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In particle physics, W′ and Z′ bosons (or W-prime and Z-prime bosons) refer to hypothetical gauge bosons that arise from extensions of the electroweak symmetry of the Standard Model. They are named in analogy with the Standard Model W and Z bosons.

Types

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Types of W′ bosons

W′ bosons often arise in models with an extra SU(2) gauge group relative to the full Standard Model gauge group SU(3) × SU(2) × U(1). The extended SU(2) × SU(2) symmetry spontaneously breaks into the diagonal subgroup SU(2)_W which corresponds to the conventional SU(2) in electroweak theory.

More generally, there could be n copies of SU(2), which are then broken down to a diagonal SU(2)_W. This gives rise to n − 1 different W′, W′, and Z′ bosons. Such models might arise from a quiver diagram, for example.

In order for the W′ bosons to couple to weak isospin, the extra SU(2) and the Standard Model SU(2) must mix; one copy of SU(2) must break around the TeV scale (to get W′ bosons with a TeV mass) leaving a second SU(2) for the Standard Model. This happens in Little Higgs models that contain more than one copy of SU(2). Because the W′ comes from the breaking of an SU(2), it is generically accompanied by a Z′ boson of (almost) the same mass and with couplings related to the W′ couplings.

Another model with W′ bosons but without an additional SU(2) factor is the so-called 331 model with ${\displaystyle \;\beta =\pm {\tfrac {1}{\sqrt {3\;}}}~.}$ The symmetry breaking chain SU(3)_L × U(1)_W → SU(2)_W × U(1)_Y leads to a pair of W′ bosons and three Z′ bosons.

W′ bosons also arise in Kaluza–Klein theories with SU(2) in the bulk.

Types of Z′ bosons

Various models of physics beyond the Standard Model predict different kinds of Z′ bosons.

Models with a new U(1) gauge symmetry

The Z′ is the gauge boson of the (broken) U(1) symmetry.

E₆ models

This type of model contains two Z′ bosons, which can mix in general.

Pati–Salam

In addition to a fourth leptonic "color", Pati–Salam includes a right handed weak interaction with W′ and Z′ bosons.

Topcolor and Top Seesaw Models of Dynamical Electroweak Symmetry Breaking

Both these models have Z′ bosons that select the formation of particular condensates.

Little Higgs models

These models typically include an enlarged gauge sector, which is broken down to the Standard Model gauge symmetry around the TeV scale. In addition to one or more Z′ bosons, these models often contain W′ bosons.

Kaluza–Klein models

The Z′ boson are the excited modes of a neutral bulk gauge symmetry.

Stueckelberg Extensions

The Z′ boson is sourced from couplings found in string theories with intersecting D-branes (see Stueckelberg action).

Searches

Direct searches for "wide resonance-width" models

The following statements pertain only to "wide resonance width" models.

A W′-boson could be detected at hadron colliders through its decay to lepton plus neutrino or top quark plus bottom quark, after being produced in quark–antiquark annihilation. The LHC reach for W′ discovery is expected to be a few TeV.

Direct searches for Z′-bosons are carried out at hadron colliders, since these give access to the highest energies available. The search looks for high-mass dilepton resonances: the Z′-boson would be produced by quark–antiquark annihilation and decay to an electron–positron pair or a pair of opposite-charged muons. The most stringent current limits come from the Fermilab Tevatron, and depend on the couplings of the Z′-boson (which control the production cross section); as of 2006, the Tevatron excludes Z′-bosons up to masses of about 800 GeV for "typical" cross sections predicted in various models.

Direct searches for "narrow resonance-width" models

Recent classes of models have emerged that naturally provide cross section signatures that fall on the edge, or slightly below the 95% confidence level limits set by the Tevatron, and hence can produce detectable cross section signals for a Z′ boson in a mass range much closer to the Z pole-mass than the "wide width" models discussed above.

These "narrow width" models which fall into this category are those that predict a Stückelberg Z′ as well as a Z′ from a universal extra dimension (see "The Z′ hunters' guide". for links to these papers).

On 7 April 2011, the CDF collaboration at the Tevatron reported an excess in proton–antiproton collision events that produce a W boson accompanied by two hadronic jets. This could possibly be interpreted in terms of a Z′ boson.

On 2 June 2015, the ATLAS experiment at the LHC reported evidence for W′-bosons at significance 3.4 σ, still too low to claim a formal discovery. Researchers at the CMS experiment also independently reported signals that corroborate ATLAS's findings.

In March 2021, there were some reports to hint at the possible existence of Z′ bosons as an unexpected difference in how beauty quarks decay to create electrons or muons. The measurement has been made at a statistical significance of 3.1 σ, which is well below the 5 σ level that is conventionally considered sufficient proof of a discovery.

Z′–Y mixings

We might have gauge kinetic mixings between the U(1)′ of the Z′ boson and U(1)_Y of hypercharge. This mixing leads to a tree level modification of the Peskin–Takeuchi parameters.

See also

• X and Y bosons – Hypothetical elementary particles

References

1. ^ J. Beringer et al. (Particle Data Group) (2012). "Review of Particle Physics". Physical Review D. 86 (1): 010001. Bibcode:2012PhRvD..86a0001B. doi:10.1103/PhysRevD.86.010001. hdl:10481/34377.
2. A. Abulencia et al. (CDF collaboration) (2006). "Search for Z′ → ee using dielectron mass and angular distribution". Physical Review Letters. 96 (21): 211801. arXiv:hep-ex/0602045. Bibcode:2006PhRvL..96u1801A. doi:10.1103/PhysRevLett.96.211801. PMID 16803227.
3. Woollacott, Emma (2011-04-07). "Tevatron data indicates unknown new particle". TG Daily.
4. "Fermilab's data peak that causes excitement". Symmetry Magazine. Fermilab/SLAC. 2011-04-07.
5. Slezak, Michael (22 August 2015). "Possible new particle hints that universe may not be left-handed". New Scientist.
6. Johnston, Hamish (23 March 2021). "Has a new particle called a 'leptoquark' been spotted at CERN?". Physics World. Archived from the original on 24 March 2021.

Further reading

• T.G. Rizzo (2006). "Z′ Phenomenology and the LHC". arXiv:hep-ph/0610104., a pedagogical overview of Z′ phenomenology (TASI 2006 lectures)
• P. Rincon (17 May 2010). "LHC particle search 'nearing', says physicist". BBC News.

More advanced:

• Abulencia, A.; CDF Collaboration; et al. (2006). "Search for Z′ → ee using dielectron mass and angular distribution". Physical Review Letters. 96 (211801): 211801. arXiv:hep-ex/0602045. Bibcode:2006PhRvL..96u1801A. doi:10.1103/PhysRevLett.96.211801. PMID 16803227.
• Amini, Hassib (2003). "Radiative corrections to Higgs masses in Z′ models". New Journal of Physics. 5 (49): 49. arXiv:hep-ph/0210086. Bibcode:2003NJPh....5...49A. doi:10.1088/1367-2630/5/1/349. S2CID 15264222.
• Aoki, Mayumi; Oshimo, Noriyuki (2000). "Supersymmetric extension of the standard model with naturally stable proton". Physical Review D. 62 (55013): 55013. arXiv:hep-ph/0003286. Bibcode:2000PhRvD..62e5013A. doi:10.1103/PhysRevD.62.055013. S2CID 14168936.
• Aoki, Mayumi; Oshimo, Noriyuki (2000). "A supersymmetric model with an extra U(1) gauge symmetry". Physical Review Letters. 84 (23): 5269–5272. arXiv:hep-ph/9907481. Bibcode:2000PhRvL..84.5269A. doi:10.1103/PhysRevLett.84.5269. PMID 10990921. S2CID 15033987.
• Appelquist, Thomas; Dobrescu, Bogdan A.; Hopper, Adam R. (2003). "Nonexotic neutral gauge bosons". Physical Review D. 68 (35012): 35012. arXiv:hep-ph/0212073. Bibcode:2003PhRvD..68c5012A. doi:10.1103/PhysRevD.68.035012. S2CID 119091245.
• Babu, K. S.; Kolda, Christopher F.; March-Russell, John (1996). "Leptophobic U(1)s and the R_b–R_c crisis". Physical Review D. 54 (7): 4635–4647. arXiv:hep-ph/9603212. Bibcode:1996PhRvD..54.4635B. doi:10.1103/PhysRevD.54.4635. PMID 10021145. S2CID 38299279.
• Barger, Vernon D.; Whisnant, K. (1987). "Use of Z lepton asymmetry to determine mixing between Z boson and Z′ boson of E₆ superstrings". Physical Review D. 36 (3): 979–82. Bibcode:1987PhRvD..36..979B. doi:10.1103/PhysRevD.36.979. PMID 9958259.
• Barr, S.M.; Dorsner, I. (2005). "The origin of a peculiar extra U(1)". Physical Review D. 72 (15011): 015011. arXiv:hep-ph/0503186. Bibcode:2005PhRvD..72a5011B. doi:10.1103/PhysRevD.72.015011. S2CID 119492913.
• Batra, Puneet; Dobrescu, Bogdan A.; Spivak, David (2006). "Anomaly-free sets of fermions". Journal of Mathematical Physics. 47 (82301): 2301. arXiv:hep-ph/0510181. Bibcode:2006JMP....47h2301B. doi:10.1063/1.2222081. S2CID 9830964.
• Carena, Marcela S.; Daleo, Alejandro; Dobrescu, Bogdan A.; Tait, Tim M. P. (2004). "Z′ gauge bosons at the Tevatron". Physical Review D. 70 (93009): 093009. arXiv:hep-ph/0408098. Bibcode:2004PhRvD..70i3009C. doi:10.1103/PhysRevD.70.093009. S2CID 118616267.
• Demir, Durmus A.; Kane, Gordon L.; Wang, Ting T. (2005). "The Minimal U(1)′ extension of the MSSM". Physical Review D. 72 (15012): 015012. arXiv:hep-ph/0503290. Bibcode:2005PhRvD..72a5012D. doi:10.1103/PhysRevD.72.015012. S2CID 17656689.
• Dittmar, Michael; Nicollerat, Anne-Sylvie; Djouadi, Abdelhak (2004). "Z′ studies at the LHC: an update". Physics Letters B. 583 (1–2): 111–120. arXiv:hep-ph/0307020. Bibcode:2004PhLB..583..111D. doi:10.1016/j.physletb.2003.09.103. S2CID 15749848.
• Emam, W.; Khalil, S. (2007). "Higgs and Z′ phenomenology in B−L extension of the standard model at LHC". European Physical Journal C. 522 (3): 625–633. arXiv:0704.1395. Bibcode:2007EPJC...52..625E. doi:10.1140/epjc/s10052-007-0411-7. S2CID 18985438.
• Erler, Jens (2000). "Chiral models of weak scale supersymmetry". Nuclear Physics B. 586 (1): 73–91. arXiv:hep-ph/0006051. Bibcode:2000NuPhB.586...73E. doi:10.1016/S0550-3213(00)00427-2. S2CID 16728305.
• Everett, Lisa L.; Langacker, Paul; Plumacher, Michael; Wang, Jing (2000). "Alternative supersymmetric spectra". Physics Letters B. 477 (1–3): 233–241. arXiv:hep-ph/0001073. Bibcode:2000PhLB..477..233E. doi:10.1016/S0370-2693(00)00187-8. S2CID 16294141.
• Fajfer, S.; Singer, P. (2002). "Constraints on heavy Z′ couplings from ΔS = 2 B → KKπ decay". Physical Review D. 65 (17301): 017301. arXiv:hep-ph/0110233. Bibcode:2001PhRvD..65a7301F. doi:10.1103/PhysRevD.65.017301. S2CID 117080415.
• Ferroglia, A.; Lorca, A.; van der Bij, J. J. (2007). "The Z′ reconsidered". Annalen der Physik. 16 (7–8): 563–578. arXiv:hep-ph/0611174. Bibcode:2007AnP...519..563F. doi:10.1002/andp.200710249. S2CID 17347199.
• Hayreter, Alper (2007). "Dilepton signatures of family non-universal U(1)′". Physics Letters B. 649 (2–3): 191–196. arXiv:hep-ph/0703269. Bibcode:2007PhLB..649..191H. doi:10.1016/j.physletb.2007.03.049. S2CID 16059648.
• Kang, Junhai; Langacker, Paul (2005). "Z′ discovery limits for supersymmetric E₆ models". Physical Review D. 71 (35014): 035014. arXiv:hep-ph/0412190. Bibcode:2005PhRvD..71c5014K. doi:10.1103/PhysRevD.71.035014. S2CID 9649745.
• Morrissey, David E.; Wells, James D. (2006). "The tension between gauge coupling unification, the Higgs boson mass, and a gauge-breaking origin of the supersymmetric μ-term". Physical Review D. 74 (15008): 15008. arXiv:hep-ph/0512019. Bibcode:2006PhRvD..74a5008M. doi:10.1103/PhysRevD.74.015008. S2CID 119467594.

External links

• The Z′ Hunter's Guide, a collection of papers and talks regarding Z′ physics
• Z′ physics on arxiv.org

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