arXiv subjects
Publications and source records attributed to J. Micheli.
We show that QCD Green functions in Landau Gauge exhibit sizable $O(1/μ^2)$ corrections to the expected perturbative behavior at energies as high as 10 GeV. We argue that these are due to a $ $-condensate which does not vanish in Landau gauge.
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 encouraging result is more a preliminary indication than a real prediction.
We present the first attempt of a new method to compute the pion light-cone wave function (LCWF) on the lattice. We compute the matrix element between the pion and the vacuum of a non-local operator: the propagator of a ``scalar quark'' (named for short "squark"). A theoretical analysis shows that for some kinematical conditions (energetic pion and hard squark) this matrix element depends dominantly on the LCWF $Φ_π(u), u\in [0,1]$. On the lattice, the discretization of the parton momenta imposes further constraints on the pion momentum. The two-point Green functions made of squark-quark and squark-squark fields show hadron-like bound-state behaviour and verify the standard energy spectrum. We show some indications that during a short time, after being created, the system of the spectator quark and the squark behave like partons, before they form a hadron-like bound state. This short time is the place where the partonic wave function has to be looked for.
We study the flavorless gluon propagator in the Landau gauge from high statistics lattice calculations. Hypercubic artifacts are efficiently eliminated by taking the $\sum p_μ^4 \to 0$ limit. The propagator is fitted to the three-loops perturbative formula in an energy window ranging form $\sim$ 2.5 GeV up to $\sim$ 5.5 GeV. $α_s$ is extracted from the best fit in a continuous set of renormalisation schemes. The fits are very good, with a $χ^2$ per d.o.f smaller than 1. We propose a more stringent test of asymptotic scaling based on scheme independence of the resulting $Λ_{\bar MS}$. This method shows that asymptotic scaling at three loops is not reached by the gluon propagator although we use rather large energies. We are only able to obtain an effective flavorless three-loops estimate $Λ_{\bar MS}^{(3)}= 353 \pm 2 ^{+25}_{-10} $ MeV. We argue that the real asymptotic value for $Λ_{\bar MS}$ should plausibly be smaller.
Using the operator product expansion we show that the $O(1/p^2)$ correction to the perturbative expressions for the gluon propagator and the strong coupling constant resulting from lattice simulations in the Landau gauge are due to a non-vanishing vacuum expectation value of the operator $A^μA_μ$. This is done using the recently published Wilson coefficients of the identity operator computed to third order, and the subdominant Wilson coefficient computed in this paper to the leading logarithm. As a test of the applicability of OPE we compare the $ $ estimated from the gluon propagator and the one from the coupling constant in the flavourless case. Both agree within the statistical uncertainty: $\sqrt{< A^μA_μ>} \simeq 1.64(15)$ GeV. Simultaneously we fit $\Lams = $ 233(28) MeV in perfect agreement with previous lattice estimates. When the leading coefficients are only expanded to two loops, the two estimates of the condensate differ drastically. As a consequence we insist that OPE can be applied in predicting physical quantities only if the Wilson coefficients are computed to a high enough perturbative order.
We perform an OPE analysis of the flavorless non-perturbative gluon propagator and the symmetric three-gluon vertex in the Landau gauge. The first subdominant operator is $A_μA^μ$ which can condensate in the Landau gauge ``vacuum'' although being a non-gauge invariant operator. We neglect all higher dimension operators. Then the gluon propagator and the symmetric three gluon vertex only depend on one common unknown condensate. We propose a consistency check from lattice data. At two loops for the leading coefficient and with $1/p^2$ corrections at tree-level order the two fitted values for the condensate do not agree. At three loops we argue that the today unknown $β_2^{\rm MOM}$ should be equal to $1.5(3)\times β_2^{\widetilde{\rm MOM}}=7400(1500)$ to fulfill the OPE relation. Inclusion of the power corrections' anomalous dimensions should improve further the agreement. We show that these techniques cannot be applied to the asymmetric three gluon vertex with one vanishing momentum.
By using suitable Ward identities, we show that it is possible to compute K0-K0bar mixing without subtracting the terms generated by explicit chiral symmetry breaking present in Wilson-like lattice actions. The accuracy in the determination of the amplitudes is of O(a), which is the best one attainable in the absence of improvement.
We report on very strong evidence of the occurrence of power terms in $\as(p)$, the QCD running coupling constant in the $\widetilde{MOM}$ scheme, by analyzing non-perturbative measurements from the lattice three-gluon vertex between 2.0 and 10.0 GeV at zero flavor. While putting forward the caveat that this definition of the coupling is a gauge dependent one, the general relevance of such an occurrence is discussed. We fit $Λ_{\bar{\rm MS}}^{(n_f=0)}= 237 \pm 3 ^{+ 0}_{-10}$ MeV in perfect agreement with the result obtained by the ALPHA group with a totally different method. The power correction to $\as(p)$ is fitted to $(0.63\pm 0.03 ^{+ 0.0}_{- 0.13}) {\rm GeV}^2/p^2$.
We pursue the study of the high energy behaviour of the gluon propagator on the lattice in the Landau gauge in the flavorless case (n_f=0). It was shown in a precedin g paper that the gluon propagator did not reach three-loop asymptotic scaling at an energy scale as high as 5 GeV. Our present high statistics analysis includes also a simulation at $β=6.8$ ($a\simeq 0.03$ fm), which allows to reach $μ\simeq 10$ GeV. Special care has been devoted to the finite lattice-spacing artifacts as well as to the finite volume effects, the latter being acute at $β=6.8$ where the volume is bounded by technical limits. Our main conclusion is a strong evidence that the gluon propagator has reached three-loop asymptotic scaling, at $μ$ ranging from 5.6 GeV to 9.5 GeV. We buttress up this conclusion on several demanding criteria of asymptoticity, including scheme independence. Our fit in the 5.6 GeV to 9.5 GeV window yields $Λ^{\bar{\rm MS}} = 319 \pm 14 ^{+10}_{-20}$ MeV, in good agreement with our previous result, $Λ^{\bar{\rm MS}} = 295 \pm 20 $ MeV, obtained from the three gluon vertex, but it is significantly above the Schrödinger functional method estimate : $238 \pm 19$ MeV. The latter difference is not understood. Confirming our previous paper, we show that a fourth loop is necessary to fit the whole ($2.8 ÷9.5$) GeV energy window.
We study the UV-scaling of the flavorless gluon propagator in the Landau gauge in an energy window up to 9 GeV. Dominant hypercubic lattice artifacts are eliminated. A large set of renormalization schemes is used to test asymptotic scaling. We compare with our results obtained directly from the triple gluon vertex. We end-up with Λ_{\bar{\rm{MS}}} = 318(12)(5) MeV and 292(5)(15) MeV respectively for these two methods, compatible which each other but significantly above the Schrodinger method estimate.
We determine the three-loop coefficient of the beta function in the asymmetric momentum subtraction scheme in Landau gauge. This scheme is convenient for lattice studies of α_s, the running coupling constant of QCD. We present high statistics lattice results for α_s in the SU(3) Yang-Mills theory without quark, compare with the three-loop running and extract the value of the corresponding Λ_\msbar parameter. We estimate the systematic error coming from four-loop terms. We obtain the result: Λ_\msbar = 295 (5) (15) {a^{-1}(β=6.0) \over 1.97 GeV} MeV.
We compute the flavorless running coupling constant of QCD from the three gluon vertex in the (regularisation independent) momentum subtraction renormalisation scheme. This is performed on the lattice with high statistics. The expected color dependence of the Green functions is verified. There are significant $O(a^2μ^2)$ effects which can be consistently controlled. Scaling is demonstrated when the renormalisation scale is varied between 2.1 GeV and 3.85 GeV. Scaling when the lattice spacing is varied is very well satisfied. The resulting flavorless conventional two loop $Λ^{(c)}_{\bar{MS}}$ is estimated to be, respectively for the MOM and $\widetilde{MOM}$ scheme, 361(6) MeV and 345(6) MeV, while the three loop results are, depending on $β_2: Λ^{(3)}_{\bar{MS}} = (412 - 59 \frac{β_2} {β_{2, \bar{MS}}} \pm 6 MeV) $ and $Λ^{(3)}_{\bar{MS}} = (382- 46\frac{β_2} {β_{2, \bar{MS}}}\pm 5 MeV) $. A preliminary computation of $β_2$ in the $\widetilde{MOM}$ scheme leads to $Λ^{(3)}_{\bar{MS}} = 303(5)\frac {a^{-1}(β=6.0)} {1.97 GeV}$ MeV.
The $B$-meson decay constant can be measured on the lattice using a $1/m_b$ expansion. To relate the physical quantity to Monte Carlo data one has to know the renormalization coefficient, $Z$, between the lattice operators and their continuum counterparts. We come back to this computation to resolve discrepancies found in previous calculations. We define and discuss in detail the renormalization procedure that allows the (perturbative) computation of $Z$. Comparing the one-loop calculations in the effective Lagrangian approach with the direct two-loop calculation of the two-point $B$-meson correlator in the limit of large $b$-quark mass, we prove that the two schemes give consistent results to order $α_s$. We show that there is, however, a renormalization prescription ambiguity that can have sizeable numerical consequences. This ambiguity can be resolved in the framework of an $O(a)$ improved calculation, and we describe the correct prescription in that case. Finally we give the numerical values of $Z$ that correspond to the different types of lattice approximations discussed in the paper.