arXiv subjects
Publications and source records attributed to Yutaka Hosotani.
When the extra dimensional space is not simply-connected, dynamics of the AB phase in the extra dimension can induce dynamical gauge symmetry breaking by the Hosotani mechanism. This opens up a new way of achieving unification of gauge forces. It leads to the gauge-Higgs unification. The Hosotani mechanism can be established nonperturbatively by lattice simulations, in which measurements of the Polyakov line give a clue.
In the $SO(5) \times U(1)$ gauge-Higgs unification in the Randall-Sundrum (RS) warped space the Higgs boson naturally becomes stable. The model is consistent with the current collider signatures only for a large warp factor $z_L > 10^{15}$ of the RS space. In order for stable Higgs bosons to explain the dark matter of the Universe the Higgs boson must have a mass $m_h = 70 \sim 75$ GeV, which can be obtained in the non-SUSY model with $z_L \sim 10^5$. We show that this discrepancy is resolved in supersymmetric gauge-Higgs unification where a stop mass is about $300 \sim 320 $GeV and gauginos in the electroweak sector are light.
The gauge bosons and Englert-Brout-Higgs (EBH) boson are unified in the five dimensional RS spacetime. The EBH boson is identified with a part of the fifth dimensional component of the gauge potential. In the SO(5) x U(1) gauge-Higgs unification the EW symmetry is dynamically broken. The EBH boson, predicted with a mass around 130 GeV, naturally becomes stable so that it appears as missing energy and momentum in collider experiments. Collider signatures such as gauge couplings of quarks and leptons and production of KK γand Z are also discussed.
Collider signatures of the $SO(5) \times U(1)$ gauge-Higgs unification model in the Randall-Sundrum warped space are explored. Gauge couplings of quarks and leptons receive small corrections from the fifth dimension whose effects are tested by the precision data. It is found that the forward-backward asymmetries in $e^+e^-$ collisions on the $Z$ pole are well explained in a wide range of the warp factor $z_L$, but the model is consistent with the branching fractions of $Z$ decay only for large $z_L \simg 10^{15}$. Kaluza-Klein (KK) spectra of gauge bosons, quarks, and leptons as well as gauge and Higgs couplings of low-lying KK excited states are determined. Right-handed quarks and leptons have larger couplings to the KK gauge bosons than left-handed ones. Production rates of Higgs bosons and KK states at Tevatron, LHC and ILC are evaluated. The first KK $Z$ has a mass 1130 GeV with a width 422 GeV for $z_L = 10^{15}$. The current limit on the $Z'$ production at Tevatron and LHC indicates $z_L >10^{15}$. A large effect of parity violation appears in the difference between the rapidity distributions of $e^+$ and $e^-$ in the decay of the first KK $Z$. The first KK gauge bosons decay into light and heavy quarks evenly.
A spherically symmetric monopole solution is found in SO(5) gauge theory with Higgs scalar fields in the vector representation in six-dimensional Minkowski spacetime. The action of the Yang-Mills fields is quartic in field strengths. The solution saturates the Bogomolny bound and is stable.
In the SO(5) x U(1) gauge-Higgs unification model in the Randall-Sundrum warped space there results the conservation of the H parity. The H parity is assigned to all 4D fields including excited modes in Kaluza-Klein towers. The neutral Higgs boson is the lightest particle of odd H parity, consequently becoming absolutely stable. Its mass is found to be 70 \sim 135 GeV for the warp factor z_L = 10^5 \sim 10^{15}.
The Higgs boson is in the backbone of the standard model of electroweak interactions. It must exist in some form for achieving unification of interactions. In the gauge-Higgs unification scenario the Higgs boson becomes a part of the extra-dimensional component of gauge fields. The Higgs boson becomes absolutely stable in a class of the gauge-Higgs unification models, serving as a promising candidate for cold dark matter in the universe. The observed relic abundance of cold dark matter is obtained with the Higgs mass around 70 GeV. The Higgs-nucleon scattering cross section is found to be close to the recent CDMS II and XENON10 bounds in the direct detection of dark matter. In collider experiments stable Higgs bosons are produced in a pair, appearing as missing energies and momenta so that the way of detecting Higgs bosons must be altered.
In the gauge-Higgs unification the 4D Higgs field becomes a part of the extra-dimensional component of the gauge potentials. In the $SO(5) \times U(1)$ gauge-Higgs unification in the Randall-Sundrum warped spacetime the electroweak symmetry is dynamically broken through the Hosotani mechanism. The Higgs bosons become absolutely stable, and become the dark matter of the universe. The mass of the Higgs boson is determined from the WMAP data to be about 70 GeV.
The electroweak currents of quarks and leptons in the $SO(5) \times U(1)$ gauge-Higgs unification model in the Randall-Sundrum warped space are determined. The 4D gauge couplings deviate from those in the standard model and the weak universality is slightly violated. It is shown that the model is free from 4D anomalies and the deviations of the gauge couplings are tiny, less than 1% except for the top quark. The $Zt_L \bar t_L$, $Zt_R \bar t_R$, $Zb_L \bar b_L$ and $Zb_R \bar b_R$ couplings deviate from those in the standard model by -7%, 18%, 0.3% and 0.9% with the warp factor $z_L = 10^{15}$, respectively. The violation of the $μ$-$e$, $τ$-$e$ and $t$-$e$ universality in the charged current interactions is ${\cal O}(10^{-8})$, ${\cal O}(10^{-6})$ and 2.3%, respectively.
In a class of the gauge-Higgs unification models the 4D neutral Higgs boson, which is a part of the extra-dimensional component of the gauge fields, becomes absolutely stable as a consequence of the gauge invariance and dynamically generated new parity, serving as a promising candidate for cold dark matter (CDM). We show that the observed relic abundance of cold dark matter is obtained in the SO(5) x U(1) model in the warped space with the Higgs mass around 70 GeV. The Higgs-nucleon scattering cross section is found to be close to the current CDMS II and XENON10 bounds in the direct detection of dark matter.
The wave functions and Yukawa couplings of the top and bottom quarks in the SO(5) x U(1) gauge-Higgs unification model are determined. The result is summarized in the effective interactions for \hat θ_H(x) = θ_H + H(x)/f_H where θ_H is the Wilson line phase and H(x) is the 4D Higgs field. The Yukawa, WWH and ZZH couplings vanish at θ_H = \onehalf π. There emerges the possibility that the Higgs particle becomes stable.
In the gauge-Higgs unification scenario the Higgs field is unified with gauge fields in higher dimensional gauge theory. The 4D Higgs field $H(x)$ corresponds to 4D fluctuations of the Aharonov-Bohm phase (Wilson line phase) $θ_H$ in the extra-dimension. An $SO(5)\times U(1)$ gauge-Higgs unification model in the Randall-Sundrum warped spacetime with top and bottom quarks is presented. Gauge couplings of the top quark multiplet induce electroweak symmetry breaking by the Hosotani mechanism. The effective potential $V_\eff (θ_H)$ is found to be minimized at $θ_H = \onehalf π$ and the Higgs mass is predicted around 50 GeV. The $ZZH$ and $WWH$ couplings vanish at $θ_H = \onehalf π$ so that the LEP2 bound for the Higgs mass is evaded. The result is summarized in the effective interactions for $\hat θ_H(x) = θ_H + H(x)/f_H$.
In the gauge-Higgs unification scenario 4D Higgs fields are unified with gauge fields in higher dimensions. The electroweak model is constructed in the Randall-Sundrum warped space. The electroweak symmetry is dynamically broken by the Hosotani mechanism due to the top quark contribution. The Higgs mass is predicted to be around 50 GeV with the vanishing ZZH and WWH couplings so that the LEP2 bound for the Higgs mass is evaded.
The gauge couplings $WWZ$, $WWWW$, and $WWZZ$ in the gauge-Higgs unification scenario in the Randall-Sundrum warped spacetime remain almost universal as in the standard model, but substantial deviation results for the Higgs couplings. In the $SO(5)\times U(1)_{B-L}$ model, the couplings $WWH$ and $ZZH$ are suppressed by a factor $\cos θ_H$ from the values in the standard model, while the bare couplings $WWHH$ and $ZZHH$ are suppressed by a factor $1-(2/3)\sin^2 θ_H$. Here $θ_H$ is the Yang-Mills AB phase (Wilson line phase) along the fifth dimension, which characterizes the electroweak symmetry breaking. The suppression can be used to test the gauge-Higgs unification scenario at LHC and ILC. It is also shown that the $WWZ$ coupling in flat spacetime deviates from the standard model value at moderate values of $θ_H$, contradicting with the LEP2 data.
In the gauge-Higgs unification scenario the 4D Higgs field is identified with the zero mode of the extra-dimensional component of gauge potentials. The mass of the Higgs particle in the unification in the Randall-Sundrum warped spacetime is predicted to be in the range 100 GeV - 300 GeV. The WWZ gauge couplings remains almost universal as in the standard model, but substantial deviation results for the Higgs couplings. The WWH and ZZH couplings are suppressed by a factor \cos θ_H from the values in the standard model, where θ_H is the Yang-Mills AB phase along the fifth dimension. These can be tested at LHC and ILC.
In the dynamical gauge-Higgs unification in the Randall-Sundrum warped spacetime, where the 4D Higgs field is unified with gauge fields and the electroweak symmetry is dynamically broken by the Hosotani mechanism, the trilinear couplings for WWZ, WWH, and ZZH, where H stands for the Higgs field, are evaluated. The latter two couplings are suppressed by a factor of \cos θ_H where θ_H is the Yang-Mills Aharonov-Bohm phase in the extra dimension, while the WWZ couplings remain the same as in the standard model to good accuracy.
In the dynamical gauge-Higgs unification the 4D Higgs field is unified with gauge fields and the electroweak symmetry is dynamically broken by the Hosotani mechanism. Interesting phenomenology is obtained in the Randall-Sundrum warped spacetime. (i) The Higgs boson mass is predicted at the LHC energies. (ii) The hierarchy in the fermion mass spectrum is naturally explained. (iii) Tiny violation of the universality in the charged current interactions is predicted. (iv) Yukawa couplings of quarks and leptons are suppressed compared with those in the standard model. (v) $WWH$, $ZZH$ couplings are suppressed compared with those in the standard model.
In the dynamical gauge-Higgs unification, it is shown that the mass of the Higgs boson (4D scalar field) in U(1) gauge theory in $M^4 \times T^n$ ($n=1,2,3,...$) is finite to all order in perturbation theory as a consequence of the large gauge invariance. It is conjectured that the Higgs boson mass is finite in non-Abelian gauge theory in $M^4 \times S^1$, $M^4 \times (S^1/Z_2)$ and the Randall-Sundrum warped spacetime to all order in the rearranged perturbation theory where the large gauge invariance is maintained.