Editing Quark (section)

=== Weak interaction ===
{{Main|Weak interaction}}
[[Image:Beta Negative Decay.svg|thumb|right|192px|upright|[[Feynman diagram]] of [[beta decay]] with time flowing upwards. The CKM matrix (discussed below) encodes the probability of this and other quark decays.|alt=A tree diagram consisting mostly of straight arrows. A down quark forks into an up quark and a wavy-arrow W[superscript minus] boson, the latter forking into an electron and reversed-arrow electron antineutrino.]]
A quark of one flavor can transform into a quark of another flavor only through the weak interaction, one of the four [[fundamental interaction]]s in particle physics. By absorbing or emitting a [[W boson]], any up-type quark (up, charm, and top quarks) can change into any down-type quark (down, strange, and bottom quarks) and vice versa. This flavor transformation mechanism causes the [[radioactive decay|radioactive]] process of [[beta decay]], in which a neutron ({{SubatomicParticle|neutron}}) "splits" into a proton ({{SubatomicParticle|proton}}), an [[electron]] ({{SubatomicParticle|electron}}) and an [[electron antineutrino]] ({{SubatomicParticle|electron antineutrino}}) (see picture). This occurs when one of the down quarks in the neutron ({{SubatomicParticle|up quark}}{{SubatomicParticle|down quark}}{{SubatomicParticle|down quark}}) decays into an up quark by emitting a [[virtual particle|virtual]] {{SubatomicParticle|W boson-}} boson, transforming the neutron into a proton ({{SubatomicParticle|up quark}}{{SubatomicParticle|up quark}}{{SubatomicParticle|down quark}}). The {{SubatomicParticle|W boson-}} boson then decays into an electron and an electron antineutrino.<ref name="SLAC">
{{cite web
 |title=Weak Interactions
 |url=http://www2.slac.stanford.edu/vvc/theory/weakinteract.html
 |work=Virtual Visitor Center
 |publisher=[[Stanford Linear Accelerator Center]]
 |year=2008
 |access-date=2008-09-28
 |archive-date=23 November 2011
 |archive-url=https://web.archive.org/web/20111123112925/http://www2.slac.stanford.edu/vvc/theory/weakinteract.html
 |url-status=dead
}}</ref>

{| style="margin:auto;" cellpadding="5%"
|-
| &nbsp; {{SubatomicParticle|Neutron}}|| → || &nbsp; {{SubatomicParticle|Proton}} ||+|| {{SubatomicParticle|electron}} ||+|| {{SubatomicParticle|electron antineutrino}} || (Beta decay, hadron notation)
|-
| {{SubatomicParticle|up quark}}{{SubatomicParticle|down quark}}{{SubatomicParticle|down quark}} || → || {{SubatomicParticle|up quark}}{{SubatomicParticle|up quark}}{{SubatomicParticle|down quark}} ||+|| {{SubatomicParticle|electron}} ||+|| {{SubatomicParticle|electron antineutrino}} || (Beta decay, quark notation)
|}

Both beta decay and the inverse process of ''[[inverse beta decay]]'' are routinely used in medical applications such as [[positron emission tomography]] (PET) and in experiments involving [[neutrino detector|neutrino detection]].
[[Image:Quark weak interactions.svg|thumb|271px|left|The [[Coupling (physics)|strengths]] of the weak interactions between the six quarks. The "intensities" of the lines are determined by the elements of the [[CKM matrix]].|alt=Three balls "u", "c", and "t" noted "up-type quarks" stand above three balls "d", "s", "b" noted "down-type quark". The "u", "c", and "t" balls are vertically aligned with the "d", "s", and b" balls respectively. Colored lines connect the "up-type" and "down-type" quarks, with the darkness of the color indicating the strength of the weak interaction between the two; The lines "d" to "u", "c" to "s", and "t" to "b" are dark; The lines "c" to "d" and "s" to "u" are grayish; and the lines "b" to "u", "b" to "c", "t" to "d", and "t" to "s" are almost white.]]

While the process of flavor transformation is the same for all quarks, each quark has a preference to transform into the quark of its own generation. The relative tendencies of all flavor transformations are described by a [[matrix (mathematics)|mathematical table]], called the [[Cabibbo–Kobayashi–Maskawa matrix]] (CKM matrix). Enforcing [[Unitary operator|unitarity]], the approximate [[absolute value|magnitudes]] of the entries of the CKM matrix are:<ref name="PDG2010">
{{cite journal
 |author=K. Nakamura
 |display-authors=etal
 |collaboration=[[Particle Data Group]]
 |year=2010
 |title=Review of Particles Physics: The CKM Quark-Mixing Matrix
 |url=http://pdg.lbl.gov/2010/reviews/rpp2010-rev-ckm-matrix.pdf
 |journal=[[Journal of Physics G]]
 |volume=37 |issue= 7A|page=075021
 |bibcode=2010JPhG...37g5021N
 |doi=10.1088/0954-3899/37/7A/075021 |doi-access=free
}}</ref>
: <math alt="|V_ud| ≅ 0.974; |V_us| ≅ 0.225; |V_ub| ≅ 0.003; |V_cd| ≅ 0.225; |V_cs| ≅ 0.973; |V_cb| ≅ 0.041; |V_td| ≅ 0.009; |V_ts| ≅ 0.040; |V_tb| ≅ 0.999.">
\begin{bmatrix} |V_\mathrm {ud}| & |V_\mathrm {us}| & |V_\mathrm {ub}| \\ |V_\mathrm {cd}| & |V_\mathrm {cs}| & |V_\mathrm {cb}| \\ |V_\mathrm {td}| & |V_\mathrm {ts}| & |V_\mathrm {tb}| \end{bmatrix} \approx
\begin{bmatrix} 0.974 & 0.225 & 0.003 \\ 0.225 & 0.973 & 0.041 \\ 0.009 & 0.040 & 0.999 \end{bmatrix},</math>
where ''V''<sub>''ij''</sub> represents the tendency of a quark of flavor ''i'' to change into a quark of flavor ''j'' (or vice versa).<ref group="nb">The actual probability of decay of one quark to another is a complicated function of (among other variables) the decaying quark's mass, the masses of the [[decay product]]s, and the corresponding element of the CKM matrix. This probability is directly proportional (but not equal) to the magnitude squared (|''V''<sub>''ij''&nbsp;</sub>|<sup>2</sup>) of the corresponding CKM entry.</ref>

There exists an equivalent weak interaction matrix for leptons (right side of the W boson on the above beta decay diagram), called the [[Pontecorvo–Maki–Nakagawa–Sakata matrix]] (PMNS matrix).<ref>
{{cite journal
 |author1=Z. Maki
 |author2=M. Nakagawa
 |author3=S. Sakata
 |title=Remarks on the Unified Model of Elementary Particles
 |journal=[[Progress of Theoretical Physics]]
 |volume=28
 |issue=5
 |page=870
 |year=1962
 |bibcode=1962PThPh..28..870M
 |doi=10.1143/PTP.28.870
 |doi-access=free
}}</ref> Together, the CKM and PMNS matrices describe all flavor transformations, but the links between the two are not yet clear.<ref>
{{cite journal
 |author1=B. C. Chauhan
 |author2=M. Picariello
 |author3=J. Pulido
 |author4=E. Torrente-Lujan
 |title=Quark–Lepton Complementarity, Neutrino and Standard Model Data Predict {{nowrap|1=θ{{su|p=PMNS|b=13}} = {{val|9|+1|-2|u=°}}}}<!-- See Section 2 -->
 |journal=[[European Physical Journal]]
 |volume=C50 |issue=3 |pages=573–578
 |year=2007
 |arxiv=hep-ph/0605032
 |bibcode = 2007EPJC...50..573C
 |doi=10.1140/epjc/s10052-007-0212-z
 |s2cid=118107624
}}</ref>
{{clear}}