Completing the Georgi-Glashow leptophobic $U(1)_X$ gauge-boson model: mixing corrections, scalar and anomaly-canceling sectors, and the feasibility of the $X\to W\xi/Z\xi$ collider signatures

The leptophobic $U(1)_X$ model of Georgi and Glashow (Phys. Lett. B 387 (1996) 341) proposed detecting a neutral gauge boson $X$ that couples to quarks but not to leptons through Higgs-mediated decays $X\to W^\pm\xi^\mp$ and $X\to Z\xi^0$, followed by $\xi\to c\bar s$, $b\bar b$, or $\tau$ modes - signatures with far smaller QCD backgrounds than the dominant $X\to q\bar q$ dijet channel. The 1996 analysis rests on acknowledged simplifications: $X$-$Z$ mass mixing is tuned to zero, $B$-$X$ kinetic mixing is neglected, the scalars are treated as unmixed mass eigenstates, the anomaly-canceling fermion content is left unspecified, the production estimate carries no QCD or PDF uncertainties, and no experimental feasibility study is performed. The open problem is the completion of this analysis in a consistent model: mixing-corrected couplings and decay widths, the realistic scalar spectrum including $H_L$ and singlet mixing, a specified anomaly-canceling fermion sector and its competing decay modes, quantified production uncertainties, and a collider feasibility assessment of the $W/Z$+heavy-flavor/$\tau$ signatures. No completion of the Georgi-Glashow model itself is known in the literature, and the original $R_b/R_c$ motivation disappeared with subsequent LEP/SLC data.

Background

In the mid-1990s the experiments at LEP, the Large Electron-Positron collider at CERN, reported deviations from Standard Model (SM) predictions in two Z-boson decay fractions: $R_b$, the fraction of hadronic Z decays producing $b\bar b$ pairs, and $R_c$, the fraction producing $c\bar c$. Several groups proposed explaining these deviations, together with an excess of high-energy jets at the Fermilab Tevatron proton-antiproton collider, by a new neutral gauge boson - a $Z'$ - that couples to quarks but not to leptons (Altarelli et al., Phys. Lett. B 375 (1996) 292; Babu, Kolda and March-Russell, Phys. Rev. D 54 (1996) 4635; Agashe, Graesser, Hinchliffe and Suzuki, Phys. Lett. B 385 (1996) 218). Such a boson is called leptophobic: having no tree-level couplings to charged leptons or neutrinos, it modifies the quark lines of electroweak observables without spoiling the precisely measured leptonic ones.

Georgi and Glashow (Phys. Lett. B 387 (1996) 341) studied the decays of such a boson in this model class. The gauge group is the SM $SU(2)\times U(1)_Y$ extended by $U(1)_X$: left-handed quark doublets carry $U(1)_X$ charge $q_Q$, right-handed up- and down-type quarks carry $q_U$ and $q_D$, and all leptons are neutral. Quark and lepton masses require three Higgs doublets $H_U$, $H_D$, $H_L$ - scalar fields whose neutral components acquire vacuum expectation values (VEVs) $v_U$, $v_D$, $v_L$ that break the electroweak symmetry - with $U(1)_X$ charges $q_U-q_Q$, $q_Q-q_D$ and $0$.

Two kinds of mixing complicate the analysis. Mass mixing between $X$ and the SM $Z$ boson would distort the precision-measured $Z$ observables; kinetic mixing between the $U(1)_Y$ gauge field $B$ and $X$ (a renormalizable $\varepsilon B_{\mu\nu}X^{\mu\nu}$ term) would induce couplings of $X$ to leptons, destroying leptophobia. Georgi and Glashow set the mass mixing to zero through the tuning $v_U^2(q_U-q_Q)+v_D^2(q_Q-q_D)=0$, neglected kinetic mixing, and assumed $v_L\ll v_U,v_D$. In this limit the Higgs kinetic terms yield their central result, the interaction

$2\,g_X\sqrt{(q_U-q_Q)(q_D-q_Q)}\left(m_W\left(\xi^+X^\mu W^-_\mu+\xi^-X^\mu W^+_\mu\right)+m_Z\,\xi^0X^\mu Z_\mu\right),$

where $g_X$ is the $U(1)_X$ gauge coupling and $\xi^\pm$, $\xi^0$ are the charged and neutral scalar fields remaining after the Higgs mechanism removes the Goldstone bosons (the field combinations eaten as the longitudinal modes of the $W$ and $Z$). The $\xi$ states form a triplet under custodial $SU(2)$, the approximate symmetry of Higgs sectors that protects the relation between the $W$ and $Z$ masses. This vertex opens the two-body decay modes $X\to W^\pm\xi^\mp$ and $X\to Z\xi^0$, whose partial widths are of the same parametric size as the dominant $X\to q\bar q$ widths because the explicit $m_W$ and $m_Z$ factors are compensated by the enhancement of longitudinal gauge-boson polarization. For representative charge assignments, such as $(q_Q,q_U,q_D)=(-1,2,1)$ and $(0,1,1)$, the branching ratios are large enough to be of experimental interest. If the $\xi$'s are light they are expected to decay mostly into heavy quarks ($\xi^+\to c\bar s$, $\xi^0\to b\bar b$) or, with small mixing with the lepton-Higgs doublet $H_L$, into tau leptons - giving $W/Z$ plus heavy-flavor or $\tau$ final states whose backgrounds are far smaller than the QCD dijet background that hides the dominant $X\to q\bar q$ resonance in CDF (the Collider Detector at Fermilab) dijet searches (Abe et al., Phys. Rev. Lett. 74 (1995) 3538).

The construction has acknowledged gaps, which define the open problem. The $U(1)_X$ symmetry has gauge anomalies - quantum effects of charged-fermion loops that violate gauge invariance and must cancel for the theory to be consistent - so extra fermions must be added, and their content and masses were not specified. The $\xi$'s were treated as unmixed mass eigenstates, although mixing with the $H_L$ components and with $SU(2)$-singlet scalars (which also contribute to $m_X$) is expected. The production cross section was estimated only approximately, at Tevatron energy $\sqrt{s}=1.8$ TeV with a chosen coupling $g_X=0.15$ and chosen parton distribution functions (PDFs, the probability distributions of quark and gluon momenta inside the proton used to compute hadron-collider rates), without higher-order QCD corrections or uncertainty bands. Finally, the proposed signatures were never subjected to a feasibility study with realistic backgrounds, detector acceptances, and selection efficiencies.

Problem Statement

Complete the theory and collider phenomenology of the leptophobic $U(1)_X$ gauge boson of Georgi and Glashow - gauge group $SU(2)\times U(1)_Y\times U(1)_X$, quark $U(1)_X$ charges $(q_Q,q_U,q_D)$, leptons neutral, three Higgs doublets $H_U,H_D,H_L$ with charges $(q_U-q_Q,\,q_Q-q_D,\,0)$ and $v_L\ll v_U,v_D$ - by removing the 1996 analysis's simplifying assumptions, and determine whether $X$ is discoverable at hadron colliders through its Higgs-mediated decays $X\to W^\pm\xi^\mp$ and $X\to Z\xi^0$ with $\xi\to c\bar s$, $b\bar b$, $\tau\nu$, $\tau^+\tau^-$. Concretely:

(1) Include $X$-$Z$ mass mixing and $B$-$X$ kinetic mixing: derive the corrected $X$-scalar-$W/Z$ interaction and the corrected partial widths $\Gamma(X\to W^\pm\xi^\mp)$, $\Gamma(X\to Z\xi^0)$ and $\Gamma(X\to f\bar f)$ for non-negligible mixing, and determine the mixing region allowed by electroweak precision data.

(2) Determine the realistic scalar spectrum: the effect of mixing among the $H_U,H_D,H_L$ components and with $SU(2)$-singlet scalars on the masses, couplings, and decay patterns of the $\xi$ states (in particular their heavy-flavor versus $\tau$ branching fractions), and hence on the $X\to W\xi/Z\xi$ branching ratios.

(3) Specify a consistent anomaly-canceling fermion content (fields and masses) and compute its consequences: new $X$ decay modes and their competition with the $W\xi/Z\xi$ channels, and the collider signatures of the new fermions.

(4) Quantify the uncertainty of the $X$ production rate from higher-order QCD corrections and PDF choices, for representative $g_X$ values and charge assignments.

(5) Assess the experimental feasibility of the proposed $W/Z$+heavy-flavor and $W/Z+\tau$ signatures at the Large Hadron Collider (LHC) with $\sqrt{s}=13$ TeV: backgrounds, detector acceptances, selection efficiencies, and the resulting discovery reach in the $(m_X,g_X)$ plane.

The five components serve one objective: in a consistent completion of the leptophobic $U(1)_X$ model, do the Higgs-mediated $W/Z+\xi$ decay modes give a quantitatively predicted, discoverable signal for the $X$ boson? The mixing, scalar-spectrum, and anomaly-sector results jointly fix the branching ratios; the production and feasibility components convert those predictions into a detection verdict.

References

1. Howard Georgi and Sheldon L. Glashow, 'Decays of a leptophobic gauge boson', Phys. Lett. B 387 (1996) 341-345. DOI: 10.1016/0370-2693(96)00997-5; arXiv:hep-ph/9607202; https://arxiv.org/abs/hep-ph/9607202
2. G. Altarelli, N. Di Bartolomeo, F. Feruglio, R. Gatto, M. Mangano, 'Rb, Rc and jet distributions at the Tevatron in a model with an extra vector boson', Phys. Lett. B 375 (1996) 292-300. DOI: 10.1016/0370-2693(96)00237-7; arXiv:hep-ph/9601324; https://arxiv.org/abs/hep-ph/9601324
3. K. S. Babu, Chris Kolda, John March-Russell, 'Leptophobic U(1)'s and the Rb - Rc anomalies', Phys. Rev. D 54 (1996) 4635-4647. DOI: 10.1103/PhysRevD.54.4635; arXiv:hep-ph/9603212; https://arxiv.org/abs/hep-ph/9603212
4. K. Agashe, M. Graesser, Ian Hinchliffe, M. Suzuki, 'A consistent model of electroweak data including Z to b bbar and Z to c cbar', Phys. Lett. B 385 (1996) 218-224. DOI: 10.1016/0370-2693(96)00831-3; arXiv:hep-ph/9604266; https://arxiv.org/abs/hep-ph/9604266
5. M. L. Mangano, G. Altarelli, N. Di Bartolomeo, F. Feruglio, R. Gatto, 'The fate of the leptophobic Z prime', arXiv:hep-ph/9610469 (1996), Proceedings of the XXVIII International Conference on High Energy Physics (Warsaw, 1996); https://arxiv.org/abs/hep-ph/9610469
6. Yoshiaki Umeda, Gi-Chol Cho, Kaoru Hagiwara, 'Constraints on leptophobic Z prime models from electroweak experiments', Phys. Rev. D 58 (1998) 115008. DOI: 10.1103/PhysRevD.58.115008; arXiv:hep-ph/9805447; https://arxiv.org/abs/hep-ph/9805447
7. Jonathan L. Rosner, 'Prominent decay modes of a leptophobic Z prime', Phys. Lett. B 387 (1996) 113-117. DOI: 10.1016/0370-2693(96)01022-2; arXiv:hep-ph/9607207; https://arxiv.org/abs/hep-ph/9607207
8. Alfredo Aranda, Christopher D. Carone, 'Limits on a light leptophobic gauge boson', Phys. Lett. B 443 (1998) 352-358. DOI: 10.1016/S0370-2693(98)01309-4; arXiv:hep-ph/9809522; https://arxiv.org/abs/hep-ph/9809522
9. P. Taxil, J.-M. Virey, 'A light leptophobic Z prime in polarized hadronic collisions', Phys. Lett. B 441 (1998) 376-382. DOI: 10.1016/S0370-2693(98)01165-4; arXiv:hep-ph/9807487; https://arxiv.org/abs/hep-ph/9807487
10. P. Taxil, E. Tugcu, J.-M. Virey, 'Constraints on leptophobic gauge bosons with polarized neutrons and protons at RHIC', Eur. Phys. J. C 24 (2002) 149-157. DOI: 10.1007/s100520200900; arXiv:hep-ph/0111242; https://arxiv.org/abs/hep-ph/0111242
11. Timothy R. Dulaney, Pavel Fileviez Perez, Mark B. Wise, 'Dark matter, baryon asymmetry, and spontaneous B and L breaking', Phys. Rev. D 83 (2011) 023520. DOI: 10.1103/PhysRevD.83.023520; arXiv:1005.0617; https://arxiv.org/abs/1005.0617
12. Michael Duerr, Pavel Fileviez Perez, 'Theory for baryon number and dark matter at the LHC', Phys. Rev. D 91 (2015) 095001. DOI: 10.1103/PhysRevD.91.095001; arXiv:1409.8165; https://arxiv.org/abs/1409.8165
13. Michael Duerr, Pavel Fileviez Perez, Juri Smirnov, 'Baryonic Higgs at the LHC', JHEP 09 (2017) 093. DOI: 10.1007/JHEP09(2017)093; arXiv:1704.03811; https://arxiv.org/abs/1704.03811
14. Pavel Fileviez Perez, Elliot Golias, Clara Murgui, Alexis D. Plascencia, 'The Higgs and leptophobic force at the LHC', JHEP 07 (2020) 087. DOI: 10.1007/JHEP07(2020)087; arXiv:2003.09426; https://arxiv.org/abs/2003.09426
15. Bogdan A. Dobrescu, 'Leptophobic boson signals with leptons, jets and missing energy', arXiv:1506.04435 (2015); https://arxiv.org/abs/1506.04435
16. V. Khachatryan et al. (CMS Collaboration), 'Search for leptophobic Z prime bosons decaying into four-lepton final states in proton-proton collisions at sqrt(s) = 8 TeV', Phys. Lett. B 773 (2017) 563-584. DOI: 10.1016/j.physletb.2017.08.069; arXiv:1701.01345; https://arxiv.org/abs/1701.01345
17. JiJi Fan, David Krohn, Paul Langacker, Itay Yavin, 'A higgsophilic s-channel Z prime and the CDF W+2j anomaly', Phys. Rev. D 84 (2011) 105012. DOI: 10.1103/PhysRevD.84.105012; arXiv:1106.1682; https://arxiv.org/abs/1106.1682
18. Matt Buckley, Pavel Fileviez Perez, Dan Hooper, Ethan Neil, 'Dark forces at the Tevatron', Phys. Lett. B 702 (2011) 256-259. DOI: 10.1016/j.physletb.2011.07.012; arXiv:1104.3145; https://arxiv.org/abs/1104.3145
19. F. del Aguila, J. A. Aguilar-Saavedra, M. Moretti, F. Piccinini, R. Pittau, M. Treccani, 'Combined analysis of Z prime to t tbar and Z prime to t tbar j production for vector resonance searches at LHC', Phys. Lett. B 685 (2010) 302-308. DOI: 10.1016/j.physletb.2010.01.068; arXiv:0912.3799; https://arxiv.org/abs/0912.3799
20. Bogdan A. Dobrescu, Felix Yu, 'Coupling-mass mapping of dijet peak searches', Phys. Rev. D 88 (2013) 035021. DOI: 10.1103/PhysRevD.88.035021; arXiv:1306.2629; https://arxiv.org/abs/1306.2629
21. P. Ko, Yuji Omura, Chaehyun Yu, 'A resolution of the flavor problem of two Higgs doublet models with an extra U(1)_H symmetry for Higgs flavor', Phys. Lett. B 717 (2012) 173-178. DOI: 10.1016/j.physletb.2012.09.019; arXiv:1204.4588; https://arxiv.org/abs/1204.4588
22. F. Abe et al. (CDF Collaboration), 'Search for new particles decaying to dijets in p pbar collisions at sqrt(s) = 1.8 TeV', Phys. Rev. Lett. 74 (1995) 3538-3543. DOI: 10.1103/PhysRevLett.74.3538; arXiv:hep-ex/9501001; https://arxiv.org/abs/hep-ex/9501001