W′ and Z′ bosons
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particle physics Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...
, 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 In particle physics, the W and Z bosons are vector bosons that are together known as the weak bosons or more generally as the intermediate vector bosons. These elementary particles mediate the weak interaction; the respective symbols are , , an ...
.


Types


Types of W′ bosons

W′ bosons often arise in models with an extra
SU(2) In mathematics, the special unitary group of degree , denoted , is the Lie group of unitary matrices with determinant 1. The more general unitary matrices may have complex determinants with absolute value 1, rather than real 1 in the special ...
gauge group In physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations (Lie group ...
relative to the full Standard Model gauge group . The extended symmetry spontaneously breaks into the
diagonal subgroup In the mathematical discipline of group theory, for a given group the diagonal subgroup of the ''n''-fold direct product is the subgroup :\. This subgroup is isomorphic to Properties and applications * If acts on a set the ''n''-fold diag ...
SU(2)W which corresponds to the conventional SU(2) in electroweak theory. More generally, there could be copies of SU(2), which are then broken down to a diagonal SU(2)W. This gives rise to different W′+, W′, and Z′ bosons. Such models might arise from a
quiver diagram In theoretical physics, a quiver diagram is a graph representing the matter content of a gauge theory that describes D-branes on orbifolds. Quiver diagrams may also be used to described \mathcal = 2 supersymmetric gauge theories in four dimens ...
, for example. In order for the W′ bosons to couple to
weak isospin In particle physics, weak isospin is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol or , with the third component written as or . It c ...
, 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 \; \beta = \pm \tfrac ~. The symmetry breaking chain 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 Bulk can refer to: Industry * Bulk cargo * Bulk liquids * Bulk mail * Bulk material handling * Bulk pack, packaged bulk materials/products * Bulk purchasing * Baking * Bulk fermentation, the period after mixing when dough is left alone to f ...
.


Types of Z′ bosons

Various models of physics beyond the Standard Model predict different kinds of Z′ bosons. ; Models with a new
U(1) In mathematics, the circle group, denoted by \mathbb T or \mathbb S^1, is the multiplicative group of all complex numbers with absolute value 1, that is, the unit circle in the complex plane or simply the unit complex numbers. \mathbb T = \. ...
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 Topcolor is a model in theoretical physics, of dynamical electroweak symmetry breaking in which the top quark and anti-top quark form a composite Higgs boson by a new force arising from massive "top gluons". The solution to composite Higgs model ...
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-brane In string theory, D-branes, short for ''Dirichlet membrane'', are a class of extended objects upon which open strings can end with Dirichlet boundary conditions, after which they are named. D-branes were discovered by Jin Dai, Leigh, and Polch ...
s (see
Stueckelberg action In field theory, the Stueckelberg action (named after Ernst Stueckelberg) describes a massive spin-1 field as an R (the real numbers are the Lie algebra of U(1)) Yang–Mills theory coupled to a real scalar field φ. This scalar field takes on ...
).


Searches


Direct searches for "wide resonance-width" models

The following statements pertain only to "wide
resonance width In physics and engineering, the quality factor or ''Q'' factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is. It is defined as the ratio of the initial energy stored in the resonator to the energ ...
" models. A W′-boson could be detected at hadron colliders through its decay to lepton plus
neutrino A neutrino ( ; denoted by the Greek letter ) is a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass ...
or
top quark The top quark, sometimes also referred to as the truth quark, (symbol: t) is the most massive of all observed elementary particles. It derives its mass from its coupling to the Higgs Boson. This coupling y_ is very close to unity; in the Standard ...
plus
bottom quark The bottom quark or b quark, also known as the beauty quark, is a third-generation heavy quark with a charge of −  ''e''. All quarks are described in a similar way by electroweak and quantum chromodynamics, but the bottom quark has exce ...
, after being produced in quark–antiquark
annihilation In particle physics, annihilation is the process that occurs when a subatomic particle collides with its respective antiparticle to produce other particles, such as an electron colliding with a positron to produce two photons. The total energy ...
. The LHC reach for W′ discovery is expected to be a few TeV. Direct searches for Z′-bosons are carried out at
hadron In particle physics, a hadron (; grc, ἁδρός, hadrós; "stout, thick") is a composite subatomic particle made of two or more quarks held together by the strong interaction. They are analogous to molecules that are held together by the e ...
colliders, since these give access to the highest energies available. The search looks for high-mass dilepton
resonances Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillat ...
: the Z′-boson would be produced by quark–antiquark annihilation and decay to an
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no ...
positron pair or a pair of opposite-charged muons. The most stringent current limits come from the
Fermilab Fermi National Accelerator Laboratory (Fermilab), located just outside Batavia, Illinois, near Chicago, is a United States Department of Energy national laboratory specializing in high-energy particle physics. Since 2007, Fermilab has been opera ...
Tevatron The Tevatron was a circular particle accelerator (active until 2011) in the United States, at the Fermi National Accelerator Laboratory (also known as ''Fermilab''), east of Batavia, Illinois, and is the second highest energy particle collider ...
, and depend on the couplings of the Z′-boson (which control the production
cross section Cross section may refer to: * Cross section (geometry) ** Cross-sectional views in architecture & engineering 3D *Cross section (geology) * Cross section (electronics) * Radar cross section, measure of detectability * Cross section (physics) **Abs ...
); as of 2006, the
Tevatron The Tevatron was a circular particle accelerator (active until 2011) in the United States, at the Fermi National Accelerator Laboratory (also known as ''Fermilab''), east of Batavia, Illinois, and is the second highest energy particle collider ...
excludes Z′-bosons up to masses of about 800 
GeV GEV may refer to: * ''G.E.V.'' (board game), a tabletop game by Steve Jackson Games * Ashe County Airport, in North Carolina, United States * Gällivare Lapland Airport, in Sweden * Generalized extreme value distribution * Gev Sella, Israeli-Sou ...
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 ' for links to these papers). On 7 April 2011, the
CDF collaboration The Collider Detector at Fermilab (CDF) experimental collaboration studies high energy particle collisions from the Tevatron, the world's former highest-energy particle accelerator. The goal is to discover the identity and properties of the partic ...
at the Tevatron reported an excess in proton–
antiproton The antiproton, , (pronounced ''p-bar'') is the antiparticle of the proton. Antiprotons are stable, but they are typically short-lived, since any collision with a proton will cause both particles to be annihilated in a burst of energy. The exis ...
collision
events Event may refer to: Gatherings of people * Ceremony, an event of ritual significance, performed on a special occasion * Convention (meeting), a gathering of individuals engaged in some common interest * Event management, the organization of ev ...
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 ATLAS is the largest general-purpose particle detector experiment at the Large Hadron Collider (LHC), a particle accelerator at CERN (the European Organization for Nuclear Research) in Switzerland. The experiment is designed to take advantage of ...
at the LHC reported evidence for W′-bosons at significance 3.4  , 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  , which is well below the 5  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 In particle physics, the hypercharge (a portmanteau of hyperon, hyperonic and charge (physics), charge) ''Y'' of a subatomic particle, particle is a quantum number conserved under the strong interaction. The concept of hypercharge provides a sin ...
. This mixing leads to a tree level modification of the Peskin–Takeuchi parameters.


See also

*


References


Further reading

* , a pedagogical overview of Z′ phenomenology ( TASI 2006 lectures) * More advanced: * * * * * * * * * * * * * * * * * * * *


External links


The Z′ Hunter's Guide
a collection of papers and talks regarding Z′ physics
Z′ physics on arxiv.org
{{DEFAULTSORT:W' and Z' bosons Gauge bosons Hypothetical elementary particles Force carriers Subatomic particles with spin 1