QCD Coupling Constant Research Articles

Renormalization group equation and QCD coupling constant in the presence of SU(3) chromo-electric field

We solve renormalization group equation in QCD in the presence of SU(3) constant chromo-electric field E^a with arbitrary color index a=1,2,...8 and find that the QCD coupling constant \alpha_s depends on two independent casimir/gauge invariants C_1=[E^aE^a] and C_2=[d_{abc}E^aE^bE^c]^2 instead of one gauge invariant C_1=[E^aE^a]. The \beta function is derived from the one-loop effective action. This coupling constant may be useful to study hadron formation from color flux tubes/strings at high energy colliders and to study quark-gluon plasma formation at RHIC and LHC.

Jets and measurements of [formula omitted

A survey is presented of recent measurements in jet physics, and improved determinations of the QCD coupling constant alpha_s that these have made possible.

Optimal spin-quantization axes for quarkonium with large transverse momentum

The gluon collision process that creates a heavy-quark-antiquark pair with small relative momentum and large transverse momentum predicts at leading-order in the QCD coupling constant that the transverse polarization of the pair should increase with its transverse momentum. Measurements at the Fermilab Tevatron of the polarization of charmonium and bottomonium states with respect to a particular spin-quantization axis are inconsistent with this prediction. However the predicted rate of approach to complete transverse polarization depends on the choice of spin-quantization axis. We introduce axes that maximize and minimize the transverse polarization from the leading-order gluon collision process. They are determined by the direction of the jet that provides most of the balancing transverse momentum.

Update: Accurate determinations ofαsfrom realistic lattice QCD

We use lattice QCD simulations, with MILC configurations (including vacuum polarization from $u$, $d$, and $s$ quarks), to update our previous determinations of the QCD coupling constant. Our new analysis uses results from 6 different lattice spacings and 12 different combinations of sea-quark masses to significantly reduce our previous errors. We also correct for finite-lattice-spacing errors in the scale setting, and for nonperturbative chiral corrections to the 22 short-distance quantities from which we extract the coupling. Our final result is ${\ensuremath{\alpha}}_{V}(7.5\text{ }\text{ }\mathrm{GeV},{n}_{f}=3)=0.2120(28)$, which is equivalent to ${\ensuremath{\alpha}}_{\overline{\mathrm{MS}}}({M}_{Z},{n}_{f}=5)=0.1183(8)$. We compare this with our previous result from Wilson loops, which differs by one standard deviation.

Systematic analysis of scaling properties in deep inelastic scattering

Using the ``quality factor'' method, we analyze the scaling properties of deep inelastic processes at the accelerator HERA and fixed target experiments for $x\ensuremath{\le}{10}^{\ensuremath{-}2}$. We look for scaling formulas of the form ${\ensuremath{\sigma}}^{{\ensuremath{\gamma}}^{*}p}(\ensuremath{\tau})$, where $\ensuremath{\tau}(L=\mathrm{log}{Q}^{2},Y)$ is a scaling variable suggested by the asymptotic properties of QCD evolution equations with rapidity $Y$. We consider four cases: ``fixed coupling,'' corresponding to the original geometric scaling proposal and motivated by the asymptotic properties of the Balitsky-Kovchegov equation with fixed QCD coupling constant; two versions, ``running coupling I, II,'' of the scaling suggested by the Balitsky-Kovchegov equation with running coupling; and ``diffusive scaling'' suggested by the QCD evolution equation with Pomeron loops. The quality factors, quantifying the phenomenological validity of the candidate scaling variables, are fitted on the total and deeply virtual Compton scattering cross-section data from HERA and predictions are made for the elastic vector meson and for the diffractive cross sections at fixed small ${x}_{\mathbb{P}}$ or $\ensuremath{\beta}$. The first three scaling formulas have comparably good quality factors while the fourth one is disfavored. Adjusting initial conditions gives a significant improvement of the running coupling II scaling.

Jet Rates in Electron-Positron Annihilation atO(αs3)in QCD

We compute production rates for two, three, four, and five jets in electron-positron annihilation at the third order in the QCD coupling constant. At this order, three-jet production is described to next-to-next-to-leading order in perturbation theory while the two-jet rate is obtained at next-to-next-to-next-to-leading order. Our results yield an improved perturbative description of the dependence of jet multiplicity on the jet resolution parameter y{cut}, particularly at small values of y{cut}.

Publisher's Note: Hot QCD equations of state and relativistic heavy ion collisions [Phys. Rev. C 76, 054909 (2007)

We study two recently proposed equations of state (EOS) which are obtained from high temperature QCD, and show how they can be adapted to use them for making predictions for relativistic heavy ion collisions. The method involves extracting equilibrium distribution functions for quarks and gluons from the EOS, which in turn will allow a determination of the transport and other bulk properties of the quark gluon plasma. Simultaneously, the method also yields a quasi particle description of interacting quarks and gluons. The first EOS is perturbative in the QCD coupling constant and has contributions of $O(g^5)$. The second EOS is an improvement over the first, with contributions upto $ O(g^6 ln(\frac{1}{g}))$; it incorporates the nonperturbative hard thermal contributions. The interaction effects are shown to be captured entirely by the effective chemical potentials for the gluons and the quarks, in both the cases. The chemical potential is seen to be highly sensitive to the EOS. As an application, we determine the screening lengths which are, indeed the most important diagnostics for QGP. The screening lengths are seen to behave drastically differently depending on the EOS considered., and yield, therefore, a way to distinguish the two equations of state in heavy ion collisions.

Hot QCD equations of state and relativistic heavy ion collisions

We study two recently proposed equations of state obtained from high-temperature QCD and show how they can be adapted to use them for making predictions for relativistic heavy ion collisions. The method involves extracting equilibrium distribution functions for quarks and gluons from the equation of state (EOS), which in turn will allow a determination of the transport and other bulk properties of the quark gluon-plasma. Simultaneously, the method also yields a quasiparticle description of interacting quarks and gluons. The first EOS is perturbative in the QCD coupling constant and has contributions of $O({g}^{5})$. The second EOS is an improvement over the first, with contributions up to $O[{g}^{6}\mathrm{ln}(1/g)]$; it incorporates the nonperturbative hard thermal contributions. The interaction effects are shown to be captured entirely by the effective chemical potentials for the gluons and the quarks, in both cases. The chemical potential is seen to be highly sensitive to the EOS. As an application, we determine the screening lengths, which are, indeed, the most important diagnostics for QGP. The screening lengths are seen to behave drastically differently depending on the EOS considered and therefore yield a way to distinguish the two equations of state in heavy ion collisions.

Perturbative QCD analysis of exclusiveJ/ψ+ηcproduction ine+e−annihilation

We analyze the exclusive charmonium $J/\ensuremath{\psi}+{\ensuremath{\eta}}_{c}$ pair production in ${e}^{+}{e}^{\ensuremath{-}}$ annihilation using the nonfactorized perturbative QCD and the light-front quark model (LFQM) that goes beyond the peaking approximation. We effectively include all orders of higher twist terms in the leading order of QCD coupling constant and compare our nonfactorized analysis with the usual factorized analysis in the calculation of the cross section. We also calculate the quark distribution amplitudes, the Gegenbauer moments, and the decay constants for $J/\ensuremath{\psi}$ and ${\ensuremath{\eta}}_{c}$ mesons using our LFQM. Our nonfactorized result enhances the nonrelativistic QCD result by a factor of $3\ensuremath{\sim}4$ at $\sqrt{s}=10.6\text{ }\text{ }\mathrm{GeV}$.

QCD COLLISIONAL ENERGY LOSS IN AN INCREASINGLY INTERACTING QUARK–GLUON PLASMA

The discovery of the jet quenching in central Au + Au collisions at the Relativistic Heavy-Ion Collider (RHIC) at Brookhaven National Laboratory has provided clear evidence for the formation of strongly interacting dense matter. It has been predicted to occur due to the energy loss of high energy partons that propagate through the quark–gluon plasma. In this paper we investigate the dependence of the parton energy loss due to elastic scatterings in a parton plasma on the value of the strong coupling and its running with the evolution of the system. We analyze different prescriptions for the QCD coupling and calculate the energy and length dependence of the fractional energy loss. Moreover, the partonic quenching factor for light and heavy quarks is estimated. We found that the predicted enhancement of the heavy to light hadrons (D/π) ratio is strongly dependent on the running of the QCD coupling constant.

Elastic energy loss in an expanding QGP

The discovery of the jet quenching in central Au + Au collisions at the Relativistic Heavy-ion Collider (RHIC) has provided clear evidence for the formation of strongly interacting dense matter. It has been predicted to occur due to the energy loss of high energy partons that propagate through the quark gluon plasma. Since the medium is not static and it cools while expands, the strong coupling is not fixed, running with the evolution of the system. In this work, we present an investigation of the dependence on the value of the strong coupling in the parton energy loss due to elastic scatterings in a parton plasma. We analyze different prescriptions for the QCD coupling and calculate the energy and length dependence of the fractional energy loss. Moreover, the quenching factor for light and heavy quarks is estimated. We found that the predicted enhancement of heavy to light hadrons (D/pi) ratio is strongly dependent on the running of the QCD coupling constant.

Modelling non-perturbative corrections to bottom-quark fragmentation

We describe B-hadron production in e + e − annihilation at the Z 0 pole by means of a model including non-perturbative corrections to b-quark fragmentation as originating, via multiple soft emissions, from an effective QCD coupling constant, which does not exhibit the Landau pole any longer and includes absorptive effects due to parton branching. We work in the framework of perturbative fragmentation functions at NLO, with NLL DGLAP evolution and NNLL large- x resummation in both coefficient function and initial condition of the perturbative fragmentation function. We include hadronization corrections via the effective coupling constant in the NNLO approximation and do not add any further non-perturbative fragmentation function. As part of our model, we perform the Mellin transforms of our resummed expressions exactly. We present results on the energy distribution of b-flavored hadrons, which we compare with LEP and SLD data, in both x- and N-spaces. We find that, within the theoretical uncertainties on our calculation, our model is able to reasonably reproduce the data at x ≲ 0.92 and the first five moments of the B cross section.

Systematics of geometric scaling

Abstract Using all available data on the deep-inelastic cross-sections at HERA at x ⩽ 10 −2 , we look for geometric scaling of the form σ γ ∗ p ( τ ) where the scaling variable τ behaves alternatively like log Q 2 − λ Y , as in the original definition, or log Q 2 − λ Y , which is suggested by the asymptotic properties of the Balitsky–Kovchegov (BK) equation with running QCD coupling constant. A “Quality Factor” (QF) is defined, quantifying the phenomenological validity of the scaling and the uncertainty on the intercept λ . Both choices have a good QF, showing that the second choice is as valid as the first one, predicted for fixed coupling constant. A comparison between the QCD asymptotic predictions and data is made and the QF analysis shows that the agreement can be reached, provided going beyond leading logarithmic accuracy for the BK equation.

Scalar form factor of the nucleon and nucleon-scalar meson coupling constant in QCD

Scalar form factor of the nucleon is calculated in the framework of light-cone QCD sum rules, using the most general form of the baryon current. Using the result on scalar form factor of the nucleon, the nucleon-scalar $\ensuremath{\sigma}$ and ${a}_{0}$ meson coupling constants are estimated. Our results on these couplings are in good agreement with the prediction of the external-field QCD sum rules method.

Hadronic interactions of ultra-high energy photons with protons and light nuclei in the dipole picture

We apply the dipole formalism that has been developed to describe low-x deep inelastic scattering to the case of ultra-high energy real photons with nucleon and nuclear targets. We hope that there will be future modelling applications in high-energy particle astrophysics. We modify the dipole model of McDermott, Frankfurt, Guzey and Strikman (MFGS) by fixing the cross section at the maximum value allowed by the unitarity constraint whenever the dipole model would otherwise predict a unitarity violation. We observe that, under reasonable assumptions, a significant fraction of the real photon cross section results from dipole interactions where the QCD coupling constant is small, and that the MFGS model is consistent with the Froissart bound. The resulting model predicts a rise of the cross section of about a factor of 12 when the photon energy is increased from 103 GeV to 1012 GeV. We extend the analysis to the case of scattering off a 12C target. We find that, due to the low thickness of the light nuclei, unitarity for the scattering off individual nucleons plays a larger role than for the scattering off the nucleus as a whole. At the same time the proximity to the black disc limit results in a substantial increase of the amount of nuclear shadowing. This, in turn, slows down the rate of increase of the total cross section with energy as compared to the proton case. As a result we find that the 12C nuclear cross section rises by about a factor of 7 when the photon energy is increased from 103 GeV to 1012 GeV. We also find that the fraction of the cross section due to production of charm reaches 30% for the highest considered energies with a 12C target.

Transverse-momentum resummation for slepton-pair production at the CERN Large Hadron Collider

We perform a first precision calculation of the transverse-momentum (${q}_{T}$) distribution of slepton pair and slepton-sneutrino associated production at the CERN Large Hadron Collider. We implement soft-gluon resummation at the next-to-leading logarithmic level and consistently match the obtained result to the pure fixed-order perturbative result at leading order in the QCD coupling constant, i.e. $\mathcal{O}({\ensuremath{\alpha}}_{s})$. We give numerical predictions for ${\stackrel{\texttildelow{}}{\ensuremath{\tau}}}_{1}{\stackrel{\texttildelow{}}{\ensuremath{\tau}}}_{1}^{*}$ and ${\stackrel{\texttildelow{}}{\ensuremath{\tau}}}_{1}{\stackrel{\texttildelow{}}{\ensuremath{\nu}}}_{\ensuremath{\tau}}^{*}+{\stackrel{\texttildelow{}}{\ensuremath{\tau}}}_{1}^{*}{\stackrel{\texttildelow{}}{\ensuremath{\nu}}}_{\ensuremath{\tau}}$ production, also implementing recent parametrizations of nonperturbative effects. The results show a relevant contribution of resummation both in the small and intermediate ${q}_{T}$-regions and little dependence on unphysical scales and nonperturbative contributions.

Properties of color-Coulomb string tension

We study the properties of the color-Coulomb string tension obtained from the instantaneous part of gluon propagators in Coulomb gauge using quenched $SU(3)$ lattice simulation. In the confinement phase, the dependence of the color-Coulomb string tension on the QCD coupling constant is smaller than that of the Wilson loop string tension. On the other hand, in the deconfinement phase, the color-Coulomb string tension does not vanish even for $T/{T}_{c}=1\ensuremath{\sim}5$, the temperature dependence of which is comparable with the magnetic scaling, dominating the high temperature QCD. Thus, the color-Coulomb string tension is not an order parameter of quark-gluon plasma phase transition.

A systematic study of QCD coupling constant from deep-inelastic measurements

We reanalyze deep-inelastic scattering data of the BCDMS Collaboration by including proper cuts of ranges with large systematic errors. We also perform the fits of high-statistic deep-inelastic scattering data of the BCDMS, SLAC, NM, and BFP Collaborations taking the data separately and in a combined way and find good agreement between these analyses. We extract the values of both the QCD coupling constant α s(M Z 2 ) up to the NLO level and of the power corrections to the structure function F 2. The fits of the combined data for the nonsinglet part of the structure function F 2 predict the coupling constant value α s(M Z 2 ) = 0.1174 ± 0.0007 (stat.) ± 0.0019 (syst.) ± 0.0010 (norm.) (or QCD parameter $$\Lambda \tfrac{{(5)}}{{MS}} = 204 \pm 25$$ (total experimental error) MeV). The fits of the combined data for both the nonsinglet part and the singlet part lead to the values α s(M Z 2 ) = 0.1177 ± 0.0007 (stat.) ± 0.0021 (syst.) ± 0.0009 (norm.) (or QCD parameter $$\Lambda \tfrac{{(5)}}{{MS}}$$ =(208±27 (total experimental error)MeV). The above values are in very good agreement with each other. We estimate theoretical uncertainties for α s(M Z 2 ) at +0.0047 and −0.0057 from fits of the combined data when complete singlet and nonsinglet Q 2 evolution is taken into account.

Can thermalization in heavy ion collisions be described by QCD diagrams?

The onset of thermalization in heavy ion collisions in the weak coupling framework can be viewed as a transition from the initial state Color Glass Condensate dynamics, characterized by the energy density scaling like ε ∼ 1 / τ with τ the proper time, to the hydrodynamics-driven expansion of the quark–gluon plasma with ε ∼ 1 / τ 4 / 3 (or higher power of 1 / τ for the boost non-invariant case). We argue that, at any order of the perturbative expansion in the QCD coupling constant, the gluon field generated in an ultrarelativistic heavy ion collision leads to energy density scaling as ε ∼ 1 / τ for late times τ ≫ 1 / Q s . Therefore, it is likely that thermalization and hydrodynamic description of the gluon system produced in heavy ion collisions cannot result from perturbative QCD diagrams at these late times. At earlier times with τ ∼ 1 / Q s the subleading corrections to ε in 1 / τ expansion (terms scaling like ∼ 1 / τ 1 + Δ with Δ > 0 ) may become important possibly leading to hydrodynamic-like behavior of the gluon system. Still, we show that such corrections do not contribute to the particle production cross section, and are likely to be irrelevant for physical observables. We generalize our results by including massless quarks into the system. Thus, it appears that the apparent thermalization of quarks and gluons, leading to success of Bjorken hydrodynamics in describing heavy ion collisions at RHIC, can only be attributed to the non-perturbative QCD effects.

Accurate Determinations ofαsfrom Realistic Lattice QCD

We obtain a new value for the QCD coupling constant by combining lattice QCD simulations with experimental data for hadron masses. Our lattice analysis is the first to (1) include vacuum polarization effects from all three light-quark flavors (using MILC configurations), (2) include third-order terms in perturbation theory, (3) systematically estimate fourth and higher-order terms, (4) use an unambiguous lattice spacing, and (5) use an $\mathcal{O}({a}^{2})$-accurate QCD action. We use 28 different (but related) short-distance quantities to obtain ${\ensuremath{\alpha}}_{\overline{\mathrm{MS}}}^{(5)}({M}_{Z})=0.1170(12)$.