Wave Function Renormalization Research Articles

Low-energy limit of the O(4) quark-meson model from the functional renormalization group approach

We compute the low-energy limit of the $O(4)$-symmetric quark-meson model as an effective field theory for Quantum Chromodynamics within the Functional Renormalization Group (FRG) approach. In particular, we analyze the renormalization group flow of momentum-dependent pion self-interactions beyond the local potential approximation. The numerical results for these couplings obtained from the FRG are confronted with a recent tree-level study. Additionally, their effect on the wave-function renormalization and the curvature masses is investigated.

Nonperturbative evaluation for anomalous dimension in 2-dimensional O(3) sigma model

We calculate the wave-function renormalization in 2-dimensional O(3) sigma model, non- perturbatively. It is evaluated in a box with a finite spatial extent. We determine the anomalous dimension in the finite volume scheme through an analysis of the step scaling function. Results are compared with a perturbative evaluation, and the reasonable behavior is confirmed.

Description of the thermodynamic properties of BiH5 and BiH6 superconductors beyond the mean-field approximation

The ab initio calculations suggest (Y. Ma et al.), that the high-pressure (p = 200 GPa) superconducting state in BiH5 and BiH6 compounds characterizes with a high value of the critical temperature (TC ∼ 100 K). Due to the large value of the electron-phonon coupling constant (λ ∼ 1.2), the thermodynamic parameters of the superconducting phase in BiH5 and BiH6 have been determined beyond the mean-field approximation - in the framework of the Eliashberg equations formalism. We have calculated the dependence of the order parameter (Δ) and the wave function renormalization factor on the temperature. Then we have estimated the free energy difference between the superconducting state and the normal state, the thermodynamic critical field (HC) and the specific heat of the superconducting state (CS) and the normal state (CN). The values of the dimensionless ratios RΔ=2Δ0/kBTC, RC=ΔCTC/CNTC and RH=TCCNTC/HC20 are equal RΔBiH5=4.17 and RΔBiH6=4.20, RCBiH5=2.54 and RCBiH6=2.58, RHBiH5=0.146 and RHBiH6=0.146 respectively.

Meson properties and phase diagrams in a SU(3) nonlocal PNJL model with lattice-QCD-inspired form factors

We study the features of a nonlocal SU(3) Polyakov-Nambu-Jona-Lasinio model that includes wave function renormalization. Model parameters are determined from vacuum phenomenology considering lattice QCD-inspired nonlocal form factors. Within this framework we analyze the properties of light scalar and pseudoscalar mesons at finite temperature and chemical potential determining characteristics of deconfinement and chiral restoration transitions.

Anatomy of the ρ resonance from lattice QCD at the physical point**Supported in part by the U.S. DOE Grant No. DE-SC0013065, the National Nature Science Foundation of China (NSFC) (11335001, 11575196, 11575197, 11621131001) (CRC110 by DFG and NSFC), A. A. is supported in part by the National Science Foundation CAREER (PHY-1151648) and by U.S. DOE (DE-FG02-95ER40907), Y. C. thanks the

We propose a strategy to access the component of the ρ resonance in lattice QCD. Through a mixed action formalism (overlap valence on domain wall sea), the energy of the component is derived at different valence quark masses, and shows a linear dependence on . The slope is determined to be , from which the valence sigma term is extracted to be MeV using the Feynman-Hellman theorem. At the physical pion mass, the mass of the component is interpolated to be , which is close to the ρ resonance mass. We also obtain the leptonic decay constant of the component to be , which can be compared with the experimental value through the relation , with being the on-shell wavefunction renormalization of ρ owing to the interaction. We emphasize that and of the component, which are obtained for the first time from QCD, can be taken as the input parameters of ρ in effective field theory studies where ρ acts as a fundamental degree of freedom.

Four-loop wave function renormalization in QCD and QED

We compute the on-shell wave function renormalization constant to four-loop order in QCD and present numerical results for all coefficients of the SU$(N_c)$ colour factors. We extract the four-loop HQET anomalous dimension of the heavy quark field and also discuss the application of our result to QED.

Functional renormalization group approach to interacting three-dimensional Weyl semimetals

We investigate the effect of long-range Coulomb interaction on the quasiparticle properties and the dielectric function of clean three-dimensional Weyl semimetals at zero temperature using a functional renormalization group (FRG) approach. The Coulomb interaction is represented via a bosonic Hubbard-Stratonovich field which couples to the fermionic density. We derive truncated FRG flow equations for the fermionic and bosonic self-energies and for the three-legged vertices with two fermionic and one bosonic external legs. We consider two different cutoff schemes --- cutoff in fermionic or bosonic propagators --- in order to calculate the renormalized quasiparticle velocity and the dielectric function for an arbitrary number of Weyl nodes and the interaction strength. If we approximate the dielectric function by its static limit, our results for the velocity and the dielectric function are in good agreement with that of A. A. Abrikosov and S. D. Beneslavski{\u{i}} [Sov. Phys. JETP \textbf{32}, 699 (1971)] exhibiting slowly varying logarithmic momentum dependence for small momenta. We extend their result for an arbitrary number of Weyl nodes and finite frequency by evaluating the renormalized velocity in the presence of dynamic screening and calculate the wave function renormalization.

Asymptotic freedom and the thermal Lee model

Dimensional regularization is used to investigate the renormalization of the fermion mass, wave function, and coupling constant in the V-sector of a thermal Lee model in arbitrary space–time dimensions D and temperature T. A closed expression of the fermion mass renormalization shows that it diverges at the high-T limit and replicates a familiar form at the zero-T limit. Corresponding expressions of the wave function renormalization and the renormalized coupling constant vanish at the high-T limit, and resume respective customary forms at the zero-T limit. Likewise, the intrinsic scattering amplitude vanishes at the high-T limit, and reduces to the original amplitude at the zero-T limit. The 1D theory is especially useful for schematically graphing expressions that show thermal effects on the probability, the bare coupling constant, and the bare mass. Bifurcation of the bare parameters is a prominent feature in these graphs for particular choice of input. The β and γ coefficients of the Callan–Symanzik equation are calculated in closed form, and correlations between the β coefficient and the probability are in evidence for dimensions less than, or greater than 4. Schematic graphs incorporating Laurent expansions of the β coefficient, the probability, and the fermion-mass show the dependency of these functions upon the physical parameters in the theory for specific values of D. The thermal model is found to be asymptotically free for D < 4, and for odd D ≥ 5 at the high-T limit.

RG-improvement of the effective action with multiple mass scales

Improving the effective action by the renormalization group (RG) with several mass scales is an important problem in quantum field theories. A method based on the decoupling theorem was proposed in [1] and systematically improved [2] to take threshold effects into account. In this paper, we apply the method to the Higgs-Yukawa model, including wave-function renormalizations, and to a model with two real scalar fields (φ, h). In the Higgs-Yukawa model, even at one-loop level, Feynman diagrams contain propagators with different mass scales and decoupling scales must be chosen appropriately to absorb threshold corrections. On the other hand, in the two-scalar model, the mass matrix of the scalar fields is a function of their field values (φ, h) and the resultant running couplings obey different RGEs on a different point of the field space. By solving the RGEs, we can obtain the RG improved effective action in the whole region of the scalar fields.

One-loop quantum gravitational corrections to the scalar two-point function at fixed geodesic distance

We study a proposal for gauge-invariant correlation functions in perturbative quantum gravity, which are obtained by fixing the geodesic distance between points in the fluctuating geometry. These correlation functions are non-local and strongly divergent, and we show how to renormalise them by performing a ‘wave function renormalisation’ of the geodesic embedding coordinates. The result is finite and gauge-independent, but displays unusual features such as double logarithms at one-loop order.

Photon splitting in strongly magnetized medium with taking into account positronium influence

The process of the photon splitting, γ → γγ, is investigated in strongly magnetized vacuum with taking into account positronium influence. The dispersion properties of photons and the new polarization selection rules are obtained. The absorption rate of the leading photon splitting channels are calculated with taking account of the photon dispersion and wave function renormalization.

Renormalization group flows and fixed points for a scalar field in curved space with nonminimal F(ϕ)R coupling

Using covariant methods, we construct and explore the Wetterich equation for a non-minimal coupling $F(\phi)R$ of a quantized scalar field to the Ricci scalar of a prescribed curved space. This includes the often considered non-minimal coupling $\xi \phi^2 R$ as a special case. We consider the truncations without and with scale- and field-dependent wave function renormalization in dimensions between four and two. Thereby the main emphasis is on analytic and numerical solutions of the fixed point equations and the behavior in the vicinity of the corresponding fixed points. We determine the non-minimal coupling in the symmetric and spontaneously broken phases with vanishing and non-vanishing average fields, respectively. Using functional perturbative renormalization group methods, we discuss the leading universal contributions to the RG flow below the upper critical dimension $d=4$.

K +–nucleus elastic scattering revisited from the perspective of partial restoration of chiral symmetry

The $K^{+}$ meson properties in the nuclear medium are investigated by considering the wavefunction renormalization as a first step to reveal the in-medium properties of the $K^{+}$ meson in the context of partial restoration of chiral symmetry. The $K^{+}N$ elastic scattering amplitude is constructed using chiral perturbation theory up to the next-to-leading order. Using the constructed amplitude, we calculate the wavefunction renormalization in the Thomas-Fermi approximation. We obtained a good description of the $K^{+}N$ elastic scattering amplitude. The obtained wavefunction renormalization factor suggests the 2 to 6% enhancement of the $K^{+}N$ interaction at the saturation density. We conclude that the wavefunction renormalization could be one of the important medium effects for the $K^{+}$ meson.

Five-loop renormalisation of QCD in covariant gauges

We present the complete set of vertex, wave function and charge renormalisation constants in QCD in a general simple gauge group and with the complete dependence on the covariant gauge parameter ξ in the minimal subtraction scheme of conventional dimensional regularisation. Our results confirm all already known results, which were obtained in the Feynman gauge, and allow the extraction of other useful gauges such as the Landau gauge. We use these results to extract the Landau gauge five-loop anomalous dimensions of the composite operator A2 as well as the Landau gauge scheme independent gluon, ghost and fermion propagators at five loops.

How nonperturbative is the infrared regime of Landau gauge Yang-Mills correlators?

We study the Landau gauge correlators of Yang-Mills fields for infrared Euclidean momenta in the context of a massive extension of the Faddeev-Popov Lagrangian which, we argue, underlies a variety of continuum approaches. Standard (perturbative) renormalization group techniques with a specific, infrared-safe renormalization scheme produce so-called decoupling and scaling solutions for the ghost and gluon propagators, which correspond to nontrivial infrared fixed points. The decoupling fixed point is infrared stable and weakly coupled, while the scaling fixed point is unstable and generically strongly coupled except for low dimensions $d\to2$. Under the assumption that such a scaling fixed point exists beyond one-loop order, we find that the corresponding ghost and gluon scaling exponents are, respectively, $2\alpha_F=2-d$ and $2\alpha_G=d$ at all orders of perturbation theory in the present renormalization scheme. We discuss the relation between the ghost wave function renormalization, the gluon screening mass, the scale of spectral positivity violation, and the gluon mass parameter. We also show that this scaling solution does not realize the standard Becchi-Rouet-Stora-Tyutin symmetry of the Faddeev-Popov Lagrangian. Finally, we discuss our findings in relation to the results of nonperturbative continuum methods.

Correlation functions and renormalization in a scalar field theory on the fuzzy sphere

We study renormalization in a scalar field theory on the fuzzy sphere. The theory is realized by a matrix model, where the matrix size plays the role of an ultraviolet cutoff. We define correlation functions by using the Berezin symbol identified with a field and calculate them nonperturbatively by Monte Carlo simulation. We find that the 2-point and 4-point functions are made independent of the matrix size by tuning a parameter and performing a wave function renormalization. The results strongly suggest that the theory is nonperturbatively renormalizable in the ordinary sense.

Radiative corrections to the magnetic moments of the proton and the neutron

We estimate the radiative corrections of order to the magnetic moments of the proton and the neutron. The photon-loop diagram of the vertex-correction type is evaluated with phenomenological nucleon vector form factors. Infrared-finiteness and gauge-invariance require the inclusion of the wave-function renormalization factor from the self-energy diagram. Using recent empirical form factor parametrizations, the corrections amount to and . We also study the effects from photon loops with internal isobars. For two customary versions of the vertex and spin-3/2 propagator, these radiative corrections have values of and , respectively. Taking these ranges as a systematic error, our estimates read and .

Pseudogap in the Eliashberg approach based on electron‐phonon and electron‐electron‐phonon interaction

The properties of the superconducting and the anomalous normal state were described by using the Eliashberg method. The pairing mechanism was reproduced with the help of the Hamiltonian, which models the electron‐phonon and the electron‐electron‐phonon interaction (EEPh). The set of the Eliashberg equations, which determines the order parameter function (φ), the wave function renormalization factor (Z), and the energy shift function (χ), was derived. It was proven that for the sufficiently large values of the EEPh potential, the doping dependence of the order parameter () has the analogous course to that observed experimentally in cuprates. The energy gap in the electron density of states is induced by Z and χ ‐ the contribution from φ is negligible. The electron density of states possesses the characteristic asymmetric form and the pseudogap is observed above the critical temperature. image

One-loop effective potential in nonlocal supersymmetric theories

Within the superfield approach, we consider the nonlocal generalization of the Wess-Zumino model and calculate the one-loop low-energy contributions to the effective action. Four different nonlocal models are considered, among which only the first model does not reduce to the standard Wess-Zumino model when we take the parameter of nonlocality of the model, $\mathrm{\ensuremath{\Lambda}}$, much greater than any energy scale; in addition, this model also depends on an extra parameter $\ensuremath{\xi}$. As to the other three models, the result looks like the renormalized effective potential for the usual Wess-Zumino model, where the normalization scale $\ensuremath{\mu}$ is replaced by the $\mathrm{\ensuremath{\Lambda}}$. Moreover, the fourth model displays a divergence which can be eliminated through the appropriate wave function renormalization.

Thermodynamics and renormalized quasiparticles in the vicinity of the dilute Bose gas quantum critical point in two dimensions

We use the functional renormalization group (FRG) to derive analytical expressions for thermodynamic observables (density, pressure, entropy, and compressibility) as well as for single-particle properties (wavefunction renormalization and effective mass) of interacting bosons in two dimensions as a function of temperature $T$ and chemical potential $\mu$. We focus on the quantum disordered and the quantum critical regime close to the dilute Bose gas quantum critical point. Our approach is based on a truncated vertex expansion of the hierarchy of FRG flow equations and the decoupling of the two-body contact interaction in the particle-particle channel using a suitable Hubbard-Stratonovich transformation. Our analytic FRG results extend previous analytical renormalization group calculations for thermodynamic observables at $\mu =0$ to finite values of $\mu$. To confirm the validity of our FRG approach, we have also performed quantum Monte Carlo simulations to obtain the magnetization, the susceptibility, and the correlation length of the two-dimensional spin-$1/2$ quantum $XY$ model with coupling $J$ in a regime where its quantum critical behavior is controlled by the dilute Bose gas quantum critical point. We find that our analytical results describe the Monte Carlo data for $\mu \leq 0$ rather accurately up to relatively high temperatures $T \lesssim 0.1 J$.