Beyond standard model (BSM) particles should be included in effective field theory in order to compute the scattering amplitudes involving these extra particles. We formulate an extension of Higgs effective field theory which contains arbitrary numbe
r of scalar and fermion fields with arbitrary electric and chromoelectric charges. The BSM Higgs sector is described by using the non-linear sigma model in a manner consistent with the spontaneous electroweak symmetry breaking. The chiral order counting rule is arranged consistently with the loop expansion. The leading order Lagrangian is organized in accord with the chiral order counting rule. We use a geometrical language to describe the particle interactions. The parametrization redundancy in the effective Lagrangian is resolved by describing the on-shell scattering amplitudes only with the covariant quantities in the scalar/fermion field space. We introduce a useful coordinate (normal coordinate), which simplifies the computations of the on-shell amplitudes significantly. We show the high energy behaviors of the scattering amplitudes determine the curvature tensors in the scalar/fermion field space. The massive spinor-wavefunction formalism is shown to be useful in the computations of on-shell helicity amplitudes.
We formulate a generalization of Higgs effective field theory (HEFT) including arbitrary number of extra neutral and charged Higgs bosons (generalized HEFT, GHEFT) to describe non-minimal electroweak symmetry breaking models. Using the geometrical fo
rm of the GHEFT Lagrangian, which can be regarded as a nonlinear sigma model on a scalar manifold, it is shown that the scalar boson scattering amplitudes are described in terms of the Riemann curvature tensor (geometry) of the scalar manifold and the covariant derivatives of the potential. The coefficients of the one-loop divergent terms in the oblique correction parameters S and U can also be written in terms of the Killing vectors (symmetry) and the Riemann curvature tensor (geometry). It is found that perturbative unitarity of the scattering amplitudes involving the Higgs bosons and the longitudinal gauge bosons demands the flatness of the scalar manifold. The relationship between the finiteness of the electroweak oblique corrections and perturbative unitarity of the scattering amplitudes is also clarified in this language: we verify that once the tree-level unitarity is ensured, then the one-loop finiteness of the oblique correction parameters S and U is automatically guaranteed.
The relic abundance of the dark matter (DM) particle $d$ is studied in a secluded DM scenario, in which the $d$ number decreasing process dominantly occurs not through the pair annihilation of $d$ into the standard model particles, but via the $dd to
mm$ scattering process with a subsequently decaying mediator particle $m$. It is pointed out that the cosmologically observed relic abundance of DM can be accomplished even with a massive mediator having a mass $m_m$ non-negligibly heavy compared with the DM particle mass $m_d$. In the degenerated $d$-$m$ case ($m_d=m_m$), the DM relic abundance is realized by adjusting the $dd to mm$ scattering amplitude large enough and by choosing an appropriate mediator particle life-time. The DM evolution in the early universe exhibits characteristic terrace behavior, or two-step number density decreasing behavior, having a fake freeze-out at the first step. Based on these observations, a novel possibility of the DM model buildings is introduced in which the mediator particle $m$ is unified with the DM particle $d$ in an approximate dark symmetry multiplet. A pionic DM model is proposed to illustrate this idea in a renormalizable field theory framework.
Introducing arbitrary number of neutral Higgs bosons in the electroweak symmetry breaking sector, we derive a set of conditions among Higgs couplings which need to be satisfied to maintain the unitarity of the high energy scattering amplitudes of wea
k gauge bosons at the tree level (unitarity sum rules). It is shown that the unitarity sum rules require the tree level $rho$ parameter to be 1, without explicitly invoking the custodial symmetry arguments. The one-loop finiteness of the electroweak oblique corrections is automatically guaranteed once these unitarity sum rules are imposed among Higgs couplings. Severe constraints on the lightest Higgs coupling (125GeV Higgs coupling) and the mass of the second lightest Higgs boson are obtained from the unitarity and the results of the electroweak precision tests (oblique parameter measurements). These results are compared with the effective theory of the light Higgs boson, and we find simple relationships between the mass of the second lightest Higgs boson in our framework and the ultraviolet cutoff in the effective theory framework.
We revisit the analysis of the improved ladder Schwinger-Dyson (SD) equation for the dynamical chiral symmetry breaking in QCD with emphasizing the importance of the scale ambiguity. Previous calculation done so far naively used one-loop MSbar coupli
ng in the improved ladder SD equation without examining the scale ambiguity. As a result, the calculated pion decay constant f_pi was less than a half of its experimental value f_pi=92.4MeV once the QCD scale is fixed from the high energy coupling alpha_s(M_Z). In order to settle the ambiguity in a proper manner, we adopt here in the present paper the next-to-leading-order effective coupling instead of a naive use of the MSbar coupling. The pion decay constant f_pi is then calculated from high energy QCD coupling strength alpha_s(M_Z)=0.1172 pm 0.0020. Within the Higashijima-Miransky approximation, we obtain f_pi=85--106MeV depending on the value of alpha_s(M_Z) which agrees well with the experimentally observed value f_pi=92.4MeV. The validity of the improved ladder SD equation is therefore ascertained more firmly than considered before.
We propose a top quark condensate scenario embedded in grand unified theories (GUTs), stressing that the gauged Nambu-Jona-Lasinio model has a nontrivial continuum limit (``renormalizability) under certain condition which is actually satisfied in all
sensible GUTs with simple group. The top quark mass prediction in this scenario is shown to be insensitive to the ultraviolet cutoff $Lambda$ thanks to the ``renormalizability. We also discuss a possibility to reduce the top mass prediction in this scenario.
We discuss the sensitivity of the $e^+ e^- rightarrow W^+ W^-$ cross section at a future $e^+ e^-$ collider with $sqrt{s}=500$GeV to the non-decoupling effects of a techni-$rho$ like vector resonance. The non-decoupling effects are parametrized by th
e chiral coefficients of the electroweak chiral perturbation theory. We define renormalization scale independent chiral coefficients by subtracting the Standard Model loop contributions. We also estimate the size of the decoupling effects of the techni-$rho$ resonance by using a phenomenological Lagrangian including the vector resonance.
Equivalence of the hidden local symmetry formulation with non-minimal interactions and the anti-symmetric tensor field method of $rho$ and $a_1$ mesons in the chiral lagrangian is shown by using the auxiliary field method. Violation of the KSRF I rel
ation, which becomes important in the application of chiral lagrangian to {em non QCD-like} technicolor models can be parametrized by non-minimal coupling in the hidden local symmetry formalism keeping low energy theorem of hidden local symmetry. We also obtain explicit correspondence of parameters in both formulations.
We formulate the chiral perturbation theory at the one loop level in the effective lagrangian including the $rho$ meson as a dynamical gauge boson of a hidden local symmetry(HLS). The size of radiative correction to the phenomenological parameter $a$
of HLS is estimated to be about $10$%. The complete list of ${cal O}(E^4)$ terms is given and the one loop counter terms are determined explicitly in the $N$ flavor model. We also obtain matching conditions to the conventional chiral perturbation of Gasser and Leutwyler in the chiral limit in a renormalization scale independent manner. We find that Gasser--Leutwylers estimates for $L_{9,10}$ are saturated by $rho$ and its one loop contributions without introducing non-minimal couplings of $pi$-$rho$ system, suggesting the absence of the tree level $a_1$ meson contributions.
Based on the Cornwall-Jackiw-Tomboulis effective potential, we extensively study nonperturbative renormalization of the gauged Nambu-Jona-Lasinio model in the ladder approximation with standing gauge coupling. Although the pure Nambu-Jona-Lasinio mod
el is not renormalizable, presence of the gauge interaction makes it possible that the theory is renormalized as an interacting continuum theory at the critical line in the ladder approximation. Extra higher dimensional operators (``counter terms) are not needed for the theory to be renormalized. By virtue of the effective potential approach, the renormalization (``symmetric renormalization) is performed in a phase-independent manner both for the symmetric and the spontaneously broken phases of the chiral symmetry. We explicitly obtain $beta$ function having a nontrivial ultraviolet fixed line for the renormalized coupling as well as the bare one. In both phases the anomalous dimension is very large ($ ge 1$) without discontinuity across the fixed line. Operator product expansion is explicitly constructed, which is consistent with the large anomalous dimension owing to the appearance of the nontrivial extra power behavior in the Wilson coefficient for the unit operator. The symmetric renormalization breaks down at the critical gauge coupling, which is cured by the generalized renormalization scheme (``$tM$-dependent renormalization). Also emphasized is the formal resemblance to the four-fermion theory in less than four dimensions which is renormalizable in $1/N$ expansion.
