Mass Renormalization Constants Research Articles

Exact results for {Z}_m^{mathrm{OS}} and {Z}_2^{mathrm{OS}} with two mass scales and up to three loops

We consider the on-shell mass and wave function renormalization constants {Z}_m^{mathrm{OS}} and {Z}_2^{mathrm{OS}} up to three-loop order allowing for a second non-zero quark mass. We obtain analytic results in terms of harmonic polylogarithms and iterated integrals with the additional letters sqrt{1-{tau}^2} and sqrt{1-{tau}^2}/tau which extends the findings from ref. [1] where only numerical expressions are presented. Furthermore, we provide terms of order mathcal{O} (ϵ2) and mathcal{O} (ϵ) at two- and three-loop order which are crucial ingredients for a future four-loop calculation. Compact results for the expansions around the zero-mass, equal-mass and large-mass cases allow for a fast high-precision numerical evaluation.

High-precision four-loop mass and wave function renormalization in QED

The 4-loop QED mass and wave function renormalization constants Z2 and Zm have been evaluated in the on-shell subtraction scheme with 1100 digits of precision. We also worked out the coefficients of the five color structures of the QCD renormalization constants Z2OS and ZmOS which can be obtained from QED-like diagrams. The results agree with lower precision results available in the literature. Analytical fits were also obtained for all these quantities.

Electron contribution to the muon anomalous magnetic moment at four loops

We present results for the QED contributions to the anomalous magnetic moment of the muon containing closed electron loops. The main focus is on perturbative corrections at four-loop order where the external photon couples to the external muon. Furthermore, all four-loop contributions involving simultaneously a closed electron and tau loop are computed. In combination with our recent results on the light-by-light-type corrections (see Ref. \cite{Kurz:2015bia}) the complete four-loop electron-loop contribution to the anomalous magnetic moment of the muon has been obtained with an independent calculation. Our calculation is based on an asymptotic expansion in the ratio of the electron and the muon mass and shows the importance of higher order terms in this ratio. We perform a detailed comparison with results available in the literature and find good numerical agreement. As a by-product we present analytic results for the on-shell muon mass and wave function renormalization constants at three-loop order including massive closed electron and tau loops, which we also calculated using the method of asymptotic expansion.

Four-loop corrections with two closed fermion loops to fermion self energies and the lepton anomalous magnetic moment

We compute the eighth-order fermionic corrections involving two and three closed massless fermion loops to the anomalous magnetic moment of the muon. The required four-loop on-shell integrals are classified and explicit analytical results for the master integrals are presented. As further applications we compute the corresponding four-loop QCD corrections to the mass and wave function renormalization constants for a massive quark in the on-shell scheme.

Two loop low temperature corrections to electron self energy

We recalculate the two loop corrections in the background heat bath using real time formalism. The procedure of the integrations of loop momenta with dependence on finite temperature before the momenta without it has been followed. We determine the mass and wavefunction renormalization constants in the low temperature limit of QED, for the first time with this preferred order of integrations. The correction to electron mass and spinors in this limit is important in the early universe at the time of primordial nucleosynthesis as well as in astrophysics.

Polymer chains in confined geometries: Massive field theory approach

The massive field theory approach in fixed space dimensions d<4 is applied to investigate a dilute solution of long-flexible polymer chains in a good solvent between two parallel repulsive walls, two inert walls, and for the mixed case of one inert and one repulsive wall. The well-known correspondence between the field theoretical phi4 O(n) -vector model in the limit n-->0 and the behavior of long-flexible polymer chains in a good solvent is used to calculate the depletion interaction potential and the depletion force up to one-loop order. In order to make the theory UV finite in renormalization-group sense in 3<or=d<4 dimensions we performed the standard mass renormalization and additional surface-enhancement constants renormalization. Besides, our investigations include modification of renormalization scheme for the case of two inert walls. The obtained results confirm that the depletion interaction potential and the resulting depletion force between two repulsive walls are weaker for chains with excluded volume interaction (EVI) than for ideal chains because the EVI effectively reduces the depletion effect near the walls. Our results are in qualitative agreement with previous theoretical investigations, experimental results, and with the results of Monte Carlo simulations.

Two-loop Script O(ααs) corrections to the on-shell fermion propagator in the standard model

In this paper we consider mixed two-loop electroweak corrections to the top quark propagator in the Standard Model. In particular, we compute the on-shell renormalization constant for the mass and wave function, which constitute building blocks for many physical processes. The results are expressed in terms of master integrals. For the latter practical approximations are derived. In the case of the mass renormalization constant we find agreement with the results in the literature.

Non-perturbative renormalization constants and light quark masses

We present the results of an extensive non-perturbative calculation of the renormalization constants of bilinear quark operators for the non-perturbativelyO(a)-improved Wilson action. The results are obtained at four values of the lattice coupling, by using the RI/MOM and the Ward identities methods. A new non-perturbative renormalization technique, which is based on the study of the lattice correlation functions at short distance in x-space, is also numerically investigated. We then use our non-perturbative determination of the quark mass renormalization constants to compute the values of the strange and the average up/down quark masses. After performing an extrapolation to the continuum limit, we obtain M s MS¯(2GeV= (106 ± 2 ± 8) MeV and m l MS¯(2 GeV) = (4.4 ± 0.1 ± 0.4) MeV.

The charm quark mass to two-loop order

The truncation of the perturbative series at one loop order for the mass renormalization constants remain a significant systematic uncertainty in the determination of heavy quark masses in lattice QCD. We present here a high beta Monte Carlo calculation of the two loop mass renormalization constant for clover-improved fermions near the charm mass in the Fermilab heavy quark formalism. A preliminary value for the charm quark mass in the MS scheme at two loop order is reported.

LIGHT QUARK MASSES FROM QUENCHED LATTICE QCD SIMULATIONS WITH DOMAIN WALL QUARKS

Values for the strange quark mass and average up/down mass have been obtained from quenched lattice QCD simulations using the domain wall fermion action. This discretization preserves the properties of flavor and chiral symmetry at nonzero lattice spacing. Results are shown for two values of the lattice spacing. The mass renormalization constant is computed nonperturbatively.

Two-loop perturbative quark mass renormalization from large β Monte Carlo

We present the calculation of heavy Wilson quark mass renormalization constants from large beta Monte Carlo simulations. Simulations were performed at various beta larger than 9, each on several spatial lattice sizes to allow for an infinite volume extrapolation. We use twisted boundary conditions to suppress tunneling and work in Coulomb gauge with appropriate adjustments for the temporal links. The one-loop coefficient obtained from this method is in agreement with the analytical result and a preliminary result for the second order coefficient is reported.

Light quark masses from lattice quark propagators at large momenta

We compute non-perturbatively the average up-down and strange quark masses from the large momentum (short-distance) behaviour of the quark propagator in the Landau gauge. This method, which has never been applied so far, does not require the explicit calculation of the quark mass renormalization constant. Calculations were performed in the quenched approximation, by using O(a)-improved Wilson fermions. The main results of this study are ml^RI(2GeV)=5.8(6)MeV and ms^RI(2GeV)=136(11)MeV. Using the relations between different schemes, obtained from the available four-loop anomalous dimensions, we also find ml^RGI=7.6(8)MeV and ms^RGI=177(14)MeV, and the MSbar-masses, ml^MS(2GeV)=4.8(5)MeV and ms^MS(2GeV)=111(9)MeV.

Quark masses and renormalization constants from quark propagator and 3-point functions

We have computed the light and strange quark masses and the renormalization constants of the quark bilinear operators, by studying the large- p 2 behaviour of the lattice quark propagator and 3-point functions. The calculation is non-perturbatively improved, at O( a), in the chiral limit. The method used to compute the quark masses has never been applied so far, and it does not require an explicit determination of the quark mass renormalization constant.

Three-loop renormalization of the SU( Nc) non-abelian Thirring model

We renormalize to three loops a version of the Thirring model where the fermion fields not only lie in the fundamental representation of a non-abelian colour group SU( N c ) but also depend on the number of flavours, N f . The model is not multiplicatively renormalizable in dimensional regularization due to the generation of evanescent operators which emerge at each loop order. Their effect in the construction of the true wave function, mass and coupling constant renormalization constants is handled by considering the projection technique to a new order. Having constructed the MS renormalization group functions we consider other massless independent renormalization schemes to ensure that the renormalization is consistent with the equivalence of the non-abelian Thirring model with other models with a four-fermi interaction. One feature to emerge from the computation is the establishment of the fact that the SU( N f ) Gross–Neveu model is not multiplicatively renormalizable in dimensional regularization. An evanescent operator arises first at three loops and we determine its associated renormalization constant explicitly.

One-loop-dimensional reduction of the linear σ model

We perform the dimensional reduction of the linear σ model at one-loop level. The effective potential of the reduced theory obtained from the integration over the nonzero Matsubara frequencies is exhibited. Thermal mass and coupling constant renormalization constants are given, as well as the thermal renormalization group equation which controls the dependence of the counterterms on the temperature. We also recover, for the reduced theory, the vacuum unstability of the model for large N.

On the evaluation of universal non-perturbative constants in O( N) σ models

We investigate the relation between on-shell and zero-momentum non-perturbative quantities entering the parametrization of the two-point Green function of two-dimensional non-linear O( N) σ models. We present accurate estimates of ratios of mass scales and renormalization constants, obtained by an analysis of the strong-coupling expansion of the two-point Green function. These ratios allow to connect the exact on-shell results of Hasenfratz et al. [Phys. Lett. B 245 (1990) 522], Hasenfratz and Niedermayer [Phys. Lett. B 245 (1990) 529] and Balog and Niedermaier [hep-th/9612039] with typical zero-momentum lattice evaluations. Our results are supported by the 1/ N-expansion.

Renormalization of N = 2, 4 Yang-Mills theories with soft breaking of an extended supersymmetry by N = 1 mass term

Abstract N = 2, 4 Yang-Mills theories with soft breaking of an extended supersymmetry by mass terms are considered. It is proved that for N = 4 there are no ultraviolet divergences in the mass renormalization constants to all orders of perturbation theory. For N = 2 our two-loop calculations show that the charge and mass renormalization constants contain only one-loop divergences and are the same in this order. It is shown by direct calculation that mass terms can acquire finite quantum corrections starting from the two-loop approximation. The renormalization scheme dependence of N = 4 renormalization group functions is investigated. We have found that unlike renormalization schemes with minimal subtractions of divergences other renormalization schemes give a nonzero β-function. At nonzero masses the β-function in MOM schemes is not zero even at the one-loop level. In the massless case β ≠0 beginning from the two-loop approximation.

Quartic mass matrix and renormalization constants in supersymmetric Yang-Mills theories

We derive the general formula for the supertrace of the quartic mass matrix in a general supersymmetric gauge theory, with arbitrary representations for the chiral multiplets. This formula clarifies the non-renormalization theorems in presence of gauge interactions and gives “extended renormalization theorems” for N = 2 and N = 4 supersymmetric Yang-Mills theories. In particular we find the known result that g ren = g bare for the N = 4 theory and the new result m ren = m bare for the N = 2 gauge interactions of massive hypermultiplets. We give arguments to the extent that the latter non-renormalization theorem persists to all orders in perturbation theory.

U and V sectors in the Bronzan-Lee model

The Lehmann-Symanzik-Zimmermann (LSZ) formalism is used in the Bronzan-Lee model to investigate the scattering processes in the lowest sectors. In this model, there are three heavy recoilless particles U, V, and N interacting with a θ particle. The processes allowed are U⇄Vθ and V⇄Nθ. In U and V sectors of this model all τ functions have been calculated, and relevant scattering and production amplitudes are evaluated. The mass, wavefunction, and vertex function renormalization constants have been found and they agree with the results previously obtained by Bronzan and later also by Liossatos.

Effect of localized spin fluctuations on the properties of dilute Al-Mn alloys

The theory of localized spin fluctuations (LSF) in dilute nearly-magnetic alloys (e.g. AlMn) due to Hargitai and Corradi is extended to include the renormalization of the spin fluctuation lifetime capital Gamma-1s. In this way the mass renormalization constant, Z1, of the localized electronic states on the impurity site and the inverse LSF lifetime capital Gammas can be related to the fundamental parameters of the Anderson model, viz. the width capital Gamma of the localized electronic states and the Coulomb repulsion U between localized electrons of opposite spin. A numerical calculation shows that Z1 and capital Gammas show no instability at the Hartree-Fock criterion for the formation of a magnetic moment (U/πcapital Gamma = 1). Expressions for the thermodynamic, magnetic and transport properties of such alloys can be written in terms of capital Gammas, Z1, U and capital Gamma. Reasonable numerical values for capital Gammas, Z1, U and capital Gamma are then obtained from experimental data for dilute AlMn alloys.