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 use an anti-de Sitter/Quantum Chromodynamics (AdS/QCD) holographic light-front wavefunction for the ρ and φ mesons, in conjunction with the Color Glass Condensate (CGC) dipole cross-section whose parameters are fitted to the most recent 2015 high precision HERA data on inclusive Deep Inelastic Scattering (DIS), in order to predict the cross-sections for diffractive ρ and φ electroproduction. Our results suggest that the holographic meson light-front wavefunction is able to give a simultaneous description of ρ and φ production data provided we use a set of light quark masses with m u,d < m s ≈

We quantify the importance of dynamical spin effects in the holographic light-front wavefunctions of the pion, kaon, η and η ′ . Using a universal AdS/QCD scale and constituent quark masses, we find that such effects are maximal in the pion where they lead to an excellent simultaneous description of a wide range of data: the decay constant, charge radius, spacelike EM and transition form factors, as well as, after QCD evolution, both the parton distribution function and the parton distribution amplitude data from Fermilab. These dynamical spin effects lead up to a 30% chance of finding the valence quark and antiquark with aligned spins in the pion. The situation is very different for the kaon, where a simultaneous description of the available data (decay constant, radius and spacelike EM form factor) prefer no dynamical spin effects at all. The situation is less clear for the η and η ′ : while their radiative decay widths data are consistent with dynamical spin effects only in η ′ , the data on their spacelike transition form factors clearly favor maximal dynamical spin effects in both mesons.

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We account for dynamical spin effects in the holographic light-front wavefunction of the pion in order to predict the mean charge radius, r 2 π , the decay constant, f π , the spacelike electromagnetic form factor, F π (Q 2 ), the twist-2 pion Distribution Amplitude and the photon-to-pion transition form factor F γπ (Q 2 ). Using a universal fundamental AdS/QCD scale, κ = 523 MeV, and a constituent quark mass of 330 MeV, we find a remarkable improvement in describing all observables.

We use QCD light-cone sum rules with holographic anti de Sitter/Chromodynamics (AdS/QCD) Distribution Amplitudes (DAs) for the K * meson in order to predict the full set of seven B → K * transition form factors for intermediate-to-high recoil of the vector meson. We provide simple parametrizations for the form factors that fit our AdS/QCD predictions. We also provide parametrizations that fit both our AdS/QCD predictions and the most recent lattice data for low recoil. We use our form factors to predict the differential and total branching fraction of the rare dileptonic decay B → K * µ + µ − which we compare to the recent LHCb data.

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.

Using renormalization-group methods, we derive differential equations for the all-orders summation of logarithmic corrections to the QCD series for R(s) = σ(e + e − → hadrons)/σ(e + e − → µ + µ − ), as obtained from the imaginary part of the purely-perturbative vector-current correlation function. We present explicit solutions for the summation of leading and up to three subsequent subleading orders of logarithms. The summations accessible from the four-loop vector-correlator not only lead to a substantial reduction in sensitivity to the renormalization scale, but necessarily impose a common infrared bound on perturbative approximations to R(s), regardless of the infrared behaviour of the true QCD couplant.For center-of-mass squared-energy s, QCD corrections to R(s) ≡ σ(e + e − → hadrons)/σ(e + e − → µ + µ − ) are scaled by a perturbative QCD series (S):This series is extracted from the imaginary part of the MS vector-current correlation function [1, 2],with coefficients T n,m tabulated in Table I for 3-5 active flavors, as appropriate for the choice of the center-of-mass squared-energy s. Each order of this series depends upon the MS renormalization scale parameter µ, both through the couplantand through powers of the logarithmNevertheless, the all-orders series S must ultimately be independent of renormalization scale. R(s) is a measurable physical quantity necessarily independent of µ, the artificial scale entering QCD calculations as a by-product of the regulation of Feynman-diagrammatic infinities. Hence,The above renormalization group equation (RGE) is simply a chain-rule relation in whichwhere known [3] MS β-function coefficients β k are also tabulated in Table I. Thus, the RGE (5) is generally employed to provide scale dependence to the couplant x. "Optimal" renormalization-group (RG) improvement is the inclusion of every term in a perturbative series of the form (2) that can be extracted by RG-methods from a perturbative computation to a given order [4]. For example,