QCD Coupling Research Articles

Hadronic parity violation at next-to-leading order

The flavor-conserving non-leptonic weak interaction can be studied experimentally through the observation of parity violation in nuclear and few-body systems. At hadronic scales, matrix elements of parity-violating four-quark operators ultimately give rise to the parity violating couplings between hadrons, and such matrix elements can be calculated non-perturbatively using lattice QCD. In this work, we investigate the running of isovector parity-violating operators from the weak scale down to hadronic scales using the renormalization group. We work at next-to-leading order in the QCD coupling, and include both neutral-current and charged-current interactions. At this order, results are renormalization scheme dependent, and we utilize 't Hooft-Veltman dimensional regularization. The evolution of Wilson coefficients at leading and next-to-leading order is compared. Next-to-leading order effects are shown to be non-negligible at hadronic scales.

Scale setting using the extended renormalization group and the principle of maximum conformality: The QCD coupling constant at four loops

A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The extended renormalization group equations, which express the invariance of the physical observables under both the renormalization scale- and scheme-parameter transformations, provide a convenient way for estimating the scale- and scheme-dependence of the physical process. In this paper, we present a solution for the scale equation of the extended renormalization group equations at the four-loop level. Using the principle of maximum conformality (PMC)/Brodsky-Lepage-Mackenzie (BLM) scale-setting method, all nonconformal ${{\ensuremath{\beta}}_{i}}$ terms in the perturbative expansion series can be summed into the running coupling, and the resulting scale-fixed predictions are independent of the renormalization scheme. The PMC/BLM scales can be fixed order-by-order. As a useful reference, we present a systematic and scheme-independent procedure for setting PMC/BLM scales up to next-to-next-to-leading order. An explicit application for determining the scale setting of ${R}_{{e}^{+}{e}^{\ensuremath{-}}}(Q)$ up to four loops is presented. By using the world average ${\ensuremath{\alpha}}_{s}^{\overline{\mathrm{MS}}}({M}_{Z})=0.1184\ifmmode\pm\else\textpm\fi{}0.0007$, we obtain the asymptotic scale for the 't Hooft scheme associated with the $\overline{\mathrm{MS}}$ scheme, ${\ensuremath{\Lambda}}_{\overline{\mathrm{MS}}}^{\ensuremath{'}tH}={245}_{\ensuremath{-}10}^{+9}\text{ }\text{ }\mathrm{MeV}$, and the asymptotic scale for the conventional $\overline{\mathrm{MS}}$ scheme, ${\ensuremath{\Lambda}}_{\overline{\mathrm{MS}}}={213}_{\ensuremath{-}8}^{+19}\text{ }\text{ }\mathrm{MeV}$.

Three-gluon contribution to the single spin asymmetry in Drell-Yan and direct-photon processes

We derive the single-spin-dependent cross section for the Drell-Yan lepton-pair production and the direct-photon production in the $pp$-collision induced by the twist-3 three-gluon correlation functions in the transversely polarized nucleon in the leading order with respect to the QCD coupling constant. Combined with the contribution from the twist-3 quark-gluon correlation functions in the literature, this completes the twist-3 cross section for these processes. We also present a model calculation of the asymmetry for the direct photon production at the RHIC energy, demonstrating the sensitivity of the asymmetry to the form of the three-gluon correlation functions. In particular, we show that the asymmetry in the backward direction of the polarized nucleon is determined by the small-$x$ behavior of the correlation functions.

Precise predictions forZ-boson+4jet production at hadron colliders

We present the cross section for production of a $Z$ boson in association with four jets at the Large Hadron Collider, at next-to-leading order in the QCD coupling. When the $Z$ decays to neutrinos, this process is a key irreducible background to many searches for new physics. Its computation has been made feasible through the development of the on-shell approach to perturbative quantum field theory. We present the total cross section for $pp$ collisions at $\sqrt{s}=7\text{ }\text{ }\mathrm{TeV}$, after folding in the decay of the $Z$ boson, or virtual photon, to a charged-lepton pair. We also provide distributions of the transverse momenta of the four jets, and we compare cross sections and distributions to the corresponding ones for the production of a $W$ boson with accompanying jets.

Suppression of high [formula omitted] hadrons in Pb + Pb collisions at LHC

Hadron production and their suppression in Pb+Pb collisions at LHC at a center-of-mass energy of sNN=2.76 TeV are studied within a multiphase transport (AMPT) model whose initial conditions are obtained from the recently updated HIJING 2.0 model. The centrality dependence of charged hadron multiplicity dNch/dη at midrapidity was found quite sensitive to the largely uncertain gluon shadowing parameter sg that determines the nuclear modification of the gluon distribution. We find final-state parton scatterings reduce considerably hadron yield at midrapidity and enforces a smaller gluon shadowing to be consistent with dNch/dη data at LHC. With such a constrained parton shadowing, charged hadron and neutral pion production over a wide transverse momenta range are investigated in AMPT. Relative to nucleon–nucleon collisions, the particle yield in central heavy ion collisions is suppressed due to parton energy loss. While the calculated magnitude and pattern of suppression is found consistent with that measured in Au+Au collisions at sNN=0.2 TeV at RHIC, at the LHC energy the suppression is overpredicted which may imply the medium formed at LHC is less opaque than expected from simple RHIC extrapolations. Reduction of the QCD coupling constant αs by ∼30% in the higher temperature plasma formed at LHC as compared to that at RHIC was found to reproduce the measured suppression at LHC.

Hadron spectrum and infrared-finite behavior of QCD running coupling

We study the behavior of the QCD effective coupling αs in the low-energy region by exploiting the conventional meson spectrum within a relativistic quantum-field model based on analytical confinement of quarks and gluons. The spectra of quark-antiquark and two-gluon bound states are defined by using a master equation similar to the ladder Bethe-Salpeter equation. A new, independent and specific infrared-finite behavior of QCD coupling is found below energy scale ∼1 GeV. Particularly, an infrared-fixed point is extracted at αs(0) ≅ 0.757 for confinement scale Λ = 345 MeV. We provide a new analytic estimate of the lowest-state glueball mass. As applications, we also estimate masses of some intermediate and heavy mesons as well as the weak-decay constants of light mesons. By introducing only a minimal set of parameters (the quark masses mf and Λ) we obtain results in reasonable agreement with recent experimental data in a wide range of energy scale ∼0.1–10 GeV. We demonstrate that global properties of some low-energy phenomena may be explained reasonably in the framework of a simple relativistic quantum-field model if one guesses correct symmetry structure of the quark-gluon interaction in the confinement region and uses simple forms of propagators in the hadronisation regime. The model may serve a reasonable framework to describe simultaneously different sectors in low-energy particle physics.

Drell-Yan Process in p–p Collisions from a Holographic Model

We study Drell-Yan process in proton–proton collisions through the exchange of vector mesons using the holographic hard wall model to describe the dynamics and interactions of vector mesons and baryons. We estimate the angular parameters λ, μ, ν of the produced dileptons in a region of \({q_{T}^2 << Q^{2}}\), where the effective coupling of perturbative QCD is large due to logarithm corrections.

Can we see from jet quenching that quark–gluon plasma becomes more perturbative at the LHC than at the RHIC?

We perform a joint jet tomographic analysis of the PHENIX RHIC and ALICE LHC data on the nuclear modification factor RAA within the light-cone path integral approach to induced gluon emission. Our results show that variation of RAA from RHIC to LHC energies indicates that the QCD coupling constant is suppressed in the quark–gluon plasma produced at the LHC.

W boson inclusive decays to quarkonium and $B_{c}^{(*)}$ meson at the LHC

In this paper, the production rates of quarkonia η c , J/ψ, η b , ϒ and \(B_{c}^{(*)}\) mesons through W + boson decay at the LHC are calculated, at the leading order in both the QCD coupling α s and in v, the typical velocity of the heavy quark inside mesons. It shows that a sizable number of quarkonia and \(B_{c}^{(*)}\) mesons from W + boson decay will be produced at the LHC. Comparison with the predictions by using quark fragmentation mechanism is also discussed. Results show that, for the charmonium production through W + decay, the difference between predictions by the fragmentation mechanism and complete leading order calculation is around 3%, and it is insensitive to the uncertainties of theoretical parameters; however, for the bottomonium and \(B_{c}^{(*)}\) productions, the difference cannot be ignored as the fragmentation mechanism is less applicable here due to the relatively large ratio m b /m w .

Expansion functions in perturbative QCD and the determination ofαs(Mτ2)

The conventional series in powers of the coupling in perturbative QCD have zero radius of convergence and fail to reproduce the singularity of the QCD correlators like the Adler function at $\alpha_s=0$. Using the technique of conformal mapping of the Borel plane, combined with the "softening" of the leading singularities, we define a set of new expansion functions that resemble the expanded correlator and share the same singularity at zero coupling. Several different conformal mappings and different ways of implementing the known nature of the first branch-points of the Adler function in the Borel plane are investigated, in both the contour-improved (CI) and fixed-order (FO) versions of renormalization group resummation. We prove the remarkable convergence properties of a set of new CI expansions and use them for a determination of the strong coupling from the hadronic $\tau$ decay width. By taking the average upon this set, with a conservative treatment of the errors, we obtain $\alpha_s(M_\tau^2)= 0.3195^{+ 0.0189}_{- 0.0138}$.

Violation of the geometric scaling behavior of the amplitude for running QCD coupling in the saturation region

In this paper we show that the intuitive guess that the geometric scaling behaviour should be violated in the case of the running QCD coupling, turns out to be correct. The scattering amplitude of the dipole with the size $r$ depends on new dimensional scale: $\Lambda_{QCD}$, even at large values $Y = \ln(1/x)$ and $l\,=\, \ln\Lb \as\Lb r^2\Rb/\as\Lb 1/Q^2_s\Rb\Rb$. However, in this region we found a new scaling behaviour: the amplitude is a function of $\zeta = Y\,l$. We state that only in the vicinity of the saturation scale $Q_s$ ($\as(Q^2_s)\,\ln \Lb r^2 Q^2_s\Rb\,\leq \, 1$), the amplitude shows the geometric scaling behaviour. Based on these finding the geometric scaling behavior that has been seen experimentally, stems from either we have not probed the proton at HERA and the LHC deeply inside the saturation region or that there exists the mechanism of freezing of the QCD coupling constant at $r^2 \approx 1/Q^2_s$.

Standard model Higgs-boson branching ratios with uncertainties

We present an update of the branching ratios for Higgs-boson decays in the Standard Model. We list results for all relevant branching ratios together with corresponding uncertainties resulting from input parameters and missing higher-order corrections. As sources of parametric uncertainties we include the masses of the charm, bottom, and top quarks as well as the QCD coupling constant. We compare our results with other predictions in the literature.

JETS and QCD: a historical review of the discovery of the quark and gluon jets and its impact on QCD

The observation of quark and gluon jets has played a crucial role in establishing Quantum Chromodynamics [QCD] as the theory of the strong interactions within the Standard Model of particle physics. The jets, narrowly collimated bundles of hadrons, reflect configurations of quarks and gluons at short distances. Thus, by analysing energy and angular distributions of the jets experimentally, the properties of the basic constituents of matter and the strong forces acting between them can be explored. In this review, which is primarily a description of the discovery of the quark and gluon jets and the impact of their observation on Quantum Chromodynamics, we elaborate, in particular, the role of the gluons as the carriers of the strong force. Focusing on these basic points, jets in $e^+ e^-$ collisions will be in the foreground of the discussion and we will concentrate on the theory that was contemporary with the relevant experiments at the electron-positron colliders. In addition we will delineate the role of jets as tools for exploring other particle aspects in $ep$ and $pp/p\bar{p}$ collisions - quark and gluon densities in protons, measurements of the QCD coupling, fundamental 2-2 quark/gluon scattering processes, but also the impact of jet decays of top quarks, and $W^\pm, Z$ bosons on the electroweak sector. The presentation to a large extent is formulated in a non-technical language with the intent to recall the significant steps historically and convey the significance of this field also to communities beyond high energy physics.

Variation of jet quenching from RHIC to LHC and thermal suppression of the QCD coupling constant

We perform a joint jet tomographic analysis of the data on the nuclear modification factor $R_{AA}$ from PHENIX at RHIC and ALICE at LHC. The computations are performed accounting for radiative and collisional parton energy loss with running coupling constant. Our results show that the observed slow variation of $R_{AA}$ from RHIC to LHC indicates that the QCD coupling constant is suppressed in the quark-gluon plasma produced at LHC.

Probing the three-gluon correlation functions by the single spin asymmetry inp↑p→DX

We study the single transverse-spin asymmetry for the inclusive open-charm production in the pp-collision, p^\uparrow p\to DX, induced by the three-gluon correlation functions in the polarized nucleon. We derive the corresponding twist-3 cross section formula in the leading order with respect to the QCD coupling constant. As in the case of the semi-inclusive deep inelastic scattering, ep^\uparrow\to eDX, our result differs from the previous result in the literature. We also derive a "master formula" which expresses the twist-3 cross section in terms of the gg\to c\bar{c} hard scattering cross section. We present a model calculation of the asymmetry at the RHIC energy, demonstrating the sensitivity of the asymmetry on the form of the three-gluon correlation functions.

Heavy octets and Tevatron signals with three or four b jets

Hypothetical color-octet particles of spin 0, pair-produced at hadron colliders through their QCD coupling, may lead to final states involving three or four b jets. We analyze kinematic distributions of the 3b final state that differentiate the scalar octets from supersymmetric Higgs bosons. Studying the scalar sector that breaks an SU(3) \times SU(3) gauge symmetry down to the QCD gauge group, we find that the scalar octet is resonantly produced in pairs via a spin-1 octet (coloron). A scalar octet of mass in the 140 - 150 GeV range can explain the nonstandard shape of the b-jet transverse energy distributions reported by the CDF Collaboration, especially when the coloron mass is slightly above twice the scalar mass. The dominant decay mode of the scalar octet is into a pair of gluons, so that the production of a pair of dijet resonances is large in this model, of about 40 pb at the Tevatron. Even when a W boson is radiated from the initial state, the inclusive cross section for producing a dijet resonance near the scalar octet mass remains sizable, around 0.15 pb.

QCD coupling constant below 1 GeV in the poincare-covariant model

The behavior of the running coupling constant α s (Q 2) phenomenologically parameterized in the region of Q < 1 GeV is considered within the framework of the Poincare-covariant quark model in a variety of regimes. An analysis was carried out for pseudoscalar and vector mesons with the lepton masses and decay constants (obtained by the model calculations) required to match their experimental counterparts. It shows that the constant α s is likely to behave with αcrit = α s (Q 2 = 0) ∼ 0.667 − 0.821 in the case of a frozen regime and αcrit =0.300 − 0.692 for peaked curves, which follows from the experimental values of the leptonic decay constants and masses.

Hard- and soft-fermion-pole contributions to single transverse-spin asymmetry for Drell–Yan process

We study the single transverse-spin asymmetry for the Drell–Yan lepton pair production based on the twist-3 mechanism in the collinear factorization. We calculate all the hard-pole (HP) and the soft-fermion-pole (SFP) contributions to the single-spin-dependent cross section originating from the quark–gluon correlation functions in the transversely polarized nucleon in the leading order with respect to the QCD coupling constant. Combined with the soft-gluon-pole (SGP) contribution, this completes the corresponding twist-3 cross section. In the real photon limit, where all the HP contributions are transformed into the SFP contribution, we find that the SFP partonic hard cross section for the two independent quark–gluon correlation functions coincides in each scattering channel, as in the case of the inclusive light-hadron production. Our result enables one to extract the quark–gluon correlation functions from the forthcoming experiments at several facilities such as RHIC and J-PARC.

Hadron Spectrum and the Infrared Behavior of QCD Coupling

A relativistic quantum-field model based on analytical confinement is developed to build stable bound states of spin-half and spin-one particles. The spectra of two-quark ground states are defined by using the ladder Bethe-Salpeter equation. An analytic expression for the running coupling in QCD is obtained that can be extended to the low energy region. By comparing the obtained result with recent experimental data on meson masses we obtain a new, independent and specific infrared-finite behavior of QCD coupling below energy scale ∼ 1 GeV. Particularly, an infrared-fixed point is extracted at αS(0) ≃ 0.757. We also calculate masses of some conventional mesons in the range of 0.8 – 9.5 GeV.

Heavy baryon–light vector meson couplings in QCD

The strong coupling constants of heavy baryons with light vector mesons are calculated in the framework of the light cone QCD sum rules using the most general form of the interpolating currents for the heavy baryons. It is shown that the sextet–sextet, sextet–antitriplet and antitriplet–antitriplet transitions are described by one invariant function for each class of transitions. The values of the electric and magnetic coupling constants for these transitions are obtained.