Two-loop Renormalization Group Research Articles

Natural effective supersymmetry

Much heavier sfermions of the first-two generations than the other superparticles provide a natural explanation for the flavor and CP problems in the supersymmetric Standard Model (SUSY SM). However, the heavy sfermions may drive the mass squareds for the light third generation sfermions to be negative through two-loop renormalization group (RG) equations, breaking color and charge. Introducing extra matters to the SUSY SM, it is possible to construct models where the sfermion masses are RG invariant at the two-loop level in the limit of vanishing gaugino-mass and Yukawa-coupling contributions. We calculate the finite corrections to the light sfermion masses at the two-loop level in the models. We find that the finite corrections to the light-squark mass squareds are negative and can be less than (0.3–1)% of the heavy-squark mass squareds, depending on the number and the parameters of the extra matters. We also discuss whether such models realized by the U(1) X gauge interaction at the GUT scale can satisfy the constraints from Δm K and ϵ K naturally. When both the left- and right-handed down-type squarks of the first-two generations have common U(1) X charges, the supersymmetric contributions to Δm K and ϵ K are sufficiently suppressed without spoiling naturalness, even if the flavor-violating supergravity contributions to the sfermion mass matrices are included. When only the right-handed squarks of the first-two generations have a common U(1) X charge, we can still satisfy the constraint from Δm K naturally, but evading the bound from ϵ K requires the CP phase smaller than 10 −2 .

Models with inverse sfermion mass hierarchy and decoupling of the SUSY FCNC effect

We study the decoupling of the first two squark and slepton families in order to lower the flavour changing neutral current effects. Models with inverse sfermion mass hierarchy based upon gauged U(1) flavour symmetries provide a natural framework where decoupling can be implemented. Decoupling requires a large gap between the Fermi scale and the supersymmetry breaking scale. Maintaining the electroweak symmetry breaking at the Fermi scale requires some fine-tuning that we investigate by solving the two-loop renormalization group equations. We show that the two-loop effects are governed by the anomaly compensated by the Green-Schwarz mechanism and can be determined from the quark and lepton masses. The electroweak breaking constraints lead to a small $\mu$ scenario where the LSP is Higgsino-like.

Dimensionality effects in half-filled random Hubbard chains

We discuss interplay of randomness, electron correlation and dimensionality effects in half-filled random Hubbard chains. Low-temperature phases are given based on the two-loop renormalization group (RG) analysis. Feedback effects of interchain processes on the umklapp process are examined by the 1+ ε expansion. We comment on the relevance of the present result to a phase diagram of a doped organic compound, (DI-DCNQI) 2Ag 1− x Cu x .

Nonperturbative power corrections to two-loopα¯s(q2)in an analytic approach to QCD

The analytic approach to perturbative QCD which allows one to remove nonphysical singularities of the QCD running coupling constant ${\overline{\ensuremath{\alpha}}}_{s}{(q}^{2})$ in the infrared region is applied to standard as well as to iterative solutions of the two-loop renormalization group equation. Nonleading at large momentum nonperturbative contributions in ${\overline{\ensuremath{\alpha}}}_{s}{(q}^{2})$ are obtained in explicit form. The coefficients of nonperturbative contribution expansions in inverse powers of the squared Euclidean momentum are calculated. For both cases considered, power series of negative terms convergent at ${q}^{2}>{\ensuremath{\Lambda}}^{2}$ with different dependences appear on term numbers.

Interplay of Correlation, Randomness and Dimensionality Effects in Weakly-Coupled Half-Filled Random Hubbard Chains

We study interplay of electronic correlation, randomness and dimensionality effects in half-filled random Hubbard chains weakly coupled via an interchain one-particle hopping. Based on the two-loop renormalization-group approach, phase diagrams are given in terms of temperature vs. strengths of the intrachain electron-electron umklapp scattering, the random scattering and the interchain one-particle hopping.

Two-loop renormalization group restrictions on the standard model and the fourth chiral family

In the framework of the two-loop renormalization group, the restrictions on the Higgs mass from the electroweak vacuum stability and from the absence of the strong coupling are refined, while the more precise value of the top mass is taken into account. When the SM cutoff is equal to the Planck scale, the Higgs mass must be $M_{\mathrm H} = (161.3 \pm 20.6)^{+4}_{-10}$ GeV and $M_{\mathrm H}\ge 140.7^{+10}_{-10}$ GeV, where the $M_{\mathrm H}$ corridor is the theoretical one and the errors are due to the top-mass uncertainty. The SM two-loop $\beta$ functions are generalized to the case with massive neutrinos from extra families. The requirement of self-consistency of the perturbative SM as an underlying theory up to the Planck scale excludes a fourth chiral family. Under the precision-experiment restriction $M_{\mathrm H}\leq 215$ GeV, the fourth chiral family, if alone, is excluded even when the SM is regarded as an effective theory. Nevertheless a pair of chiral families constituting a vector-like one could exist.

Anisotropic renormalization-group flow of quasiparticle weight in a two-dimensional electron system with a partially flat Fermi surface

Two-loop renormalization-group (RG) analysis for a two-dimensional electron system with a partially flat Fermi surface has been carried out. We found that the RG flow of the quasiparticle weight depends on the location of the electron wave number $\mathit{k}$ on the Fermi surface due to the kinematical restriction to the logarithmically divergent processes in the flat regions of the Fermi surface.

The ΔI = 1/2 rule in the chiral limit

We discuss the matching between long-distance and short-distance at next-to-leading in $1/N_c$ and show how the scheme-dependence from the two-loop renormalization group running can be treated. We then use this method to study the three $O(p^2)$ terms contributing to non-leptonic kaon decays, namely the usual octet and 27-plet derivative terms as well as the weak mass term using the Extended Nambu--Jona-Lasinio model as the low energy approximation. We also discuss subtleties in the momentum routing in the low energy theory and a problem in separating factorizable and non-factorizable contributions from the $Q_6$ operator in the chiral limit. We update our earlier results on the $B_K$ parameter as well.

Effects of a 126-dimensional Higgs scalar on bottom-tau unification and the quasi-infrared fixed point

In the presence of ${\bf 126 + \bar{126}}$ Higgs multiplets in a SO(10) theory, the fermion masses get contributions from an induced vacuum expectation value (VEV) of a $SU(2)_L$ doublet residing in ${\bf 126}$ which differentiates between quarks and leptons by a relative sign leading to a significant correction to the prediction of the mass ratio of the bottom quark and the tau lepton for ranges of the mass of this extra doublet. We perform a two-loop renormalization group analysis of the minimal version of the one-step supersymmetric SO(10) model to display this and re-calculate the corrections to the top quark mass in the presence of such an induced VEV. We show that these effects make the infra-red fixed point scenario consistent with experimental results.

Two-loop renormalization group restrictions on the standard model and the fourth chiral family

In the framework of the two-loop renormalization group, the global profile of the Standard Model (SM) in its full parameter space is investigated up to the scale of the gauge singularity. The critical Higgs masses bordering the strong coupling, unstable and the safe regions are explicitly found. Restrictions on the Higgs boson mass as a function of a cutoff scale are obtained from the stability of the electroweak vacuum and from the absence of the strong coupling both in the Higgs and Yukawa sectors. The cutoff being equal to the Plank scale requires the Higgs mass to be M=(161.3+-20.6)+4-10 GeV and M>=140.7+-10 GeV, where the M corridor is the theoretical one and the errors are due to the top mass uncertainty. The SM two-loop beta-functions are generalized to the massive neutrino case. Modification of the two-loop global profile of the SM extended by one new chiral family is studied, and bounds on the masses of the family are found. The requirement of self-consistency of the perturbative SM as an underlying theory up to the Planck or GUT scale excludes the fourth chiral family with the mass up to 250 GeV depending on the Higgs mass and the cutoff scale. Under precision experiment restriction M<=200 GeV, the fourth chiral family, taken alone, is excluded. Nevertheless a pair of the chiral families constituting the vector-like one could still exist.

Supersymmetry breaking and the supersymmetric flavor problem: An analysis of decoupling the first two generation scalars

The supersymmetric contributions to the Flavor Changing Neutral Current processes may be suppressed by decoupling the scalars of the first and second generations. It is known, however, that the heavy scalars drive the stop mass squareds negative through the two-loop Renormalization Group evolution. This tension is studied in detail. Two new items are included in this analysis: the effect of the top quark Yukawa coupling and the QCD corrections to the supersymmetric contributions to $\Delta m_K$. Even with Cabibbo-like degeneracy between the squarks of the first two generations, these squarks must be heavier than $\sim 40$ TeV to suppress $\Delta m_K$. This implies, in the case of a high scale of supersymmetry breaking, that the boundary value of the stop mass has to be greater than $\sim 7$ TeV to keep the stop mass squared positive at the weak scale. Low-energy supersymmetry breaking at a scale that is of the same order as the mass of the heavy scalars is also considered. In this case the finite parts of the two-loop diagrams are computed to estimate the contribution of the heavy scalar masses to the stop mass squared. It is found that for Cabibbo-like mixing between the squarks, the stop mass at the boundary needs to be larger than $\sim 2$ TeV. Thus, for both cases, the large boundary value of the stop masses leads to an unnatural amount of fine tuning to obtain the correct $Z$ mass.

Correct scaling relation for the conserved Kardar-Parisi-Zhang equation and growth models

Department of Physics and Research Institute for Basic Sciences, Kyung-Hee University, Seoul 130-701, Korea~Received 29 May 1998!To test the corrected scaling relation a1z5423dof the conserved Kardar-Parisi-Zhang~CKPZ! equationsuggested by Janssen @Phys. Rev. Lett. 78, 1082 ~1997!#, a stochastic growth model that follows the CKPZequation with the conserved noise is restudied. We have found a consistent nonzero correction term d, whichis somewhat larger than that estimated from the two-loop renormalization group calculation.@S1063-651X~98!10010-7#PACS number~s!: 05.40.1j, 05.70.Ln, 68.35.Fx

Spreading of damage and susceptibility in the quantumS=1/2Heisenberg ferromagnet

In this work we extend a recently proposed prescription for studying the dynamical properties of quantum Heisenberg ferromagnets which is based on the spreading of the damage technique. Within the Handscomb Monte Carlo method, we introduce a Hamming distance defined as a difference in the cyclic structure of Mayers diagrams in such a way that the quantum nature of the Hamiltonian is accounted for. We show that the cyclic Hamming distance is closely related to the static spin susceptibility and illustrate our results by comparing them with previous two-loop renormalization group calculations of the susceptibility low-temperature behavior in two-dimensional quantum Heisenberg models.

Two-Loop RG Calculation of Sound Attenuation and Dispersion Near the Liquid-Gas Critical Point

We calculate the singular part of the sound attenuation and dispersion near the liquid-gas critical point on the critical isochore above T c . It is shown that the corresponding scaling function is related to the correlation function &lt;ψ2ψ2&gt; of two composite operators of the Halperin-Hohenberg–Siggia model H.1 Using the renormalization group (RG) and ∊-expansion we obtain this scaling function in second order in ∊.

Building models of gauge-mediated supersymmetry breaking without a messenger sector

We propose a general scheme for constructing models in which the Standard Model (SM) gauge interactions are the mediators of supersymmetry breaking to the fields in the supersymmetric SM, but where the SM gauge groups couple directly to the sector which breaks supersymmetry dynamically. Despite the direct coupling, the models preserve perturbative unification of the SM gauge coupling constants. Furthermore, the supergravity contributions to the squark and slepton masses can be naturally small, typically being much less than 1% of the gauge-mediated (GM) contributions. Both of these goals can be achieved without need of a fine-tuning or a very small coupling constant. This scheme requires run-away directions at the renormalizable level which are only lifted by non-renormalizable terms in the superpotential. To study the proposed scheme in practice, we develop a modified class of models based on SU(N) × SU(N − 1) which allows us to gauge an SU(N − 2) global symmetry. However, we point out a new problem which can exist in models where the dynamical supersymmetry breaking sector and the ordinary sector are directly coupled - the two-loop renormalization group has contributions which can induce negative (mass)2 for the squarks and sleptons. We clarify the origin of the problem and argue that it is likely to be surmountable. We give a recipe for a successful model.

Can the supersymmetric flavor problem be solved by decoupling?

It has been argued that the squarks and sleptons of the first and second generations can be relatively heavy without destabilizing the weak scale, thereby improving the situation with too-large flavor-changing neutral current (FCNC) and CP violating processes. In theories where the soft supersymmetry breaking parameters are generated at a high scale (such as the Planck scale), we show that such a mass spectrum tends to drive the scalar top mass squared $m_{\tilde{Q}_3}^2$ negative from two-loop renormalization group evolution. Even ignoring CP violation and allowing $O(\lambda) \sim .22$ alignment, the first two generation scalars must be heavier than 22 TeV to suppress FCNC. This in turn requires the boundary condition on $m_{\tilde{Q}_3} > 4 TeV$ to avoid negative $m_{\tilde{Q}_3}^2$ at the weak scale. Some of the models in the literature employing the anomalous U(1) in string theory are excluded by our analysis.

Localization and Metal-Insulator Transition in Multilayer Quantum Hall Structures

We study the phase structure and Hall conductance quantization in weakly coupled multilayer electron systems in the integer quantum Hall regime. We derive an effective field theory and perform a two-loop renormalization group calculation. It is shown that (i) finite interlayer tunnelings (however small) give rise to successive metallic and insulating phases and metal-insulator transitions in the unitary universality class; (ii) the Hall conductivity is not renormalized in the metallic phases in the 3D regime; and (iii) the Hall conductances are quantized in the insulating phases. In the bulk quantum Hall phases, the effective field theory describes the transport on the surface.

A Model of Direct Gauge Mediation of Supersymmetry Breaking

We present the first phenomenologically viable model of gauge meditation of supersymmetry breaking without a messenger sector or gauge singlet fields. The standard model gauge groups couple directly to the sector which breaks supersymmetry dynamically. Despite the direct coupling, it can preserve perturbative gauge unification thanks to the inverted hierarchy mechanism. There is no dangerous negative contribution to ${m}_{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{q}}^{2}$, ${m}_{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{l}}^{2}$ due to two-loop renormalization group equation. The potentially nonuniversal supergravity contribution to ${m}_{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{q}}^{2}$ and ${m}_{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{l}}^{2}$ can be suppressed enough. The model is completely chiral, and one does not need to forbid mass terms for the messenger fields by hand. Cosmology of the model is briefly discussed.

Single-Electron Box and the Helicity Modulus of an Inverse SquareXYModel

We calculate the average number of electrons on a metallic single-electron-box as a function of the gate voltage for arbitrary values of the tunneling conductance. In the vicinity of the plateaus the problem is equivalent to calculating the helicity modulus of a classical inverse square XY-model in one dimension. By a combination of perturbation theory, a two-loop renormalization group calculation and a Monte-Carlo simulation in the intermediate regime we provide a complete description of the smearing of the Coulomb staircase at zero temperature with increasing conductance.

Threshold effects and radiative electroweak symmetry breaking in SU(5) extensions of the MSSM

We make a complete analysis of radiative symmetry breaking in the MSSM and its $SU(5)$ extensions including low- and high-energy threshold effects in the framework of the two-loop renormalization group. In particular, we consider minimal $SU(5)$, the ``missing-doublet'' $SU(5)$, a Peccei-Quinn invariant version of $SU(5)$ as well as a version with light adjoint remnants. We derive permitted ranges for the parameters of these models in relation to predicted $\alpha_{s}$ and $M_G$ values within the present experimental accuracy. The parameter regions allowed under the constraints of radiative symmetry breaking, perturbativity and proton stability, include the experimentally designated domain for $\alpha_s$. In the case of the minimal $SU(5)$, the values of $\alpha_s$ obtained are somewhat large in comparison with the experimental average. The ``missing-doublet'' $SU(5)$, generally, predicts smaller values of $\alpha_s$. In both versions of the ``missing-doublet'', the high energy threshold effects on $\alpha_s$ operate in the opposite direction than in the case of the minimal model, leading to small values. In the case of the Peccei-Quinn version however the presence of an extra intermediate scale allows to achieve an excellent agreement with the experimental $\alpha_s$ values. Finally, the last considered version, with light remnants, exhibits unification of couplings at string scale at the expense however of rather large $\alpha_s$ values.