Walking Technicolor Research Articles

One-loop corrections to theSandTparameters in a three site Higgsless model

In this paper we compute the one-loop chiral logarithmic corrections to the $S$ and $T$ parameters in a highly deconstructed Higgsless model with only three sites. In addition to the electroweak gauge bosons, this model contains a single extra triplet of vector states (which we denote ${\ensuremath{\rho}}^{\ifmmode\pm\else\textpm\fi{}}$ and ${\ensuremath{\rho}}^{0}$), rather than an infinite tower of Kaluza-Klein modes. We compute the corrections to $S$ and $T$ in 't Hooft-Feynman gauge, including the ghost, unphysical Goldstone-boson, and appropriate pinch contributions required to obtain gauge-invariant results for the one-loop self-energy functions. We demonstrate that the chiral-logarithmic corrections naturally separate into two parts, a model-independent part arising from scaling below the $\ensuremath{\rho}$ mass, which has the same form as the large Higgs-mass dependence of the $S$ or $T$ parameter in the standard model, and a second model-dependent contribution arising from scaling between the $\ensuremath{\rho}$ mass and the cutoff of the model. The form of the universal part of the one-loop result allows us to correctly interpret the phenomenologically derived limits on the $S$ and $T$ parameters (which depend on a reference Higgs-boson mass) in this three-site Higgsless model. Higgsless models may be viewed as dual to models of dynamical symmetry breaking akin to ``walking technicolor,'' and in these terms our calculation is the first to compute the subleading $1/N$ corrections to the $S$ and $T$ parameters. We also discuss the reduction of the model to the ``two-site'' model, which is the usual electroweak chiral Lagrangian, noting the ``nondecoupling'' contributions present in the limit ${M}_{\ensuremath{\rho}}\ensuremath{\rightarrow}\ensuremath{\infty}$.

Conformal technicolor

We point out that the flavor problem in theories with dynamical electroweak symmetry breaking can be effectively decoupled if the physics above the TeV scale is strongly conformal, and the electroweak order parameter has a scaling dimension d = 1 + epsilon with epsilon \simeq 1/few. There are many restrictions on small values of epsilon: for epsilon << 1, electroweak symmetry breaking requires a fine-tuning similar to that of the standard model; large-N conformal field theories (including those obtained from the AdS/CFT correspondence) require fine-tuning for d < 2; `walking technicolor' theories cannot have d < 2, according to gap equation analyses. However, strong small-N conformal field theories with epsilon \simeq 1/few avoid all these constraints, and can give rise to natural dynamical electroweak symmetry breaking with a top quark flavor scale of order 10^{1/epsilon} TeV, large enough to decouple flavor. Small-N theories also have an acceptably small Peskin-Takeuchi S parameter. This class of theories provides a new direction for dynamical electroweak symmetry breaking without problems from flavor or electroweak precision tests. A possible signal for these theories is a prominent scalar resonance below the TeV scale with couplings similar to a heavy standard model Higgs.

Electroweak symmetry breaking

In this note I provide a brief description of models of dynamical electroweak symmetry breaking, including walking technicolor, top-color assisted technicolor, the top-quark seesaw model, and little higgs theories. Preprint MSU-041021

LIGHT COMPOSITE HIGGS: LCH @ LHC

Here I summarize some of the salient features of technicolor theories with technifermions in higher dimensional representations of the technicolor gauge group. The expected phase diagram as function of number of flavors and colors for the two index (anti)symmetric representation of the gauge group is reviewed. After having constructed the simplest walking technicolor theory one can show that it is not at odds with the precision measurements. The simplest theory also requires, for consistency, a fourth family of heavy leptons. The latter may result in an interesting signature at LHC. In the case of a fourth family of leptons with ordinary lepton hypercharge the new heavy neutrino can be a natural candidate of cold dark matter. New theories will also be proposed in which the critical number of flavors needed to enter the conformal window is higher than in the one with fermions in the two-index symmetric representation, but lower than in the walking technicolor theories with fermions only in the fundamental representation of the gauge group. Due to the near conformal/chiral phase transition the composite Higgs is very light compared to the intrinsic scale of the technicolor theory. For the two technicolor theory the composite Higgs mass is predicted not to exceed 150 GeV.

Light composite Higgs boson from higher representations versus electroweak precision measurements: Predictions for CERN LHC

We investigate theories in which the technifermions in higher dimensional representations of the technicolor gauge group dynamically break the electroweak symmetry of the standard model. For the two-index symmetric representation of the gauge group the lowest number of techniflavors needed to render the underlying gauge theory quasi conformal is two. We confront the models with the recent electroweak precision measurements and demonstrate that the two technicolor theory is a valid candidate for a dynamical breaking of the electroweak symmetry. The electroweak precision measurements provide useful constraints on the relative mass splitting of the new leptons needed to cure the Witten anomaly. In the case of a fourth family of leptons with ordinary lepton hypercharge the new heavy neutrino can be a natural candidate of cold dark matter. We also propose theories in which the critical number of flavors needed to enter the conformal window is higher than the one with fermions in the two-index symmetric representation, but lower than in the walking technicolor theories with fermions only in the fundamental representation of the gauge group. Due to the near conformal/chiral phase transition, we show that the composite Higgs is very light compared to the intrinsic scale of the technicolor theory. For the two technicolor theory we predict the composite Higgs mass not to exceed 150 GeV.

Distinguishing technicolor models viatt¯production at polarized photon colliders

We study top quark pair productions at a polarized photon collider from an e{sup +}e{sup -} linear collider (LC) in various improved technicolor models, namely, the one-family walking technicolor model, the top-color-assisted technicolor model, and the top-color-assisted multiscale technicolor model. Recent constraint on the top-pion mass from the precision data of R{sub b} is considered. It is shown that, considering only the statistical errors, a polarized photon collider from a 500 GeV LC with an integrated luminosity of 500 fb{sup -1} is sufficient for distinguishing the three improved technicolor models experimentally.

Collider phenomenology of technihadrons in the technicolor straw man model

We discuss the phenomenology of the lightest SU(3)_C singlet and non-singlet technihadrons in the Straw Man Model of low-scale technicolor (TCSM). The technihadrons are assumed to be those arising in topcolor--assisted technicolor models in which topcolor is broken by technifermion condensates. We improve upon the description of the color--singlet sector presented in our earlier paper introducing the TCSM (hep-ph/9903369). These improvements are most important for subprocess energies well below the masses of the technirho and techniomega, and, therefore, apply especially to e+e- colliders such as LEP and a low--energy linear collider. In the color--octet sector, we consider mixing of the gluon, the coloron V_8 from topcolor breaking, and four isosinglet color--octet technirho mesons. We assume, as expected in walking technicolor, that these technirhos decay into qbar-q, gg, and g-technipion final states, but not into technipion pairs. All the TCSM production and decay processes discussed here are included in the event generator Pythia. We present several simulations appropriate for the Tevatron Collider, and suggest benchmark model lines for further experimental investigation.

Top mode standard model with extra dimensions

We critically examine a version of the top mode standard model recently cast in extra dimensions by Arkani-Hamed, Cheng, Dobrescu, and Hall, based on the (improved) ladder Schwinger-Dyson (SD) equation for the D-(=6,8-)-dimensional gauge theories. We find that the bulk QCD cannot have larger coupling beyond the non-trivial ultraviolet (UV) fixed point, the existence of which is supported by a recent lattice analysis. The coupling strength at the fixed point is evaluated by using the one-loop renormalization group equation. It is then found that, in a version with only the third family (as well as the gauge bosons) living in the D-dimensional bulk, the critical (dimensionless) coupling for dynamical chiral symmetry breaking to occur is larger than the UV fixed point of the bulk QCD coupling for D=6, while smaller for D=8. We further find that the improved ladder SD equation in D dimensions has an approximate scale-invariance due to the running of the coupling and hence has an essential-singularity scaling of the ``conformal phase transition,'' similar to Miransky scaling in the four-dimensional ladder SD equation with a nonrunning coupling. This essential-singularity scaling can resolve the fine-tuning even when the cutoff (``string scale'') is large. Such a theory has a large anomalous dimension \gamma_m=D/2 - 1 and is expected to be free from the flavor-changing-neutral-current problem as in walking technicolor for D=4. Furthermore, the induced bulk Yukawa coupling becomes finite even at infinite cutoff limit (in the formal sense), similarly to the renormalizability of the gauged Nambu-Jona-Lasinio model. Comments are made on the use of the ``effective'' coupling, which includes finite renormalization effects, instead of the \bar{MS} running coupling in the improved ladder SD equation.

Corrections from PGB to the Single-Top-Quark Production at the Fermilab Tevatron in the Technicolor Models

We calculate one-loop PGB (pseudo-Goldstone bosons) corrections to the cross section for the single-topquarkproduction via at the Fermilab Tevatron in the MWTCM (multiscale walking technicolor model) and topcolor assisted MWTCM. The corrections from PGB in the topcolor assisted MWTCM decrease the production cross section only a few percent, and the corrections from PGB in the MWTCM are found to exceed , which might be observable at a high-luminosity Tevatron.

Search for color singlet technicolor particles in p&pmacr; collisions at radicals = 1.8 TeV

We search for color singlet technirho and technipion production in p&pmacr; collisions at sqrt[s] = 1.8 TeV recorded with the Collider Detector at Fermilab. These exotic technimesons are present in a model of walking technicolor. The signatures studied are lepton plus two jets plus E(T) and multijet final states. No excess of events is seen in either final state. We set an upper limit on the technirho production cross section and exclude a region in the technipion mass versus technirho mass plane.

Study on the Radiative Decays of B Mesons in the Multiscale Walking Technicolor Model

We calculate PGB (pseudo-Goldstone boson) corrections to the decays B → Xsγ and B → K*γ in the MWTCM (multiscale walking technicolor model). The presence of PGBs in the MWTCM leads to large enhancements in the rates of B → Xsγ and B → K*γ. But these results are in conflict with the recent CLEO data on the branching ratios B → Xsγ and B → K*γ. If topcolor is further introduced, the calculated results in the topcolor assisted MWTCM can be suppressed and be in agreemet with the CLEO data for a certain range of parameters. We also estimate the branching ratio BR(B → Xsg) in the topcolor assisted MWTCM, and this estimate is roughly one order higher than that in the standard model.

Constraints on Technicolor Models from Inclusive Decay of B Meson**The project supported by National Natural Science Foundation of China under Grant Nos 19575015 and 19775012, and Natural Science Foundation of Scientific Committee of Henan Province

Corrections to the branching ratio BR(B → Xsγ) from technipions and top pions appeared in technicolor models are investigated. We found that: (a) the multiscale walking technicolor model is ruled out since it is conflict with the CLEO data; (b) the topcolor-assisted technicolor model is consistent with the CLEO data of BR(B → Xsγ) for a certain range of parameters.

The Signatures of the Neutral Top-Pion at the NLC and the Tevatron in Topcolor-Assisted MWTC Model**The project supported by National Natural Science Foundation of China and the Natural Science Foundation of Henan Scientific Committee

The neutral top-pion can couple to the gluons and the photons through the top quark triangle-loop. we calculate the corrections of the neutral top-pion to the production cross section in topcolor-assisted multiscale walking technicolor model. We find that, for a heavy neutral top-pion, the corrections are quite significant. For , and , the relative correction is larger than 10% which might be observed at a high-luminosity Tevatron. We further estimate the production cross section of at the NLC experiment. We find that the production rate is significantly large. The neutral top-pion may be detected in future linear collider experiments.

Can a light technipion be discovered at the Tevatron if it decays to two gluons?

In multiscale and topcolor-assisted models of walking technicolor, light, spin-one technihadrons can exist with masses of a few hundred GeV; they are expected to decay as ρ T → Wπ T . For M ρ T ≃200 GeV and M π T ≃100 GeV , the process p p ̄ →ρ T→Wπ T has a cross section of about a picobarn at the Tevatron. We demonstrate the detectability of this process with simulations appropriate to Run II conditions, for the challenging case where the technipion decays dominantly into two gluons.

The rare K-decays in the Multiscale Walking Technicolor Model

We calculate the one-loop $Z^0$-penguin contributions to the rare K-decays, $K^+ \to \pi^+ \nu \bar \nu$, $K_L \to \pi^0 \nu \bar \nu$ and $K_L \to \mu^+ \mu^-$, from the unit-charged technipions $\pi_1$ and $\pi_8$ in the framework of the Multiscale Walking Technicolor Model. We find that: (a) the $\pi_1$ and $\pi_8$ can provide one to two orders enhancements to the branching ratios of the rare K-decays; (b) by comparing the experimental data of $Br(K^+ \to \pi^+ \nu \bar \nu)$ with the theoretical prediction one finds the lower mass bounds, $m_{p8} \geq 249 GeV$ for $F_Q=40GeV$ and $m_{p1}=100 GeV$; (c) by comparing the experimental data of $Br(K_L \to \mu^+ \mu^-)$ with the theoretical predictions one finds the lower bounds on $m_{p1}$ and $m_{p8}$, $m_{p1} \geq 210 GeV$ if only the contribution from $\pi_1$ is taken into account, and $m_{p8} \geq 580 GeV$ for $m_{p1}=210 GeV$, assuming $F_Q=40GeV$; (d) the assumed ranges of the masses $m_{p1}$ and $m_{p8}$ in the Multiscale Walking Technicolor Model are excluded by the rare K-decay data.

Finding low-scale technicolor at hadron colliders

In multiscale and topcolor-assisted models of walking technicolor, relatively light spin-one technihadrons $\rho_T$ and $\omega_T$ exist and are expected to decay as $\rho_T \to W \pi_T, Z \pi_T$ and $\omega_T \to \gamma \pi_T$. For $M_{\rho_T} \simeq 200 GeV$ and $M_{\pi_T} \simeq 100 GeV$, these processes have cross sections in the picobarn range in $\bar p p$ colisions at the Tevatron and about 10 times larger at the Large Hadron Collider. We demonstrate their detectability with simulations appropriate to Run II conditions at the Tevatron.

Multiscale technicolor and b → sγ

Correction to the b → sγ branching ratio in the multiscale walking technicolor model (MWTCM) is examined. For the original MWTCM, the correction is too large to explain the recent CLEO data. We show that if topcolor is further introduced, the branching ratio in the topcolor assisted MWTCM can be in agreement with the CLEO data for a certain range of the parameters.

Multiscale technicolour and the vertex

Correction to the branching ratio in the multiscale walking technicolour model (MWTCM) is examined. For the original MWTCM, the correction is too large to explain the recent LEP data in most of the parameter space. We show that the branching ratio in the topcolour assisted MWTCM can be in agreement with the LEP data for a certain range of the parameters and the flavour diagonal ETC boson exchange gives very small contribution to the parameter T.

Low-scale technicolor at the Tevatron

In multiscale models of walking technicolor, relatively light color-singlet technipions are produced in q q annihilation in association with longitudinal W and Z bosons and with each other. The technipions decay as π T 0 → b b and π T + → c b . Their production rates are resonantly enhanced by isovector technirho vector mesons with mass M W + M πT ≲ M ϱT ≲ 2 M πT . At the Tevatron, these associated production rates are 1–10 picobarns for M πT ⋍ 100 GeV . Such a low mass technipion requires topcolor-assisted technicolor to suppress the decay t → π T + b. Searches for πTπT production will also be rewarding. Sizable rates are expected if M ϱT ≳ 2 M πT + 10 GeV. The isoscalar ωT is nearly degenerate with ϱT and is expected to be produced at roughly the same rate. The ωT should have the distinctive decay modes ωT → γπ T 0 and Zπ T 0.

Study on the rare radiative decay Bc-->Ds* gamma in the standard model and multiscale walking technicolor model.

Applying the perturbative QCD method, we study the decay {ital B}{sub {ital c}}{r_arrow}{ital D}{sub {ital s}}{sup {asterisk}}{gamma} in the standard model (SM) and multiscale walking technicolor model (MWTCM). In the SM, we find that the contribution of weak annihilation is more important than that of the electromagnetic penguin diagram. The presence of pseudo Goldstone bosons in the MWTCM leads to a large enhancement in the rate of {ital B}{sub {ital c}}{r_arrow}{ital D}{sub {ital s}}{sup {asterisk}}{gamma}, but this model is in conflict with the branching ratio of {ital Z}{r_arrow}{ital b{bar b}}({ital R}{sub {ital b}}) and the CLEO data on the branching ratio {ital B}({ital b}{r_arrow}{ital s}{gamma}). If top-color is further introduced, the calculated results in the top-color-assisted MWTCM can be suppressed and be in agreement with the CLEO data for a certain range of parameters. {copyright}{ital 1996 The American Physical Society.}