# Masafumi Kurachi - Nagoya Univ.

## Contact Details

NameMasafumi Kurachi |
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AffiliationNagoya Univ. |
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CityToyoake-shi |
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CountryJapan |
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## Pubs By Year |
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## External Links |
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## Pub CategoriesHigh Energy Physics - Phenomenology (37) High Energy Physics - Lattice (29) High Energy Physics - Theory (4) High Energy Physics - Experiment (4) |

## Publications Authored By Masafumi Kurachi

We discuss the properties of the topological soliton, or the Electroweak-Skyrmion, in the system of the Standard Model Higgs Lagrangian with addition of general O(p^4) terms. We show that the upper bound on the mass of the Electroweak-Skyrmion is about 10 TeV, which is obtained from currently available experimental constraints on coefficients of O(p^4) terms. The impact on the properties of the Electroweak-Skyrmion due to further modification of the Lagrangian is also discussed, and comments on possible mechanisms for the generation of the Electroweak-Skyrmion in the early Universe as a dark matter are given. Read More

**Authors:**Yasumichi Aoki

^{1}, Tatsumi Aoyama

^{2}, Ed Bennett

^{3}, Masafumi Kurachi

^{4}, Toshihide Maskawa

^{5}, Kohtaroh Miura

^{6}, Kei-ichi Nagai

^{7}, Hiroshi Ohki

^{8}, Enrico Rinaldi

^{9}, Akihiro Shibata

^{10}, Koichi Yamawaki

^{11}, Takeshi Yamazaki

^{12}

**Affiliations:**

^{1}the LatKMI Collaboration,

^{2}the LatKMI Collaboration,

^{3}the LatKMI Collaboration,

^{4}the LatKMI Collaboration,

^{5}the LatKMI Collaboration,

^{6}the LatKMI Collaboration,

^{7}the LatKMI Collaboration,

^{8}the LatKMI Collaboration,

^{9}the LatKMI Collaboration,

^{10}the LatKMI Collaboration,

^{11}the LatKMI Collaboration,

^{12}the LatKMI Collaboration

Based on the highly improved staggered quark action, we perform lattice simulations of $N_f=8$ QCD and confirm our previous observation of a flavor-singlet scalar meson (denoted as $\sigma$) as light as the pion and various "walking signals" through low-lying spectra, with higher statistics, smaller fermion masses $m_f$, and larger volumes. We measure $M_\pi$, $F_\pi$, $M_\rho$, $M_{a_0}$, $M_{a_1}$, $M_{b_1}$, $M_N$, $M_\sigma$, $F_\sigma$, $\langle \overline{\psi} \psi\rangle$ (both directly and through the GMOR relation), and the string tension. The data are consistent with the spontaneously broken phase of the chiral symmetry, in agreement with the previous results: ratios of the quantities to $M_\pi$ monotonically increase in the smaller $m_f$ region towards the chiral limit similarly to $N_f=4$ QCD, in sharp contrast to $N_f=12$ QCD where the ratios become flattened. Read More

We show the existence of a nontrivial topological configuration of the Higgs field in the Standard Model with the Skyrme term. It is shown that the current upper bound of the mass of the topological object is about 34 TeV. We discuss the impact of the existence of the topological object on cosmology. Read More

**Authors:**LatKMI collaboration, Yasumichi Aoki

^{1}, Tatsumi Aoyama

^{2}, Ed Bennett

^{3}, Masafumi Kurachi

^{4}, Toshihide Maskawa

^{5}, Kohtaroh Miura

^{6}, Kei-ichi Nagai

^{7}, Hiroshi Ohki

^{8}, Enrico Rinaldi

^{9}, Akihiro Shibata

^{10}, Koichi Yamawaki

^{11}, Takeshi Yamazaki

^{12}

**Affiliations:**

^{1}KMI,

^{2}KMI,

^{3}Swansea,

^{4}KEK,

^{5}KMI,

^{6}CPT Marseille,

^{7}KMI,

^{8}RIKEN-BNL,

^{9}LLNL,

^{10}KEK,

^{11}KMI,

^{12}Tsukuba

**Category:**High Energy Physics - Lattice

SU(3) gauge theory with eight massless fundamental fermions seems to be near the conformal boundary, and is a candidate theory of walking technicolor. Along the series of study by LatKMI collaboration using HISQ fermions, S-parameter and vector decay constant, which provide important constraints in the model of electroweak symmetry breaking, are calculated for this theory. Use of various volumes allows a systematic investigation of finite volume effects. Read More

SU(3) gauge theory with eight massless flavours is believed to be walking, while the corresponding twelve- and four-flavour appear IR-conformal and confining respectively. Looking at the simulations performed by the LatKMI collaboration of these theories, we use the topological susceptibility as an additional probe of the IR dynamics. By drawing a comparison with SU(3) pure gauge theory, we see a dynamical quenching effect emerge at larger number of flavours, which is suggestive of emerging near-conformal and conformal behaviour. Read More

In the search for a realistic walking technicolor model, QCD with many flavors is an attractive candidate. From the series of studies by the LatKMI collaboration, we present updated results of the scaling properties of various hadron spectra, including the (pseudo)scalar, vector, and baryon channels, for $N_f=8$ QCD analyzed with the HISQ action. By comparing these with $N_f=12$ QCD, which has properties consistent with conformality, possible signals of walking dynamics are discussed. Read More

As a part of the project studying large $N_f$ QCD, the LatKMI Collaboration has been investigating the SU(3) gauge theory with four fundamental fermions (four-flavor QCD). The main purpose of studying four-flavor QCD is to provide a qualitative comparison to $N_f= 8$, $12$, $16$ QCD; however, a quantitative comparison to real-world QCD is also interesting. To make such comparisons more meaningful, it is desirable to use the same kind of lattice action consistently, so that qualitative difference of different theories are less affected by artifacts of lattice discretization. Read More

In the search for a composite Higgs boson in walking technicolor models, many flavor QCD, in particular with $N_f=8$, is an attractive candidate, and has been found to have a composite flavor-singlet scalar as light as the pion. Based on lattice simulations of this theory with the HISQ action, we will present our preliminary results on the scalar decay constant using the fermionic bilinear operator, and on the mass of the lightest baryon state which could be a dark matter candidate. Combining these two results, implications for dark matter direct detection are also discussed. Read More

LatKMI Collaboration discusses the topological insights in many-flavor QCD on the lattice. We explore walking/conformal/confining phase in $N_\mathrm{f}$ = 4, 8 and 12 (in particular $N_\mathrm{f}$ = 8) lattice QCD via the topological charge and susceptibility, eigenvalues and anomalous dimension. Read More

The ATLAS collaboration has recently reported an excess of about 2.5 $\sigma$ global significance at around 2 TeV in the diboson channel with the boson-tagged fat dijets, which may imply a new resonance beyond the standard model. We provide a possible explanation of the excess as the isospin-triplet technivector mesons (technirhos, denoted as $\rho_\Pi^{\pm,3}$) of the walking technicolor in the case of the one-family model as a benchmark. Read More

The spectrum of twelve-flavor QCD has been studied in details by the LatKMI collaboration. In this proceeding we present our updated results for the spectrum obtained with the HISQ action at two lattice spacings, several volumes and fermion masses. In particular, we emphasize the existence of a flavor-singlet scalar state parametrically light with respect to the rest of the spectrum, first reported in our paper. Read More

In technicolor theories using an SU($N_{TC}$) gauge group, the value of $N_{TC}$ is not, {\it a priori}, determined and is typically chosen by phenomenological criteria. Here we present a novel way to determine $N_{TC}$ from the embedding of a one-family technicolor model, with fermions in the fundamental represention of SU($N_{TC}$), in an extended technicolor theory, and use it to deduce that $N_{TC}=4$ in this framework. Read More

We study the vacuum alignment of the top-mode pseudo-Nambu-Goldstone boson Higgs (TMpNGBH) model, which has recently been proposed as a variant of the top quark condensate model in light of the 126 GeV Higgs boson discovered at the LHC. It is shown that the vacuum of the model, determined from the one-loop effective potential with all the explicit breaking effects included, realizes the electroweak symmetry breaking with the appropriate breaking scale. Phenomenologies of two characteristic particles in the TMpNGBH model, namely the CP-odd partner of the Higgs and the vectorlike partner of the top quark are also studied based on the newly identified vacuum. Read More

We formulate a scale-invariant hidden local symmetry (HLS) as a low-energy effective theory of walking technicolor (WTC) which includes the technidilaton, technipions, and technirho mesons as the low-lying spectra. As a benchmark for LHC phenomenology, we in particular focus on the one-family model of WTC having eight technifermion flavors, which can be, at energy scales relevant to the reach of the LHC, described by the scale-invariant HLS based on the manifold $[SU(8)_L \times SU(8)_R]_{\rm global} \times SU(8)_{\rm local}/SU(8)_V$, where $SU(8)_{\rm local}$ is the HLS and the global $SU(8)_L \times SU(8)_R$ symmetry is partially gauged by $SU(3) \times SU(2)_L \times U(1)_Y$ of the standard model. Based on the scale-invariant HLS, we evaluate the coupling properties of the technirho mesons and place limits on the masses from the current LHC data. Read More

**Authors:**Yasumichi Aoki

^{1}, Tatsumi Aoyama

^{2}, Masafumi Kurachi

^{3}, Toshihide Maskawa

^{4}, Kohtaroh Miura

^{5}, Kei-ichi Nagai

^{6}, Hiroshi Ohki

^{7}, Enrico Rinaldi

^{8}, Akihiro Shibata

^{9}, Koichi Yamawaki

^{10}, Takeshi Yamazaki

^{11}

**Affiliations:**

^{1}the LatKMI Collaboration,

^{2}the LatKMI Collaboration,

^{3}the LatKMI Collaboration,

^{4}the LatKMI Collaboration,

^{5}the LatKMI Collaboration,

^{6}the LatKMI Collaboration,

^{7}the LatKMI Collaboration,

^{8}the LatKMI Collaboration,

^{9}the LatKMI Collaboration,

^{10}the LatKMI Collaboration,

^{11}the LatKMI Collaboration

We present the first observation of a flavor-singlet scalar meson as light as the pion in $N_f=8$ QCD on the lattice, using the Highly Improved Staggered Quark action. Such a light scalar meson can be regarded as a composite Higgs with mass 125 GeV. In accord with our previous lattice results showing that the theory exhibits walking behavior, the light scalar may be a technidilaton, a pseudo Nambu-Goldstone boson of the approximate scale symmetry in walking technicolor. Read More

We calculate masses of the technipions in the walking technicolor model with the anomalous dimension gamma_m =1, based on a holographic model which has a naturally light technidilaton phi as a composite Higgs with mass m_phi simeq 125 GeV. The one-family model (with 4 weak-doublets) is taken as a concrete example in such a framework, with the inputs being F_pi=v/2 simeq 123 GeV and m_phi simeq 125 GeV as well as gamma_m=1. It is shown that technipion masses are enhanced by the large anomalous dimension to typically O(1) TeV. Read More

We report the calculation of the flavor-singlet scalar in the SU(3) gauge theory with the degenerate twelve fermions in the fundamental representation using a HISQ-type action at a fixed $\beta$. In order to reduce the large statistical error coming from the vacuum-subtracted disconnected correlator, we employ a noise reduction method and a large number of configurations. We observe that the flavor-singlet scalar is lighter than the pion in this theory from the calculations with the fermion bilinear and gluonic operators. Read More

In the spirit of the top quark condensation, we propose a model which has a naturally light composite Higgs boson, "tHiggs", to be identified with the 126 GeV Higgs discovered at the LHC. The tHiggs, a bound state of the top quark and its flavor (vector-like) partner, emerges as a pseudo Nambu-Goldstone boson (NGB), "Top-Mode Pseudo", together with the exact NGBs to be absorbed into the W and Z bosons as well as another (heavier) Top-Mode Pseudo (CP-odd composite scalar). Those five composite (exact/pseudo) NGBs are dynamically produced simultaneously by a single supercritical four-fermion interaction having U(3) x U(1) symmetry which includes the electroweak symmetry, where the vacuum is aligned by small explicit breaking term so as to break the symmetry down to a subgroup, U(2) x U(1)', in a way not to retain the electroweak symmetry, in sharp contrast to the little Higgs models. Read More

We measure glueball masses and the string tension in twelve-flavour QCD, aiming at comparing the emerging gluonic spectrum to the mesonic one. When approaching the critical surface at zero quark mass, the hierarchy of masses in the different sectors of the spectrum gives a new handle to determine the existence of an infrared fixed point. We describe the details of our gluonic measurements and the results obtained on a large number of gauge configurations generated with the HISQ action. Read More

In search for a composite Higgs boson (techni-dilaton) in the walking technicolor, we present our preliminary results on the first observation of a light flavor-singlet scalar in a candidate theory for the walking technicolor, the Nf=8 QCD, which was found in our previous paper to have spontaneous chiral symmetry breaking together with remnants of the conformality. Based on simulations with the HISQ-type action on several lattice sizes with various fermion masses, we find evidence of a flavor-singlet scalar meson with mass comparable to that of the Nambu-Goldstone pion in both the small fermion-mass region, where chiral perturbation theory works, and the intermediate fermion-mass region where the hyperscaling relation holds. We further discuss its chiral limit extrapolation in comparison with other states studied in our previous paper: the scalar has a mass much smaller than that of the vector meson, which is compared to the Nambu-Goldstone pion having a vanishing mass in that limit. Read More

We study "gluonic effects" (gluon condensation effects) on the hadronic leading order (HLO) contributions to the anomalous magnetic moment (g-2) of leptons, based on a holographic model having explicit gluonic mode introduced for consistency with the operator product expansion of QCD. We find gluonic enhancement of HLO contributions to the muon g-2 by about 6%, which nicely fills in the gap between the holographic estimate without gluonic effects and the phenomenological one using the experimental data as inputs. Similar calculations including the gluonic effects for the electron and the tau lepton g-2 are also carried out in good agreement with the phenomenological estimates. Read More

Based on lattice simulations using highly improved staggered quarks for twelve-flavor QCD with several bare fermion masses, we observe a flavor-singlet scalar state lighter than the pion in the correlators of fermionic interpolating operators. The same state is also investigated using correlators of gluonic interpolating operators. Combined with our previous study, that showed twelve-flavor QCD to be consistent with being in the conformal window, we infer that the lightness of the scalar state is due to infrared conformality. Read More

We investigate chiral and conformal properties of the lattice QCD with eight flavors (Nf=8) through meson spectrum using the Highly Improved Staggered Quark (HISQ) action. We also compare our results with those of Nf=12 and Nf=4 which we study on the same systematics. We find that the decay constant F_pi of the pseudoscalar meson "pion" is non-zero, with its mass M_pi consistent with zero, both in the chiral limit extrapolation of the chiral perturbation theory (ChPT). Read More

The LatKMI collaboration is studying systematically the dynamical properties of N_f = 4,8,12,16 SU(3) gauge theories using lattice simulations with (HISQ) staggered fermions. Exploring the spectrum of many-flavour QCD, and its scaling near the chiral limit, is mandatory in order to establish if one of these models realises the Walking Technicolor scenario. Although lattice technologies to study the mesonic spectrum are well developed, scalar flavour-singlet states still require extra effort to be determined. Read More

We present the report of the LatKMI collaboration on the lattice QCD simulation for the cases of 4 and 8 flavors. The Nf=8 in particular is interesting from the model-building point of view: The typical walking technicolor model with the large anomalous dimension is the so-called one-family model (Farhi-Susskind model). Thus we explore the walking behavior in LQCD with 8 HISQ quarks by comparing with the 4-flavor case (in which the chiral symmetry is spontaneously broken). Read More

We present our result of the many-flavor QCD. Information of the phase structure of many-flavor SU(3) gauge theory is of great interest, since the gauge theories with the walking behavior near the infrared fixed point are candidates of new physics for the origin of the dynamical electroweak symmetry breaking. We study the SU(3) gauge theories with 12 and 16 fundamental fermions. Read More

We study infrared conformality of the twelve-flavor QCD on the lattice. Utilizing the highly improved staggered quarks (HISQ) type action which is useful to study the continuum physics, we analyze the lattice data of the mass and the decay constant of a pseudoscalar meson and the mass of a vector meson as well at several values of lattice spacing and fermion mass. Our result is consistent with the conformal hypothesis for the mass anomalous dimension $\gamma_m \sim 0. Read More

Information of the phase structure of many flavor SU(3) gauge theory is of great interest for finding a theory which dynamically breaks the electro-weak symmetry. We study the SU(3) gauge theory with fermions for $N_f=12$ and 16 in fundamental representation. Both of them, through perturbation theory, reside in the conformal phase. Read More

We present the first report of the LatKMI collaboration on the the lattice QCD simulation performed at the KMI computer, "$\varphi$", for the cases of 4 flavors and 8 flavors, the latter being expected to be a candidate for the walking technicolor having an approximate scale invariance near the infrared fixed point. The simulation was carried out based on the highly improved staggered quark (HISQ) action. In this proceedings, we report preliminary results on the spectrum, analyzed through the chiral perturbation theory and the finite-size hyperscaling. Read More

We study corrections to the conformal hyperscaling relation in the conformal window of the large Nf QCD by using the ladder Schwinger-Dyson (SD) equation as a concrete dynamical model. From the analytical expression of the solution of the ladder SD equation, we identify the form of the leading mass correction to the hyperscaling relation. We find that the anomalous dimension, when identified through the hyperscaling relation neglecting these corrections, yields a value substantially lower than the one at the fixed point \gamma_m^* for large mass region. Read More

The technique of Weinberg's spectral-function sum rule is a powerful tool for a study of models in which global symmetry is dynamically broken. It enables us to convert information on the short-distance behavior of a theory to relations among physical quantities which appear in the low-energy picture of the theory. We apply such technique to general supersymmetry breaking models to derive new sum rules. Read More

Incorporated with twisted boundary condition, Polyakov loop correlators can give a definition of the renormalized coupling. We employ this scheme for the step scaling method (with step size s = 2) in the search of conformal fixed point of SU(3) gauge theory with 12 massless flavors. Staggered fermion and plaquette gauge action are used in the lattice simulation with six different lattice sizes, L/a = 20, 16, 12, 10, 8 and 6. Read More

We study the infrared properties of SU(3) gauge theory coupled to 12 massless Dirac fermions in the fundamental representation. The renormalized running coupling constant is calculated in the Twisted Polyakov loop scheme on the lattice. From the step-scaling analysis, we find that the infrared behavior of the theory is governed by a non-trivial fixed point. Read More

We measure the renormalized coupling in the Twisted Polyakov loop scheme for SU(3) gauge theory coupled with $N_f=12$ fundamental fermions. To find the infrared fixed point of this theory, we focus on the step scaling function for the renormalized coupling. We take the continuum limit using the linear function of $(a/L)^2$ and a constant fit function. Read More

We present our preliminary study of the SU(2) gauge theory with 8 flavors of fermions in fundamental representation. This theory could be a candidate of the gauge theory with conformal fixed point. By using Wilson/Polyakov loop in a finite volume with twisted boundary conditions, we study the renormalization group flow of the gauge coupling constant. Read More

We study the flavor structure in the three site Higgsless model. In this model, the gauge bosons and fermions have heavy partners, coming from the Kaluza-Klein excitation in the dimensional deconstruction picture. The yukawa couplings are introduced in a way to minimize the flavor chaning neutral current in the light sector at the tree level. Read More

The three site Higgsless model has been offered as a benchmark for studying the collider phenomenology of Higgsless models. In this talk, we present how well the three site Higgsless model performs as a general representative of Higgsless models in describing W_L W_L scattering, and which modifications can make it more representative. We employ general sum rules relating the masses and couplings of the Kaluza-Klein (KK) modes of the gauge fields in continuum and deconstructed Higgsless models as a way to compare the different theories. Read More

We present a non-perturbative study of the running coupling constant in the Twisted Polyakov Loop (TPL) scheme. We investigate how the systematic and statistical errors can be controlled {\it via} a feasibility study in SU(3) pure Yang-Mills theory. We show that our method reproduces the perturbative determination of the running coupling in the UV. Read More

We present a simple formulation of non-linear supersymmetry where superfields and partnerless fields can coexist. Using this formalism, we propose a supersymmetric Standard Model without the Higgsino as an effective model for the TeV-scale supersymmetry breaking scenario. We also consider an application of the Hidden Local Symmetry in non-linear supersymmetry, where we can naturally incorporate a spin-two resonance into the theory in a manifestly supersymmetric way. Read More

**Authors:**Alexander S. Belyaev

^{1}, R. Sekhar Chivukula

^{2}, Neil D. Christensen

^{3}, Elizabeth H. Simmons

^{4}, Hong-Jian He

^{5}, Masafumi Kurachi

^{6}, Masaharu Tanabashi

^{7}

**Affiliations:**

^{1}Southampton U.,

^{2}Michigan State U.,

^{3}Michigan State U.,

^{4}Michigan State U.,

^{5}Tsinghua U., Beijing,

^{6}LANL,

^{7}Nagoya U.

**Category:**High Energy Physics - Phenomenology

The three-site model has been offered as a benchmark for studying the collider phenomenology of Higgsless models. In this paper we analyze how well the three-site model performs as a general exemplar of Higgsless models in describing W_L W_L scattering, and which modifications can make it more representative. We employ general sum rules relating the masses and couplings of the Kaluza-Klein (KK) modes of the gauge fields in continuum and deconstructed Higgsless models as a way to compare the different theories. Read More

We propose a new renormalization scheme of the running coupling constant in general gauge theories using the Wilson loops. The renormalized coupling constant is obtained from the Creutz ratio in lattice simulations and the corresponding perturbative coefficient at the leading order. The latter can be calculated by adopting the zeta-function resummation techniques. Read More

We propose a new method to compute the running coupling constant of gauge theories on the lattice. We first give the definition of the running coupling in the new scheme using the Wilson loops in a finite volume, and explain how the running of the coupling constant is extracted from the measurement of the volume dependence. The perturbative calculation of the renormalization constant to define the scheme is also given at the leading order. Read More

We analyze inelastic 2 to 2 scattering amplitudes for gauge bosons and Nambu-Goldstone bosons in deconstructed Higgsless models. Using the (KK) Equivalence Theorem in 4D (5D), we derive a set of general sum rules among the boson masses and multi-boson couplings that are valid for arbitrary deconstructed models. Taking the continuum limit, our results naturally include the 5D Higgsless model sum rules for arbitrary 5D geometry and boundary conditions; they also reduce to the elastic sum rules when applied to the special case of elastic scattering. Read More

We calculate the Z boson propagator correction, as described by the S parameter, in technicolor theories with extended technicolor interactions included. Our method is to solve the Bethe-Salpeter equation for the requisite current-current correlation functions. Our results suggest that the inclusion of extended technicolor interactions has a relatively small effect on S. Read More

Based on recent works [1,2], we present the results of calculations for several physical quantities (meson masses, the S parameter, etc.) in a vectorial gauge theory, as a function of the number of fermions, N_f. Solutions of the Schwinger-Dyson and the Bethe-Salpeter equations with the improved ladder approximation are used for the calculations. Read More

We study elastic pion-pion scattering in global linear moose models and apply the results to a variety of Higgsless models in flat and AdS space using the Equivalence Theorem. In order to connect the global moose to Higgsless models, we first introduce a block-spin transformation which corresponds, in the continuum, to the freedom to perform coordinate transformations in the Higgsless model. We show that it is possible to make an "f-flat" deconstruction in which all of the f-constants f_j of the linear moose model are identical; the phenomenologically relevant f-flat models are those in which the coupling constants of the groups at either end of the moose are small - corresponding to the global linear moose. Read More

We consider a vectorial, confining SU(N) gauge theory with a variable number, $N_f$, of massless fermions transforming according to the fundamental representation. Using the Schwinger-Dyson and Bethe-Salpeter equations, we calculate the $S$ parameter in terms of the current-current correlation functions. We focus on values of $N_f$ such that the theory is in the crossover region between the regimes of walking behavior and QCD-like (non-walking) behavior. Read More

We analyze the spectrum and properties of a highly-deconstructed Higgsless model with only three sites. Such a model contains sufficient complexity to incorporate interesting physics issues related to fermion masses and electroweak observables, yet remains simple enough that it could be encoded in a Matrix Element Generator program for use with Monte Carlo simulations. The gauge sector of this model is equivalent to that of the BESS model; the new physics of interest here lies in the fermion sector. Read More

We study a vectorial gauge theory with gauge group SU(Nc) and a variable number, Nf, of massless fermions in the fundamental representation of this group. Using approximate solutions of Schwinger-Dyson and Bethe-Salpeter equations, we calculate meson masses and investigate how these depend on Nf. We focus on the range of Nf extending from near the boundary with a non-Abelian Coulomb phase, where the theory exhibits a slowly running ("walking") gauge coupling, toward smaller values where the theory has non-walking behavior. Read More

In the framework of the Schwinger-Dyson equation and the Bethe-Salpeter equation in the improved ladder approximation, we calculate the S parameter and an analogue of the \pi^+ - \pi^0 mass difference \Delta m_\pi^2 \equiv m_{\pi^+}^2 -m_{\pi^0}^2 as well as the NG boson decay constant f_\pi on the same footing in the large N_f QCD, through the difference between the vector current correlator \Pi_{VV} and the axial-vector current correlator \Pi_{AA}. Approaching the chiral phase transition point \alpha_*\to \alpha_{\rm cr} (=\pi/4) from the broken phase, where \alpha_* is the the gauge coupling on the infrared fixed point, \Delta m_\pi^2 as well as f_\pi^2 goes to zero with the essential-singularity scaling (Miransky scaling), while the ratio indicates a blowing up enhancement reflecting the characteristic behavior of the large N_f QCD as a walking theory which is expected to scale as \Delta m_\pi^2/f_\pi^2 \sim (\alpha_*/\alpha_{\rm cr}-1)^{-1/2}. On the other hand, the S parameter takes values somewhat smaller than that of the real-life QCD and indicates slightly decreasing tendency as we approach the phase transition point. Read More