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Register a new userQuark Mass Corrections to the Perturbative Thrust and its Effect on the determination of $alpha_s$
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We consider the effects of quark masses to the perturbative thrust in $e^+e^-$ annihilation. In particular we show that perturbative power corrections resulting from non-zero quark masses considerably alters the size of the non-perturbative power corrections and consequently, significantly changes the fitted value of $alpha_s$.
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The order $alpha_s^2$ perturbative QCD correction to the Gottfried sum rule is obtained. The result is based on numerical calculation of the order $alpha_s^2$ contribution to the coefficient function and on the new estimate of the three-loop anomalous dimension term. The correction found is negative and rather small. Therefore it does not affect the necessity to introduce flavour-asymmetry between $bar{u}$ and $bar{d}$ antiquarks for the description of NMC result for the Gottfried sum rule.
From soft-collinear effective theory one can derive a factorization formula for the e+e- thrust distribution dsigma/dtau with tau = 1-T that is applicable for all tau. The formula accommodates available O(alpha_s^3) fixed-order QCD results, resummation of logarithms at NNNLL order, a universal nonperturbative soft function for hadronization effects, factorization of nonperturbative effects in subleading power contributions, bottom mass effects and QED corrections. We emphasize that the use of Monte Carlos to estimate hadronization effects is not compatible with high-precision, high-order analyses. We present a global analysis of all available e+e- thrust data measured at Q = 35 to 207 GeV in the tail region, where a two-parameter fit can be carried out for alpha_s(m_Z) and Omega_1, the first moment of the soft function. To obtain small theoretical errors it is essential to define Omega_1 in a short-distance scheme, free of an O(Lambda_QCD) renormalon ambiguity. We find alpha_s(m_Z) = 0.1135 +- (0.0002)_expt +- (0.0005)_Omega_1 +- (0.0009)_pert with chi^2/dof = 0.9.
In the paper, we study the properties of the top-quark $overline{rm MS}$ running mass computed from its on-shell mass by using both the four-loop $overline{rm MS}$-on-shell relation and the principle of maximum conformality (PMC) scale-setting approach. The PMC adopts the renormalization group equation to set the correct magnitude of the strong running coupling of the perturbative series, its prediction avoids the conventional renormalization scale ambiguity, and thus a more precise pQCD prediction can be achieved. After applying the PMC to the four-loop $overline{rm MS}$-on-shell relation and taking the top-quark on-shell mass $M_t=172.9pm0.4$ GeV as an input, we obtain the renormalization scale-invariant $overline{rm MS}$ running mass at the scale $m_t$, e.g., $m_t(m_t)simeq 162.6pm 0.4$ GeV, in which the error is the squared average of those from $Delta alpha_s(M_Z)$, $Delta M_t$, and the approximate error from the uncalculated five-loop terms predicted by using the Pad{e} approximation approach.
We compute in order alpha_s the nonrelativistic QCD (NRQCD) short-distance coefficients that match quark-antiquark operators of all orders in the heavy-quark velocity v to the electromagnetic current. We employ a new method to compute the one-loop NRQCD contribution to the matching condition. The new method uses full-QCD expressions as a starting point to obtain the NRQCD contribution, thus greatly streamlining the calculation. Our results show that, under a mild constraint on the NRQCD operator matrix elements, the NRQCD velocity expansion for the quark-antiquark-operator contributions to the electromagnetic current converges. The velocity expansion converges rapidly for approximate J/psi operator matrix elements.
Hadron colliders offer a unique opportunity to test perturbative QCD because, rather than producing events at a specific beam energy, the dynamics of the hard scattering is probed simultaneously at a wide range of momentum transfers. This makes the determination of $al$ and the parton density functions (PDF) at hadron colliders particularly interesting. In this paper we restrict ourselves to extracting $al$ for a given PDF at a scale which is directly related to the transverse energy produced in the collision. As an example, we focus on the single jet inclusive transverse energy distribution and use the published 88-89 CDF data with an integrated luminosity of 4.2 pb$^{-1}$. The evolution of the coupling constant over a wide range of scales (from 30~GeV to 500~GeV) is clearly shown and is in agreement with the QCD expectation. The data to be obtained in the current Tevatron run (expected to be well in excess 100 pb$^{-1}$ for both the CDF and DO experiments) will significantly decrease the experimental errors.
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