For any perturbative series that is known to k-subleading orders of perturbation theory, we utilize the process-appropriate renormalization-group ͑RG͒ equation in order to obtain all-orders summation of series terms proportional to ␣ n log nϪk ( 2 ) with kϭ͕0,1,2,3͖, corresponding to the summation to all orders of the leading and subsequent-three-subleading logarithmic contributions to the full perturbative series. These methods are applied to the perturbative series for semileptonic b decays in both MS and pole-mass schemes, and they result in RG-summed series for the decay rates which exhibit greatly reduced sensitivity to the renormalization scale . Such summation via RG methods of all logarithms accessible from known series terms is also applied to perturbative QCD series for vector-and scalar-current correlation functions, the perturbative static potential function, the ͑single-doublet standard-model͒ Higgs decay amplitude into two gluons, as well as the Higgs-mediated high-energy cross section for W ϩ W Ϫ →ZZ scattering. The resulting RG-summed expressions are also found to be much less sensitive to the renormalization scale than the original series for these processes.and the successive-order series coefficients within S͓x,L͔, as defined by Eq. ͑1.1͒, are ͓1͔T 0,0 ϭ1, T 1,0 ϭ4.25360, T 1,1 ϭ5, T 2,0 ϭ26.7848, T 2,1 ϭ36.9902, T 2,2 ϭ17.2917. ͑1.5͒The five active-flavor pole-mass expression for the same rate is obtained by replacing m b () with the renormalizationscale independent pole mass m b pole in Eqs. ͑1.4͒ and ͑1.2͒, as well as a concomitant alteration of the following series coefficients ͓1͔: PHYSICAL REVIEW D 66, 014010 ͑2002͒

We construct asymptotically safe extensions of the standard model by adding gauged vectorlike fermions. Using large number-of-flavor techniques we argue that all gauge couplings, including the hypercharge and, under certain conditions, the Higgs coupling, can achieve an interacting ultraviolet fixed point.

We have extended the calculation of the correlation functions of heavy quarkonium hybrid operators with various J P C quantum numbers to include QCD condensates up to dimension six. In contrast to previous analyses which were unable to optimize the QCD sum-rules for certain J P C , recent work has shown that inclusion of dimension six condensates stabilizes the hybrid sum-rules and permits reliable mass predictions. In this work we have investigated the effects of the dimension six condensates on the remaining channels. After performing the QCD sum-rule analysis, we update the mass spectra of charmonium and bottomonium hybrids with exotic and non-exotic quantum numbers. We identify that the negative-parity states with J P C = (0, 1, 2) −+ , 1 −− form the lightest hybrid supermultiplet while the positive-parity states with J P C = (0, 1) +− , (0, 1, 2) ++ belong to a heavier hybrid supermultiplet, confirming the supermultiplet structure found in other approaches. The hybrid with J P C = 0 −− has a much higher mass which may suggest a different excitation of the gluonic field compared to other channels. In agreement with previous results, we find that the J P C = 1 ++ charmonium hybrid is substantially heavier than the X(3872), which seems to preclude a pure charmonium hybrid interpretation for this state.

Masses of the pseudoscalar (J PC ¼ 0 Àþ ) charmonium and bottomonium hybrids are determined using QCD Laplace sum-rules. The effects of the dimension-six gluon condensate are included in our analysis and result in a stable sum-rule analysis, whereas previous studies of these states were unable to optimize mass predictions. The pseudoscalar charmonium hybrid is predicted to have a mass of approximately 3.8 GeVand the corresponding bottomonium prediction is 10.6 GeV. Calculating the full correlation function, rather than only the imaginary part, is shown to be necessary for accurate formulation of the sum-rules. The charmonium hybrid mass prediction is discussed within the context of the XYZ resonances.

Axial vector (J P C = 1 ++ ) charmonium and bottomonium hybrid masses are determined via QCD Laplace sum-rules. Previous sum-rule studies in this channel did not incorporate the dimension-six gluon condensate, which has been shown to be important for 1 −− and 0 −+ heavy quark hybrids. An updated analysis of axial vector charmonium and bottomonium hybrids is presented, including the effects of the dimension-six gluon condensate. The axial vector charmonium and bottomonium hybrid masses are predicted to be 5.13 GeV and 11.32 GeV, respectively. We discuss the implications of this result for the charmonium-like "XYZ" states and the charmonium hybrid multiplet structure observed in recent lattice calculations.

D ecem ber 19,2013A bstract W e uti l i ze asym ptoti c Pad e-approxi m ant m ethods to esti m ate the three-l oop order M S-schem e coe ci ents w i thi n the i ncl usi ve b ! u ' ' decay rate for four and ve acti ve quark avours. T he esti m ates w e obtai n for the three renorm al i zati on-group-accessi bl e coe ci ents w i thi n the three-l oop contri buti on are al l found to be w i thi n 5. 1% of thei r true val ues,usi ng a l east-squares procedure i n conjuncti on w i th an asym ptoti c Pad eapproxi m ant esti m ate ofthe three-l oop term over the enti re m b dom ai n. G i ven the i nput val ues s(M Z )= 0: 118 0: 004 and m b (m b )= 4: 17 0: 05 G eV ,the three-l oop expressi on for the purel y-perturbati ve contri buti on to the b ! u ' ' decay rate i s m i ni m al l y sensi ti ve to renorm al i zati on scal e at = 1: 775 G eV ,at w hi ch scal e the three-l oop contri buti on i s esti m ated to be onl y 1. 4% ofthe l eadi ng tree-ordercontri buti on. W e esti m ate the ful lperturbati ve decay rate to be 192 3 (b ! u ' ' )= G 2 F j V u b j 2 = 2070 G eV 5 16% ,i ncl usi ve oftheoreti cal uncertai nti es from seri es truncati on,the i nput param eters,and the esti m ati on procedure.

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We investigate the recent evidence for a charged X(5568) meson as an exotic open-flavor tetraquark state subd with J P = 0 + /1 + in the framework of QCD sum rules. We use the color antisymmetric [3 c ] su ⊗ [3 c ]¯bd tetraquark currents in both scalar and axial-vector channels to perform evaluations and numerical analyses. Our results imply that the X(5568) can be interpreted as both the scalar subd tetraquark state and the axial-vector one, which are in good agreement with the experimental measurement. We also discuss the possible decay patterns of the X(5568) and suggest to search for its neutral partner in the radiative decay into B 0 s γ and B * s γ, which can be used to determine its spin-parity quantum numbers. Moreover, we predict its charmed partner state around 2.55 GeV with the quark content sucd and J P = 0 + /1 + .