共查询到20条相似文献,搜索用时 31 毫秒
1.
The paper is devoted to the calculation of renormalization-group (RG) functions in the O(n)-symmetry two-dimensional model of the λ? 4 type in the five-loop approximation and to an analysis of the critical behavior of systems described by this model. Five-loop expansions for the β function and the critical indices are determined in bulk theory. They are summed up using the Padé-Borel and Padé-Borel-Le Roy methods, making it possible to optimize the summation procedure and to estimate the accuracy of the obtained numerical values. It is shown that in the Ising (n=1) case, as well as in other cases, the inclusion of the five-loop contribution to the β function displaces the coordinate of the Wilson fixed point only insignificantly, leaving it outside the interval formed by the results of computations on lattices; even “spreads” of the error in the renormalization group and lattice estimates do not overlap. This discrepancy is attributed to the effect of the nonanalytic com-ponent of the β function, which cannot be determined in perturbation theory. A computation of critical indices proves that, although the inclusion of the five-loop terms in the corresponding RG expansion slightly improves the concordance with the exact results, the nonanalytic contributions are apparently also significant in this case. 相似文献
2.
A procedure for calculating critical exponents directly at finite ? is proposed. It relies on the invariance of the critical exponents at the critical coupling gc of the full theory with respect to finite changes in the renormalization point. This is expressed as the coincidence of curves at the point β = 0 in the plane of β versus a critical exponent parametrically described by the renormalized coupling for various values of the renormalization point (the “twisted fan”). If more than one critical exponent is present the fan is a set of curves in a multidimensional space with the twist at β = 0 and the exact values of the critical exponents. In perturbative approximations, an approximate invariance may result whether or not a zero of β exists to that order. We show that in the one and two loop approximations to the Reggeon calculus this approximate invariance does occur. The values of the critical exponents at the approximate twists show remarkable stability properties. We obtain σtot ≈ (lns)?γ where ?γ ≈ 0.11 and 0.17 for one and two loops respectively. 相似文献
3.
By associating the triple-pomeron coupling gp(t) with the renormalization of the pomeron propagator and requiring the latter to correctly reproduce a dual fo trajectory, as well as the magnitude and width of the ππ diffraction peak, we obtain gp(0) ≈ 1 GeV−1. 相似文献
4.
Statistics of fluctuations in a spatially distributed system describing the interaction of nonequilibrium phase transitions is studied. It is shown that for a certain value of the intensity of external white noise acting on phase transitions, the time and spatial spectra of fluctuations exhibit power dependences S(f) ~ f ?α and S(k) ~ k ?γ. The dependence of exponents α and γ on the diffusion coefficient determining the spatial interaction of fluctuations is determined. Extremal low-frequency fluctuations are singled out and the distribution functions of their duration (P(τ) ~ τ?β) and size (P(s) ~ s?ν)) are constructed. It is found that exponent α in the time spectral dependence and exponent β in the duration of fluctuations are connected via the relation α + β = 2. Exponents γ and ν in the spatial spectral dependence and in the size distribution function are connected via an analogous relation (γ + ν = 2). 相似文献
5.
A consistent field theoretic computation of the first-order correction to the total decay of a non-relativistic heavy quarkonium state must consider contributions from the annihilation amplitude, with a typical scale of the order of the quark mass m, and from the bound-state wave function, where the typical scale is of the order of the Bohr momentum αsm. Therefore, not only the latter smaller scale is the one to be taken for the total decay rate, but also a quite specific renormalization, the “bound-state renormalization scheme”, must be used for a computation of the total inclusive decay rate of 0?+→hadrons. Due to important cancellations between large individual contributions, the net result turns out to be small, encouraging the use of pure perturbative QCD in such systems. 相似文献
6.
Lee Smolin 《Nuclear Physics B》1982,208(3):439-466
Using the 1/N expansion a fixed point of the renormalization group is found for quantized gravitational theories which is non-trivial in all dimensions, d, including four. Using the fixed point it is shown how Einstein's theory can be renormalized for 3<d<4. In four dimensions the pure Einstein theory does not exist, but the R + Cμναβ2 theory does. It is shown how gravitational theories whose quantum lagrangians are scale invariant may be renormalized such that the scale invariance is broken only by the choice of the critical renormalization group trajectory. A comparison is made with the renormalization of four-fermion and Yukawa theories in 4?? dimensions which suggests that quantum gravity might exist in four dimensions even if those theories do not. 相似文献
7.
《Nuclear Physics B》1995,445(1):81-105
We propose a non-perturbative method for computing the renormalization constants of generic composite operators. This method is intended to reduce some systematic errors, which are present when one tries to obtain physical predictions from the matrix elements of lattice operators. We also present the results of a calculation of the renormalization constants of several two-fermion operators, obtained, with our method, by numerical simulation of QCD, on a 163 x 32 lattice, at β = 6.0. The results of this simulation are encouraging, and further applications to four-fermion operators and to the heavy quark effective theory are proposed. 相似文献
8.
F. Jegerlehner 《Zeitschrift fur Physik C Particles and Fields》1986,32(2):195-207
Usinge + e ?-data, an updated analysis of hadronic contributions to electroweak parameter renormalizations is presented. We emphasize the estimate of uncertainties which is important for precision tests at LEP and SLC. ForM z =93 GeV and sin2 Θ 0=0.22 hadronic contributions from 5 flavors are found to be $$\Delta r_{had}^{(5)} = 0.0326 \pm 0.0007(\Delta r_{QED,had}^{(5)} = 0.0286 \pm 0.0007)$$ and $$\Delta g_{had}^{(5)} = 0.0602 \pm 0.0016(\Delta g_{3\gamma ,had}^{(5)} = 0.0619 \pm 0.0016)$$ for the renormalization of α and α g =α/sin2 Θ 0, respectively. Parameter shifts are calculated and uncertainties due to higher order effects are estimated. 相似文献
9.
A. G. Aleksejevs S. G. Barkanova A. N. Ilyichev Yu. G. Kolomensky V. A. Zykunov 《Physics of Particles and Nuclei》2013,44(2):161-174
Using two different approaches, we perform detailed calculations of the one-loop (Next-to-Leading Order (NLO)) electroweak radiative corrections to the parity violating e ? e ? → e ? e ?(γ) scattering asymmetry. First approach, more classical, relies on calculations “by hand” with reasonable approximations, second approach relies on program packages FeynArts, FormCalc, LoopTools, and FORM. The detailed numerical analysis of the various contributions is provided for a wide range of energies relevant for the ultraprecise 11 GeV MOLLER experiment planned at the JLab, as well as future experiments at the International Linear Collider (ILC). The numerical results obtained within the on-shell renormalization scheme using two different sets of renormalization conditions are in excellent agreement. We also calculate the total NLO correction in the Constrained Differential Renormalization (CDR) scheme. Analysis of the results, along with the increasing experimental precision, shows that it is feasible that the corrections at the Next-to-Next-to-Leading Order (NNLO) level may be important for the next generation of experiments. 相似文献
10.
K. Ishikawa A. Sato G. Schierholz M. Teper 《Zeitschrift fur Physik C Particles and Fields》1983,21(1):167-188
We calculate the glueball mass spectrum in theSU (3) lattice regularized gauge theory. We find fourlight glueballs: the 0++, 2++, 0?+ and, most interestingly from the experimental point of view, the oddball 1?+. We calculate the 0++ and 2++ masses over a range of β values and find thatboth states conform to continuum renormalization group behaviour to a very significant degree. The question of metastable states and temperature is addressed in detail. Finally we discuss and resolve contrary claims in the recent literature. 相似文献
11.
The strong coupling limit of the gφ4 theory in the framework of the path integral formalism. An expansion of the Green's functions in negative powers of the coupling constant is obtained; at each order the dependence on the external momenta is of polynomial type. A renormalization procedure is proposed; the asymptotic behaviour of the Callan-Symanzik β function is studied and the existence of a stable ultraviolet fixed point is established. 相似文献
12.
《Nuclear Physics A》1998,641(4):461-475
We present a computationally reliable and accurate method for solving the Gribov-Lipatov-Altarelli-Parisi equations at next to leading order, both in the non-singlet and in the singlet case. It requires solving numerically the renormalization group equations for the anomalous dimensions of composite operators in the complex plane, and finally performing an inverse Mellin transformation. In this way the group property of renormalization is exactly preserved, i.e. performing two successive scale transformations coincides exactly with a direct one making parton distributions independent of the integration path used to connect two different scales. This is relevant when large scale differences are involved and makes upward or downward evolution fully equivalent. Thus, it becomes possible to evolve the known parton distributions and leading twist contributions to the structure functions from Q2 = mb2 to the lowest possible scale imposed by positivity and unitarity. 相似文献
13.
Takeshi Fukuyama 《Zeitschrift fur Physik C Particles and Fields》1981,10(1):9-15
General relativity is formulated in the framework of Yang-Mills theory whose gauge group isO(3, 2). This theory allows the global topological charge of spin without breaking Bianchi identity. β function in the renormalization group equation is negative and the confinement of gravity is expected. The confinement radius is, however, actually infinite and we can read off the relation that the average mass density of the present universe is exactly equal to the critical value ρ c (t)=6H 2(t)/K 2. 相似文献
14.
The existence of a metric, which enables the renormalisation group β functions of a multicomponent field theory to be written as a gradient, has very important implications for the asymptotic behavior of the renormalisation group equations. It is shown that a very simple metric exists in a field theory with n-component Bose fields and arbitrary φ4 interaction, when the β functions are calculated perturbatively up to and including the 2-loop diagrams. This same metric is shown to work for all irreducible diagrams, but it must and can be modified to accommodate reducible 3-loop contributions. The prospects and outlook of this aspect of the renormalisation group are discussed. 相似文献
15.
In this work, we made five samples of SrAl2O4: Eu2+, Dy3+, the α phase and β phase SrAl2O4:Eu2+,Dy3+ powder and pellet samples, and α phase single crystal. We have measured the emission spectra of all the samples. All the emission peaks are around 520 nm, which correspond to the transition from 4f65d1(2Eg) to 4f7(8S7/2) of Eu2+ in SrAl2O4 host. The intensity of emission of the β phase is stronger than that of the α phase. We believe that it is because the Eu2+ ions have occupied the two types of sites in the α phase SrAl2O4 host and the lifetime of the transition of Eu2+ in the A site is longer than that in the B site. This result also proves that the β phase of the material is brighter than the α phase. In addition, the β phase can be achieved by quenching technique. 相似文献
16.
A. I. Feoktistov A. A. Val’chuk V. T. Kupryashkin L. P. Sidorenko I. P. Shapovalova 《Bulletin of the Russian Academy of Sciences: Physics》2008,72(2):262-265
The yields of near-zero (e0) electrons from the surface of targets with different Z under their bombardment by α particles from 226Ra decay were measured by the method of eα coincidences. The ratios of the e0-electron yields for α particles with different energies E α are described well by the dependence Y e (E α) ~ υ α ?1 , where υ α is the α-particle velocity. The e0-electron yield from the surface of thin films under their bombardment by β particles from radioactive sources with 152Eu, 154Eu, and 226Ra has been investigated by the method of eγ coincidences. It is established that ionization rate of target atoms in this case is inversely proportional to the velocity of incident β particles (υ β ?1 ), i.e., is proportional to the time of atomic electron perturbation induced by a β particle passing near an atom. 相似文献
17.
R. Flume 《Nuclear Physics B》1983,217(2):531-543
It is assumed that N = 1 supersymmetric Yang-Mills fields coupled to chiral matter fields can be renormalized in a covariant Wess-Zumino gauge with a minimal number of subtractions so that the Ward identities of supersymmetry, ordinary gauge invariance and matter-field-flavour symmetries are satisfied. The chiral Yukawa couplings are supposed to remain unrenormalized. I show that on the basis of these assumptions an N = 4 extended manifestly O(4) invariant theory can be constructed with finite Yukawa and φ4 couplings. A consequence of these non-renormalizations is the vanishing of the renormalization group β function. 相似文献
18.
A method, independently proposed by Kaiser and by us, to study the strong coupling limit of the Green functions is described and discussed. Although its quantum mechanical version exhibits unusual features, an application to the anharmonic oscillator indicates that the method is able to reproduce correctly known numerical results. In spite of difficulties in the setting up of a renormalization program for the theory, a preliminary study of the CS β function for the gφ4 interaction shows that is asymptotically linear in the renormalization coupling constant. Evidence is given for the compatibility of this behaviour with the information that can be drawn from the known perturbative expansion. 相似文献
19.
20.
Pseudopotential calculations have been carried out for the α, β and γ polytypic forms of the layer semiconductor ZnIn2S4, respectively, corresponding to space groups C53v, C13v and D33d. The required form factors are consistent with those used in our previous calculations for ZnS and CdIn2S4. The band structure of the α phase, the only one up to now for which optical data are available, compares quite satisfyingly with very recent photoemission and reflectivity experimental data. The computed band structures of the β and γ phases are very alike; on the contrary, interesting differences exist between these structures and the α phase which could easily be verified by experimental investigations. 相似文献