Perturbative QCD Calculations Research Articles

Calculations for deep inelastic scattering using fast interpolation grid techniques at NNLO in QCD and the extraction of alpha _{mathrm {s}} from HERA data

The extension of interpolation-grid frameworks for perturbative QCD calculations at next-to-next-to-leading order (NNLO) is presented for deep inelastic scattering (DIS) processes. A fast and flexible evaluation of higher-order predictions for any a posteriori choice of parton distribution functions (PDFs) or value of the strong coupling constant is essential in iterative fitting procedures to extract PDFs and Standard Model parameters as well as for a detailed study of the scale dependence. The APPLfast project, described here, provides a generic interface between the parton-level Monte Carlo program NNLOjet and both the APPLgrid and fastNLO libraries for the production of interpolation grids at NNLO accuracy. Details of the interface for DIS processes are presented together with the required interpolation grids at NNLO, which are made available. They cover numerous inclusive jet measurements by the H1 and ZEUS experiments at HERA. An extraction of the strong coupling constant is performed as an application of the use of such grids and a best-fit value of alpha _{mathrm {s}} (M_{{mathrm {Z}}}) = 0.1170,(15)_text {exp},(25)_text {th} is obtained using the HERA inclusive jet cross section data.

Higher-order perturbative coefficients in QCD from series acceleration by conformal mappings

The present calculations in perturbative QCD reach the order ${\ensuremath{\alpha}}_{s}^{4}$ for several correlators calculated to five loops, and the huge computational difficulties make unlikely the full six-loop calculation in the near future. This situation has practical consequences; in particular the treatment of the higher orders of the perturbation series for the current-current correlator of light quarks is one of the main sources of errors in the extraction of the strong coupling from hadronic $\ensuremath{\tau}$ decays. Several approximate estimates of the next coefficients of the corresponding Adler function have been proposed, using various arguments. In the present paper we exploit the analytic structure of the Adler function in the Borel plane, which allows the definition of an improved perturbative expansion in powers of a conformal variable which maps the cut Borel plane onto the unit disk. The new expansions converge in a larger domain of the Borel plane and, when reexpanded in powers of the strong coupling, yield definite values for the higher perturbative coefficients. We apply the method to the Adler function in the $\overline{\mathrm{MS}}$ scheme and to a suitable weighted integral of this function in the complex $s$ plane, chosen such as to avoid model-dependent assumptions on analyticity. Our results ${c}_{5,1}=287\ifmmode\pm\else\textpm\fi{}40$, ${c}_{6,1}=2948\ifmmode\pm\else\textpm\fi{}208$ and ${c}_{7,1}=(1.89\ifmmode\pm\else\textpm\fi{}0.75)\ifmmode\times\else\texttimes\fi{}{10}^{4}$, for the six-, seven- and eight-loop coefficients, respectively, agree with a recent determination from Pad\'e approximants applied to the perturbative expansion of the hadronic $\ensuremath{\tau}$ decay rate.

Charm and Beauty Production Cross-Section Measurements in Deep Inelastic Electron-Proton Scattering at HERA

The open charm and beauty production cross-sections in the deep inelastic ep scattering (DIS) at HERA from the H1 and ZEUS Collaborations are combined. Reduced cross-sections are obtained in the kinematic range of negative four-momentum transfer squared of a photon 2.5≤ Q2 ≤2000 GeV2 and the Bjorken scaling variable 3×10¬5 ≤ xBj ≤5×10¬2. The different charm- and beauty-tagging methods are used for the heavy-flavor production study in DIS. The combined method accounts for the correlations of systematic uncertainties, as well as statistical uncertainties among the different datasets. Perturbative QCD (pQCD) calculations are compared to the measured combined data. A NLO QCD analysis is performed using these data together with the combined inclusive deep inelastic scattering cross-sections from HERA. The running charm- and beauty-quark masses are determined as mc(mc) = 1,290+0,046−0,041(exp /fit)+0,062−0,014(model)+0,03−0,031(parametrization) GeV and mb(mb) = 4,049+0,104−0,109(exp /fit)+0,090−0,032(model)+0,001−0,031(parametrization) GeV.

Radiative decays of hc to the light mesons η(′) : A perturbative QCD calculation

We study the radiative decays $h_{c}\rightarrow\gamma\eta^{(\prime)}$ in the framework of perturbative QCD and evaluate analytically the one-loop integrals with the light quark masses kept. Interestingly, the branching ratios $\mathcal{B}(h_{c}\rightarrow\gamma\eta^{(\prime)})$ are insensitive to both the light quark masses and the shapes of $\eta^{(\prime)}$ distribution amplitudes. And it is noticed that the contribution of the gluonic content of $\eta^{(\prime)}$ is almost equal to that of the quark-antiquark content of $\eta^{(\prime)}$ in the radiative decays $h_{c} \rightarrow \gamma\eta^{(\prime)}$. By employing the ratio $R_{h_{c}}=\mathcal{B}(h_{c}\rightarrow\gamma\eta)/\mathcal{B}(h_{c}\rightarrow\gamma\eta^{\prime})$, we extract the mixing angle $\phi=33.8^{\circ}\pm2.5^{\circ}$, which is in clear disagreement with the Feldmann-Kroll-Stech result $\phi=39.0^{\circ}\pm1.6^{\circ}$ extracted from the ratio $R_{J/\psi}$ with nonperturbative matrix elements $\langle 0\mid G^{a}_{\mu\nu}\tilde{G}^{a,\mu\nu}\mid\eta^{(\prime)}\rangle$, but in consistent with $\phi=33.5^{\circ}\pm0.9^{\circ}$ extracted from the asymptotic limit of the $\gamma^{\ast}\gamma-\eta^{\prime}$ transition form factor and $\phi=33.9^{\circ}\pm0.6^{\circ}$ extracted from $R_{J/\psi}$ in perturbative QCD. We also briefly discuss possible reasons for the difference in the determinations of the mixing angle.

Measurement of prompt photon production in [formula omitted] TeV p + Pb collisions with ATLAS

The inclusive production rates of isolated, prompt photons in p+Pb collisions at sNN=8.16 TeV are studied with the ATLAS detector at the Large Hadron Collider using a dataset with an integrated luminosity of 165 nb−1 recorded in 2016. The cross-section and nuclear modification factor RpPb are measured as a function of photon transverse energy from 20 GeV to 550 GeV and in three nucleon–nucleon centre-of-mass pseudorapidity regions, (−2.83,−2.02), (−1.84,0.91), and (1.09,1.90). The cross-section and RpPb values are compared with the results of a next-to-leading-order perturbative QCD calculation, with and without nuclear parton distribution function modifications, and with expectations based on a model of the energy loss of partons prior to the hard scattering. The data disfavour a large amount of energy loss and provide new constraints on the parton densities in nuclei.

Measurement of [formula omitted] meson production in pp and PbPb collisions at [formula omitted] TeV

The production cross sections of Bs0 mesons and charge conjugates are measured in proton-proton (pp) and PbPb collisions via the exclusive decay channel Bs0→J/ψϕ→μ+μ−K+K− at a center-of-mass energy of 5.02 TeV per nucleon pair and within the rapidity range |y|<2.4 using the CMS detector at the LHC. The pp measurement is performed as a function of transverse momentum (pT) of the Bs0 mesons in the range of 7 to 50 GeV/c and is compared to the predictions of perturbative QCD calculations. The Bs0 production yield in PbPb collisions is measured in two pT intervals, 7 to 15 and 15 to 50 GeV/c, and compared to the yield in pp collisions in the same kinematic region. The nuclear modification factor (RAA) is found to be 1.5±0.6(stat)±0.5(syst) for 7–15 GeV/c, and 0.87±0.30(stat)±0.17(syst) for 15–50 GeV/c, respectively. Within current uncertainties, the Bs0 results are consistent with models of strangeness enhancement, and suppression by parton energy loss, as observed for the B+ mesons.

Measurement of charm and bottom production from semileptonic hadron decays in p+p collisions at s=200 GeV

Measurements of the differential production of electrons from open-heavy-flavor hadrons with charm- and bottom-quark content in $p$$+$$p$ collisions at $\sqrt{s}=200$ GeV are presented. The measurements proceed through displaced-vertex analyses of electron tracks from the semileptonic decay of charm and bottom hadrons using the PHENIX silicon-vertex detector. The relative contribution of electrons from bottom decays to inclusive heavy-flavor-electron production is found to be consistent with fixed-order-plus-next-to-leading-log perturbative-QCD calculations within experimental and theoretical uncertainties. These new measurements in $p$$+$$p$ collisions provide a precision baseline for comparable forthcoming measurements in A$+$A collisions.

A Short Review on Recent Developments in TMD Factorization and Implementation

In the latest years the theoretical and phenomenological advances in the factorization of several collider processes using the transverse momentum dependent distributions (TMD) have greatly increased. I attempt here a short resume of the newest developments discussing also the most recent perturbative QCD calculations. The work is not strictly directed to experts in the field and it wants to offer an overview of the tools and concepts which are behind the TMD factorization and evolution. I consider both theoretical and phenomenological aspects, some of which have still to be fully explored. It is expected that actual colliders and the Electron Ion Collider (EIC) will provide important information in this respect.

Measurement of {{mathrm{D}}^0}, {{mathrm{D}}^+}, {{mathrm{D}}^{*+}} and {{mathrm{D}}^+_{mathrm{s}}} production in pp collisions at {sqrt{{textit{s}}}~=~5.02~{text {TeV}}} with ALICE

The measurements of the production of prompt {{mathrm{D}}^0}, {{mathrm{D}}^+}, {{mathrm{D}}^{*+}}, and {{mathrm{D}}^+_{mathrm{s}}} mesons in proton–proton (pp) collisions at sqrt{s}=5.02~mathrm {TeV} with the ALICE detector at the Large Hadron Collider (LHC) are reported. D mesons were reconstructed at mid-rapidity (|y|<0.5) via their hadronic decay channels mathrm{D}^0 rightarrow {mathrm{K}}^-pi ^+, mathrm{D}^+rightarrow {mathrm{K}}^-pi ^+pi ^+, {mathrm{D}}^{*+} rightarrow {mathrm{D}}^0 pi ^+ rightarrow {mathrm{K}}^- pi ^+ pi ^+, {{mathrm{D}}^{+}_{mathrm{s}}rightarrow phi pi ^+rightarrow {mathrm{K}}^{+} {mathrm{K}}^{-} pi ^{+}}, and their charge conjugates. The production cross sections were measured in the transverse momentum interval 0<p_{mathrm{T}}<36~mathrm {GeV}/c for {{mathrm{D}}^0}, 1<p_{mathrm{T}}<36~mathrm {GeV}/c for {{mathrm{D}}^+} and {{mathrm{D}}^{*+}}, and in 2<p_{mathrm{T}}<24~mathrm {GeV}/c for {{mathrm{D}}^+_{mathrm{s}}} mesons. Thanks to the higher integrated luminosity, an analysis in finer p_{mathrm{T}} bins with respect to the previous measurements at sqrt{s}=7~mathrm {TeV} was performed, allowing for a more detailed description of the cross-section p_{mathrm{T}} shape. The measured p_{mathrm{T}}-differential production cross sections are compared to the results at sqrt{s}=7 TeV and to four different perturbative QCD calculations. Its rapidity dependence is also tested combining the ALICE and LHCb measurements in pp collisions at sqrt{s}=5.02~mathrm {TeV}. This measurement will allow for a more accurate determination of the nuclear modification factor in p–Pb and Pb–Pb collisions performed at the same nucleon–nucleon centre-of-mass energy.

Measurement of the ratio of cross sections for inclusive isolated-photon production in pp collisions at sqrt{s} = 13 and 8 TeV with the ATLAS detector

The ratio of the cross sections for inclusive isolated-photon production in pp collisions at centre-of-mass energies of 13 and 8 TeV is measured using the ATLAS detector at the LHC. The integrated luminosities of the 13 TeV and 8 TeV datasets are 3.2 fb−1 and 20.2 fb−1, respectively. The ratio is measured as a function of the photon transverse energy in different regions of the photon pseudorapidity. The predictions from next-to-leading-order perturbative QCD calculations are compared with the measured ratio. The experimental systematic uncertainties as well as the uncertainties affecting the predictions are evaluated taking into account the correlations between the two centre-of-mass energies, resulting in a reduction of up to a factor of 2.5 (5) in the experimental (theoretical) systematic uncertainties. The predictions based on several parameterisations of the proton parton distribution functions agree with the data within the reduced experimental and theoretical uncertainties. In addition, this ratio to that of the fiducial cross sections for Z boson production at 13 and 8 TeV using the decay channels Z → e+e− and Z → μ+μ− is made and compared with the theoretical predictions. In this double ratio, a further reduction of the experimental uncertainty is obtained because the uncertainties arising from the luminosity measurement cancel out. The predictions describe the measurements of the double ratio within the theoretical and experimental uncertainties.

Charged jet cross section and fragmentation in proton-proton collisions at s=7 TeV

We report the differential charged jet cross section and jet fragmentation distributions measured with the ALICE detector in proton-proton collisions at a centre-of-mass energy $\sqrt{s}=$ 7 TeV. Jets with pseudo-rapidity $\left| \eta \right| < {\rm 0.5}$ are reconstructed from charged particles using the anti-$k_{\rm T}$ jet finding algorithm with a resolution parameter $R$ = 0.4. The jet cross section is measured in the transverse momentum interval 5 $\leq p_{\rm T}^{\rm ch \; jet} <$ 100 GeV/$c$. Jet fragmentation is studied measuring the scaled transverse momentum spectra of the charged constituents of jets in four intervals of jet transverse momentum between 5 GeV/$c$ and 30 GeV/$c$. The measurements are compared to calculations from the PYTHIA model as well as next-to-leading order perturbative QCD calculations with POWHEG + PYTHIA8. The charged jet cross section is described by POWHEG for the entire measured range of $p_{\rm T}^{\rm ch \; jet}$. For $p_{\rm T}^{\rm ch \; jet}$ $>$ 40 GeV/$c$, the PYTHIA calculations also agree with the measured charged jet cross section. PYTHIA6 simulations describe the fragmentation distributions to 15%. Larger discrepancies are observed for PYTHIA8.

Combination and QCD Analysis of Charm and Beauty Production Cross-section Measurements in Deep Inelastic $ep$ Scattering at HERA

Measurements of open charm and beauty production cross sections in ep deep inelastic scattering (DIS) at HERA from the H1 and ZEUS collaborations are combined. Reduced cross sections are obtained in a restricted kinematic range. Perturbative QCD calculations are compared to the combined data. Next-to-leading order QCD analysis is performed using these data together with combined inclusive HERA DIS cross sections.

Moli\xe8re scattering in quark-gluon plasma: finding point-like scatterers in a liquid

By finding rare (but not exponentially rare) large-angle deflections of partons within a jet produced in a heavy ion collision, or of such a jet itself, experimentalists can find the weakly coupled short-distance quark and gluon particles (scatterers) within the strongly coupled liquid quark-gluon plasma (QGP) produced in heavy ion collisions. This is the closest one can come to probing QGP via a scattering experiment and hence is the best available path toward learning how a strongly coupled liquid emerges from an asymptotically free gauge theory. The short-distance, particulate, structure of liquid QGP can be revealed in events in which a jet parton resolves, and scatters off, a parton from the droplet of QGP. The probability for picking up significant transverse momentum via a single scattering was calculated previously, but only in the limit of infinite parton energy which means zero angle scattering. Here, we provide a leading order perturbative QCD calculation of the Molière scattering probability for incident partons with finite energy, scattering at a large angle. We set up a thought experiment in which an incident parton with a finite energy scatters off a parton constituent within a “brick” of QGP, which we treat as if it were weakly coupled, as appropriate for scattering with large momentum transfer, and compute the probability for a parton to show up at a nonzero angle with some energy. We include all relevant channels, including those in which the parton that shows up at a large angle was kicked out of the medium as well as the Rutherford-like channel in which what is seen is the scattered incident parton. The results that we obtain will serve as inputs to future jet Monte Carlo calculations and can provide qualitative guidance for how to use future precise, high statistics, suitably differential measurements of jet modification in heavy ion collisions to find the scatterers within the QGP liquid.

Novel mechanism for suppression of heavy flavored mesons in heavy ion collisions

Production of heavy flavored hadrons from fragmentation of heavy quarks represents an alternative probe for a medium created after heavy ion collisions. We demonstrate that observed strong suppression of heavy flavored D and B mesons, produced with high transverse momenta pT, is caused by final state interactions with such a medium. The space-time pattern of hadronization of a highly virtual heavy quark is controlled predominantly by intensive gluon radiation, which is ceased at a short time scale in accordance with perturbative QCD calculations and LEP measurements of the fragmentation functions. However, production of heavy flavored hadrons lasts a long time due to prompt multiple breakups of produced colorless (pre)hadrons in the medium. This fact together with the specific shape of heavy quark fragmentation function, peaked at large z, allows to explain the observed strong suppression of D and B mesons in a good accord with data.

Measurement of dijet azimuthal decorrelations in pp collisions at s=8 TeV with the ATLAS detector and determination of the strong coupling

A measurement of the rapidity and transverse momentum dependence of dijet azimuthal decorrelations is presented, using the quantity $R_{\Delta \phi}$. The quantity $R_{\Delta \phi}$ specifies the fraction of the inclusive dijet events in which the azimuthal opening angle of the two jets with the highest transverse momenta is less than a given value of the parameter $\Delta \phi_\mathrm{max}$. The quantity $R_{\Delta \phi}$ is measured in proton--proton collisions at $\sqrt{s}=$8 TeV as a function of the dijet rapidity interval, the event total scalar transverse momentum, and $\Delta \phi_\mathrm{max}$. The measurement uses an event sample corresponding to an integrated luminosity of 20.2 fb$^{-1}$ collected with the ATLAS detector at the CERN Large Hadron Collider. Predictions of a perturbative QCD calculation at next-to-leading order in the strong coupling with corrections for non-perturbative effects are compared to the data. The theoretical predictions describe the data in the whole kinematic region. The data are used to determine the strong coupling $\alpha_{\mathrm{S}}$ and to study its running for momentum transfers from 260 GeV to above 1.6 TeV. An analysis that combines data at all momentum transfers results in $\alpha_{\mathrm{S}}(m_{Z}) = 0.1127^{+0.0063}_{-0.0027}$.

Study of isolated-photon and jet momentum imbalance in pp and PbPb collisions

In this paper, we study the production of isolated-photon plus a jet in pp and PbPb collisions, which can be used as an important probe to the jet transport property in quark gluon plasma created in heavy ion collisions. Normally, there are two types of observables associated with the production of isolated-photon plus a jet, namely, the azimuthal angular correlation and the transverse momentum imbalance. To understand both observables in the full kinematical region, we need to employ the perturbative QCD calculation, which takes into account the hard splitting of partons, together with the Sudakov resummation formalism, which resums soft gluon splittings. Furthermore, by introducing energy-loss into the system, we calculate the enhancement of the momentum imbalance distribution for AA as compared to pp collisions and make predictions for future unfolded experimental data. In addition, in order to extract the jet transport coefficient more precisely in our numerical calculation, we also distinguish quark jets from gluon jets, since they interact with quark gluon plasma with different strengths. This work provides a reliable theoretical tool for the calculation of the gamma-jet correlation, which can lead us to a more precise extraction of the jet transport coefficient in relativistic heavy-ion collisions.

Production of single-charm hadrons by the quark-combination mechanism in p -Pb collisions at sNN=5.02 TeV

If QGP-like medium is created in $p$-Pb collisions at extremely high collision energies, charm quarks that move in the medium can hadronize by capturing the co-moving light quark(s) or anti-quark(s) to form the charm hadrons. Using light quark $p_{T}$ spectra extracted from the experimental data of light-flavor hadrons and a charm quark $p_{T}$ spectrum that is consistent with perturbative QCD calculations, the central-rapidity data of $p_{T}$ spectra and the spectrum ratios for $D$ mesons in the low $p_{T}$ range ($p_{T}\lesssim7$ GeV/$c$) in minimum-bias $p$-Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV are well described by quark combination mechanism in equal-velocity combination approximation. The $\Lambda_{c}^{+}/D^{0}$ ratio in quark combination mechanism exhibits the typical increase-peak-decrease behavior as the function of $p_{T}$, and the shape of the ratio for $p_{T}\gtrsim3$ GeV/$c$ is in agreement with the data of ALICE collaboration in central rapidity region $-0.96<y<0.04$ and the preliminary data of LHCb collaboration in forward rapidity region $1.5<y<4.0$. The global production of single-charm baryons is quantified using the data and the possible enhancement (relative to light flavor baryons) is discussed. The $p_{T}$ spectra of $\Xi_{c}^{0}$, $\Omega_{c}^{0}$ in minimum-bias events and those of single-charm hadrons in high-multiplicity event classes are predicted, which serves as the further test of the possible change of the hadronization characteristic for low $p_{T}$ charm quarks in the small system created in $p$-Pb collisions at LHC energies.

Combination and QCD analysis of charm and beauty production cross-section measurements in deep inelastic ep scattering at HERA

Measurements of open charm and beauty production cross sections in deep inelastic ep scattering at HERA from the H1 and ZEUS Collaborations are combined. Reduced cross sections are obtained in the kinematic range of negative four-momentum transfer squared of the photon 2.5~hbox {GeV}^2le Q^2 le 2000, hbox {GeV}^2 and Bjorken scaling variable 3 cdot 10^{-5} le x_mathrm{Bj} le 5 cdot 10^{-2}. The combination method accounts for the correlations of the statistical and systematic uncertainties among the different datasets. Perturbative QCD calculations are compared to the combined data. A next-to-leading order QCD analysis is performed using these data together with the combined inclusive deep inelastic scattering cross sections from HERA. The running charm- and beauty-quark masses are determined as m_c(m_c) = 1.290^{+0.046}_{-0.041} mathrm{(exp/fit)}{}^{+0.062}_{-0.014} mathrm{(model)}{}^{+0.003}_{-0.031} mathrm{(parameterisation)} GeV and m_b(m_b) = 4.049^{+0.104}_{-0.109} mathrm{(exp/fit)}{}^{+0.090}_{-0.032} mathrm{(model)}{}^{+0.001}_{-0.031} mathrm{(parameterisation)}~mathrm{GeV}.

Nuclear modification factor of D0 mesons in PbPb collisions at [formula omitted

The transverse momentum (pT) spectrum of prompt D0 mesons and their antiparticles has been measured via the hadronic decay channels D0→K−π+ and D‾0→K+π− in pp and PbPb collisions at a centre-of-mass energy of 5.02 TeV per nucleon pair with the CMS detector at the LHC. The measurement is performed in the D0 meson pT range of 2–100GeV/c and in the rapidity range of |y|<1. The pp (PbPb) dataset used for this analysis corresponds to an integrated luminosity of 27.4 pb−1 (530 μb−1 ). The measured D0 meson pT spectrum in pp collisions is well described by perturbative QCD calculations. The nuclear modification factor, comparing D0 meson yields in PbPb and pp collisions, was extracted for both minimum-bias and the 10% most central PbPb interactions. For central events, the D0 meson yield in the PbPb collisions is suppressed by a factor of 5–6 compared to the pp reference in the pT range of 6–10GeV/c. For D0 mesons in the high-pT range of 60–100GeV/c, a significantly smaller suppression is observed. The results are also compared to theoretical calculations.

Measurement of inclusive jet and dijet cross-sections in proton-proton collisions at sqrt{s}=13 TeV with the ATLAS detector

Inclusive jet and dijet cross-sections are measured in proton-proton collisions at a centre-of-mass energy of 13 TeV. The measurement uses a dataset with an integrated luminosity of 3.2 fb−1 recorded in 2015 with the ATLAS detector at the Large Hadron Collider. Jets are identified using the anti-kt algorithm with a radius parameter value of R = 0.4. The inclusive jet cross-sections are measured double-differentially as a function of the jet transverse momentum, covering the range from 100 GeV to 3.5 TeV, and the absolute jet rapidity up to |y| = 3. The double-differential dijet production cross-sections are presented as a function of the dijet mass, covering the range from 300 GeV to 9 TeV, and the half absolute rapidity separation between the two leading jets within |y| < 3, y∗, up to y∗ = 3. Next-to-leading-order, and next-to-next-to-leading-order for the inclusive jet measurement, perturbative QCD calculations corrected for non-perturbative and electroweak effects are compared to the measured cross-sections.