Consistent Renormalization Research Articles

Higgs triplets and limits from precision measurements

In this letter, they present the results on a global fit to precision electroweak data in a Higgs triplet model. In models with a triplet Higgs boson, a consistent renormalization scheme differs from that of the Standard Model and the global fit shows that a light Higgs boson with mass of 100-200 GeV is preferred. Triplet Higgs bosons arise in many extensions of the Standard Model, including the left-right model and the Little Higgs models. The result demonstrates the importance of the scalar loops when there is a large mass splitting between the heavy scalars. It also indicates the significance of the global fit.

Renormalization group calculation of the uniform susceptibilities in low-dimensional systems

We analyze the one-dimensional (1D) and the two-dimensional (2D) repulsive Hubbard models (HM) for densities slightly away from half-filling through the behavior of two central quantities of a system: the uniform charge and spin susceptibilities. We point out that a consistent renormalization group treatment of them can only be achieved within a two-loop approach or beyond. In the 1D HM, we show that this scheme reproduces correctly the metallic behavior given by the well-known Luttinger liquid fixed-point result. Then, we use the same approach to deal with the more complicated 2D HM. In this case, we are able to show that both uniform susceptibilities become suppressed for moderate interaction parameters as one take the system towards the Fermi surface. Therefore, this result adds further support to the interpretation that those systems are in fact insulating spin liquids. Later, we perform the same calculations in 2D using the conventional random phase approximation, and establish clearly a comparison between the two schemes.

From big bang to asymptotic de Sitter: complete cosmologies in a quantum gravityframework

Using the Einstein–Hilbert approximation of asymptotically safe quantum gravity wepresent a consistent renormalization group based framework for the inclusion of quantumgravitational effects into the cosmological field equations. Relating the renormalizationgroup scale to cosmological time via a dynamical cutoff identification this frameworkapplies to all stages of the cosmological evolution. The very early universe is found tocontain a period of ‘oscillatory inflation’ with an infinite sequence of time intervals duringwhich the expansion alternates between acceleration and deceleration. For asymptoticallylate times we identify a mechanism which prevents the universe from leaving the domain ofvalidity of the Einstein–Hilbert approximation and obtain a classical de Sitter era.

Few-body physics in effective field theory

Effective field theory (EFT) provides a powerful framework that exploits a separation of scales in physical systems to perform systematically improvable, model-independent calculations. Particularly interesting are few-body systems with short-range interactions and large two-body scattering length. Such systems display remarkable universal features. In systems with more than two particles, a three-body force with limit cycle behaviour is required for consistent renormalization already at leading order. We will review this EFT and some of its applications in the physics of cold atoms and nuclear physics. In particular, we will discuss the possibility of an infrared limit cycle in QCD. Recent extensions of the EFT approach to the four-body system and N-boson droplets in two spatial dimensions will also be addressed.

Linking the quark meson model with QCD at high temperature

We model the transition of a system of quarks and gluons at high energies to a system of quarks and mesons at low energies in a consistent renormalization group approach. Flow equations interpolate between the physics of the high-temperature degrees of freedom and the low-temperature dynamics at a scale of 1 GeV. We also discuss the dependence of the equation of state on baryon density and compare our results with recent lattice gauge simulations.

Instanton determinant with arbitrary quark mass: WKB phase-shift method and derivative expansion

The fermion determinant in an instanton background for a quark field of arbitrary mass is studied using the Schwinger proper-time representation with WKB scattering phase shifts for the relevant partial-wave differential operators. Previously, results have been obtained only for the extreme small and large quark mass limits, not for intermediate interpolating mass values. We show that consistent renormalization and large-mass asymptotics requires up to third-order in the WKB approximation. This procedure leads to an almost analytic answer, requiring only modest numerical approximation, and yields excellent agreement with the well-known extreme small and large mass limits. We estimate that it differs from the exact answer by no more than 6% for generic mass values. In the philosophy of the derivative expansion the same amplitude is then studied using a Heisenberg–Euler-type effective action, and the leading order approximation gives a surprisingly accurate answer for all masses.

One-loop radiative corrections to theρparameter in the littlest Higgs model

We perform a one-loop analysis of the $\ensuremath{\rho}$ parameter in the littlest Higgs model, including the logarithmically enhanced contributions from both fermion and scalar loops. We find that the one-loop contributions are comparable to the tree level corrections in some regions of parameter space. The fermion loop contribution dominates in the low cutoff scale f region. On the other hand, the scalar loop contribution dominates in the high cutoff scale f region and it grows with the cutoff scale f. This in turn implies an upper bound on the cutoff scale. A low cutoff scale is allowed for a non-zero triplet vacuum expectation value. Constraints on various other parameters in the model are also discussed. The role of triplet scalars in constructing a consistent renormalization scheme is emphasized.

Renormalization of Φ-derivable approximations in scalar field theories

We discuss the renormalization of Φ-derivable approximations for scalar field theories. In such approximations, the self-energy is obtained as the solution of a self-consistent equation which effectively resums infinite subsets of diagrams of perturbation theory. We show that a consistent renormalization can be carried out, and we provide an explicit construction of the counterterms needed to eliminate the subdivergences. These counterterms are calculated from the solution of an auxiliary gap equation which determines the dominant part of the self-energy at large momentum. This auxiliary gap equation may be chosen as the gap equation of the massless theory at zero temperature. We verify explicitly that, as expected, the counterterms determined at zero temperature are sufficient to eliminate the divergences which occur in finite temperature calculations.

Linked-cluster Tamm–Dancoff field theory

To solve the relativistic bound-state problem one needs to systematically and simultaneously decouple the high-energy from the low-energy modes and the many-body from the few-particle states using a consistent renormalization scheme. In a recent Letter we have shown that one such approach can be a combination of the coupled cluster method as used in many-body theory and the Wilsonian exact renormalization group. Even though the method is intrinsically non-perturbative, one can easily implement a loop expansion within it. In this Letter we provide further support for this aspect of our formalism by obtaining results for the two-loop renormalized φ4 theory. We show that the non-unitary representation inherent in our method leads to an economic computation and does not produce any non-Hermiticity in the relevant terms.

Effective theory of NN interactions in a separable representation

We consider the effective field theory of the NN system in a separable representation. The pionic part of the effective potential is included nonperturbatively and approximated by a separable potential. The use of a separable representation allows for the explicit solution of the Lippmann-Schwinger equation and a consistent renormalization procedure. The phase shifts in the $^1S_0$ channel are calculated to subleading order.

Drastic violation of the U-matrix boundary condition by quantum-field theoretical on-shell renormalization and a new consistent renormalization concept involving bound-state problems

By generalizing the Gell-Mann–Low formula and applying the self-consistent projection-operator method, developed a decade ago by the present author, a connecting equation between the fermion propagator (involving the interaction with the quantum electromagnetic field in the presence of an external field) and the U-matrix elements, being valid to any order of the fermion–photon interaction, is derived. After proving rigorously, the drastic violation of the U-matrix boundary condition ( U( t, t)=1) by the conventional on-shell renormalization of the fermion propagator (removal of free-fermion pole and residue corrections), the absolute necessity for the formulation of a new renormalization concept becomes self-evident. This latter is achieved in the present paper by elaborating a consistent renormalization procedure, based on the self-consistent projection-operator method (which, unlike the standard perturbation method, guarantees the consistency of the applied approximation to any order as to the strength of the interaction). The new complete renormalization, unlike the conventional one, removes completely the experimentally unobservable free-electron Dyson self-energy from the fermion propagator. By applying the new concept, for the first time, consistently renormalized contributions (up to the fourth order) to the bound-electron self-energy function with the corresponding Feynman diagrams are derived.

The hypertriton in effective field theory

Doublet Λd scattering and the hypertriton are studied in the framework of an effective field theory for large scattering lengths. As in the triton case, consistent renormalization requires a one-parameter three-body force at leading order whose renormalization group evolution is governed by a limit cycle. Constraining unknown parameters from symmetry considerations and the measured binding energy of the hypertriton, we calculate the low-energy phase shifts for doublet Λd scattering. For the low-energy parameters, we find a Λd =(16.8 +4.4 −2.4) fm and r Λd =(2.3±0.3) fm, where the errors are due to the uncertainty in the hypertriton binding energy. Since the hypertriton is extremely shallow, low-energy three-body observables in this channel are very insensitive to the exact values of the ΛN low-energy parameters.

Serious inconsistency implied in conventional on-shell renormalization and a new renormalization concept involving bound-state problems in QED

In an earlier Invited Comment, the present author, as all other authors, advocated the generally accepted conception about the applicability of the conventional on-shell renormalization (elimination of the free-electron pole and residue corrections) for the renormalization of the complete electron propagator in QED. In the present Letter, for the first time, it is proved rigorously that this renormalization procedure, applied for more than 50 years in the literature, drastically violates the U-matrix boundary condition ( U( t, t)=1) and, therefore, its application for the renormalization of the electron propagator is not permitted. As a consequence, a new consistent renormalization concept is formulated and applied for the derivation of, for the first time, correctly renormalized bound-electron propagator with the corresponding self-energy function and Feynman diagrams.

Investigation on the Nature of the Concentration-Induced Non-Fermi-Liquid Behavior in YbCu3.5Al1.5

YbCu5−xAlx exhibits long range antiferromagnetic order for x>1.5 with TN rising up to 2 K for the composition YbCu3Al2. This development of antiferromagnetic order is due to a valence shift from the non-magnetic Yb 4f 14 ground state in YbCu5 to the magnetic 4f13 ground state in YbCu3Al2. At the critical concentration x=1.5 the system is in a state of magnetic instability, where typical non-Fermi-liquid (nFl)-properties are observed, e.g., a−log T contribution in C/T and a power law in ρ=ρ0+cTα with α<2. We have measured the specific heat and electrical resistance of YbCu3.5Al1.5 in various magnetic fields in order to clarify the nature of the non-Fermi- liquid behavior in this series. The specific heat divided by temperature in zero field can be described by a Self Consistent Renormalization (SCR)-model for a 3D antiferromagnet down to the lowest measured temperature and over more than a decade of temperature. The resistance data clearly deviate from the Fermi-liquid (Fl)-T2-behavior in zero magnetic field, whereas with increasing field, the range of the Fl-behavior enlarges. The derived SCR parameters indicate that the system is not exactly at the quantum critical point (QCP) and application of external magnetic field pushes the system further away from the QCP. A hyperscaling analysis of the specific heat data taken in various magnetic fields in the region where C/T is proportional to −log T points to collective effects responsible for the nFl-behavior in YbCu3.5Al1.5. The scaling disappears for T<240 mK which would point to a crossover from weakly interacting to non Gaussian strongly interacting spin fluctuations as the cause of the nFl-behavior.

Renormalization group in quantum mechanics

We establish the renormalization group equation for the running action in the context of a one quantum particle system. This equation is deduced by integrating each fourier mode after the other in the path integral formalism. It is free of the well known pathologies which appear in quantum field theory due to the sharp cutoff. We show that for an arbitrary background path the usual local form of the action is not preserved by the flow. To cure this problem we consider a more general action than usual which is stable by the renormalization group flow. It allows us to obtain a new consistent renormalization group equation for the action.

CORRECT ELECTRON-PROPAGATOR AND U-MATRIX RENORMALIZATION REPLACING THE INCONSISTENT ON-MASS-SHELL RENORMALIZATION AND THE RENORMALIZED NATURAL LINE SHAPE

After pointing out the drastic violation of the U-matrix boundary condition by the conventional quantum-field–theoretical on-mass-shell renormalization of the electron propagator, a new consistent renormalization concept (without mass and charge renormalization) is presented. From the correctly renormalized bound-electron propagator (respectively, U-matrix), the natural line shape is for the first time, after 50 years, correctly calculated in QFT.

The O(N) model at nonzero temperature: renormalization of the gap equations in Hartree and large-N approximations

The temperature dependence of the sigma meson and pion masses is studied in the framework of the O(N ) model. The Cornwall-Jackiw-Tomboulis formalism is applied to derive gap equations for the masses in the Hartree and large-N approximations. Renormalization of the gap equations is carried out within the cut-off and counter-term renormalization schemes. A consistent renormalization of the gap equations within the cut-off scheme is found to be possible only in the large-N approximation and for a finite value of the cut-off. On the other hand, the counter-term scheme allows for a consistent renormalization of both the large-N and Hartree approximations. In these approximations, the meson masses at a given nonzero temperature depend in general on the choice of the cut-off or renormalization scale. As an application, we also discuss the in-medium on-shell decay widths for sigma mesons and pions at rest.

Renormalization equations in gravitational theory with higher derivatives

The structure of renormalization equations in gravitational theories with higher derivatives is considered. The gauge dependence of invariant divergences of the effective action is found to be nontrivial. The external source technique is used to construct a consistent Green's function renormalization. One- and two-loop divergences of the effective action are explicitly calculated for an arbitrary parametrization and gauge. These calculations fit the general structure of the obtained renormalization equations.

Spin dynamics in itinerant heavy electron system Ce(Ru 1− xRh x) 2Si 2 ( x=0 and 0.03) near the magnetic instability point

We report on specific heat and inelastic neutron scattering experiments of the heavy electron system Ce(Ru 1− x Rh x ) 2Si 2 ( x ⩽ 0.03). A spin density wave (SDW) transition was observed for 0.03 < x<0.4. We applied the self consistent renormalization (SCR) theory for the low Rh concentration region ( x ⩽ 0.03) of this system, and well explained the temperature dependence of the specific heats. We obtained the dynamical susceptibilities χ( q, ω) in the q- and ω-space by inelastic neutron scattering experiments. We discuss the effect of antiferromagnetic spin fluctuations on the dynamical properties of Ce(Ru 1− x Rh x ) 2Si 2 near the magnetic instability point on the basis of the SCR theory.

Chiral Symmetry Breaking in Strongly Coupled U(1) Gauge Theory Coupled to Scalar and Fermion Matter

We construct a transformation for scalar QED (U(1) gauge theory coupled with a charged scalar field) which leads to a dual effective gauge theory having a perturbation theory expansion in inverse powers of the (electric charge) coupling constant. The dual formulation is applied to the special case of scalar QED coupled to a massless charged fermion. A four-fermion interaction term arises naturally under the duality mapping. As an extension to discussions initiated by Miransky, Bardeen and Kondo and their collaborators in the late 1980's, we use this formulation to explore the possibility of a dynamical breakdown of chiral symmetry for the strongly coupled U(1) gauge theory interacting with both scalar and fermion degrees of freedom. Assuming that scalar QED is realized in the Higgs phase, we examine the Schwinger–Dyson equation approach to the fermion propagator in next-to-leading order of the strong coupling expansion (quenched approximation, i.e. no fermion loops). We construct a consistent renormalization procedure to deal with the ultraviolet infinities. For fixed scalar field vacuum expectation values, we obtain in the plane of the two important parameters of the theory (electric charge and four-fermion coupling constant) critical transition lines to a chirality broken phase.