What can we learn from the finite temperature renormalization group?

The renormalization group for finite temperature quantum field theories is studied, in particular for λ?⁴. It is shown that the “high” temperature limit can only be discussed perturbatively ifT dependent renormalization schemes are implemented. Zero temperature renormalization schemes or renormalization at some fixed reference temperatureT _o are both inadequate as they imply perturbative expansions about fixed points of the renormalization group which are associated with a zero temperature system and a system at temperatureT _o respectively.T dependent schemes give rise to an expansion about the true fixed point of the system, the resulting renormalization group allows the entire crossover between high and low temperature behaviour to be investigated.     

Continuum regularization of quantum field theory

As an extension of our earlier one-loop renormalization studies at the regularized Schwinger-Dyson level, we report here on equivalent renormalization programs for regularized Langevin systems. Proper structure is discussed, and proper one-loop renormalizations of the Green functions of φ ₆ ³ and QCD₄ are given. An optional apparent?-renormalization is discussed as a technical simplificaiton for gauge theories with Zwanziger's gauge-fixing.     

Conformally covariant composite operators in quantum chromodynamics

Conformal covariance is shown to determine renormalization properties of composite operators in QCD and in the ϕ₆³-model at the one-loop level. Its relevance to higher-order (renormalization group improved) perturbative calculations in the short-distance limit is also discussed. Light cone operator product expansions and spectral representations for wavefunctions in QCD are derived.     

Mixing renormalization in Majorana neutrino theories

The renormalization of general theories with inter-family mixing of Dirac and/or Majorana fermions is studied at the one-loop electroweak order. The phenomenological significance of the mixing-matrix renormalization is discussed, within the context of models based on the SU(2)_L⊗U(1)_Y gauge group. The effect of radiative neutrino masses present in these models is naturally taken into account in this formulation. As an example, charged-lepton universality in pion decays is investigated in the heavy-neutrino limit. Non-decoupling heavy-neutrino effects induced by mixing renormalization are found to considerably affect the predictions in these new-physics scenarios.     

Quantization and Renormalization of the Manifest Left–Right Symmetric Model of Electroweak Interactions

Quantization and renormalization of the left–right symmetric model is the main purpose of the paper. First the model at tree level with a Higgs sector containing one bidoublet and two triplets is precisely discussed. Then the canonical quantization and Faddeev–Popov Lagrangian are carried out ('t Hooft gauge). The BRST symmetry is discussed. Subsequently the on-mass-shell renormalization is performed and, as a test of consistency, the renormalization of the ZN_iN_j vertex is analyzed.     

Soluble renormalization groups and scaling fields for low-dimensional Ising systems

A variety of one-dimensional Ising spin systems, including staggered and parallel magnetic fields, alternating and second neighbor interactions, four-spin coupling, etc., are discussed in terms of renormalization group theory. A continuous range of distinct renormalization groups is constructed in exact closed form, analyzed in detail, and compared with exactly calculated thermodynamic properties. Fixed point linearization yields relevant, irrelevant, and marginal operators. All groups yield identical “critical” behavior (at T = 0) with η = 1, δ = ∞, γ = ν = 2 ? α, and with identical linear scaling fields. A generalization of Wegner's analysis to discrete groups yields explicit power series for the nonlinear scaling fields; these are seen to depend on the particular renormalization group and, hence, are physically nonunique. A planar, multiconnected “truncated tetrahedron” model of effective dimensionality log₂ 3 is analyzed via a dedecoration and star-triangle group revealing highly singular behavior as T → T_c = 0.     

Renormalization Group Invariance in Pionless Effective Field Theory for the NN System

We consider the NN interaction in pionless effective field theory (EFT) up to next-to-next-to-leading order (NNLO) and use a recursive subtractive renormalization scheme to describe NN scattering in the ¹ S ₀ channel. We fix the strengths of the contact interactions at a reference scale, chosen to be the one that provides the best fit for the phase-shifts, and then slide the renormalization scale by evolving the driving terms of the subtracted Lippmann?CSchwinger equation through a non-relativistic Callan?CSymanzik equation. The results show that such a systematic renormalization scheme with multiple subtractions is fully renormalization group invariant.     

An introduction to the fundamentals of the renormalization group in critical phenomena

The fundamental concepts underlying the application of the renormalization group and related techniques to critical phenomena are reviewed at an elementary level. Topics discussed include: the definition of the renormalization group as a functional integral over high momentum components of the spin field, the behaviour of the renormalization group near the fixed point and the derivation of scaling, Wilson's approximate recursion relation, trivial and non-trivial fixed points of isotropic spin systems near d = 4, Feynman graph expansions for critical exponents, ? = 4 ? d and 1/n-expansions, the derivation of exact recursion relations and co-ordinate space transformations for d = 2 Ising systems     

Renormalization group analysis of the theory of interacting pomerons

A detailed analysis of the behaviour near J = 1 and k_⊥ = 0 of the theory of interacting pomerons is performed by means of the renormalization group techniques in the version developed by Wilson. Those techniques deal with the bare field theoretical Langrangian and allow one to study very general forms of the interactions. Following those procedures the strong coupling solution and two different forms of the weak coupling solution are found. The relevance of those solutions for the behaviour of diffractive scattering is briefly discussed.     

The renormalization of the string operator in QCD

We shall observe that the renormalization of the string operator U(x₁, x₂; C) = Pexp{ig∫_x1^x2dx_μA^μ(x)} with an open path C (smooth and non-intersecting) is path-independently performed in any order of perturbation. To demonstrate this, the renormalization constants will be calculated up to order g⁴. Next the renormalization effect on the algebraic identity $\text{U(x}{}_1\text{, x}{}_2\text{;}\text{C}\text{)U(x}{}_2\text{, x}{}_3\text{;}\text{C}\text{) = U(x}{}_1\text{, x}{}_3\text{;}\text{C}\text{∪}\text{C}\text{)}$ will be discussed and it will be proved that the renormalization preserves the algebraic identity in any order of perturbation if the paths C and $\text{C}$ are smoothly connected at x₂. Finally, the string operator renormalization is extended to the case when the path C is smoothly closed (the Wilson loop operator). It is then shown that the renormalization factor which multiplicatively renormalizes the string operator in the case of the open path, is cancelled in any order of perturbation by the divergence appearing in the coincidence of the end points. As a results, the Wilson loop operator can be renormalized by the coupling constant renormalization alone.     

LDA’+DMFT investigation of electronic structure of K1 − x Fe2 − y Se2 superconductor

We investigate electronic structure of the new iron chalcogenide high temperature superconductor K_1?x Fe_2?y Se₂ (hole doped case with x = 0.24, y = 0.28) in the normal phase using the novel LDA’+DMFT computational approach. We show that this iron chalcogenide is more correlated in a sense of bandwidth renormalization (energy scale compression by factor about 5 in the interval ±1.5 eV), than typical iron pnictides (compression factor about 2), though the Coulomb interaction strength is almost the same in both families. Our results for spectral densities are in general agreement with recent ARPES data on this system. It is found that all Fe-3d(t _2g ) bands crossing the Fermi level have equal renormalization, in contrast to some previous interpretations. Electronic states at the Fermi level are of predominantly xy symmetry. Also we show that LDA’+DMFT results are in better agreement with experimental spectral function maps, than the results of conventional LDA+DMFT. Finally we make predictions for photoemission spectra lineshape for K_0.76Fe_1.72Se₂.     

Uncertainties in the proton lifetime

We discuss the masses of the leptoquark bosons m_x and the proton lifetime in grand unified theories based principally on SU(5). It is emphasized that estimates of m_x based on the QCD coupling and the fine structure constant are probably more reliable than those using the experimental value of sin²θ_w. Uncertainties in the QCD Λ parameter and the correct value of α are discussed. We estimate higher-order effects on the evolution of coupling constants in a momentum-space renormalization scheme. It is shown that increasing the number of generations of fermions beyond the minimal three increases m_x by almost a factor of 2 per generation. Additional uncertainties exist for each generation of technifermions that may exist. We discuss and discount the possibility that proton decay could be “Cabibbo rotated” away, and a speculation that Lorentz invariance may be violated in proton decay at a detectable level. We estimate that in the absence of any substantial new physics beyond that in the minimal SU(5) model the proton lifetime is 8 × 10^30±2 years.     

Renormalization in non-Abelian gauge theories

The renormalization is performed in a manifestly covariant approach. The simplest form of the Ward identities z₁=z₂=…=z_n=… is fulfilled automatically in every gauge. In the Yang-Mills theory the counter-terms are gauge-invariant and depend on the charge renormalization constant only. In pure gravitation the analysis of all divergences is reduced in the present approach to some special classification of the kth order scalar densities in a Riemannian space.     

Renormalization group estimate of the hadronic decay width of the Higgs boson

The total hadronic decay width of the Weinberg-Salam type Higgs boson is estimated in QCD for the Higgs boson mass much larger than the ordinary hadronic mass scale, by use of the operator product expansion and renormalization group equation. We give an explicit formula for the decay width in terms of quark masses including strong interaction corrections up to the next-to-leading order. A numerical analysis of the hadronic decay width of the Higgs boson is made in the six-quark model. The next-to-leading order correction is found to be significant, e.g., 30-20% of the leading term for m_H of oue interest, m_H ? 1 TeV. Application of our scheme to the decay rates of heavy Higgs bosons of other types is also discussed.     

A new theoretical constraint on the static critical behaviour of the specific heat

We show from a field-theoretical approach that, if we admit that the additive renormalization function of the specific heat C is singular at the fixed point, we obtain a coherent formulation of the critical behaviour of C. Especially we show that the α<0 case, which corresponds to a cusp for C, is dominated by a critical constant B_cr generated by the long-range correlations of the fluctuations. We derive a universal combination between the leading and first correction amplitudes and B_cr, which will have a great importance in the analysis of experimental data.     

Continuum regularization of quantum field theory

As a complement to our earlier study of renormalization at the Langevin regularized level, we report here on equivalent renormalization programs for regularized Schwinger-Dyson systems. Both one-loop and iterated loop renormalizations of the Green functions of QCD₄ are given, and are shown to be equivalent to the Langevin results. The optional apparent ?-renormalization discussed in IV is shown to apply as well to Schwinger-Dyson systems as to Langevin systems.     

The non-perturbative renormalization group in the ordered phase

We study some analytical properties of the solutions of the non-perturbative renormalization group flow equations for a scalar field theory with Z₂ symmetry in the ordered phase, i.e. at temperatures below the critical temperature. The study is made in the framework of the local potential approximation. We show that the required physical discontinuity of the magnetic susceptibility χ(M) at M=±M₀ (M₀ spontaneous magnetization) is reproduced only if the cut-off function which separates high and low energy modes satisfies to some restrictive explicit mathematical conditions; we stress that these conditions are not satisfied by a sharp cut-off in dimensions of space d<4.By generalizing a method proposed earlier by Bonanno and Lacagnina [Nucl. Phys. B 693 (2004) 36] to any kind of cut-off we propose to solve numerically the renormalization group flow equations for the threshold functions rather than for the local potential. It yields an algorithm sufficiently robust and precise to extract universal as well as non-universal quantities from numerical experiments at any temperature, in particular at sub-critical temperatures in the ordered phase. Numerical results obtained for the φ⁴ potential with three different cut-off functions are reported and compared. The data confirm our theoretical predictions concerning the analytical behavior of χ(M) at M=±M₀.Fixed point solutions of the adimensioned renormalization group flow equations are also obtained in the same vein, that is by solving the fixed points equations and the associated eigenvalue problem for the threshold functions rather than for the potential. We report high precision data for the odd and even spectra of critical exponents for different cut-offs obtained in this way.     

Observation of quasi-universal magnetic behavior in a random exchange Heisenberg antiferromagnetic chain: Neutron irradiated quinolinium (TCNQ)2

Low field electron spin resonance measurements of the magnetic susceptibility (χ) and absorption linewidth over the temperature range 0.04 – 300 K are reported for quinolinium (TCNQ)₂ into which increased amounts of disorder have been introduced by fast neutron irradiation. It is found that below 20 K, χ = AT^-α; A increases linearly with the irradiation dose, but $\text{α (? 0.8)}$ is almost independent of it, in agreement with the quasi universal behavior predicted by recent renormalization calculations for a random exchange Heisenberg antiferromagnetic chain. Measurements of the g-shift at 4.2 K range indicate that all of χ is associated with TCNQ chains. These results are discussed in terms of the renormalization calculation of Soos and Bondeson.     

Improved renormalization group equations with dimensional regularization and the ε expansions

Due to the absence of dimensional cut-off parameters in the dimensional regularization scheme, vanishing of the renormalized mass of the scalar boson implies vanishing of its renormalized mass; thus the masses of both bosons and fermions in renormalizable field theories can be made finite by multiplicative mass renormalizations. The improved renormalization group equations in D dimensions are derived in such a way that both the large (or the small) momentum limits and the Wilson ? expansions can be uniformly treated for the fermion as well as the boson cases. We discuss the improved equations for φ₆³ theory, φ₄⁴ theory, quantumelectrodynamics, massive vector-gluon model, and non-Abelian guage theories incorporating fermions. For the latter three classes of theories, the gauge dependent problem of the coefficient functions in the improved renormalization group equations is discussed.