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# W′ and Z′ bosons

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### W′ and Z′ bosons

 Composition Elementary particle Bosonic Standard-Model Extension[1] Hypothetical unknown similar to W and Z bosons W′: ±1 e Z′: 0 e 1[1] 2

In particle physics, W′ and Z′ bosons (or W-prime and Z-prime bosons) refer to hypothetical new 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.

## Contents

• Types 1
• Types of W′ bosons 1.1
• Types of Z′ bosons 1.2
• Searches 2
• Direct searches 2.1
• Indirect searches 2.2
• Z′–Y mixings 3
• References 5

## Types

### Types of W′ bosons

W′ bosons often arise in models with an extra SU(2) gauge group. SU(2) × SU(2) is spontaneously broken to the diagonal subgroup SU(2)W which corresponds to the electroweak SU(2). More generally, we might have n copies of SU(2), which are then broken down to a diagonal SU(2)W. This gives rise to n−1 W+′, W′ and Z′ bosons. Such models might arise from quiver diagram, for example. In order for the W′ bosons to couple to 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 β = ± 1/3. 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.
• Topcolor and Top Seesaw Models of Dynamical Electroweak Symmetry Breaking have Z′ bosons to 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 (see Stueckelberg action). The Z′ boson is sourced from couplings found in string theories with intersecting D-branes.

## Searches

### Direct searches

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.[2]

The above statements apply to "wide 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′ Hunter's Guide for links to these papers).

On April 7, 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.[3][4]

### Indirect searches

The most stringent limits on new W′ bosons are set by their indirect effects on low-energy processes like muon decay, where they can substitute for the Standard Model W boson exchange.

Indirect searches for Z′ bosons are carried out at electron-positron colliders, since these give access to high-precision measurements of the properties of the Standard Model Z boson. The constraints come from mixing between the Z′ and the Z, and are model dependent because they depend not only on the Z′ mass but also its mixing with the Z. The current most stringent limits are from the CERN LEP collider, which constrains Z′ bosons to be heavier than a few hundred GeV, for typical model parameters. The ILC will extend this reach up to 5 to 10 TeV depending on the model under consideration, providing complementarity with the LHC because it will offer measurements of additional properties of the Z′ boson.

## 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.

## References

1. ^ a b J. Beringer et al. (
2. ^ A. Abulencia et al. (
3. ^ Emma Woollacott (2011-04-07). "Tevatron data indicates unknown new particle". TG Daily.
4. ^ "Fermilab’s data peak that causes excitement". Fermilab/SLAC. 2011-04-07.

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

• Abulencia, A.; et al. (CDF Collaboration) (2006). "Search for Z′ → e+e using dielectron mass and angular distribution". Physical Review Letters 96 (211801).
• Amini, Hassib (2003). "Radiative corrections to Higgs masses in Z′ models". New Journal of Physics 5 (49).
• Aoki, Mayumi; Oshimo, Noriyuki (2000). "Supersymmetric extension of the standard model with naturally stable proton". Physical Review D 62 (055013): 55013.
• Aoki, Mayumi; Oshimo, Noriyuki (2000). "A supersymmetric model with an extra U(1) gauge symmetry". Physical Review Letters 84 (23): 5269–5272.
• Appelquist, Thomas; Dobrescu, Bogdan A.; Hopper, Adam R. (2003). "Nonexotic neutral gauge bosons". Physical Review D 68 (035012): 35012.
• Babu, K. S.; Kolda, Christopher F.; March-Russell, John (1996). "Leptophobic U(1)s and the Rb–Rc crisis" 54. pp. 4635–4647.
• 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.
• Barr, S.M.; Dorsner, I. (2005). "The origin of a peculiar extra U(1)". Physical Review D 72 (015011).
• Batra, Puneet; Dobrescu, Bogdan A.; Spivak, David (2006). "Anomaly-free sets of fermions". Journal of Mathematical Physics 47 (082301): 2301.
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• Demir, Durmus A.; Kane, Gordon L.; Wang, Ting T. (2005). "The Minimal U(1)′ extension of the MSSM". Physical Review D 72 (015012).
• Dittmar, Michael; Nicollerat, Anne-Sylvie; Djouadi, Abdelhak (2004). "Z′ studies at the LHC: an update". Physical Letters B 583: 111–120.
• Emam, W.; Khalil, S. (2007). "Higgs and Z′ phenomenology in BL extension of the standard model at LHC". European Physical Journal C 522: 625–633.
• Erler, Jens (2000). "Chiral models of weak scale supersymmetry". Nuclear Physics B 586: 73–91.
• Everett, Lisa L.; Langacker, Paul; Plumacher, Michael; Wang, Jing (2000). "Alternative supersymmetric spectra". Physics Letters B 477: 233–241.
• Fajfer, S.; Singer, P. (2002). "Constraints on heavy Z′ couplings from ΔS = 2 B → KKπ+ decay". Physical Review D 65 (017301).
• Ferroglia, A.; Lorca, A.; van der Bij, J. J. (2007). "The Z′ reconsidered". Annalen der Physik 16: 563–578.
• Hayreter, Alper (2007). "Dilepton signatures of family non-universal U(1)′". Physical Letters B 649 (2–3): 191–196.
• Kang, Junhai; Langacker, Paul (2005). "Z′ discovery limits for supersymmetric E6 models". Physical Review D 71 (035014).
• 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 (015008): 15008.