Next-to-leading Order Cross Sections Research Articles

Confronting electroweak MSSM through one-loop renormalized neutralino-Higgs interactions for dark matter direct detection and the muon g−2

We compute the next-to-leading order (NLO) corrections to the vertices where a pair of the lightest neutralino couples to CP-even (light or heavy) Higgs scalars. In particular, the lightest neutralino is assumed to be a dominantly binolike mixed state, composed of bino and Higgsino or bino, wino, and Higgsino. After computing all the three-point functions in the electroweak minimal supersymmetric Standard Model (MSSM), we detail the contributions from the counterterms that arise in renormalizing these vertices in one-loop order. The amendment of the renormalized vertices impacts the spin-independent direct detection cross sections of the scattering of nucleons with dark matter. We perform a comprehensive numerical scan over the parameter space where all the points satisfy the present B-physics constraints and accommodate the muon’s anomalous magnetic moment. Finally, we exemplify a few benchmark points, which indulge the present searches of supersymmetric particles. After including the renormalized one-loop vertices, the spin-independent DM-nucleon cross sections may be enhanced up to 20% compared to its tree-level results. Finally, with the NLO cross section, we use the recent LUX-ZEPLIN (LZ) results on the neutralino-nucleon scattering to display the relative rise in the lowest allowed band of the Higgsino mass parameter in the M1−μ plane of the electroweak MSSM. Published by the American Physical Society 2024

Precision predictions for dark matter with DM@NLO in the MSSM

We present DM@NLO, a Fortran 77 based program with a C++ interface dedicated to precision calculations of dark matter (DM) (co)annihilation cross-sections and elastic dark matter-nucleon scattering amplitudes in the minimal supersymmetric (SUSY) Standard Model (MSSM) at next-to-leading order (NLO) in perturbative (SUSY) QCD. If the annihilating initial particles carry an electric or colour charge, the Sommerfeld enhanced cross section is included as well and can be matched to the NLO cross section. We review these calculations including technical details relevant for using the code. We illustrate their impact by applying DM@NLO to an example scenario in the constrained MSSM.

Tests of the parametrizations of fragmentation functions using data on inclusive pion and kaon production in unpolarized pp collisions from the STAR collaboration and at the NICA project

The goal of this study is to check which, if any, of the published versions of the pion and kaon fragmentation functions (FFs) is compatible with the STAR data on semi-inclusive pion and kaon production in proton–proton collisions, and on the basis of this analysis to make reliable predictions for the [Formula: see text] spectra of the pions and kaons in inclusive pion and kaon production at the future NICA proton–proton collider. The calculations are carried out in next-to-leading order (NLO) of perturbative quantum chromodynamics (pQCD), using the well-tested CTEQ6 parton distributions. We consider the following pion and kaon FFs — DSEHS-14 [D. de Florian, R. Sassot, M. Epele, R. J. Hernández-Pinto and M. Stratmann, Phys. Rev. D 91, 014035 (2015), 1410.6027], DSEHS-17 [D. de Florian, M. Epele, R. J. Hernandez-Pinto, R. Sassot and M. Stratmann, Phys. Rev. D 95, 094019 (2017), 1702.06353], LSS-15 [E. Leader, A. V. Sidorov and D. B. Stamenov, Phys. Rev. D 93, 074026 (2016), 1506.06381], HKNS-07 [M. Hirai, S. Kumano, T. H. Nagai and K. Sudoh, Phys. Rev. D 75, 094009 (2007), hep-ph/0702250] and AKK-08 [S. Albino, B. A. Kniehl and G. Kramer, Nucl. Phys. B 803, 42 (2008), 0803.2768]. Our analysis shows that within the experimental errors all tested sets of FFs provide a good fit to STAR data at the c.m. energy [Formula: see text], and the best ones are both LSS-15 and DSEHS-14 for pions and DSEHS-17 for kaons. From comparison of the LO and NLO results it is clear that the latter fit data much better, specially in the region of small [Formula: see text]. The NLO cross-sections are also less scale-[Formula: see text] dependent, where [Formula: see text], than the LO ones. In order to make predictions for NICA energies, we compare the NLO pQCD results with the existing experimental BES STAR data on semi-inclusive hadron production in the most peripheral Au+Au collisions where the nuclear effects can be neglected. The comparison for lower energy scales, like at NICA, shows that a purely pQCD approach is inadequate and suggests the necessity to take into account also higher-order effects of initial-state soft-gluon radiation. Nevertheless, these data on the [Formula: see text] spectra of [Formula: see text], [Formula: see text] and also the ratios [Formula: see text] and [Formula: see text] seem to favor LSS-15 and DSEHS-14 FFs for pions and DSEHS-17 for kaons, similarly as at the energy scale [Formula: see text][Formula: see text]GeV.

Exclusive J/ψ photoproduction in ultraperipheral Pb+Pb collisions at the CERN Large Hadron Collider calculated at next-to-leading order perturbative QCD

We present the first next-to-leading-order (NLO) perturbative QCD (pQCD) study of rapidity-differential cross sections of coherent exclusive photoproduction of $J/\psi$ mesons in heavy-ion ultraperipheral collisions (UPCs) at the LHC, $d\sigma/dy(\text{Pb} + \text{Pb} \rightarrow \text{Pb} + J/\psi + \text{Pb})$. For this, we account for the photon-nucleon NLO cross sections at the forward limit, the $t$ dependence using a standard nuclear form factor, and the photon fluxes of the colliding nuclei. Approximating the generalized parton distributions with their forward-limit parton distribution functions (PDFs), we quantify the NLO contributions in the cross sections, show that the real part of the amplitude and quark-PDF contributions must not be neglected, quantify the uncertainties arising from the scale-choice and PDFs, and compare our results with ALICE, CMS and LHCb $J/\psi$ photoproduction data in Pb+Pb UPCs, exclusive $J/\psi$ photoproduction data from HERA, and LHCb data in p+p. The scale dependence in $d\sigma/dy(\text{Pb} + \text{Pb} \rightarrow \text{Pb} + J/\psi + \text{Pb})$ is significant, but we can find a scale-choice that reproduces the Pb+Pb UPC data both at 2.76 and 5.02 TeV collision energies. This process has traditionally been suggested to be a direct probe of nuclear gluon distributions. We show that the situation changes rather dramatically from LO to NLO: the NLO cross sections reflect the nuclear effects of both gluons and quarks in a complicated manner where the relative signs of the LO and NLO terms in the amplitude play a significant role.

Single inclusive jet production in pA collisions at NLO in the small-x regime

We present the first complete next-to-leading-order (NLO) prediction with full jet algorithm implementation for the single inclusive jet production in pA collisions at forward rapidities within the color glass condensate (CGC) effective theory. Our prediction is fully differential over the final state physical kinematics, which allows the implementation of any infra-red safe observable including the jet clustering procedure. The NLO calculation is organized with the aid of the observable originated power counting proposed in [1] which gives rise to the novel soft contributions in the CGC factorization. We achieve the fully-differential calculation by constructing suitable subtraction terms to handle the singularities in the real corrections. The subtraction contributions can be exactly integrated analytically. We present the NLO cross section with the jets constructed using the anti-kT algorithm. The NLO calculation demonstrates explicitly the validity of the CGC factorization in jet production. Furthermore, as a byproduct of the subtraction method, we also derive the fully analytic cross section for the forward jet production in the small-R limit. We show that in the small-R approximation, the forward jet cross section can be factorized into a semi-hard cross section that produces a parton and the semi-inclusive jet functions (siJFs). We argue that this feature holds for generic jet production and jet substructure observables in the CGC framework. Last, we show numerical analyses of the derived formula to validate our calculations. We justify when the small-R approximation is appropriate. Like forward hadron production, the obtained NLO result also exhibits the negativity of the cross section in the large jet transverse regime, which signals the need for the threshold resummation. A sketch of the threshold resummation in the CGC framework is presented based on the multiple emission picture and it is found to agree with the approach using the rapidity renormalization group equation developed in [2].

Soft gluon resummation for associated squark-electroweakino production at the LHC

We perform a threshold resummation calculation for the associated production of squarks and electroweakinos at the LHC to the next-to-leading logarithmic (NLL) accuracy. Analytical results for the process-dependent soft anomalous dimension and the hard matching coefficient are presented. The resummed results are matched to fixed-order predictions at next-to-leading order (NLO) in QCD, which are generalised to scenarios with non-universal squark masses and mixings. Numerically, the NLL contributions increase the total NLO cross section by 2% to 6% for squark masses ranging from 1 TeV to 3 TeV, respectively, and they reduce the dependence of the predictions on the factorisation and renormalisation scales from typically ±10% to below ±5%. Our NLO and NLO+NLL calculations have been implemented in the publicly available program Resummino.

Matrix element method at NLO for (anti-) kt -jet algorithms

In this article, we present a method to calculate a posteriori event weights at next-to-leading-order (NLO) QCD accuracy for a given jet event defined by the (anti-)$k_t$ algorithm relying on the conventional $2\to 1$ recombination. This is an important extension compared to existing Monte-Carlo tools which generate jet events together with the corresponding weight but do not allow one to calculate the weight for a given event. The method can be used to generate unweighted events distributed according to the fixed-order NLO cross section. In addition, the method allows one to calculate NLO accurate weights for events recorded by experiments. The potential of this ability is illustrated by applying the Matrix Element Method (MEM) to single top-quark events generated with POWHEG in combination with Pythia. For the first time, a systematic study of parton shower effects within the MEM is provided. The method is completely general and can be applied to arbitrary LHC processes.

Detailed k-Factor Studies Using Inclusive Production of W Bosons in pp Collisions

The theoretical k-Factor describes the difference between leading and higher order cross sections and its proper usage has a crucial importance for theoretical predictions. In this paper, three different ways are considered to define the k-Factor of W bosons at $$\sqrt s $$ = 14 TeV in proton-proton collisions. First, we calculate k-Factors using inclusive W± boson leading order (LO), next-toleading order (NLO) and next-to-next-to-leading order (NNLO) quantum chromodynamics (QCD) cross sections with LO, NLO, NNLO parton distribution function (PDF) models, respectively. The second approach used is the calculation of k-Factors based on LO, NLO and NNLO QCD cross sections with the NNLO PDF model. The last method used here is the calculation of k-Factors using the LO QCD cross section with LO, NLO and NNLO PDF models. We further investigated the dependencies of the k-Factor on the renormalization (μR) and the factorization (μF) scales, the strong coupling constant (α s ), the charges of W boson and the collision energy of protons in a range of 7 to 100 TeV.

Next-to-leading-order QCD corrections to e+e− → H + γ

The associated production of Higgs boson with a hard photon at lepton collider, i.e., e+e−→Hγ, is known to bear a rather small cross section in Standard Model, and can serve as a sensitive probe for the potential new physics signals. Similar to the loop-induced Higgs decay channels H→γγ,Zγ, the e+e−→Hγ process also starts at one-loop order provided that the tiny electron mass is neglected. In this work, we calculate the next-to-leading-order (NLO) QCD corrections to this associated H+γ production process, which mainly stem from the gluonic dressing to the top quark loop. The QCD corrections are found to be rather modest at lower center-of-mass energy range (s<300 GeV), thus of negligible impact on Higgs factory such as CEPC. Nevertheless, when the energy is boosted to the ILC energy range (s≈400 GeV), QCD corrections may enhance the leading-order cross section by 20%. In any event, the e+e−→Hγ process has a maximal production rate σmax≈0.08 fb around s=250 GeV, thus CEPC turns out to be the best place to look for this rare Higgs production process. In the high energy limit, the effect of NLO QCD corrections become completely negligible, which can be simply attributed to the different asymptotic scaling behaviors of the LO and NLO cross sections, where the former exhibits a milder decrement ∝1/s , but the latter undergoes a much faster decrease ∝1/s2.

CGC factorization for forward particle production in proton-nucleus collisions at next-to-leading order

Within the Color Glass Condensate effective theory, we reconsider the next-to-leading order (NLO) calculation of the single inclusive particle production at forward rapidities in proton-nucleus collisions at high energy. Focusing on quark production for definiteness, we establish a new factorization scheme, perturbatively correct through NLO, in which there is no `rapidity subtraction'. That is, the NLO correction to the impact factor is not explicitly separated from the high-energy evolution. Our construction exploits the skeleton structure of the (NLO) Balitsky-Kovchegov equation, in which the first step of the evolution is explicitly singled out. The NLO impact factor is included by computing this first emission with the exact kinematics for the emitted gluon, rather than by using the eikonal approximation. This particular calculation has already been presented in the literature [1,2], but the reorganization of the perturbation theory that we propose is new. As compared to the proposal in [1,2], our scheme is free of the fine-tuning inherent in the rapidity subtraction, which might be the origin of the negativity of the NLO cross-section observed in previous studies.

Squark production and decay matched with parton showers at NLO

Extending previous work on the predictions for the production of supersymmetric (SUSY) particles at the LHC, we present the fully differential calculation of the next-to-leading order (NLO) SUSY-QCD corrections to the production of squark and squark–antisquark pairs of the first two generations. The NLO cross sections are combined with the subsequent decay of the final state (anti)squarks into the lightest neutralino and (anti)quark at NLO SUSY-QCD. No assumptions on the squark masses are made, and the various subchannels are taken into account independently. In order to obtain realistic predictions for differential distributions the fixed-order calculations have to be combined with parton showers. Making use of the Powheg method we have implemented our results in the Powheg-Box framework and interfaced the NLO calculation with the parton shower Monte Carlo programs Pythia6 and Herwig++. The code is publicly available and can be downloaded from the Powheg-Box webpage. The impact of the NLO corrections on the differential distributions is studied and parton shower effects are investigated for different benchmark scenarios.

Search for neutralino pair production at the CERN LHC

We provide the next-to-leading order (NLO) predictions for the neutralino pair production via quark-antiquark annihilation and gluon-gluon fusion at the CERN Large Hadron Collider, focusing on the lightest neutralino which is likely to be the lightest supersymmetric particle. The dependence of total LO, NLO cross sections, and $K$ factor on the center-of-mass energy, the ${M}_{2}\ensuremath{-}\ensuremath{\mu}$ mass plane, the squark mass, and the factorization and renormalization scales is comprehensively analyzed for three different scenarios in the minimal supersymmetric standard model and the constrained minimal supersymmetric standard model. We find that the LO cross section is considerably increased by the NLO correction, and the $K$ factor value is clearly related to the Higgsino/gaugino mass parameters, the squark mass, and the factorization and renormalization scales.

Hard-photon production withbjets at hadron colliders

We present total and differential cross sections for the production of a hard photon with up to two b jets at both the Tevatron with center-of-mass energy 1.96 TeV and the Large Hadron Collider with center-of-mass energy 8 TeV, including Next-to-Leading Order (NLO) QCD corrections and full b-quark mass effects. We study the theoretical uncertainty due to the residual renormalization- and factorization-scale dependence and explain its origin on the basis of the different subprocesses contributing to the NLO cross section. We specifically address the case of the production of a hard photon with at least one b jet and compare the NLO QCD predictions in both the Four- and Five-Flavor-Number Schemes to the experimental measurements obtained by CDF and D0.

QCD corrections to excited lepton (pair) production at the LHC

We consider excited lepton ($\bar{l^*}l {\rm or} \bar{l^*}l^*$) production in the context of effective theories with being four-fermion contact interaction at LHC. We also consider the two body decay mode of excited lepton ($l^*$) to standard model fermion($l$) and a gauge boson $V(\equiv \gamma,Z,W)$. We have performed next-to-leading order (NLO) QCD corrections to this process. In spite of non-renormalizable nature of the interaction, the higher order QCD corrections are possible and meaningful. We have shown that these corrections can be substantial and significant. By considering the issue of scale dependence, it is shown that the scale dependence of the NLO cross sections are greatly reduced as compare to leading order (LO) cross section.

Threshold resummed and approximate next-to-next-to-leading order results forW+W−pair production at the LHC

The next-to-leading order (NLO) QCD radiative corrections to ${W}^{+}{W}^{\ensuremath{-}}$ production at hadron colliders are well understood. We combine NLO perturbative QCD calculations with soft-gluon resummation of threshold logarithms to find a next-to-next-to-leading logarithmic (NNLL) prediction for the total cross section and the invariant mass distribution at the LHC. We also obtain approximate next-to-next-to-leading order (NNLO) results for the total ${W}^{+}{W}^{\ensuremath{-}}$ cross section at the LHC which includes all contributions from the scale dependent leading singular terms. Our result for the approximate NNLO total cross section is the most precise theoretical prediction available. Uncertainties due to scale variation are shown to be small when the threshold logarithms are included. NNLL threshold resummation increases the ${W}^{+}{W}^{\ensuremath{-}}$ invariant mass distribution by $\ensuremath{\sim}3%--4%$ in the peak region for both $\sqrt{S}=8$ and 14 TeV. The NNLL threshold resummed and approximate NNLO cross sections increase the NLO cross section by 0.5%--3% for $\sqrt{S}=7$, 8, 13, and 14 TeV.

Application of the principle of maximum conformality to top-pair production

A major contribution to the uncertainty of finite-order perturbative QCD predictions is the perceived ambiguity in setting the renormalization scale ${\ensuremath{\mu}}_{r}$. For example, by using the conventional way of setting ${\ensuremath{\mu}}_{r}\ensuremath{\in}[{m}_{t}/2,2{m}_{t}]$, one obtains the total $t\overline{t}$ production cross section ${\ensuremath{\sigma}}_{t\overline{t}}$ with the uncertainty $\ensuremath{\Delta}{\ensuremath{\sigma}}_{t\overline{t}}/{\ensuremath{\sigma}}_{t\overline{t}}\ensuremath{\sim}(\genfrac{}{}{0}{}{+3%}{\ensuremath{-}4%})$ at the Tevatron and LHC even for the present next-to next-to-leading-order level. The principle of maximum conformality (PMC) eliminates the renormalization scale ambiguity in precision tests of Abelian QED and non-Abelian QCD theories. By using the PMC, all nonconformal ${{\ensuremath{\beta}}_{i}}$ terms in the perturbative expansion series are summed into the running coupling constant, and the resulting scale-fixed predictions are independent of the renormalization scheme. The correct scale displacement between the arguments of different renormalization schemes is automatically set, and the number of active flavors ${n}_{f}$ in the ${{\ensuremath{\beta}}_{i}}$ function is correctly determined. The PMC is consistent with the renormalization group property that a physical result is independent of the renormalization scheme and the choice of the initial renormalization scale ${\ensuremath{\mu}}_{r}^{\mathrm{init}}$. The PMC scale ${\ensuremath{\mu}}_{r}^{\mathrm{PMC}}$ is unambiguous at finite order. Any residual dependence on ${\ensuremath{\mu}}_{r}^{\mathrm{init}}$ for a finite-order calculation will be highly suppressed since the unknown higher-order ${{\ensuremath{\beta}}_{i}}$ terms will be absorbed into the PMC scales' higher-order perturbative terms. We find that such renormalization group invariance can be satisfied to high accuracy for ${\ensuremath{\sigma}}_{t\overline{t}}$ at the next-to next-to-leading-order level. In this paper we apply PMC scale setting to predict the $t\overline{t}$ cross section ${\ensuremath{\sigma}}_{t\overline{t}}$ at the Tevatron and LHC colliders. It is found that ${\ensuremath{\sigma}}_{t\overline{t}}$ remains almost unchanged by varying ${\ensuremath{\mu}}_{r}^{\mathrm{init}}$ within the region of $[{m}_{t}/4,4{m}_{t}]$. The convergence of the expansion series is greatly improved. For the ($q\overline{q}$) channel, which is dominant at the Tevatron, its next-to-leading-order (NLO) PMC scale is much smaller than the top-quark mass in the small $x$ region, and thus its NLO cross section is increased by about a factor of 2. In the case of the ($gg$) channel, which is dominant at the LHC, its NLO PMC scale slightly increases with the subprocess collision energy $\sqrt{s}$, but it is still smaller than ${m}_{t}$ for $\sqrt{s}\ensuremath{\lesssim}1\text{ }\text{ }\mathrm{TeV}$, and the resulting NLO cross section is increased by $\ensuremath{\sim}20%$. As a result, a larger ${\ensuremath{\sigma}}_{t\overline{t}}$ is obtained in comparison to the conventional scale setting method, which agrees well with the present Tevatron and LHC data. More explicitly, by setting ${m}_{t}=172.9\ifmmode\pm\else\textpm\fi{}1.1\text{ }\text{ }\mathrm{GeV}$, we predict ${\ensuremath{\sigma}}_{\mathrm{Tevatron},1.96\text{ }\mathrm{TeV}}={7.626}_{\ensuremath{-}0.257}^{+0.265}\text{ }\text{ }\mathrm{pb}$, ${\ensuremath{\sigma}}_{\mathrm{LHC},7\text{ }\mathrm{TeV}}={171.8}_{\ensuremath{-}5.6}^{+5.8}\text{ }\text{ }\mathrm{pb}$ and ${\ensuremath{\sigma}}_{\mathrm{LHC},14\text{ }\mathrm{TeV}}={941.3}_{\ensuremath{-}26.5}^{+28.4}\text{ }\text{ }\mathrm{pb}$.

NLO QCD corrections to dijet production via quark contact interactions

We present the exact next-to-leading order (NLO) QCD corrections to dijet production at the LHC via quark contact interactions, with different color and chiral structures induced from new physics. Following the recent analysis of quark compositeness search at the LHC, we find that the NLO QCD corrections can lower the dijet cross sections by several tens percent, depending on the theory parameters and the selected kinematic regions, and reduce the dependence of the cross sections on factorization and renormalization scales. We also calculate the renormalization group (RG) improved NLO cross sections by summing over the large logarithms from the RG running of Wilson coefficients. Moreover, we investigate the NLO QCD effects on various experimental observables and exclusion limits of quark compositeness scale.

Soft function for exclusiveN-jet production at hadron colliders

The N-jettiness event shape divides phase space into N+2 regions, each containing one jet or beam. Using a geometric measure these regions correspond to jets with circular boundaries. We give a factorization theorem for the cross section fully differential in the (transverse) mass of each jet, and compute the corresponding soft function at next-to-leading order (NLO). The ultraviolet divergences are analytically extracted by exploiting hemispheres for interactions between each pair of hard partons, leaving only convergent integrals that are sensitive to the precise boundaries. This method can be applied in general to N-jet soft functions, including other observables. For N-jettiness, the final result for the soft function involves stable one-dimensional numerical integrals, and all ingredients are now available to extend NLO cross sections to resummed predictions at next-to-next-to-leading logarithmic order.

Suppression factors in diffractive photoproduction of dijets

Now that new publications of H1 data for the diffractive photoproduction of dijets, which overlap with the earlier published H1 data and the recently published data of the ZEUS collaboration, have appeared, we have recalculated the cross sections for this process in next-to-leading order (NLO) of perturbative QCD to see whether they can be interpreted consistently. The results of these calculations are compared to the data of both collaborations. We find that the NLO cross sections disagree with the data, showing that factorization breaking occurs at that order. If direct and resolved contributions are both suppressed by the same amount, the global suppression factor depends on the transverse-energy cut. However, by suppressing only the resolved contribution, also reasonably good agreement with all the data is found with a suppression factor independent of the transverse-energy cut.

QCD corrections to associated production oftt¯γat hadron colliders

We report on the next-to-leading order (NLO) QCD computation of top-quark pair production in association with a photon at the Fermilab Tevatron RUN II and CERN Large Hadron Collider. We describe the impact of the complete NLO QCD radiative corrections to this process, and provide the predictions of the leading order (LO) and NLO integrated cross sections, distributions of the transverse momenta of the top quark and photon for the LHC and Tevatron, and the LO and NLO forward-backward top-quark charge asymmetries for the Tevatron. We investigate the dependence of the LO and NLO cross sections on the renormalization/factorization scale, and find the scale dependence of the LO cross section is obviously improved by the NLO QCD corrections. The $K$-factor of the NLO QCD correction is 0.977(1.524) for the Tevatron (LHC).