We present an up-to-date analysis for a precise determination of the effective fine structure constant and discuss the prospects for future improvements. We advocate to use a determination monitored by the Adler function which allows us to exploit perturbative QCD in an optimal well controlled way. Together with a long term program of hadronic cross section measurements at energies up to a few GeV, a determination of alpha(M_Z) at a precision comparable to the one of the Z mass M_Z should be feasible. Presently alpha(E) at E>1 GeV is the least precisely known of the fundamental parameters of the SM. Since, in spite of substantial progress due to new BaBar exclusive data, the region 1.4 to 2.4 GeV remains the most problematic one a major step in the reduction of the uncertainties are expected from VEPP-2000 and from a possible ``high-energy'' option DAFNE-2 at Frascati. The up-to-date evaluation reads Delta alpha^{(5)}_{had}(M_Z^2) = 0.027515 +/- 0.000149 or alpha^{-1}(M_Z)=128.957 +/- 0.020.
We compute, for the first time, the order alpha_s^4 contributions to the Bjorken sum rule for polarized electron-nucleon scattering and to the (non-singlet) Adler function for the case of a generic colour gauge group. We confirm at the same order a (generalized) Crewther relation which provides a strong test of the correctness of our previously obtained results: the QCD Adler function and the five-loop beta-function in quenched QED. In particular, the appearance of an irrational contribution proportional to zeta_3 in the latter quantity is confirmed. We obtain the commensurate scale equation r…
The current status of the Adler function and two closely related Deep Inelastic Scattering (DIS) sum rules, namely, the Bjorken sum rule for polarized DIS and the Gross-Llewellyn Smith sum rule are briefly reviewed. A new result is presented: an analytical calculation of the coefficient function of the latter sum rule in a generic gauge theory in order O(alpha_s^4). It is demonstrated that the corresponding Crewther relation allows to fix two of three colour structures in the O(alpha_s^4) contribution to the singlet part of the Adler function.
The analytic result for the singlet part of the Adler function of the vector current in a general gauge theory is presented in five-loop approximation. Comparing this result with the corresponding singlet part of the Gross-Llewellyn Smith sum rule [1], we successfully demonstrate the validity of the generalized Crewther relation for the singlet part. This provides a non-trivial test of both our calculations and the generalized Crewther relation. Combining the result with the already available non-singlet part of the Adler function [2,3] we arrive at the complete ${\cal O}(α_s^4)$ expression fo…
Various moments of the hadronic spectral functions have been employed in the determination of the strong coupling alpha_s from tau decays. In this work we study the behaviour of their perturbative series under different assumptions for the large-order behaviour of the Adler function, extending previous work on the tau hadronic width. We find that the moments can be divided into a small number of classes, whose characteristics depend only on generic features of the moment weight function and Adler function series. Some moments that are commonly employed in alpha_s analyses from tau decays shoul…
The tau hadronic width provides a determination of the strong coupling constant alpha_s at low energies, since it can be related to a weighted integral of the Adler function in the complex energy plane. Using Operator Product Expansion, one sees that the sensitivity to alpha_s comes from the perturbative contribution, which can be obtained by integrating the perturbative expansion of the Adler function. Two different prescriptions proposed to perform this integral, called Fixed-Order Perturbation Theory and Contour-Improved Perturbation Theory (FOPT and CIPT), yield different results for the s…
By using a non-perturbative expansion and the dispersion relation for the Adler $D$--function we propose a new method for constructing the QCD effective coupling constant in the timelike region.
The contribution from hadronic vacuum polarisation effects is responsible for a large fraction of the theoretical uncertainty in the running of the QED coupling. The current level of uncertainty has become a limitation for electroweak precision tests. We use lattice QCD simulations with two flavours of O$(a)$ improved Wilson fermions to determine the Adler function in a broad range of the momentum transfer $Q^2$. The running of the QED coupling, including valence contributions from $u$, $d$, $s$ and $c$ quarks, is compared to phenomenological results at intermediate $Q^2$ values. In the large …
We describe the Adler function in Quantum Chromodynamics using a transseries representation within a resurgent framework. The approach is based on a Borel-Ecalle resummation of the infrared renormalons combined with an effective running for the strong coupling. The new approach is flexible enough to give values in agreement with the current Adler function determinations. We then apply our finding to the muon's anomalous magnetic moment studying the possibility of saturating, solely in terms of the vacuum polarization function, the current discrepancy between the best Standard Model value for t…
A method to determine the running of alpha from a measurement of small-angle Bhabha scattering is proposed and worked out. The method is suited to high statistics experiments at e+e- colliders, which are equipped with luminometers in the appropriate angular region. A new simulation code predicting small-angle Bhabha scattering is also presented
In the determination of alpha_s from tau decays several different moments of the hadronic spectral functions have been used. In a recent work, we performed an analysis of their perturbative behaviour under two different assumptions for the higher-order coefficients of the Adler function. We showed that the various moments can be divided in a small number of classes. We concluded that some of the moments commonly employed in alpha_s extractions should be avoided due to their bad perturbative behaviour. Furthermore, for the moments that have a good perturbative behaviour, and under reasonable as…
We propose a method to determine the running of $α_{QED}$ from the measurement of small-angle Bhabha scattering. The method is suited to high statistics experiments at $e^{+} e^{-}$ colliders, which are equipped with luminometers in the appropriate angular region. We present a new simulation code predicting small-angle Bhabha scattering. A detailed description of this idea can be found in A.B. Arbuzov, D. Haidt, C. Matteuzzi, M. Paganoni and L. Trentadue, The running of the electromagnetic coupling alpha in small-angle Bhabha scattering, Eur. Phys. J. C34, 267 (2004).
We present the next-to-next-to-leading order ($alpha alpha_s^2$) corrections to the first moment of the polarized virtual photon structure function $g_1^gamma(x,Q^2,P^2)$ in the kinematical region $Lambda^2 ll P^2 ll Q^2$, where $-Q^2(-P^2)$ is the mass squared of the probe (target) photon and $Lambda$ is the QCD scale parameter. In order to evaluate the three-loop-level photon matrix element of the flavor singlet axial current, we resort to the Adler-Bardeen theorem for the axial anomaly and we calculate in effect the two-loop diagrams for the photon matrix element of the gluon operator. The …
A gluino in the mass range 12--16 GeV combined with a light (2--5.5 GeV) bottom squark, as has been proposed recently to explain an excess of b quark hadroproduction, would affect the momentum-scale dependence (``running'') of the strong coupling constant alpha_s in such a way as to raise its value at M_Z by about 0.014 +/- 0.001. If one combines sources of uncertainty at low (m_b) and high (M_Z) mass scales, one can only distinguish such an effect at slightly more than the 2 sigma level. Prospects for improvement in this situation, which include better lattice QCD simulations and better measu…
We study the inclusion of running coupling corrections into the non-linear small-x JIMWLK and BK evolution equations by resumming all powers of alpha_s N_f in the evolution kernels. We demonstrate that the running coupling corrections are included in the JIMWLK/BK evolution kernel by replacing the fixed coupling constant alpha_s in it with alpha_s (1/r_1^2) alpha_s (1/r_2^2) / alpha_s (1/R^2), where r_1 and r_2 are transverse distances between the emitted gluon and the harder gluon (or quark) off of which it was emitted to the left and to the right of the interaction with the target. In the fo…
The leading hadronic effects in electroweak theory derive from vacuum polarization which are non-perturbative hadronic contributions to the running of the gauge couplings, the electromagnetic alpha_{em}(s) and the SU(2)_L coupling alpha_2(s). I will report on my recent package "alphaQED", which besides the effective fine structure constant alpha_{em}(s) also allows for a fairly precise calculation of the SU(2)_L gauge coupling alpha_2(s). I will briefly review the role, future requirements and possibilities. Applied together with the "Rhad" package by Harlander and Steinhauser, the package all…
In this paper we compute the $\mathcal{O}(α_s α_t)$ threshold corrections to the running strong coupling constant, the top-Yukawa coupling and the top-quark mass within the MSSM. These parameters present a non-decoupling behaviour with the supersymmetry scale $M_{\rm SUSY}$. Our numerical analysis shows that the mixed QCD-Yukawa corrections can amount to few GeV for the running top-quark mass and range at the percent level for the top-Yukawa coupling.
The quark gluon plasma is a novel state of matter in which quarks are no longer confined to bound states such as baryons and mesons. the freezing of quarkvgluon deconfined degrees of freedom is the essential ingredient in determining the conditions in a transition between phases that has time to develop into equilibrium. The degree of freedom in the confined hadronic matter phase and the deconfined phase, that is, the QGP, is important in the study of phase transition in the early universe. It is calculated according to the strong coupling constant. But in the present work, we try to figure ou…
The 1/k contribution to the heavy quark potential is first generated at one loop order in QCD. We compute the two loop anomalous dimension for this potential, and find that the renormalization group running is significant. The next-to-leading-log coefficient for the heavy quark production current near threshold is determined. The velocity renormalization group result includes the alpha_s^3 ln^2(alpha_s) ``non-renormalization group logarithms'' of Kniehl and Penin.
In this talk, we present an explanation for the Delta I = 1/2 rule in K-decays based on the premise of an infrared fixed point alpha_IR in the running coupling alpha_s of quantum chromodynamics (QCD) for three light quarks u,d,s. At the fixed point, the quark condensate spontaneously breaks scale and chiral SU(3)_L x SU(3)_R symmetry. Consequently, the low-lying spectrum contains nine Nambu-Goldstone bosons: pi,K,eta and a QCD dilaton sigma. We identify sigma as the f_0(500) resonance and construct a chiral-scale perturbation theory CHPT_sigma for low-energy amplitudes expanded in alpha_s abou…
We study QCD hard processes at scales of order k^2 > Lambda^2 in the limit in which the beta-function coefficient - b is taken to be small, but alphas(k) is kept fixed. The (nonperturbative) Pomeron is exponentially suppressed in this limit, making it possible to define purely perturbative high-energy Green's functions. The hard Pomeron exponent acquires diffusion and running coupling corrections which can be expanded in the b parameter and turn out to be dependent on the effective coupling b alphas^2 Y. We provide a general setup for this b-expansion and we calculate the first few terms both …
We present new results concerning the masses and the decay widths of the most interesting hybrid meson states taking as inputs the gluon mass mg and the non-perturbative QCD running coupling constant ?alpha_s(0) comming from both LQCD and SDE recent estimations.
Motivated by speculations about infrared deviations from the standard behavior of local quantum field theories, we explore the possibility that such effects might show up as an anomalous running of coupling constants. The most sensitive probes are presently given by the anomalous magnetic moments of the electron and the muon, that suggest that alpha_{em} runs 1.00047 +- 0.00018 times faster than predicted by the Standard Model. The running of alpha_{em} and alpha_s up to the weak scale is confirmed with a precision at the % level.
We perform an all-orders resummation of the QCD Adler D-function for the vector correlator, in which the portion of perturbative coefficients involving the leading power of b, the first beta-function coefficient, is resummed. To avoid a renormalization scale dependence when we match the resummation to the exactly known NLO and NNLO results, we employ the Complete Renormalization Group Improvement (CORGI) approach. These fixed-order and resummed CORGI results are analytically continued by numerically performing a contour integral to obtain corresponding fixed and all-orders ``contour-improved''…
The QCD analytic running coupling alpha_{an} which has no nonphysical singularities for all Q^2>0 is considered for the initial perturbation theory approximations up to four loop order. The finiteness of the analytic coupling at zero is shown to be a consequence of the asymptotic freedom property of the initial theory. The nonperturbative contributions to the analytic coupling are extracted explicitly. For all Q>Lambda they are represented in the form of an expansion in inverse powers of Euclidean momentum squared. The effective method for a precise calculation of the analytic running coupling…
I calculate the anomalous dimension governing the Q^2 evolution of the gluon (and structure functions) coming from the running coupling BFKL equation. This may be expressed in an exact analytic form, up to a small ultraviolet renormalon contribution, and hence the corresponding splitting function may be determined precisely. Rather surprisingly it is most efficient to expand the gluon distribution in powers of alpha_s(Q^2) rather than use the traditional expansion where all orders of alpha_s\ln(1/x) are kept on an equal footing. The anomalous dimension is very different from that obtained from…
We update our Standard Model predictions for g-2 of the muon and for the hadronic contributions to the running of the QED coupling, Delta alpha^5_had(M_Z^2). Particular emphasis is put on recent changes in the hadronic contributions from new data in the 2pi channel and from the energy region just below 2 GeV.
We revisit the determination of alpha_s(m_tau) using a fit to inclusive tau hadronic spectral moments in light of (1) the recent calculation of the fourth-order perturbative coefficient K_4 in the expansion of the Adler function, (2) new precision measurements from BABAR of e+e- annihilation cross sections, which decrease the uncertainty in the separation of vector and axial-vector spectral functions, and (3) improved results from BABAR and Belle on tau branching fractions involving kaons. We estimate that the fourth-order perturbative prediction reduces the theoretical uncertainty, introduced…
We compute the fully-differential B -> X_u l nu decay width to all orders in perturbation theory in the large-beta0 limit. Each of the five structure functions that build the hadronic tensor is expressed as a Borel integral, summing up O(CF beta0^{n-1} alpha_s^n) corrections for any n. We derive analytic expressions for the Borel transforms of both real and virtual diagrams with a single dressed gluon, and perform an all-order infrared subtraction, where the Borel parameter serves also as an infrared regulator. Expanding the result we recover the known triple-differential NLO coefficient, and …
We investigate the occurrence of power terms in the running QCD coupling by analysing non-perturbative measurements of alpha_s (p) at low momenta obtained from the lattice three-gluon vertex. Our exploratory study provides some evidence for power contributions to alpha_s (p) proportional to 1/p^2. Possible implications for physical observables are discussed.
A generalization of the leading-order DGLAP evolution at small x is performed for the non-singlet structure function by resumming the leading-order DGLAP anomalous dimension to all orders in the QCD coupling. Explicit expressions are obtained for the non-singlet structure function of the deep inelastic scattering, taking into account both the double-logarithmic and the single-logarithmic contributions, including the running alpha_s effects. It is shown that when these contributions are included, the asymptotic small-x behaviour is power-like, with an exponent of about 0.4.
Phenomenology of a double dilaton soft-wall model: Alpha strong from Ricci flow and pion Form Factors at intermediate-energy region
Universitat Autònoma de Barcelona（巴塞罗那自治大学）；Institut de Física d’Altes Energies (IFAE)（高能物理研究所）；The Barcelona Institute of Science and Technology (BIST)（巴塞罗那科学与技术研究院）
The total cross section for electron-positron annihilation into hadrons is calculated in the region just below the B meson threshold. QCD corrections up to third order, quark mass effects, initial state radiation, the running of alpha_QED and the tails of the Upsilon resonances are included in the prediction. For given alpha_s the prediction is accurate to 0.5 percent. An experimental measurement with the corresponding precision would allow to determine alpha_s with high accuracy at intermediate energies.
In line with some previous works, we study in this paper the meson spectrum in the framework of a second order quark-antiquark Bethe-Salpeter formalism which includes confinement. An analytic one loop running coupling constant alpha_s(Q), as proposed by Shirkov and Sovlovtsov, is used in the calculations. As for the quark masses, the case of a purely phenomenological running mass for the light quarks in terms of the c. m. momentum is further investigated. Alternatively a more fundamental expression m_P(Q) is introduced for light and strange quarks, combining renormalization group and analytici…
Two-loop corrections for the <VVA> correlator of the singlet axial and vector currents in QCD are calculated in the chiral limit for arbitrary momenta. Explicit calculations confirm the non-renormalization theorems derived recently by Vainshtein and Knecht et.al. We find that as in the one-loop case also at the two loops the <VVA> correlator has only 3 independent form-factors instead of 4. From the explicit results we observe that the two-loop correction to the correlator is equal to the one-loop result times the constant factor C_2(R) alpha_s/pi in the MSbar scheme. This holds for the full c…
A main feature of high-energy scattering in QCD is saturation in the number density of gluons. This phenomenon is described by non-linear evolution equations, JIMWLK and BK, which have been derived at leading logarithmic accuracy. In this paper we generalize this framework to include running coupling corrections to the evolution kernel. We develop a dispersive representation of the dressed gluon propagator in the background of Weiszacker Williams fields and use it to compute O(beta_0^{n-1} alpha_s^n) corrections to the kernel to all orders in perturbation theory. The resummed kernels present i…
We reevaluate the hadronic contribution to the running of the QED fine structure constant alpha(s) at s = M_Z^2. We use data from e+e- annihilation and tau decays at low energy and at the qq-bar thresholds, where resonances occur. Using so-called spectral moments and the Operator Product Expansion (OPE), it is shown that a reliable theoretical prediction of the hadronic production rate R(s) is available at relatively low energies. Its application improves significantly the precision on the hadronic vacuum polarization contribution. We obtain delta_alpha^had = (277.8 +/- 2.6) x 10^-4 yielding a…
We discuss phenomenological tests for the frozen infrared behavior of the running coupling constant and gluon propagators found in some solutions of Schwinger-Dyson equations of the gluonic sector of QCD. We verify that several observables can be used in order to select the different expressions of alpha_s found in the literature. We test the effect of the nonperturbative coupling in the tau-lepton decay rate into nonstrange hadrons, in the rho vector meson helicity density matrix that are produced in the chi_{c2} --> rho rho decay, in the photon to pion transition form factor, and compute the…
We present approximate non-perturbative solutions for the propagators as well as the running coupling of QCD from a coupled system of renormalised, truncated Dyson--Schwinger equations. We employ ansaetze for the dressed vertices such that the running coupling and the quark mass function are independent of the renormalisation point. Our solutions are in good agreement with the results of recent lattice calculations. We find a weakly vanishing gluon propagator at small momenta and an infrared singular ghost propagator in agreement with Zwanziger's horizon condition and the Kugo-Ojima confinemen…
We update our Standard Model predictions for g-2 of the muon and for the hadronic contributions to the running of the QED coupling, Delta alpha_had^(5)(M_Z^2). Particular emphasis is put on recent changes in the hadronic contributions from new data in the 2pi channel and from the energy region just below 2 GeV. In particular, for the e+e- -> pi+pi- contribution we include the recent `radiative return' data from KLOE and BaBar. We also include the recent BaBar data on other exclusive channels. We make a detailed study of the effect of replacing the measurements of the inclusive cross section, s…
We have reevaluated the hadronic contribution to the anomalous magnetic moment of the muon (g-2) and to the running of the QED fine structure constant alpha(s) at s=M_Z**2. We incorporated new data from hadronic tau decays, recently published by the ALEPH Collaboration. In addition, compared to previous analyses, we use more extensive e+e- annihilation data sets. The integration over the total hadronic cross section is performed using experimental data up to 40 GeV and results from perturbative QCD above 40 GeV. The improvement from tau data concerns mainly the pion form factor, where the unce…
The present knowledge on the strong coupling is briefly summarized. The most precise determinations of alpha_s, at different energies, are reviewed and compared at the Z mass scale, using the predicted QCD running. The impressive agreement achieved between experimental measurements and theoretical predictions constitutes a beautiful and very significant test of Asymptotic Freedom, establishing QCD as the fundamental theory of the strong interaction. The world average value of the strong coupling is found to be alpha_s(M_Z^2)= 0.1186 \pm 0.0007.
I explicitly calculate the anomalous dimensions and splitting functions governing the Q^2 evolution of the parton densities and structure functions which result from the running coupling BFKL equation at LO, i.e. I perform a resummation in powers of ln(1/x) and in powers of beta_0 simultaneously. This is extended as far as possible to NLO. These are expressed in an exact, perturbatively calculable analytic form, up to small power-suppressed contributions which may also be modelled to very good accuracy by analytic expressions. Infrared renormalons, while in principle present in a solution in t…
The pseudoscalar sum rules of the heavy-light quark systems are used for extracting simultaneously the c,b quark masses and the decay constants f_D_(s),f_B_(s) of the D_(s),B_(s) mesons. To order alpha_s^2, one obtains the running quark masses: m_c(m_c)=(1.10 \pm 0.04) GeV, m_b(m_b)=(4.05\pm 0.06) GeV, the perturbative pole masses: M_c=(1.46\pm 0.04) GeV, M_b=(4.69\pm 0.06) GeV, and the decay constants: f_D=(205\pm 20) MeV, f_B=(203\pm 23) MeV and f_D_s=(235\pm 24) MeV, f_B_s=(236\pm 30) MeV, in the normalization where f_π= 130.56 MeV. The fitted values of the pole and running masses satisfy q…
In the framework of the Bethe-Salpeter formalism used in previous papers to evaluate the quarkonium spectrum, here we reverse the point of view to extract an ``experimental'' running coupling alpha_s(Q^2) in the infrared (IR) region from the data. The values so obtained agree within the errors with the Shirkov-Solovtsov analytic coupling for 200 MeV <Q< 1.2 GeV, thus giving a very satisfactory unifying description of high and low energy phenomena. Below 1 GeV however alpha_s(Q^2) seems to vanish as Q to 0. The paper is based on a work in progress in collaboration with D.V.Shirkov.
We present a determination of the strong coupling constant using ATLAS inclusive jet cross section data at sqrt{s} = 7TeV, with their full information on the bin-to-bin correlations. Several procedures for combining the statistical information from the data inputs are compared. The theoretical prediction is obtained using NLO QCD with non-perturbative corrections. Our determination uses inputs with transverse momenta between 45 and 600 GeV, the running of the strong coupling being also tested in this range. Good agreement is observed when comparing our result with the world average at the Z-bo…
We present preliminary results on the computation of the QCD running coupling constant in the MOM_tilde scheme and Landau gauge with two flavours of dynamical Wilson quarks. Gluon momenta range up to about 7 GeV (beta=5.6, 5.8 and 6.0) with a constant dynamical quark mass. This range already allows to exhibit some evidence for a sizeable 1/mu^2 correction to the asymptotic behaviour, as in the quenched approximation. We find Lambda_MS^(N_f=2) = 264(27) MeV x [a^{-1}(5.6,0.1560)/(2.19 GeV)], which leads to alpha_s(M_Z) = 0.113(3)(4). In view of the systematics error to be controlled, this encou…
The (absence of detecting) lensing dispersion of Supernovae type Ia (SNIa) can be used as a novel and extremely efficient probe of cosmology. In this preliminary example we analyze its consequences for the primordial power spectrum. The main setback is the knowledge of the power spectrum in the non-linear regime, 1 Mpc^{-1} < k < 10^2-10^3 Mpc^{-1} up to redshift of about unity. By using the lensing dispersion and conservative estimates in this regime of wavenumbers, we show how the current upper bound sigma_mu(z=1) < 0.12on existing data gives strong indirect constraints on the primordial pow…
Results on the resummation of non-power-series expansions of the Adler function of a scalar, $D_S$, and a vector, $D_V$, correlator are presented within fractional analytic perturbation theory (FAPT). The first observable can be used to determine the decay width $Γ_{H\to b\bar{b}}$ of a scalar Higgs boson to a bottom-antibottom pair, while the second one is relevant for the $e^+e^-$ annihilation cross section. The obtained estimates are compared with those from fixed-order (FOPT) and contour-improved perturbation theory (CIPT), working out the differences. We prove that although FAPT and CIPT …
We perform a determination of the strong coupling constant using the latest ATLAS inclusive jet cross section data, from proton-proton collisions at sqrt{s}=7 TeV, and their full information on the bin-to-bin correlations. Several procedures for combining the statistical information from the different data inputs are studied and compared. The theoretical prediction is obtained using NLO QCD, and it also includes non-perturbative corrections. Our determination uses inputs with transverse momenta between 45 and 600 GeV, the running of the strong coupling being also tested in this range. Good agr…
We extract (for the first time) the ratio of the gluon condensate < g^3f_{abc}G^3 >/< alpha_s G^2 > expressed in terms of the liquid instanton radius rho_c from charmonium moments sum rules by examining the effects of < alpha_s G^2 > in the determinations of both rho_c and the running MS mass m_c(m_c). Using a global analysis of selected ratios of moments at different Q^2=0, 4m_c^2 and 8m_c^2 and taking < alpha_s G^2 > from 0.06 GeV^4, where the estimate of rho_c is almost independent of < alpha_s G^2 >, we deduce: rho_c=0.98(21) GeV^{-1} which corresponds to < g^3f_{abc}G^3 > = (31+- 13) GeV^…
We present a non-perturbative computation of the running of the coupling alpha_s in QCD with two flavours of dynamical fermions in the Schroedinger functional scheme. We improve our previous results by a reliable continuum extrapolation. The Lambda-parameter characterizing the high-energy running is related to the value of the coupling at low energy in the continuum limit. An estimate of Lambda*r_0 is given using large-volume data with lattice spacings a from 0.07 fm to 0.1 fm. It translates into Lambda_{MSbar}^{(2)}=245(16)(16) MeV [assuming r_0=0.5 fm]. The last step still has to be improved…
We compute the running QCD coupling on the lattice by evaluating two-point and three-point off-shell gluon Green's functions in a fixed gauge and imposing non-perturbative renormalisation conditions on them. Our exploratory study is performed in the quenched approximation at beta=6.0 on 16^4 and 24^4 lattices. We show that, for momenta in the range 1.8-2.3 Gev, our coupling runs according to the two-loop asymptotic formula, allowing a precise determination of the corresponding Lambda parameter. The role of lattice artifacts and finite-volume effects is carefully analysed and these appear to be…
The fine structure constant, alpha, is shown to be proportional to the ratio of the quanta of electric and magnetic flux of force of the electron, and provides a new representation, which is global across all unit systems. Consequently, a variation in alpha was shown to manifest due to a differential change in the fraction of the quanta of electric and magnetic flux of force, while a variation in hcross.c was shown to manifest due to the common mode change. The representation is discussed with respect to the running of the fine structure constant at high energies (small distances), and a putat…
