Light composite Higgs boson from the normalized Bethe-Salpeter equation

We discuss the possibility of generating a light composite scalar boson, in a scenario that we may generically call Technicolor, or in any variation of a strongly interacting theory, where by light we mean a scalar composite mass about one order of magnitude below the characteristic scale of the strong theory. Instead of most of the studies about a composite Higgs boson, which are based on effective Lagrangians, we consider this problem in the framework of nonperturbative solutions of the fermionic Schwinger–Dyson and Bethe–Salpeter equations. We study a range of mechanisms proposed during the recent years to form such light composite boson, and verify that such possibility seems to be necessarily associated to a fermionic self-energy that decreases slowly with the momentum.

The scalar Higgs boson mass in a Technicolor model was obtained by Elias and Scadron with the analysis of an homogeneous Bethe–Salpeter equation (BSE), however it was performed before the most recent developments of walking gauge theories. It was not observed in their work that dynamically generated technifermion mass may vary according to the theory dynamics that forms the scalar bound state. This will be done in this work and we also call attention that their calculation must change to take into account the normalization condition of the BSE. We compute the width of the composite boson and show how the gauge group and fermion content of a technicolor theory can be inferred from the measurement of the mass and width of the scalar boson.

We discuss phenomenological consequences of requiring the cancellation of one-loop quadratic divergences in corrections to scalar masses within Two-Higgs-Doublet Models (2HDM). It is shown that the Inert Doublet Model (IDM) can not accommodate the requirement of the cancellation. A general 2HDM is also analyzed taking into account existing experimental constraints. Allowed regions in the parameter space, permitting the above cancellation, are determined. A degeneracy between masses of scalar bosons is observed for tanbeta \gsim 40. The possibility for CP violation in the scalar potential is discussed and regions of tanbeta-M_{H^\pm} with substantial amount of CP violation are determined. In order to provide a source for dark matter in a minimal manner, a scalar gauge singlet is introduced and discussed. The model allows to ameliorate the little hierarchy problem by lifting the minimal scalar Higgs boson mass and by suppressing the one-loop quadratic corrections to scalar masses. The cutoff originating from the naturality arguments is therefore lifted to \gsim 15 TeV depending on the mass of the lightest scalar.

Introducing the most general expression for the corresponding axial-vector vertex, the flavor nonsinglet, chiral axial-vector Ward-Takahashi (WT) identity is investigated in the framework of dynamical chiral symmetry breaking (DCSB). A chiral perturbation theory at the quark level (CHPTq) is proposed in terms of a Taylor series expansions in powers of the external momenta q (momentum of a massless pion) for the direct solution of the above identity at small momentum transfer q (momentum of a massless pion). Correct treatment of initial dynamical singularities at q=0 within the CHPTq approach in accordance with the Ball and Chiu procedure makes it possible to decompose the axial-vector vertex into pole and regular parts in a self-consistent way. The Bethe-Salpeter (BS) bound-state amplitude of a massless pion restored from the identity is shown to coincide with the residue at pole q2=0, which is proportional to the pion decay constant. We find exact solution for the regular piece of the corresponding vertex at zero momentum transfer in terms of the quark propagator dynamical variables alone. This solution automatically satisfies asymptotic freedom (it approaches the point-like vertex at infinity). Applying the proposed CHPTq approach to the matrix element of the axial-vector current determining the pion decay constant, we find “exact” (within the BS bound-state amplitude, restored fom the axial WT identity), nonperturbative expression for the pion decay constant in the current algebra (CA) representation. We show explicitly that the well-known formula of Pagels-Stokar-Cornwall for the pion decay constant is a particular case of the CHPTq approach. We find also new, nonperturbative formulae for the pion decay constant in the Jackiw-Johnson (JJ) representation as well. They now have full physical sense within the CHPTq approach. Renormalization of these expressions as well as their application in technicolor theories with slowly running couplings are briefly discussed. We also propose to distinguish between the scales of DCSB at the quark and hadronic levels (the scale of effective field theory) as well as advocate a simple relation between them based on naive counting arguments.

SU(3) gauge theory with overlap fermions in the 2-index symmetric (sextet) and fundamental representations is considered. A priori it is not known what the pattern of chiral symmetry breaking is in a higher dimensional representation although the general expectation is that if two representations are both complex, the breaking pattern will be the same. This expectation is verified for the sextet at N_f = 0 in several exact zero mode sectors. It is shown that if the volume is large enough the same random matrix ensemble describes both the sextet and fundamental Dirac eigenvalues. The number of zero modes for the sextet increases approximately 5-fold relative to the fundamental in accordance with the index theorem for small lattice spacing but zero modes which do not correspond to integer topological charge do exist at larger lattice spacings. The zero mode number dependence of the random matrix model predictions correctly match the simulations in each sector and each representation.

Limits to possible scalar-boson mass and coupling from e +e − collisions

In a previous paper \cite{Khlopov:2007ic}, we showed how the minimal walking technicolor model (WTC) can provide a composite dark matter candidate, by forming bound states between a -2 electrically charged techniparticle and a $^4He^{++}$. We studied the properties of these \emph{techni-O-helium} $tOHe$ "atoms", which behave as warmer dark matter rather than cold. In this paper we extend our work on several different aspects. We study the possibility of a mixed scenario where both $tOHe$ and bound states between +2 and -2 electrically charged techniparticles coexist in the dark matter density. We argue that these newly proposed bound states solely made of techniparticles, although they behave as Weakly Interacting Massive Particles (WIMPs), due to their large elastic cross section with nuclei, can only account for a small percentage of the dark matter density. Therefore we conclude that within the minimal WTC, composite dark matter should be mostly composed of $tOHe$. Moreover in this paper, we put cosmological bounds in the masses of the techniparticles, if they compose the dark matter density. Finally we propose within this setup, a possible explanation of the discrepancy between the DAMA/NaI and DAMA/LIBRA findings and the negative results of CDMS and other direct dark matter searches that imply nuclear recoil measurement, which should accompany ionization.

We investigate the scope of the Large Hadron Collider (LHC) in probing the\nparameter space of a 4-Site (4S) model supplemented by one composite Higgs\nstate. We concentrate on the yield of `mixed' di-boson production giving three\nleptons and missing (transverse) energy in the final state, i.e., events\ninduced via the sub-process $q\\bar q' -> l^+\\nu_l l^{'+}l^{'-}$ +\n${\\rm{c.c.}}$, where $q,q'$ are quarks and $l,l'=e,\\mu$ in all possible\ncombinations, signature which enables the production in the intermediate steps\nof all additional -- with respect to the Standard Model (SM) -- neutral and\ncharged gauge bosons belonging to the spectrum of this scenario, all of which\nin resonant topologies. We not only find this channel to be accessible over the\nbackground but also show that, after a dedicated cut-based analysis,\nkinematical reconstruction of all such resonances is always possible. We\nfinally compare the yield of the mixed di-boson mode to that of the `charged'\ndi-boson one and find that the former is of lesser scope than the latter at\nsmaller gauge boson masses but it overcomes it at higher values, thereby\nrevealing itself a viable search mode covering new regions of parameter space.\n

Gauge boson masses in the 3D, SU(2) gauge-Higgs model

It has been argued by Pisarski and Wilczek that finite temperature restoration of the chiral symmetry SU(Nf) x SU(Nf) is first-order for Nf >=3. This type of chiral symmetry with a large Nf may appear in the Higgs sector if one considers models such as walking technicolor theories. We examine the first-order restoration of the chiral symmetry from the point of view of the electroweak phase transition. The strength of the transition is estimated in SU(2) x U(1) gauged linear sigma model by means of the finite temperature effective potential at one-loop with the ring improvement. Even if the mass of the neutral scalar boson corresponding to the Higgs boson is larger than 114 GeV, the first-order transition can be strong enough for the electroweak baryogenesis, as long as the extra massive scalar bosons (required for the linear realization) are kept heavier than the neutral scalar boson. Explicit symmetry breaking terms reduce the strength of the first-order transition, but the transition can remain strongly first-order even when the masses of pseudo Nambu-Goldstone bosons become as large as the current lower bound of direct search experiments.

The flatness of the inflaton potential and lightness of the Higgs could have the common origin of the breaking of a global symmetry. This scenario provides a unified framework of Goldstone Inflation and Composite Higgs, where the inflaton and the Higgs both have a pseudo--Goldstone boson nature. The inflaton reheats the Universe via decays to the Higgs and subsequent secondary production of other SM particles via the top and massive vector bosons. We find that inflationary predictions and perturbative reheating conditions are consistent with CMB data for sub--Planckian values of the fields, as well as opening up the possibility of inflation at the TeV scale. We explore this exciting possibility, leading to an interplay between collider data and cosmological constraints.

The renormalization group equations for heavy fermion Higgs-Yukawa coupling constants possess low energy fixed points. The masses of fourth generation quarks and leptons, or an ultra-heavy top quark are predicted. These also correspond to upper bounds on fermion masses in SU(5)-like theories.

In this work we study constraints from new searches for heavy particles at the LHC on the allowed masses and couplings of a KK Graviton in a holographic composite Higgs model. Keeping new electroweak states heavy such that electroweak precision tests are satisfied, we control the mass of the lightest KK graviton using a brane kinetic term. With this we study KK graviton masses from 0.5-3 TeV. In our analysis we also employ Little Randall-Sundrum (RS) Models, characterised by a lower UV scale in the 5D model which in turn implies modified couplings to massless bulk fields. Viewing this scenario as a strongly coupled 4D theory with a composite Higgs boson, the KK graviton is interpreted as a composite spin-2 state and the varying UV scale corresponds to a varying intermediate scale between the cutoff of the low energy effective theory and the Planck scale. We find that KK gravitons with masses in the range 0.5-3 TeV are compatible with current collider constraints, where the most promising channels for detecting these states are the di-photon and ZZ channels. A detection is more likely in the little RS models, in which the dual gauge theory has a larger number of colours than in traditional RS models.

Several measurements of B-meson decay observables show deviations from Standard Model (SM) predictions, some of them hinting at violation of lepton flavour universality (LFU). I discusses how the anomalies in rare B decays can be explained by partial compositeness. Partial compositeness is a key ingredient of models with a composite Higgs boson and generically leads to violation of LFU. After presenting a simple model with partial compositeness that is able to explain the anomalies in rare B decays, the flavour phenomenology of a minimal UV completion of a composite Higgs model with partial compositeness is discussed: the minimal fundamental partial compositeness (MFPC) model. A virtue of the MFPC model is its capability of serving both as a solution to the naturalness problem of the SM and as an explanation of the flavour anomalies in rare B-meson decays. In view of recent new measurements, the results on which this proceedings contribution is based are updated.

The study of the Bethe-Salpeter equation for lepton-lepton interaction mediated by charged vector mesons is continued. Starting from the exact integral equation, an improved approximation procedure is developed. This reproduces the low-energy results for "allowed" processes given in a previous paper. Beyond that, it is now found that to leading order the BS equation gives the value $\frac{3{g}^{2}}{4{\ensuremath{\pi}}^{2}}$ for the zero-energy ratio between "forbidden" and "allowed" amplitudes, where $g$ is the bare meson-lepton coupling constant. Some information on the momentum dependence of the forbidden amplitude is also obtained. The mathematical methods developed in an earlier paper are then applied to the corresponding Bethe-Salpeter equation of the Fermi field theory. It is shown that the calculated amplitudes for both allowed and forbidden processes are equal to zero. This illustrates the fact that if higher order effects are taken seriously, there is no reason to consider the Fermi field theory as the limiting case of a vector meson theory with a boson mass which tends to infinity.