Chiral-symmetric technicolor with standard model Higgs boson

Roman Pasechnik, Vitaly Beylin, Vladimir Kuksa, and Grigory Vereshkov

Phys. Rev. D 88, 075009 – Published 22 October 2013

Abstract

Most of the traditional technicolor-based models are known to be in a strong tension with the electroweak precision tests. We show that this serious issue is naturally cured in strongly coupled sectors with chiral-symmetric vectorlike gauge interactions in the framework of the gauged linear $σ$ model. We discuss possible phenomenological implications of such a nonstandard chiral-symmetric technicolor scenario in its simplest formulation preserving the standard model (SM) Higgs mechanism. For this purpose, we assume the existence of an extra technifermion sector confined under extra $S U (3)_{TC}$ at the energy scales reachable at the LHC, $Λ_{TC} \sim 0.1 - 1 TeV$ and interacting with the SM gauge bosons in a chiral-symmetric (vectorlike) way. In the framework of this scenario, the SM Higgs vacuum expectation value acquires a natural interpretation in terms of the condensate of technifermions in confinement in the nearly conformal limit. We study the influence of the lowest-lying composite physical states, namely, technipions, technisigma, and constituent technifermions, on the Higgs sector properties in the SM and other observables at the LHC. We find that the predicted Higgs boson signal strengths in $γ γ$ , vector-boson $V V^{*}$ , and fermion $f \bar{f}$ decay channels can be sensitive to the new strongly coupled dynamics and are consistent with the current SM-like Higgs boson observations in the limit of relatively small Higgs-technisigma mixing. At the same time, the chiral-symmetric technicolor provides us with rich technipion phenomenology at the LHC, and its major implications are discussed in detail.

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Received 26 April 2013

DOI:https://doi.org/10.1103/PhysRevD.88.075009

Authors & Affiliations

Roman Pasechnik^1,*, Vitaly Beylin^2,†, Vladimir Kuksa^2,‡, and Grigory Vereshkov^2,3,§

¹Department of Astronomy and Theoretical Physics, Lund University, SE-223 62 Lund, Sweden
²Research Institute of Physics, Southern Federal University, 344090 Rostov-on-Don, Russian Federation
³Institute for Nuclear Research of Russian Academy of Sciences, 117312 Moscow, Russian Federation

^*Roman.Pasechnik@thep.lu.se
^†vbey@rambler.ru
^‡vkuksa47@mail.ru
^§gveresh@gmail.com

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Vol. 88, Iss. 7 — 1 October 2013

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Figure 1
An illustration of the interactions of (techni)fermion and (techni)meson fields with the SM gauge bosons via (techni)hadronization in hadron physics (left panel) and in the pointlike approximation adopted in the considered CSTC scenario (right panel).Reuse & Permissions
Figure 2
Typical radiative corrections to the quartic Higgs-TC coupling $λ$ (in particular, giving rise to the $h \tilde{σ}$ mixing) before the EWSB (left) and after the EWSB (right).Reuse & Permissions
Figure 3
Dependence of the quartic TC self-coupling $λ_{TC}$ on the $h \tilde{σ}$ mixing $s_{θ}$ with dashed, dash-dotted, and solid lines corresponding to (i) $g_{TC} = 2$ , 5, 8, $M_{\tilde{Q}} = 300 GeV$ , $m_{\tilde{π}} = 150 GeV$ , and $M_{\tilde{σ}} = 500 GeV$ ; (ii) $g_{TC} = 8$ , $M_{\tilde{Q}} = 300$ , 400, 500 GeV, $m_{\tilde{π}} = 150 GeV$ , and $M_{\tilde{σ}} = 500 GeV$ ; (iii) $g_{TC} = 8$ , $M_{\tilde{Q}} = 300 GeV$ , $m_{\tilde{π}} = 150$ , 250, 350 GeV, and $M_{\tilde{σ}} = 500 GeV$ ; (iv) $g_{TC} = 8$ , $M_{\tilde{Q}} = 300 GeV$ , $m_{\tilde{π}} = 150 GeV$ , and $M_{\tilde{σ}} = 400$ , 500, 700 GeV, in each plot from top to bottom and left to right, respectively. Here and below, $M_{h} = 125 GeV$ . The coupling $λ_{TC}$ is symmetric with respect to $s_{θ} \to - s_{θ}$ .Reuse & Permissions
Figure 4
Dependence of the quartic Higgs-TC coupling $λ$ on the $h \tilde{σ}$ mixing $s_{θ}$ with dashed, dash-dotted, and solid lines corresponding to (i) $g_{TC} = 2$ , 5, 8, $M_{\tilde{Q}} = 300 GeV$ , and $M_{\tilde{σ}} = 500 GeV$ ; (ii) $g_{TC} = 8$ , $M_{\tilde{Q}} = 300$ , 400, 500 GeV, and $M_{\tilde{σ}} = 500 GeV$ ; (iii) $g_{TC} = 8$ , $M_{\tilde{Q}} = 300 GeV$ , and $M_{\tilde{σ}} = 400$ , 500, 700 GeV, in each plot from left to right, respectively. It does not depend on $m_{\tilde{π}}$ . The coupling $λ$ is antisymmetric with respect to $s_{θ} \to - s_{θ}$ .Reuse & Permissions
Figure 5
Dependence of the quartic Higgs boson self-coupling $λ_{H}$ on the $h \tilde{σ}$ mixing $s_{θ}$ with dashed, dash-dotted, and solid lines corresponding to $M_{\tilde{σ}} = 400$ , 500, and 700 GeV, respectively. It does not depend on other free parameters of the CSTC model. The coupling $λ_{H}$ is symmetric with respect to $s_{θ} \to - s_{θ}$ .Reuse & Permissions
Figure 6
Dependence of the $h \tilde{σ}$ mixing $s_{θ}$ and the Higgs/TC self-couplings $λ_{TC}$ , $λ_{H}$ , and $λ$ on $M_{\tilde{Q}}$ in the minimal CSTC scenario with dashed, dash-dotted, and solid lines corresponding to $m_{\tilde{π}} = 150$ , 250, and 350 GeV, respectively. The no $h \tilde{σ}$ -mixing limit corresponds to zeros of the curves at $M_{\tilde{σ}} = \sqrt{3} m_{\tilde{π}}$ .Reuse & Permissions
Figure 7
The dimensionless ${\bar{g}}_{TC} / v^{3}$ (left) and $\tilde{σ}$ VEV $u$ (right) parameters with respect to $M_{\tilde{σ}}$ in the minimal CSTC scenario with dashed, dash-dotted, and solid lines corresponding to $m_{\tilde{π}} = 150$ , 250, and 350 GeV, respectively. The no $h \tilde{σ}$ -mixing limit corresponds to positions of the singularities on the curves at $M_{\tilde{σ}} = \sqrt{3} m_{\tilde{π}}$ , and the vicinity of those are excluded from the plots.Reuse & Permissions
Figure 8
The additional new (via $\tilde{π}$ , $\tilde{Q}$ , and $\tilde{σ}$ ) and modified (via Higgs boson $h$ ) contributions to the gauge bosons $Z^{0}$ , $W^{\pm}$ , and $γ$ vacuum polarization functions $δ Π_{XY} (q^{2})$ .Reuse & Permissions
Figure 9
The complete $S$ and $U$ parameters in the CSTC scenario (the nonminimal case with $μ_{S}$ and $μ_{H}$ included) as functions of (i) ${cos }^{2} θ$ for fixed $m_{\tilde{π}} = 150 GeV$ , $M_{\tilde{Q}} \equiv M_{U} = M_{D} = 300 GeV$ , and $M_{\tilde{σ}} = 400$ , 600, 800 GeV, corresponding to dashed, dash-dotted, and solid lines, respectively (first row); (ii) $M_{\tilde{σ}}$ for fixed $m_{\tilde{π}} = 150 GeV$ , ${cos }^{2} θ = 0.9$ , and $M_{\tilde{Q}} = 300$ , 500, 700 GeV, corresponding to dashed, dash-dotted, and solid lines, respectively (second row); and (iii) $m_{\tilde{π}}$ for fixed $M_{\tilde{σ}} = 500 GeV$ , ${cos }^{2} θ = 0.9$ , $M_{\tilde{Q}} = 300 GeV$ , and $Δ M_{\tilde{Q}} \equiv M_{D} - M_{U} = 0$ , 5, 10 GeV, corresponding to dashed, dash-dotted, and solid lines, respectively (third row). Also, here and for other PT parameters below, the sine of the mixing angle due to symmetry is chosen to be positive: $s_{θ} > 0$ .Reuse & Permissions
Figure 10
The complete $T$ parameter in the CSTC scenario (the nonminimal case with $μ_{S}$ and $μ_{H}$ included) as a function of ${cos }^{2} θ$ for two different cases: (i) $Δ M_{\tilde{Q}} = 0$ and $M_{\tilde{σ}} = 400$ , 600, 800 GeV, corresponding to dashed, dash-dotted, and solid lines, respectively (left panel); (ii) $M_{\tilde{σ}} = 500 GeV$ and $Δ M_{\tilde{Q}} \equiv M_{D} - M_{U} = 0$ , 5, 10 GeV, corresponding to dashed, dash-dotted, and solid lines, respectively (right panel). The $T$ parameter does not depend on degenerated $M_{\tilde{Q}} \equiv M_{U} = M_{D}$ mass and $m_{\tilde{π}}$ .Reuse & Permissions
Figure 11
The complete $V$ and $W$ parameters in the CSTC scenario (the nonminimal case with $μ_{S}$ and $μ_{H}$ included) as functions of (i) ${cos }^{2} θ$ for fixed $M_{U} = M_{D} = 300 GeV$ and $m_{\tilde{π}} = 150$ , 250, 350 GeV, corresponding to dashed, dash-dotted, and solid lines, respectively (first row); and (ii) $m_{\tilde{π}}$ for fixed ${cos }^{2} θ = 0.9$ and $M_{\tilde{Q}} = 300$ , 500, 700 GeV, corresponding to dashed, dash-dotted, and solid lines, respectively (second row). Both $V$ and $W$ parameters do not depend on $M_{\tilde{σ}}$ and $Δ M_{\tilde{Q}}$ .Reuse & Permissions
Figure 12
The $X$ parameter $m_{\tilde{π}}$ for fixed $M_{\tilde{Q}} = 300$ , 500, and 700 GeV, corresponding to dashed, dash-dotted, and solid lines, respectively. It does not depend on ${cos }^{2} θ$ , $M_{\tilde{σ}}$ , and $Δ M_{\tilde{Q}}$ .Reuse & Permissions
Figure 13
Typical FCNC contributions in the CSTC model. The rightmost diagrams with scalar exchanges are the only weakly affected contributions due to a small $h \tilde{σ}$ -mixing and additional $\tilde{σ}$ meson, which are however negligibly small (see the main text).Reuse & Permissions
Figure 14
The Higgs boson signal strength in the tree-level $f \bar{f}$ , $Z Z^{*}$ , and $W W^{*}$ channels $μ_{f \bar{f}, W W, Z Z}$ as a function of $s_{θ}$ calculated according to Eq. (4.6) for $δ E = 0$ (dotted line), $δ E = Γ_{tot}^{h, SM} ≃ 4.03 MeV$ (dash-dotted line), $δ E = Γ_{tot}^{h, SM} / 2$ (long-dashed line), and $δ E = 2 Γ_{tot}^{h, SM}$ (solid line), and the $c_{θ}^{4} = (1 - s_{θ}^{2})^{2}$ curve is also shown for reference (dashed line).Reuse & Permissions
Figure 15
Typical one-loop contributions to the $h$ , $\tilde{σ} \to γ γ$ decay channel in the CSTC.Reuse & Permissions
Figure 16
The Higgs boson decay widths in the loop-induced $γ γ$ and $γ Z$ channels in the nonminimal CSTC (with scalar $μ_{S, H}$ terms included) as functions of physical parameters of the model. The corresponding SM predictions are shown for comparison. The parameters in each figure are set as follows: (top left) $m_{\tilde{π}} = 200 GeV$ , $c_{θ}^{2} = 0.8$ , and $g_{TC} = 8$ ; (top left) $M_{\tilde{Q}} = 300 GeV$ , $c_{θ}^{2} = 0.8$ , and $g_{TC} = 8$ ; (bottom left) $M_{\tilde{Q}} = 300 GeV$ , $m_{\tilde{π}} = 200 GeV$ , and $g_{TC} = 8$ ; (bottom right) $M_{\tilde{Q}} = 300 GeV$ , $m_{\tilde{π}} = 200 GeV$ , and $c_{θ}^{2} = 0.8$ . These results do not depend on $M_{\tilde{σ}}$ , and the positive sign of the mixing angle, or $s_{θ} > 0$ , is fixed here.Reuse & Permissions
Figure 17
Dependence of the Higgs boson signal strength in the resonance given by Eq. (4.7) in the nonminimal case of the CSTC model (with scalar $μ_{S, H}$ terms included), $μ_{γ γ}^{res}$ , on $s_{θ}$ for different sets of the physical parameters: (top left) $g_{TC} = 8$ , $M_{\tilde{Q}} = 300 GeV$ , and $m_{\tilde{π}} = 150$ , 250, 350 GeV, corresponding to dashed, dash-dotted, and solid lines, respectively; (top right) $g_{TC} = 8$ , $m_{\tilde{π}} = 150 GeV$ , and $M_{\tilde{Q}} = 400$ , 500, 700 GeV, corresponding to dashed, dash-dotted, and solid lines, respectively; (bottom left) $m_{\tilde{π}} = 150 GeV$ , $M_{\tilde{Q}} = 500 GeV$ , and $g_{TC} = 2$ , 8, 15, corresponding to dashed, dash-dotted, and solid lines, respectively. Finally, the bottom-right figure corresponds to smeared $μ_{γ γ} (δ E)$ given by Eq. (4.6) as a function of $s_{θ}$ for fixed $m_{\tilde{π}} = 150 GeV$ , $M_{\tilde{Q}} = 500 GeV$ , and $g_{TC} = 8$ and with different smearing parameters: no smearing $δ E = 0$ (dashed line), $δ E = Γ_{tot}^{h, SM} ≃ 4.03 MeV$ (dash-dotted line), and $δ E = 1 GeV$ (solid line). Here and below, $Y_{\tilde{Q}} = 1 / 3$ , unless noted otherwise.Reuse & Permissions
Figure 18
Dependence of the Higgs boson signal strength in the resonance given by Eq. (4.7) in the minimal CSTC model (with scalar $μ_{S, H}$ terms excluded), $μ_{γ γ}^{res}$ , on $M_{\tilde{σ}}$ for different sets of the physical parameters: (top left) $g_{TC} = 8$ , $M_{\tilde{Q}} = 300 GeV$ , and $m_{\tilde{π}} = 150$ , 250, 350 GeV, corresponding to dashed, dash-dotted, and solid lines, respectively; (top right) $g_{TC} = 8$ , $m_{\tilde{π}} = 350 GeV$ , and $M_{\tilde{Q}} = 400$ , 500, 700 GeV, corresponding to dashed, dash-dotted, and solid lines, respectively; (bottom left) $m_{\tilde{π}} = 350 GeV$ , $M_{\tilde{Q}} = 500 GeV$ , and $g_{TC} = 2$ , 8, 15, corresponding to dashed, dash-dotted, and solid lines, respectively. Finally, the bottom-right figure corresponds to smeared $μ_{γ γ} (δ E)$ given by Eq. (4.6) as a function of $M_{\tilde{σ}}$ for fixed $m_{\tilde{π}} = 350 GeV$ , $M_{\tilde{Q}} = 500 GeV$ , and $g_{TC} = 8$ and with different smearing parameters: no smearing $δ E = 0$ (dashed line), $δ E = Γ_{tot}^{h, SM} ≃ 4.03 MeV$ (dash-dotted line), and $δ E = 1 GeV$ (solid line).Reuse & Permissions
Figure 19
Partial contributions to the $μ_{γ γ}^{res}$ in the nonminimal CSTC (with scalar $μ_{S, H}$ terms included) as functions of $s_{θ}$ with $m_{\tilde{π}} = 150 GeV$ , $M_{\tilde{Q}} = 500 GeV$ , and $g_{TC} = 8$ (left panel) and in the minimal CSTC without scalar $μ_{S, H}$ terms as functions of $M_{\tilde{σ}}$ with $m_{\tilde{π}} = 350 GeV$ , $M_{\tilde{Q}} = 500 GeV$ , and $g_{TC} = 8$ (right panel), corresponding to the $W$ loop (dashed lines), $top-quark loop \times 10$ (dash-dotted lines), $technifermion loop \times 10$ (dotted lines), and $technipion loop \times 1000$ (short-dashed lines). In both panels, solid lines correspond to the total Higgs boson signal (resonant) strengths shown for comparison. The rescaling of the curves is made for better visibility and comparison.Reuse & Permissions
Figure 20
Light technipion loop-induced (two- and three-body) decay modes in the leading order through constituent technifermion loops.Reuse & Permissions
Figure 21
The technipion decay widths in the loop-induced $γ γ$ , $γ Z$ , $γ W$ , $Z Z$ , and $Z W$ channels in the nonminimal CSTC (with scalar $μ_{S, H}$ terms included) as functions of physical parameters of the model. The parameters in each figure are set as follows: (left) $M_{\tilde{Q}} = 300 GeV$ , $c_{θ}^{2} = 0.8$ , and $g_{TC} = 8$ ; (middle) $M_{\tilde{Q}} = 300 GeV$ , $m_{\tilde{π}} = 200 GeV$ , and $c_{θ}^{2} = 0.8$ ; (right) $m_{\tilde{π}} = 200 GeV$ , $c_{θ}^{2} = 0.8$ , and $g_{TC} = 8$ . These results do not depend on $M_{\tilde{σ}}$ .Reuse & Permissions
Figure 22
The neutral and charged technipion branching ratios of the loop-induced $γ γ$ , $γ Z$ , $γ W$ , $Z Z$ , and $Z W$ channels in the nonminimal CSTC (with scalar $μ_{S, H}$ terms included) as functions of $m_{\tilde{π}}$ for fixed $M_{\tilde{Q}} = 300 GeV$ , $c_{θ}^{2} = 0.8$ , and $g_{TC} = 8$ .Reuse & Permissions
Figure 23
The technisigma tree-level decay widths in the $\tilde{π} \tilde{π}$ and $h h$ channels in the nonminimal CSTC (with scalar $μ_{S, H}$ terms included) as functions of physical parameters of the model. The parameters in each figure are fixed as $m_{\tilde{π}} = 200 GeV$ , $M_{\tilde{Q}} = 300 GeV$ , $M_{\tilde{σ}} = 500 GeV$ , $c_{θ}^{2} = 0.8$ , and $g_{TC} = 8$ , such that in each figure one drops off a variable from this list corresponding to the one at the respective $x$ axis while keeping the others fixed.Reuse & Permissions
Figure 24
The technisigma tree-level decay widths in the fermion ( $t \bar{t}$ and $b \bar{b}$ ) and gauge boson ( $γ γ$ , $γ Z$ , $Z Z$ , and $W W$ ) channels in the nonminimal CSTC (with scalar $μ_{S, H}$ terms included) as functions of physical parameters of the model. The setup of parameters is the same as in Fig. 23.Reuse & Permissions
Figure 25
Typical production channels of the Higgs boson at tree level (left) and technipion via a triangle technifermion loop (right) via gauge boson fusion in the quark-(anti)quark scattering.Reuse & Permissions
Figure 26
The one-technipion (T-pion) production cross sections via the VBF mechanism at the parton level for different incoming and outgoing quark $q$ and (anti)quark $q^{'}$ states as functions of $q q^{'}$ invariant mass, or c.m.s. energy $E_{c . m . s .}^{q q} = \sqrt{\hat{s}}$ (left), corresponding total hadron level cross sections of one technipion production for given incoming $q q^{'}$ states in picobarns (before cuts) at the maximal LHC energy $\sqrt{s} = 14 TeV$ as a function of the technipion mass $m_{\tilde{π}}$ (middle), and corresponding VBF hadronic cross sections of the Higgs boson as functions of its mass $M_{h}$ shown for comparison. Here, $g_{TC} = 8$ and $M_{\tilde{Q}} = 300 GeV$ are fixed, and the results do not depend on other CSTC parameters. In calculations of the hadronic cross sections in this paper, we have used quark CTEQ5LO PDFs [51].Reuse & Permissions
Figure 27
Typical technipion production channels in the leading order, relevant for collider phenomenology. Here, $V = Z$ , $W$ , $γ$ in appropriate places. The $g g h$ and $g g \tilde{σ}$ couplings are heavy quark loop-induced ones in the leading order.Reuse & Permissions
Figure 28
The one-technipion (T-pion) pair production cross sections via the VBF mechanism at the parton level for different incoming and outgoing quark $q$ and (anti)quark $q^{'}$ states as functions of $q q^{'}$ invariant mass, or c.m.s. energy $E_{c . m . s .}^{q q} = \sqrt{\hat{s}}$ (left), corresponding total hadron level cross sections of the technipion pair production for given incoming $q q^{'}$ states in picobarns (before cuts) at the maximal LHC energy $\sqrt{s} = 14 TeV$ as a function of the technipion mass $m_{\tilde{π}}$ (right). Here, $g_{TC} = 8$ , $c_{θ}^{2} = 0.8$ , $M_{\tilde{σ}} = 600 GeV$ , and $M_{\tilde{Q}} = 300 GeV$ are fixed.Reuse & Permissions

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