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Register a new userSub-GeV $U(1)_{R}$ gauge boson to address the proton radius discrepancy
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We propose a Standard Model extension by a $U(1)_{R}$ gauge symmetry where only right-handed chiral fermions can carry a non-trivial charge. Here we show that the simplest anomaly-free solution to accommodate the proton charge radius discrepancy takes right-handed muons $mu_R$ and first generation quarks, $u_R$ and $d_R$. Consistency with the latest muons $(g-2)$ measurements is achieved through an extra light scalar, which itself must lie in the tens of MeV mass range to be viable.
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The Higgs boson mass $m_H=126 $GeV in the $SO(5) times U(1)$ gauge-Higgs unification in the Randall-Sundrum space leads to important consequences. An universal relation is found between the Kaluza-Klein (KK) mass scale $m_{KK}$ and the Aharonov-Bohm phase $theta_H$ in the fifth dimension; $m_{KK} sim 1350,{rm GeV}/(sin theta_H)^{0.787}$. The cubic and quartic self-couplings of the Higgs boson become smaller than those in the SM, having universal dependence on $theta_H$. The decay rates $H rightarrow gamma gamma, gg$ are evaluated by summing contributions from KK towers. Corrections coming from KK excited states turn out very small. With $theta_H= 0.1 sim 0.35$, the mass of the first KK $Z$ is predicted to be $2.5 sim 6 , $TeV.
We derive perturbativity constraints on beyond standard model scenarios with extra gauge groups, such as $SU(2)$ or $U(1)$, whose generators contribute to the electric charge, and show that there are both upper and lower limits on the additional gauge couplings, from the requirement that the couplings remain perturbative up to the grand unification theory (GUT) scale. This leads to stringent constraints on the masses of the corresponding gauge bosons and their collider phenomenology. We specifically focus on the models based on $SU(2)_Ltimes U(1)_{I_{3R}} times U(1)_{B-L}$ and the left-right symmetric models based on $SU(2)_Ltimes SU(2)_Rtimes U(1)_{B-L}$, and discuss the implications of the perturbativity constraints for new gauge boson searches at current and future colliders. In particular, we find that the stringent flavor constraints in the scalar sector of left-right model set a lower bound on the right-handed scale $v_R gtrsim 10$ TeV, if all the gauge and quartic couplings are to remain perturbative up to the GUT scale. This precludes the prospects of finding the $Z_R$ boson in the left-right model at the LHC, even in the high-luminosity phase, and leaves only a narrow window for the $W_R$ boson. A much broader allowed parameter space, with the right-handed scale $v_R$ up to $simeq 87$ TeV, could be probed at the future 100 TeV collider.
A phenomenological study of CP-violating dimension-six operators via the $e^+e^-to u bar{ u} H$ process is performed in a model-independent Standard Model effective field theory framework at all energy stages of CLIC using the updated baseline integrated luminosities. All signal and relevant background events are generated in MadGraph and passed through PYTHIA for parton showering and hadronization at parton level. Detector effects are considered via tuned CLIC detector cards in Delphes. Since we reconstruct the Higgs boson from a pair of b-jets, limits on CP-violating dimension-six couplings are obtained at three $b$-tagging working points: tight, medium and loose defined in the CLIC Delphes card for all three energy stages of CLIC. Our best 95 % C.L. limits at the loose working point (90 % b-tagging efficiency) on $tilde c_{HW}$ and $tilde c_{HB}$ are $[-7.0times10^{-3};7.0times10^{-3}]$ and $[-3.0times10^{-2};3.0times10^{-2}]$, respectively at the 3 TeV energy stage of CLIC with an integrated luminosity of 5.0 ab$^{-1}$. Considering a 0.3 % systematic uncertainty from possible experimental sources worsens the limits on these couplings by a factor of two.
Motivated by the recent PAMELA and ATIC data, one is led to a scenario with heavy vector-like dark matter in association with a hidden $U(1)_X$ sector below GeV scale. Realizing this idea in the context of gauge mediated supersymmetry breaking (GMSB), a heavy scalar component charged under $U(1)_X$ is found to be a good dark matter candidate which can be searched for direct scattering mediated by the Higgs boson and/or by the hidden gauge boson. The latter turns out to put a stringent bound on the kinetic mixing parameter between $U(1)_X$ and $U(1)_Y$: $theta lesssim 10^{-6}$. For the typical range of model parameters, we find that the decay rates of the ordinary lightest neutralino into hidden gauge boson/gaugino and photon/gravitino are comparable, and the former decay mode leaves displaced vertices of lepton pairs and missing energy with distinctive length scale larger than 20 cm for invariant lepton pair mass below 0.5 GeV. An unsatisfactory aspect of our model is that the Sommerfeld effect cannot raise the galactic dark matter annihilation by more than 60 times for the dark matter mass below TeV.
Signatures of the $SO(5)times U(1)$ gauge-Higgs unification at LHC and future colliders are explored. The Kaluza-Klein (KK) mass spectra of $gamma, Z, Z_R$ and the Higgs self-couplings obey universality relations with the Aharonov-Bohm (AB) phase $theta_H$ in the fifth dimension. The current data at low energies and at LHC indicate $theta_H <0.2$. Couplings of quarks and leptons to KK gauge bosons are determined. Three neutral gauge bosons, the first KK modes $Z_R^{(1)}$, $Z^{(1)}$, and $gamma^{(1)}$, appear as $Z$ bosons in dilepton events at LHC. For $theta_H = 0.114$, the mass and decay width of $Z_R^{(1)}$, $Z^{(1)}$, and $gamma^{(1)}$ are (5.73TeV, 482GeV), (6.07TeV, 342GeV), and (6.08TeV, 886GeV), respectively. For $theta_H = 0.073$ their masses are 8.00TeV$sim$8.61TeV. An excess of events in the dilepton invariant mass should be observed in the $Z$ search at the upgraded LHC at 14TeV.
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