to do the numerical solutions, based on Monte Carlo method, has this feature that all the results are obtained in a proper wall clock time by computer. The algorithms are implemented in FORTRAN and the employed coding ideas can be used in other numerical computations as well. Our results for the evolved parton densities are in good agreement with some phenomenological models. They also indicate better behavior with respect to the results of similar numerical calculations.

Next-to-next-to-leading order QCD analysis of spin-dependent parton distribution functions and their uncertainties: Jacobi polynomials approach

We present a first QCD analysis of next-to-next-leading-order (NNLO) contributions of the spin-dependent parton distribution functions (PPDFs) in the nucleon and their uncertainties using the Jacobi polynomial approach. Having the NNLO contributions of the quark-quark and gluon-quark splitting functions in perturbative QCD (Nucl. Phys. B 889 (2014) 351-400), one can obtain the evolution of longitudinally polarized parton densities of hadrons up to NNLO accuracy of QCD. A very large sets of recent and up-to-date experimental data of spin structure functions of the proton $g_1^p$, neutron $g_1^n$, and deuteron $g_1^d$ have been used in this analysis. The predictions for the NNLO calculations of the polarized parton distribution functions as well as the proton, neutron and deuteron polarized structure functions are compared with the corresponding results of the NLO approximation. We form a mutually consistent set of polarized PDFs due to the inclusion of the most available experimental data including the recently high-precision measurements from {\tt COMPASS16} experiments (Phys. Lett. B 753 (2016) 18-28). We have performed a careful estimation of the uncertainties using the most common and practical method, the Hessian method, for the polarized PDFs originating from the experimental errors. The proton, neutron and deuteron structure functions and also their first moments, $\Gamma^{\rm p, n, d}$, are in good agreement with the experimental data at small and large momentum fraction of $x$. We will discuss how our knowledge of spin-dependence structure functions can improve at small and large value of $x$ by the recent {\tt COMPASS16} measurements at CERN, the {\tt PHENIX} and {\tt STAR} measurements at RHIC, and at the future proposed colliders such as Electron-Ion collider (EIC).

Fragmentation functions of neutral mesons π0 and k0 with Laplace transform approach

With an analytical solutions of DGLAP evolution equations based on the Laplace transform method, we find the fragmentation functions (FFs) of neutral mesons, [Formula: see text] and [Formula: see text] at NLO approximation. We also calculated the total fragmentation functions of these mesons and compared them with experimental data and those from global fits. The results show a good agreement between our solutions and other models and they are compatible with experimental data.

Update of the MCSANC Monte Carlo integrator, v. 1.20

New features of the MCSANC v.1.20 program, a Monte Carlo tool for calculation of the next-to-leading order electroweak and QCD corrections to various Standard Model processes, have been presented. The extensions concern implementation of Drell–Yan-like processes and include a systematic treatment of the photon-induced contribution in proton–proton collisions and electroweak corrections beyond the NLO approximation. There are also technical improvements such as calculation of the forward–backward asymmetry for the neutral current Drell–Yan process. The updated code is suitable for studies of the effects due to EW and QCD radiative corrections to Drell–Yan (and several other) processes at the LHC and for forthcoming high-energy proton–proton colliders.

Diphoton production at the Tevatron and the LHC in the NLO approximation of the parton Reggeization approach

The hadroproduction of prompt isolated photon pairs at high energies is studied in the NLO* framework of the Parton Reggeization Approach. The real part of the NLO corrections is computed, and the procedure for the subtraction of double counting between real parton emissions in the hard-scattering matrix element and unintegrated PDF is constructed for the amplitudes with Reggeized quarks in the initial state. The matrix element of the important NNLO subprocess RR->2gamma with full dependence on the transverse momenta of the initial-state Reggeized gluons is obtained. We compare obtained numerical results with diphoton spectra measured at Tevatron and the LHC, and find a good agreement of our predictions with experimental data at the high values of diphoton transverse momentum, pT, and especially at the pT larger than the diphoton invariant mass, M. In this multi-Regge kinematics region, the NLO correction is strongly suppressed, demonstrating the self-consistency of the Parton Reggeization Approach.

Fragmentation functions of the pion, kaon, and proton in the NLO approximation: Laplace transform approach

Using repeated Laplace transform, We find an analytical solution for DGLAP evolution equations for extracting the pion, kaon and proton Fragmentation Functions (FFs) at NLO approximation. We also study the symmetry breaking of the sea quarks Fragmentation Functions, $D_{\bar q}^h (z,Q^2)$ and simply separated them according to their mass ratio. Finally, we calculate the total Fragmentation Functions of these hadrons and compare them with experimental data and those from global fits. Our results show a good agreement with the FFs obtained from global parameterizations as well as with the experimental data.

Longitudinal Proton Structure Function at LO and NLO Approximations

The purpose of this paper is to calculate the longitudinal structure function of proton through the well-known equation FL=F2−2xF1. To determine this structure function, we need to identify parton distribution functions to find F2. In this case, the valon model and DGLAP equations are utilized to obtain the parton distributions. Our calculations are carried out in two approximations LO and NLO. The results at the NLO approximation are in better agreement with the experimental data.

Effects of QCD Vacuum and the Instanton Induced-Contributions to the Nucleon Structure Functions

The instanton induced cross section in deep inelastic kinematics is a subject which people are tendentious to investigate it. Instanton induced contributions are well defined for the nucleon structure function. The non-perturbative contribution to the quark distributions of structure function, F2(x,Q2), is considered within an instanton model for the QCD vacuum. We find that the structure function may possess numerically large non-perterbative contributions which are related to the violation of chirality and correspond to the correction of parton distribution of the leading twist. It is shown that the instantons give a negative contribution to the structure function at the NLO approximation. A comparison between our results, considering instantaon effect, and the case when we do not take this effect is done. Taking into account the instanton size, ρ, via the modified running coupling constant we get to a good agreement between our results at the NLO and NNLO approximations and the available experimental data, specially at the low values of the Bjorken variable x < 0.1 which confirms the validity of our calculations.

NLO inspired effective Lagrangians for Higgs physics

Either late autumn this year or latest early next year ATLAS/CMS should have results with 2–3 times the current data which might give first clues on the couplings of the light narrow resonance discovered at the LHC in July 2012, compatible with the Higgs boson of the Standard Model. A strategy for measuring deviations from the Standard Model can be based on using the “full” Standard Model, including all available QCD and electroweak higher-order corrections, and supplement it with d=6 local operators. Their Wilson coefficients are assumed to be small enough that they can be treated at leading order. Examples of the connection of local operators with BSM Lagrangians are presented as well as a discussion of Lagrangians with/without decoupling of heavy degrees of freedom. The whole strategy is critically reviewed in the light of internal consistency and an “Effective NLO Approximation” is proposed.

Nonequilibrium two-particle irreducible evolution of theO(N)model with longitudinal expansion

Motivated by the problem of thermalization in heavy-ion collisions, we present numerical simulations of the nonequilibrium evolution of the O(N) model in 1+2 dimensions with longitudinal expansion and in the presence of a background field. We work in the NLO approximation of the 1/N expansion and consider both the strong and weak coupling cases. Special emphasis is put on the difference between the 2PI formalism and the classical statistical approach. In the 2PI case at strong coupling, we find some evidence of the Bose-Einstein (exponential) distribution in the expanding system.

SPIN-DEPENDENT STRUCTURE FUNCTION OF 3He and 3H

We present the results of our QCD analysis for quark distributions and structure functions for polarized deep inelastic scattering of leptons on nucleons and nuclei using the Jacobi polynomials up to NLO approximation. Finally by having proton and also neutron structure functions, we have enough motivation to extract 3 He and 3 H polarized structure functions.

Markovian Monte Carlo program EvolFMC v.2 for solving QCD evolution equations

Abstract We present the program EvolFMC v.2 that solves the evolution equations in QCD for the parton momentum distributions by means of the Monte Carlo technique based on the Markovian process. The program solves the DGLAP-type evolution as well as modified-DGLAP ones. In both cases the evolution can be performed in the LO or NLO approximation. The quarks are treated as massless. The overall technical precision of the code has been established at 5 × 10 − 4 . This way, for the first time ever, we demonstrate that with the Monte Carlo method one can solve the evolution equations with precision comparable to the other numerical methods. New version program summary Program title: EvolFMC v.2 Catalogue identifier: AEFN_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEFN_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including binary test data, etc.: 66 456 (7407 lines of C++ code) No. of bytes in distributed program, including test data, etc.: 412 752 Distribution format: tar.gz Programming language: C++ Computer: PC, Mac Operating system: Linux, Mac OS X RAM: Less than 256 MB Classification: 11.5 External routines: ROOT ( http://root.cern.ch/drupal/ ) Nature of problem: Solution of the QCD evolution equations for the parton momentum distributions of the DGLAP- and modified-DGLAP-type in the LO and NLO approximations. Solution method: Monte Carlo simulation of the Markovian process of a multiple emission of partons. Restrictions: 1. Limited to the case of massless partons. 2. Implemented in the LO and NLO approximations only. 3. Weighted events only. Unusual features: Modified-DGLAP evolutions included up to the NLO level. Additional comments: Technical precision established at 5 × 10 − 4 . Running time: For the 10 6 events at 100 GeV: DGLAP NLO: 27s; C ′ -type modified DGLAP NLO: 150s (MacBook Pro with Mac OS X v.10.5.5, 2.4 GHz Intel Core 2 Duo, gcc 4.2.4, single thread).