arXiv subjects

C. S. Lim

Publications and source records attributed to C. S. Lim.

At least 19 recordsLinked to original sources

arXiv2025

Dyons in higher-dimensional gauge theories

We discuss the 't Hooft-Polyakov (TP) monopole and then dyon in the framework of higher dimensional gauge theories, such as gauge-Higgs unification models. First, we point out that the Bogomol'nyi-Prasad-Sommerfield (BPS) monopole is nothing but a self-dual gauge field in the 4-dimensional (4D) space including the extra dimension, which is argued to lead to a consequence that the mass of the BPS monopole $M_{{\rm TPM}}$ and therefore the vacuum expectation value (VEV) of the Higgs field are topologically quantized. In literatures, there exist related arguments on the calorons, which may be understood to be a composition of a pair of constituent monopole and anti-monopole, with each constituent carrying fractional topological charge, while the net topological charge carried by the caloron is unity. From the viewpoint of the caloron, our conclusion of the quantized monopole mass corresponds to the special case, where only a single monopole exists that carries the net topological charge. Next, the argument is generalized to the case of dyon. The mass of the BPS dyon, $M_{{\rm BPS}}$, is still proportional to the quantized Higgs VEV, though it also depends on a parameter $\mu$, denoting the ratio of the electric and magnetic charges of the dyon. In the 5D gauge theories the Chern-Simons term is induced at the quantum level, which, after the extra space component of the gauge field is replaced by its VEV, produces the $\theta$ term. Then, through the Witten effect we reach to an interesting conclusion that the parameter $\mu$ and therefore $M_{{\rm BPS}}$ are discretized. In addition, we propose a numerical method to obtain the field configurations and the mass of the non-BPS dyons by use of ``modified" gradient flow equations.

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arXiv2023

Analytic construction of sphaleron-like solution invoking higher dimensional gauge theory

We perform analytic construction of a sphaleron-like solution in the 4-dimensional (4D) space-time invoking the framework of 5D SU(2) gauge theory. By the sphaleron-like solution we mean a static finite energy solution to the equation of motion, which carries the Chern-Simons number $N_\text{CS}=\frac{1}{2}$. Since we are interested in the static solution in the low-energy effective theory, we focus on the part of the action which contains only the gauge fields in the 4D space (not space-time), $(A_{i}, A_{y}) (i = 1,2,3)$ and keep only the Kaluza-Klein zero modes of these fields. Interestingly, the self-duality condition in this 4D space is known to be nothing but the BPS condition for the 't Hooft-Polyakov monopole, once the extra-space component $A_y$ is identified with the adjoint scalar, needed for the monopole solution. Thus, the sphaleron-like solution is based on the BPS monopole embedded in the higher dimensional space-time, which may be interpreted as a self-dual gauge field. By use of the lesson we learn in the case of the instanton in ordinary 4D space-time, we achieve the sphaleron-like configuration of $A_{i}$, which carries $N_\text{CS} = \frac{1}{2}$. As a characteristic feature of this construction invoking higher dimensional gauge theory, in clear contrast to the case of the ordinary BPS monopole, the VEV of the adjoint scalar is topologically fixed, and therefore the mass of the sphaleron-like solution is determined to be $M_\text{sp} = \frac{4π}{g_{4}^{2}}\frac{1}{R}$ ($g_{4}$: 4D gauge coupling constant, $R$: the radius of the circle as the extra space). We also argue that the sphaleron-like solution may be regarded as a saddle point of the energy in the space of static field configurations.

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arXiv2022

On the vacuum structure of gauge-Higgs unification models

In this paper, we discuss the vacuum structure of the gauge-Higgs unification theory, which is one of the attractive candidates of physics beyond the standard model. This scenario has a remarkable feature, namely it has infinitely degenerate vacua due to the characteristic periodic potential of the Higgs filed, to be identified with the extra space component of the higher dimensional gauge field. We address a question, whether to form the superposition of such degenerate vacua, like the $θ$-vacuum in QCD, is necessary or not, in order to realize the true vacuum state of the theory. We derive gauge field configuration which describes the transition between neighboring vacua, like the instanton (or anti-instanton) solution in QCD, and the corresponding Euclidean action in two models. In a simplified 2-dimensional U(1) model, the derived configuration to describe the transition is shown to have finite Euclidean action, and accordingly the "$θ$-vacuum" and the resultant "$θ$-term" are formulated. In a realistic 5D U(1) model, however, the gauge field configuration to describe the transition is shown to have infinite Euclidean action and therefore the tunneling probability between the degenerate vacua vanishes. Thus the superposition of the degenerate vacua is not necessary.

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arXiv2021

The strong CP problem and higher dimensional gauge theories

We discuss a natural scenario to solve the strong CP problem in the framework of the higher dimensional gauge theory. An axion-like field $A_y$ has been built-in as the extra-space component of the higher dimensional gauge field. The coupling of $A_y$ with gluons is attributed to the radiatively induced "Chern-Simons" (CS) term. We adopt a toy model with some unknown gauge symmetry U(1)$_X$. The CS term is obtained in two ways: first by a concrete 1-loop calculation and next by use of the Fujikawa's method to deal with the chiral anomaly in 4D space-time. The obtained results are identical, which implies that the radiative correction to the CS term is "1-loop exact" and is also free from UV-divergence even though the theory itself is non-renormalizable. As a novel feature of this scenario, such obtained CS term is no longer linear in the field $A_y$ as in the usually discussed CS term in 5D space-time but a periodic function of $A_y$, since $A_y$ has a physical meaning as the Wilson-loop phase. We argue how such novel feature of this scenario causes the modification of the ordinary solutions of the strong CP problem based on the axion fields.

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arXiv2020

't Hooft-Polyakov monopole and instanton-like topological solution in gauge-Higgs unification

We consider 't Hooft-Polyakov monopole (TPM) as a topological soliton in the 5-dimensional (5D) theory of gauge-Higgs unification. This scenario provides a very natural framework to incorporate the TPM, since the adjoint scalar is builtin as the extra-space component of higher dimensional gauge field. In the process of the analysis, we realize that the condition to be satisfied by the Bogomolny-Prasad-Sommerfield (BPS) state of TPM, the BPS monopole, is equivalent to an (anti-)self-dual condition for the higher dimensional gauge field. This observation, in turn, suggests the presence of instanton-like topological soliton living in the 4D space (including the extra dimension), instead of the 4D space-time in the case of ordinary instanton, say "space-like instanton" with finite energy, instead of finite action. We construct the field configuration for the space-like instanton and calculate its mass, handled by the compactification scale. Next we discuss the BPS monopole, as an anti-self-dual gauge field. We start by constructing a hedgehog-type solution as what is obtained by a local gauge transformation from a trivial vacuum. We also argue in some detail that the relation between these two types of topological solitons becomes manifest through the unified description by use of the ansatz adopted by 't Hooft.

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arXiv2018

Majorana neutrino masses in the scenario of gauge-Higgs unification

In this paper we consider possible mechanisms to generate small Majorana neutrino masses for active neutrinos in the scenario of gauge-Higgs unification, a candidate for physics beyond the standard model. We stress that it is non-trivial to find a gauge-invariant operator, responsible for the Majorana masses, which is the counterpart of the well-known SU(2)$_L \times$ U(1)$_Y$ invariant higher-mass-dimensional ($d = 5$) operator. As the first possibility we discuss the seesaw mechanism by assigning leptonic fields to the adjoint representation of the gauge group, so that a $d = 5$ gauge-invariant operator can be formed. It turns out that the mechanism leading to the small Majorana masses is the admixture of the Type I and Type III seesaw mechanisms. As the second possibility, we consider the case where the relevant operator has $d = 7$, by introducing a matter scalar belonging to the fundamental representation of the gauge group. Reflecting the fact that the mass dimension of the operator is higher than usually expected, the Majorana masses are generated by a "double seesaw mechanism."

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arXiv2018

The implication of gauge-Higgs unification to the hierarchical fermion masses

The observed hierarchical charged fermion masses of three generations seem to imply that these masses are originally universal for three generations and then get exponential suppression with "quantized exponents" by some mechanism. We argue that such remarkable feature of hierarchical fermion mass spectrum may be naturally understood in the scenario of gauge-Higgs unification, where the universality of fermion masses is guaranteed by the fact that Higgs boson is originally gauge boson in this scenario and also the quantized exponents may be attributed to the well-known quantization condition of magnetic charge of the magnetic monopole placed inside the torus, as the extra dimensional space. Because of the presence of the magnetic monopole, we get a chiral theory and multiple Kaluza-Klein zero modes even if we introduce only a single 6-dimensional Weyl fermion. We present two types of three generation model, which succeed to realize the remarkable hierarchical mass spectrum.

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arXiv2016

Few remarks on the Higgs boson decays in gauge-Higgs unification

In the scenario of gauge-Higgs unification, the origin of the Higgs boson is higher dimensional gauge boson. Reflecting its origin, very characteristic predictions are made of the Higgs boson interactions in this scenario. Especially, a remarkable claim has been made: the contribution of non-zero Kaluza-Klein modes to the Higgs decay $H \to Z γ$ exactly vanishes in the minimal SU(3) electro-weak unified model, at least at the one-loop level. In this brief report, in order to see whether this prediction is a general feature of the scenario or the consequence of the specific choice of the model, matter content or the order of perturbative expansion, we perform an operator analysis. We demonstrate that there does not exist any relevant operator, respecting the gauge symmetry SU(3) in the bulk. We also comment on the possibly important contribution to the photonic decay $H \to γγ$ due to the non-zero Kaluza-Klein modes of light quarks.

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arXiv2016

Predictions of the Higgs mass and the weak mixing angle in the 6D gauge-Higgs unification

In the gauge-Higgs unification with multiple extra spaces, the Higgs self-coupling is of the order of $g^2$ and Higgs is predicted to be light, being consistent with the LHC results. When the gauge group is simple, the weak mixing angle is also predictable. We address a question whether there exists a model of gauge-Higgs unification in 6-dimensional space-time, which successfully predicts the mass ratios of the Higgs boson and weak gauge bosons. First, by use of a useful formula we give a general argument on the condition to get a realistic prediction of the weak mixing angle $sin^{2}theta_{W} = 1/4$, and find that triplet and sextet representations of the minimal SU(3) gauge group lead to the realistic prediction. Concerning the Higgs mass, we notice that in the models with one Higgs doublet, the predicted Higgs mass is always the same: $M_H = 2 M_W$. However, by extending our discussion to the models with two Higgs doublets, the situation changes: we obtain an interesting prediction $M_{H} leq 2M_{W}$ at the leading order of the perturbation. Thus it is possible to recover the observed Higgs mass, 125 GeV, for a suitable choice of the parameter. The situation is in clear contrast to the case of the minimal supersymmetric standard model, where $M_{H} leq M_{Z}$ at the classical level and the predicted Higgs mass cannot recover the observed value.

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arXiv2015

Is the 126 GeV Higgs Boson Mass Calculable in Gauge-Higgs Unification?

We address a question whether the recently observed Higgs mass $M_{H} = 126$ GeV, of the order of the weak scale $M_{W}$, is calculable as a finite value in the scnenario of gauge-Higgs unification. In the scenario formulated on a flat 5-dimensional space-time, the Higgs mass is calculable, being protected under the quantum correction by gauge invariance, though the predicted Higgs mass is generally too small compared with $M_{W}$. In the 6-dimensional SU(3) model, however, a suitable orbifolding is known to lead to a mass of the order of $M_{W}$: $M_{H} = 2M_{W}$ at the tree level, which has some similarity to the corresponding prediction by the MSSM, $M_{H}$ leq (cos beta) $M_{Z}$. We demonstrate first by a general argument and secondly by explicit calculations that, even though the quantum correction to the quartic self-coupling of the Higgs field is UV-divergent, its deviation from that of $g^{2}$ is calculable, and therefore two observables, $M_{H}^{2}$ and Delta equiv $(M_{H}/2M_{W})^{2}-1$, are both calculable in the gauge-Higgs unification scenario. The implication of the precise value 126 GeV to the compactification scale and the bulk mass of the matter field in our model is also discussed.

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arXiv2014

Distinguishing between Extra Natural Inflation and Natural Inflation after BICEP2

In this paper, we carefully calculated the tensor-to-scalar ratio, the running spectral index, and the running of running spectrum for (extra) natural inflation in order to compare with recent BICEP2 data, PLANCK satellite data and future 21 cm data. We discovered that the prediction for running spectral index and the running of running spectrum in natural inflation is different from that in the case of extra natural inflation. Near future observation for the running spectral index may achieve enough accuracy to allow us distinguishing between extra natural inflation from natural inflation. Distinguishing the models by using the running of running spectrum is not impossible but would be more challenging for future experiments.

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arXiv2014

Anomalous Higgs interactions in dimensional deconstruction

Recent LHC experiments have revealed that Higgs is light. As an interesting candidate to accommodate light Higgs, in this paper we adopt the scenario of dimensional deconstruction, where Higgs is redarded as a pseudo-Nambu-Goldstone boson. Though the scenario is formulated in ordinary 4-dimensional space-time, it may also be interpreted as "latticized" gauge-Higgs unification. We point out that in this scenario Higgs interaction with matter field is anomalous, i.e. its coupling deviates from what the standard model predicts. The interplay between the periodicity of physical observables in the Higgs field and the violation of translational invariance along the extra-space due to the latticization is argued to play an essential role to get the anomalous interaction. Though the predicted anomalous Higgs interaction has much similarity to the one in the gauge-Higgs unification, in the case of dimensional deconstruction the anomaly exists even if we do not introduce bulk mass term for the chiral fermion realized by orbifolding, in clear contrast to the case of gauge-Higgs unification. It in turn means that the anomaly goes away in the continuum limit of the extra-space.

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arXiv2014

Hilltop Supernatural Inflation and SUSY Unified Models

In this paper, we consider high scale (100 TeV) supersymmetry (SUSY) breaking and realize the idea of hilltop supernatural inflation in concrete particle physics models based on flipped-SU(5) and Pati-Salam models in the framework of supersymmetric grand unified theories (SUSY GUTs). The inflaton can be a flat direction including right-handed sneutrino and the waterfall field is a GUT Higgs. The spectral index is $n_s=0.96$ which fits very well with recent data by PLANCK satellite. There is no both thermal and non-thermal gravitino problems. Non-thermal leptogenesis can be resulted from the decay of right-handed sneutrino which plays (part of) the role of inflaton.

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arXiv2013

The Higgs Particle and Higher-Dimensional Theories

In spite of the great success of LHC experiments, we do not know whether the discovered "standard model-like" Higgs particle is really what the standard model predicts or a particle some new physics has in its low energy effective theory. Also the long-standing problems concerning the property of Higgs and its interactions are still there, and we still do not have any conclusive argument of the origin of the Higgs itself. In this article we focus on higher-dimensional theories as new physics. First we give a brief review of their representative scenarios and closely related 4-dimensional scenarios. Among them, we mainly discuss two interesting possibilities of the origin of the Higgs: Higgs as a gauge boson and Higgs as a (pseudo) Nambu-Goldstone boson. Next, we argue that theories of new physics are divided into two categories, i.e. theories with normal Higgs interactions and those with anomalous Higgs interactions. Interestingly both of two candidates concerning the origin of the Higgs mentioned above predict characteristic "anomalous" Higgs interactions, such as the deviation of the Yukawa couplings from the standard model predictions. Such deviations can be hopefully investigated by the precision tests of Higgs interactions at the planned ILC experiment. Also discussed is the main decay mode of the Higgs, $H \to γγ$. Again, theories belonging different categories are known to predict remarkably different new physics contributions to this important process.

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arXiv2012

Flavor Mixing in the Gauge-Higgs Unification

Gauge-Higgs unification is the fascinating scenario solving the hierarchy problem without supersymmetry. In this scenario, the Standard Model (SM) Higgs doublet is identified with extra component of the gauge field in higher dimensions and its mass becomes finite and stable under quantum corrections due to the higher dimensional gauge symmetry. On the other hand, Yukawa coupling is provided by the gauge coupling, which seems to mean that the flavor mixing and CP violation do not arise at it stands. In this talk, we discuss that the flavor mixing is originated from simultaneously non-diagonalizable bulk and brane mass matrices. Then, this mechanism is applied to various flavor changing neutral current (FCNC) processes via Kaluza-Klein (KK) gauge boson exchange at tree level and constraints for compactification scale are obtained.

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arXiv2012

Anomalous Higgs Interactions in Gauge-Higgs Unification

We discuss anomalous Higgs interactions in the scenario of gauge-Higgs unification. In the scenario Higgs originates from higher dimensional gauge field and has a physical meaning as AB phase or Wilson loop. As its inevitable consequence, physical observables are expected to be periodic in the Higgs field. In particular, the Yukawa coupling is expected to show some periodic and non-linear behavior as the function of the Higgs VEV. For a specific choice of the VEV, the Yukawa coupling of KK zero mode fermion even vanishes. On the other hand, the Yukawa coupling is originally provided by gauge interaction, which is linear in the Higgs field. We discuss how such two apparent contradiction about the non-linearity of the Yukawa coupling can be reconciled and at the same time how these two "pictures" give different predictions in the simplest framework of the scenario: SU(3) electroweak model in 5-dimensional flat space-time with orbifolding. The deviation of the Yukawa coupling from the standard model prediction is also calculated for arbitrary VEV. We study "$H$-parity", which guarantees the stability of the Higgs for a specific choice of the VEV. Also discussed is the Higgs interaction with $W^\pm$ and $Z^0$. It turns out that in our framework of flat space-time the interaction does not show deviation from the standard model prediction, except for the specific case of the VEV.

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arXiv2011

D^0-\bar D^0 Mixing in Gauge-Higgs Unification

We discuss flavor mixing and resulting Flavor Changing Neutral Current (FCNC) in the SU(3) \otimes SU(3)_color gauge-Higgs unification. As the FCNC process we calculate the rate of D^0-\bar D^0 mixing due to the exchange of non-zero Kaluza-Klein gluons at the tree level. Flavor mixing is argued to be realized by the fact that the bulk mass term and brane localized mass term is not diagonalized simultaneously unless bulk masses are degenerate. It is shown that automatic suppression mechanism is operative for the FCNC processes of light quarks. We therefore obtain a lower bound on the compactification scale of order \cal O(TeV) by comparing our prediction on the mass difference of neutral D meson with the recent experimental data, which is much milder than what we naively expect assuming only the decoupling of non-zero Kaluza-Klein gluons.

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arXiv2011

Flavor Mixing in Gauge-Higgs Unification

We discuss flavor mixing and resultant flavor changing neutral current processes in the SU(3) \otimes SU(3)_\text{color} gauge-Higgs unification scenario. To achieve flavor violation is a challenging issue in the scenario, since the Yukawa couplings are originally higher dimensional gauge interactions. We argue that the presence of Z_2-odd bulk masses of fermions plays a crucial role as the new source of flavor violation. Although introducing brane-localized mass terms in addition to the bulk masses is necessary to realize flavor mixing, if the bulk masses were universal among generations, the flavor mixing and flavor changing neutral current processes are known to disappear. We also discuss whether natural flavor conservation is realized in the scenario. It is shown that the new source of flavor violation leads to flavor changing neutral current processes at the tree level due to the exchange of non-zero Kaluza-Klein gauge bosons. As a typical example we calculate the rate of K^0 - \bar{K}^0 mixing due to the non-zero Kaluza-Klein gluon exchange at the tree level. The obtained result for the mass difference of neutral kaon is suppressed by the inverse powers of the compactification scale. By comparing our prediction with the data we obtain the lower bound of the compactification scale as a function of one unfixed parameter of the theory, which is of {\cal O}(10) TeV, except for some extreme cases. We argue that the reason to get such rather mild lower bound is the presence of "GIM-like" mechanism, which is a genuine feature of GHU scenario.

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