Analysis Of Renormalization Group Equations Research Articles

Criterion of perturbativity with the mass-dependent beta function in extended Higgs models

In order to realize an electroweak first-order phase transition, a category of extended Higgs models with relatively large self-coupling constants is often considered. In such a scenario, the running coupling constants can blow up at an energy scale much below the Planck scale. To clarify the allowed parameter space of the model, it is important to evaluate the scale where perturbative calculation breaks down. In the renormalization group equation analysis using the mass-independent renormalization scheme, we need a matching condition to connect the low energy theory and the high energy theory. Consequently, the analysis depends on the details of the matching condition. On the other hand, an analysis with the mass-dependent beta function can be performed in a simpler way because the threshold effect is automatically included in the beta function. In this paper, using the mass-dependent beta function, we discuss the application limit of perturbative calculations at the one-loop level. First, we explain the essence of our method and compare our results with those based on the mass-independent beta function in a toy model with two complex scalar fields. We then apply our method to a more realistic model, i.e., the inert doublet model. We find that, in our method, in which the threshold effect is automatically included, the energy scale where the perturbative calculation breaks down can be higher than the one using the mass-independent beta function, especially when the blowup scale is relatively low. Published by the American Physical Society 2024

Fermiophobic light Higgs boson in the type-I two-Higgs-doublet model

The null results in the new physics searches at the LHC do not exclude a light new particle if the particle is fermiophobic. A good example is the fermiophobic Higgs boson hf in the type-I two-Higgs-doublet model, which occurs if we adopt α=π/2 and the inverted scenario where the heavier CP-even Higgs boson is the observed one at a mass of 125 GeV. We first obtain the still-valid parameter space satisfying the theoretical requirements, flavor-changing neutral currents in B physics, the cutoff scale above 1 TeV, Higgs precision data, and the direct search bounds at high energy colliders. We also study the high energy scale behavior of the allowed parameter points via the renormalization group equation analysis. An important result is that the fermiophobic type-I can maintain the stability of the scalar potential all the way up to the Planck scale if mhf is larger than half the observed Higgs boson mass. Since the decay modes of hf→γγ, H±→hfW±, and A→hfZ are dominant, the productions of pp→Ahf/H±hf/H±A/H+H− yield the four-photon final states at the LHC. We suggest the processes of 4γ+VV′ (V(′)=Z,W±) as the discovery channels that supplement 4γ+V, since they have compatible cross sections and enjoy the background-free environment.

CDF W -boson mass and muon g−2 in a type-X two-Higgs-doublet model with a Higgs-phobic light pseudoscalar

The recent measurement of the $W$ boson mass by the CDF collaboration adds an anomaly to the longstanding discrepancy in the muon anomalous magnetic moment, $\mathrm{\ensuremath{\Delta}}{a}_{\ensuremath{\mu}}$. Although type-X in the two-Higgs-doublet model provides an attractive solution to $\mathrm{\ensuremath{\Delta}}{a}_{\ensuremath{\mu}}$ through a light pseudoscalar $A$, the model confronts the exotic Higgs decays of $h\ensuremath{\rightarrow}AA$ and the lepton flavor universality data in the $\ensuremath{\tau}$ and $Z$ decays. To save the model, we propose that the light pseudoscalar be Higgs-phobic. Through the random scanning over the entire parameter space, we perform a comparative study of the Higgs-phobic type-X with and without the CDF ${m}_{W}$ measurement, called the CDF and PDG cases, respectively. Both cases can explain the two anomalies as well as all the other constraints, but have significant differences in the finally allowed parameter space. For example, a small region with almost degenerate masses of new Higgs bosons around 100 GeV is allowed only in the PDG case. The cutoff scale of the model is also studied via the analysis of renormalization group equations, which reaches up to ${10}^{5}\text{ }\text{ }\mathrm{GeV}$ (${10}^{7}\text{ }\text{ }\mathrm{GeV}$) in the CDF (PDG) case. Since the dominant decay modes are $A\ensuremath{\rightarrow}\ensuremath{\tau}\ensuremath{\tau}$, $H\ensuremath{\rightarrow}ZA$, and ${H}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{W}^{\ifmmode\pm\else\textpm\fi{}}A$ in most of the viable parameter space, we propose the $4\ensuremath{\tau}+V{V}^{\ensuremath{'}}$ states as the golden discovery channel at the LHC.

Unification of inflation and dark matter in the Higgs\u2013Starobinsky model

In this work, we propose unified picture of inflation and dark matter in the Higgs–Starobinsky (HS) model. As pointed out in the literature, Starobinsky R^2 inflation is induced by quantum correction effect from the large Higgs-curvature (graviton) coupling. We start with non-minimal coupling HS action in Jordan frame. We then transform the Jordan frame action into the Einstein one using the conformal transformation. The inflation potential is derived from the gravitational action of non-minimal-Higgs coupling and Starobinsky term in Einstein frame where the R^2 term is dominated in the inflationary phase of the universe. For model of inflation, we compute the inflationary parameters and confront them with Planck 2015 data. We discover that the predictions of the model are in excellent agreement with the Planck analysis. In addition, we find that the HS model is equivalent to a scalar singlet dark matter (SSDM) or Higgs-portal model. The renormalization group equations (RGEs) of HS scenario with standard model at one-loop level is qualitatively analyzed. By using the solutions of parameter spaces from RGE analysis, the coupling constants of the HS model will be verified and can be used to constrain the SSDM using dark matter relic abundance.

High scale impact in alignment and decoupling in two-Higgs-doublet models

The two-Higgs doublet model (2HDM) provides an excellent benchmark to study physics beyond the Standard Model (SM). In this work we discuss how the behaviour of the model at high energy scales causes it to have a scalar with properties very similar to those of the SM -- which means the 2HDM can be seen to naturally favor a decoupling or alignment limit. For a type II 2HDM, we show that requiring the model to be theoretically valid up to a scale of 1 TeV, by studying the renormalization group equations (RGE) of the parameters of the model, causes a significant reduction in the allowed magnitude of the quartic couplings. This, combined with $B$-physics bounds, forces the model to be naturally decoupled. As a consequence, any non-decoupling limits in type II, like the wrong-sign scenario, are excluded. On the contrary, even with the very constraining limits for the Higgs couplings from the LHC, the type I model can deviate substantially from alignment. An RGE analysis similar to that made for type II shows, however, that requiring a single scalar to be heavier than about 500 GeV would be sufficient for the model to be decoupled. Finally, we show that not only a 2HDM where the lightest of the CP-even scalars is the 125 GeV one does not require new physics to be stable up to the Planck scale but this is also true when the heavy CP-even Higgs is the 125 GeV and the theory has no decoupling limit for the type I model.

Renormalization group equation analysis of a pseudoscalar portal dark matter model

We investigate the vacuum stability and perturbativity of a pseudoscalar portal dark matter (DM) model with a Dirac DM candidate, through the renormalization group equation analysis at one-loop order. The model has a particular feature which can evade the direct detection upper bounds measured by XENON100 and even that from planned experiment XENON1T. We first find the viable regions in the parameter space which will give rise to correct DM relic density and comply with the constraints from Higgs physics. We show that for a given mass of the pseudoscalar, the mixing angle plays no significant role in the running of the couplings. Then we study the running of the couplings for various pseudoscalar masses at mixing angle , and find the scale of validity in terms of the dark coupling, . Depending on our choice of the cutoff scale, the resulting viable parameter space will be determined.

Z→bb¯and chiral currents in Higgsless models

In this paper we compute the flavor-dependent chiral-logarithmic corrections to the decay $Z\ensuremath{\rightarrow}b\overline{b}$ in the three-site Higgsless model. We compute these corrections diagrammatically in the gaugeless limit in which the electroweak couplings vanish. We also compute the chiral-logarithmic corrections to the decay $Z\ensuremath{\rightarrow}b\overline{b}$ using a renormalization group equation analysis in effective field theory, and show that the results agree. In the process of this computation, we compute the form of the chiral current in the gaugeless limit of the three-site model, and consider the generalization to the $N$-site case. We elucidate the Ward-Takahashi identities which underlie the gaugeless limit calculation in the three-site model, and describe how the result for the $Z\ensuremath{\rightarrow}b\overline{b}$ amplitude is obtained in unitary gauge in the full theory. We find that the phenomenological constraints on the three-site Higgsless model arising from measurements of $Z\ensuremath{\rightarrow}b\overline{b}$ are relatively mild, requiring only that the heavy Dirac fermion be heavier than 1 TeV or so, and are satisfied automatically in the range of parameters allowed by other precision electroweak data.

Refining the predictions of supersymmetricCP-violating models: A top-down approach

We explore in detail the consequences of the CP-violating phases residing in the supersymmetric and soft SUSY breaking parameters in the approximation that family flavour mixings are ignored. We allow for non-universal boundary conditions and in such a consideration the model is described by twelve independent CP-violating phases and one angle which misaligns the vacuum expectation values (VEVs) of the Higgs scalars. We run two-loop renormalization group equations (RGEs), for all parameters involved, including phases, and we properly treat the minimization conditions using the one-loop effective potential with CP-violating phases included. We show that the two-loop running of phases may induce sizable effects for the electric dipole moments (EDMs) that are absent in the one-loop RGE analysis. Also important corrections to the EDMs are induced by the Higgs VEVs misalignment angle which are sizable in the large tan β region. Scanning the available parameter space we seek regions compatible with accelerator and cosmological data with emphasis on rapid neutralino annihilations through a Higgs resonance. It is shown that large CP-violating phases, as required in Baryogenesis scenarios, can be tuned to obtain agreement with WMAP3 cold dark matter constraints, EDMs and all available accelerator data, in extended regions of the parameter space which may be accessible to LHC.

Low energy theorems and the unitarity bounds in the extraU(1)superstring inspiredE6models

The conventional method using low energy theorems derived by Chanowitz et al. [Phys. Rev. Lett. 57, 2344 (1986);] does not seem to lead to an explicit unitarity limit in the scattering processes of longitudinally polarized gauge bosons for the high energy case in the extra U(1) superstring inspired models, commonly known as {eta} model, emanating from E{sub 6} group of superstring theory. We have made use of an alternative procedure given by Durand and Lopez [Phys. Lett. B 217, 463 (1989);], which is applicable to supersymmetric grand unified theories. Explicit unitarity bounds on the superpotential couplings (identified as Yukawa couplings) are obtained from both using unitarity constraints as well as using renormalization group equations (RGE) analysis at one-loop level utilizing critical couplings concepts implying divergence of scalar coupling at M{sub G}. These are found to be consistent with finiteness over the entire range M{sub Z}{<=}{radical}(s){<=}M{sub G} i.e. from grand unification scale to weak scale. For completeness, the similar approach has been made use of in other models i.e., {chi}, {psi}, and {nu} models emanating from E{sub 6} and it has been noticed that at weak scale, the unitarity bounds on Yukawa couplings do not differ among E{sub 6} extra U(1)more » models significantly except for the case of {chi} model in 16 representations. For the case of the E{sub 6}-{eta} model ({beta}{sub E} congruent with 9.64), the analysis using the unitarity constraints leads to the following bounds on various parameters: {lambda}{sub t(max.)}(M{sub Z})=1.294, {lambda}{sub b(max.)}(M{sub Z})=1.278, {lambda}{sub H(max.)}(M{sub Z})=0.955, {lambda}{sub D(max.)}(M{sub Z})=1.312. The analytical analysis of RGE at the one-loop level provides the following critical bounds on superpotential couplings: {lambda}{sub t,c}(M{sub Z}) congruent with 1.295, {lambda}{sub b,c}(M{sub Z}) congruent with 1.279, {lambda}{sub H,c}(M{sub Z}) congruent with 0.968, {lambda}{sub D,c}(M{sub Z}) congruent with 1.315. Thus superpotential coupling values obtained by both the approaches are in good agreement. Theoretically we have obtained bounds on physical mass parameters using the unitarity constrained superpotential couplings. The bounds are as follows: (i) Absolute upper bound on top quark mass m{sub t}{<=}225 GeV (ii) the upper bound on the lightest neutral Higgs boson mass at the tree level is m{sub H{sub 2}{sup 0}}{sup tree}{<=}169 GeV, and after the inclusion of the one-loop radiative correction it is m{sub H{sub 2}{sup 0}}{<=}229 GeV when {lambda}{sub t}{ne}{lambda}{sub b} at the grand unified theory scale. On the other hand, these are m{sub H{sub 2}{sup 0}}{sup tree}{<=}159 GeV, m{sub H{sub 2}{sup 0}}{<=}222 GeV, respectively, when {lambda}{sub t}={lambda}{sub b} at the grand unified theory scale. A plausible range on D-quark mass as a function of mass scale M{sub Z{sub 2}} is m{sub D}{approx_equal}O(3 TeV) for M{sub Z{sub 2}}{approx_equal}O(1 TeV) for the favored values of tan{beta}{<=}1. The bounds on aforesaid physical parameters in the case of {chi}, {psi}, and {nu} models in the 27 representation are almost identical with those of {eta} model and are consistent with the present day experimental precision measurements.« less

Fixed-Point Analysis of the Low-Energy Constants in the Pion-Nucleon Chiral Lagrangian

In the framework of heavy-baryon chiral perturbation theory, we investigate the fixed point structure of renormalization group equations (RGE) for the ratios of the renormalized low energy constants (LECs) that feature in the pion-nucleon chiral Lagrangian. The ratios of the LECs deduced from our RGE analysis are found to be in semi-quantitative agreement with those obtained from direct fit to the experimental data. The naturalness of this agreement is discussed using a simple dimensional analysis combined with Wilsonian RGEs.

Method for renormalization group equation analysis and its application.

We develop a general method for analyzing the renormalization group equations (RGE's) to one-loop and two-loop order in grand unified theories (GUT's) which can have an arbitrary number of symmetry-breaking scales and/or mass scales. The method is more efficient, convenient, and accurate than the current method for determining the ranges of symmetry-breaking scales and/or mass scales, as well as the ranges of unified gauge couplings. It does not involve the usual numerical integration of the RGE's at all, but in fact solves the RGE's analytically by a perturbative approach. The results are presented graphically and analyzed using simple geometrical considerations. We apply the method to two-step symmetry-breaking chains of SO(10) GUT's and compare the results with those obtained by numerical integration. We discover that the numerical method itself often introduces errors which are comparable with two-loop corrections. Our method avoids these. We also apply our method to two-step symmetry-breaking chains of supersymmetric SO(10) GUT's.

TOWARD THE REALISTIC THREE-GENERATION MODEL IN THE (2, 0) HETEROTIC STRING COMPACTIFICATION

In the three-generation models with SUSY SO(10) or SU(5) GUTs derived from the (2, 0) compactification of E8×E′8 heterotic string, the massless matter field spectra at the GUT scale Mx and the breaking directions of GUT symmetries are discussed. A pseudo-left-right symmetric Pati-Salam model is naturally deduced in the SUSY SO(10) GUT and shown to have an interesting property, Mx≃MP1, MR≃1010 GeV and Ms (the scale of superpartner masses) ≃104 GeV, as a result of the renormalization group equation analysis using the new precise LEP data.

Three-generation superstring models with Z 3R-symmetry

A class of three-generation superstring models with Z 3 R-symmetry is investigated. Three different definitions of matter-parity are considered in the investigation. It is found that only two models can provide phenomenologically interesting results: all but the known quarks are superheavy; there is one and only one pair of light Higgs doublets; a proton does not decay fast; renormalization group equation analysis gives sin 2 θ W ≈ 0.23−0.25; and two or three additional light lepton doublets and charged singlets are predicted to have mass ∼ 10 3 GeV.