Difference between revisions of "Fermi's interaction"

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{{distinguish|Fermi contact interaction}}
 
{{distinguish|Fermi contact interaction}}
  
In [[particle physics]], '''Fermi's interaction''' (also the '''Fermi Theory of Beta Decay''') is an explanation of the [[beta decay]], proposed by [[Enrico Fermi]] in 1933.<ref>"Tentativo di una teoria dei raggi ß", Ricerca Scientifica, 1933 (also Z. Phys., 1934)</ref><ref>
+
[[Image:Beta-minus Decay.svg|thumb|360px|{{SubatomicParticle|Beta-}} decay in an [[atomic nucleus]] (the accompanying antineutrino is omitted).<br>
{{Cite web
+
The inset shows beta decay of a free neutron.<br>
| last = Fermi | first = E.
+
In both processes, the intermediate emission of a virtual [[W boson|{{SubatomicParticle|W boson-}} boson]] (which then decays to electron and antineutrino) is not shown.]]In [[particle physics]], '''Fermi's interaction''' (also the '''Fermi Theory of Beta Decay''') is an explanation of the [[beta decay]], proposed by [[Enrico Fermi]] in 1933.<ref>
| title = Fermi's Theory of Beta Decay (English translation by Fred L. Wilson, 1968)
+
{{cite journal
| work = [[American Journal of Physics]]
+
|last=Fermi |first=E.
| year = 1934
+
|year=1933
| url = http://microboone-docdb.fnal.gov/cgi-bin/RetrieveFile?docid=953;filename=FermiBetaDecay1934.pdf;version=1
+
|title=Tentativo di una teoria dei raggi β
}}</ref> The theory posits four [[fermion]]s directly interacting with one another, at one vertex. For example, this interaction explains beta decay of a [[neutron]] by direct coupling of a neutron  with an [[electron]], [[antineutrino]] and a [[proton]].<ref name="Feynman">{{cite book|last=Feynman|first=R.P.|title=Theory of Fundamental Processes|year=1962|publisher=W.A. Benjamin }} Chapters 6&7</ref> Fermi first introduced this coupling in his description of beta decay in 1933.<ref name="griffiths">{{cite book|last=Griffiths|first=David|title=Introduction to Elementary Particles |year=2009|isbn=978-3-527-40601-2|pages=314–315}}</ref>
+
|journal=[[La Ricerca Scientifica]]
 +
|volume=2 |issue=12 |pages=
 +
|bibcode=
 +
|doi=
 +
|language=Italian
 +
}}</ref><ref>
 +
{{cite journal
 +
|last=Fermi |first=E.
 +
|year=1934
 +
|title=Tentativo di una teoria dei raggi β
 +
|journal=[[Il Nuovo Cimento]]
 +
|volume=11 |issue=1 |pages=1–19
 +
|bibcode=
 +
|doi=10.1007/BF02959820
 +
|language=Italian
 +
}}</ref><ref>
 +
{{cite journal
 +
|last=Fermi |first=E.
 +
|year=1934
 +
|title=Versuch einer Theorie der beta-Strahlen. I
 +
|journal=[[Zeitschrift für Physik]]
 +
|volume=88 |issue= |pages=161
 +
|bibcode= 1934ZPhy...88..161F
 +
|doi= 10.1007/BF01351864
 +
|language=German
 +
}}</ref><ref>
 +
{{cite journal
 +
|last=Wilson |first=F. L.
 +
|year=1968
 +
|title=Fermi's Theory of Beta Decay
 +
|url=http://microboone-docdb.fnal.gov/cgi-bin/RetrieveFile?docid=953;filename=FermiBetaDecay1934.pdf;version=1
 +
|work=[[American Journal of Physics]]
 +
|volume=36 |issue=12 |pages=1150
 +
|bibcode= 1968AmJPh..36.1150W
 +
|doi= 10.1119/1.1974382
 +
}}</ref> The theory posits four [[fermion]]s directly interacting with one another, at one vertex.<br>
 +
For example, this interaction explains beta decay of a [[neutron]] by direct coupling of a neutron  with:
 +
# an [[electron]],  
 +
# an [[antineutrino]] and  
 +
# a [[proton]].<ref name="Feynman">
 +
{{cite book
 +
|last=Feynman|first=R.P.
 +
|title=Theory of Fundamental Processes
 +
|year=1962
 +
|publisher=[[W. A. Benjamin]]
 +
|at=Chapters 6 & 7
 +
}}</ref>  
 +
 
 +
Fermi first introduced this coupling in his description of beta decay in 1933.<ref name="griffiths">
 +
{{cite book
 +
|last=Griffiths |first=D.
 +
|year=2009
 +
|title=Introduction to Elementary Particles
 +
|edition=2nd |pages=314–315
 +
|isbn=978-3-527-40601-2
 +
}}</ref> The Fermi interaction was the precursor to the theory for the [[weak interaction]] where the interaction between the proton-neutron and electron-antineutrino is mediated by a virtual [[W and Z bosons|W<sup>-</sup> boson]].
  
 
== History of initial rejection and later publication ==
 
== History of initial rejection and later publication ==
Fermi first submitted his "tentative" theory of beta decay to the famous science journal ''[[Nature (journal)|Nature]]'', which rejected it for being "too speculative." ''Nature'' later admitted the rejection to be one of the great editorial blunders in its history. Fermi then submitted the paper to Italian and German publications, which accepted and published it in 1933 in those languages, but it did not appear at the time in a primary publication in English (''[[Nature (journal)|Nature]]'' finally belatedly republished Fermi's report on beta decay in English on January&nbsp;16, 1939).
+
Fermi first submitted his "tentative" theory of beta decay to the famous science journal ''[[Nature (journal)|Nature]]'', which rejected it for being "too speculative." ''Nature'' later admitted the rejection to be one of the great editorial blunders in its history. Fermi then submitted the paper to [[italian language|Italian]] and [[german language|German]] publications, which accepted and published it in 1933 in those languages, but it did not appear at the time in a primary publication in English (''[[Nature (journal)|Nature]]'' finally belatedly republished Fermi's report on beta decay in English on January&nbsp;16, 1939).
  
Fermi found the initial rejection of the paper so troubling that he decided to take some time off from theory, and do only experimental physics. This would lead shortly to his famous work with activation of nuclei with slow neutrons.
+
Fermi found the initial rejection of the paper so troubling that he decided to take some time off from [[theoretical physics]], and do only experimental physics. This would lead shortly to his famous work with [[neutron temperature|activation of nuclei]] with slow neutrons.
  
 
==The nature of the interaction==
 
==The nature of the interaction==
  
The interaction could also explain [[muon]] decay via a coupling of a muon, electron-antineutrino, muon-neutrino and electron, with the same fundamental strength of the interaction. This hypothesis was put forward by [[Gershtein]] and [[Zeldovich]] and is known as the [[Conserved Vector Current]] hypothesis.<ref name="gerstein1958">Gerstein, S S; Zeldovich Ya B. (1958) Soviet Physics. JFTP. 8, 570</ref>
+
The interaction could also explain [[muon]] decay via a coupling of a muon, electron-antineutrino, muon-neutrino and electron, with the same fundamental strength of the interaction. This hypothesis was put forward by [[Gershtein]] and [[Zeldovich]] and is known as the [[Conserved Vector Current]] hypothesis.<ref name="gerstein1958">
 +
{{cite journal
 +
|last1=Gerstein |first1=S. S.
 +
|last2=Zeldovich |first2=Ya. B.
 +
|year=1958
 +
|journal=[[Soviet Physics JETP]]
 +
|volume=8 |pages=570
 +
|bibcode=
 +
|doi=
 +
}}</ref>
  
Fermi's four-fermion theory describes the [[weak interaction]] remarkably well. Unfortunately, the calculated cross-section grows as the square of the energy <math> \sigma \approx G_F^2 E^2 </math>, making it unlikely that the theory is valid at energies much higher than about 100 GeV. The solution is to replace the four-fermion contact interaction by a more complete theory ([[UV completion]])—an exchange of a [[W and Z bosons|W or Z boson]] as explained in the [[electroweak theory]].
+
Fermi's four-fermion theory describes the [[weak interaction]] remarkably well. Unfortunately, the calculated cross-section grows as the square of the energy <math> \sigma \approx G_{\rm F}^2 E^2 </math>, making it unlikely that the theory is valid at energies much higher than about 100 GeV. The solution is to replace the four-fermion contact interaction by a more complete theory ([[UV completion]])—an exchange of a [[W and Z bosons|W or Z boson]] as explained in the [[electroweak theory]].
  
 
In the original theory, Fermi assumed that the form of interaction is a contact coupling of two vector currents. Subsequently, it was pointed out by [[Tsung-Dao Lee|Lee]] and [[Chen Ning Yang|Yang]] that nothing prevented the appearance of an axial, parity violating current, and this was confirmed by [[Wu Experiment|experiments]] carried out by [[Chien-Shiung Wu]].<ref>
 
In the original theory, Fermi assumed that the form of interaction is a contact coupling of two vector currents. Subsequently, it was pointed out by [[Tsung-Dao Lee|Lee]] and [[Chen Ning Yang|Yang]] that nothing prevented the appearance of an axial, parity violating current, and this was confirmed by [[Wu Experiment|experiments]] carried out by [[Chien-Shiung Wu]].<ref>
Line 44: Line 108:
 
  |bibcode=1957PhRv..105.1413W
 
  |bibcode=1957PhRv..105.1413W
 
  |doi=10.1103/PhysRev.105.1413
 
  |doi=10.1103/PhysRev.105.1413
}}</ref>  
+
}}</ref>
  
 
{| class="wikitable" style="float:right; clear:right; margin-top:0; margin-left:10px; margin-bottom:8px; margin-right:0; padding:7px; font-size:85%; width:230px;"
 
{| class="wikitable" style="float:right; clear:right; margin-top:0; margin-left:10px; margin-bottom:8px; margin-right:0; padding:7px; font-size:85%; width:230px;"
Line 50: Line 114:
 
| {{nowrap|[[File:MuonFermiDecay.gif|x110px]]&nbsp;}}
 
| {{nowrap|[[File:MuonFermiDecay.gif|x110px]]&nbsp;}}
 
|-
 
|-
| [[Fermi's interaction]] showing the 4-point fermion vector current, coupled under Fermi's Coupling Constant, "Gf". Fermi's Theory was the first theoretical effort in describing nuclear  decay rates for Beta-Decay.  
+
| Fermi's interaction showing the 4-point fermion vector current, coupled under Fermi's Coupling Constant {{math|''G''<sub>F</sub>}}. Fermi's Theory was the first theoretical effort in describing nuclear  decay rates for Beta-Decay.  
 
|}
 
|}
  
The inclusion of Parity violation in Fermi's interaction was done by [[George Gamow]] and [[Edward Teller]] in the so-called Gamow-Teller Transitions which described Fermi's interaction in terms of Parity violating "allowed" decays and Parity conserving "superallowed" decays in terms of anti-parallel and parallel electron and neutrino spin states respectively. Before the advent of the electroweak theory and the [[Standard Model]], [[George Sudarshan]] and [[Robert Marshak]], and also independently [[Richard Feynman]] and [[Murray Gell-Mann]], were able to determine the correct [[tensor]] structure ([[vector (geometric)|vector]] minus [[axial vector]], {{nowrap|''V'' − ''A''}}) of the four-fermion interaction.
+
The inclusion of Parity violation in Fermi's interaction was done by [[George Gamow]] and [[Edward Teller]] in the so-called Gamow-Teller Transitions which described Fermi's interaction in terms of Parity violating "allowed" decays and Parity conserving "superallowed" decays in terms of anti-parallel and parallel electron and neutrino spin states respectively. Before the advent of the electroweak theory and the [[Standard Model]], [[George Sudarshan]] and [[Robert Marshak]], and also independently [[Richard Feynman]] and [[Murray Gell-Mann]], were able to determine the correct [[tensor]] structure ([[vector (geometric)|vector]] minus [[axial vector]], {{math|''V'' − ''A''}}) of the four-fermion interaction.
  
 
==Fermi constant==
 
==Fermi constant==
The strength of Fermi's interaction is given by the Fermi coupling constant ''G''<sub>F</sub>. The most precise experimental determination of the Fermi constant comes from measurements of the muon [[Exponential decay|lifetime]], which is inversely proportional to the square of ''G''<sub>F</sub>.<ref name="mulan">D. Chitwood et al., Phys.Rev.Lett. 99 (2007) 032001</ref> In modern terms:<ref name=griffiths />
+
The strength of Fermi's interaction is given by the Fermi coupling constant {{math|''G''<sub>F</sub>}}. The most precise experimental determination of the Fermi constant comes from measurements of the muon [[Exponential decay|lifetime]], which is inversely proportional to the square of {{math|''G''<sub>F</sub>}} (when neglecting the muon mass against the mass of the W boson).<ref name="mulan">
 +
{{cite journal
 +
|last=Chitwood |first=D. B.
 +
|coauthors=et al. ([[MuLan|MuLan Collaboration]])
 +
|year=2007
 +
|title=Improved Measurement of the Positive-Muon Lifetime and Determination of the Fermi Constant
 +
|journal=[[Physical Review Letters]]
 +
|volume=99 |issue= |pages=032001
 +
|arxiv= 0704.1981
 +
|bibcode= 2007PhRvL..99c2001C
 +
|doi=10.1103/PhysRevLett.99.032001
 +
}}</ref> In modern terms:<ref name=griffiths />
  
 
<math>
 
<math>
\frac{G_\text{F}}{(\hbar c)^3}=\frac{\sqrt{2}}{8}\frac{g^{2}}{m_\text{W}^{2}}=1.16637(1)\times10^{-5} \; \textrm{GeV}^{-2} \ .</math>
+
\frac{G_{\rm F}}{(\hbar c)^3}=\frac{\sqrt{2}}{8}\frac{g^{2}}{m_{\rm W}^{2}}=1.16637(1)\times10^{-5} \; \textrm{GeV}^{-2} \ .</math>
  
Here ''g'' is the [[coupling constant]] of the [[weak interaction]], and ''m''<sub>W</sub> is the mass of the [[W boson]] which mediates the decay in question.
+
Here {{mvar|g}} is the [[coupling constant]] of the [[weak interaction]], and {{math|''m''<sub>W</sub>}} is the mass of the [[W boson]] which mediates the decay in question.
  
In the Standard Model, Fermi's constant is related to the [[Higgs_mechanism|Higgs vacuum expectation value]] <math>v = (\sqrt{2}G_\text{F})^\text{-1/2} \simeq 246.22 \; \textrm{GeV}</math><ref>{{cite journal|last=Plehn|first=Tilman|coauthors=Rauch, Michael|journal=Phys. Rev. D|year=2005|volume=72|pages=053008|doi=10.1103/PhysRevD.72.053008|arxiv = hep-ph/0507321 |bibcode = 2005PhRvD..72e3008P }}</ref>  
+
In the Standard Model, Fermi's constant is related to the [[Higgs mechanism|Higgs vacuum expectation value]] <math>v = (\sqrt{2}G_{\rm F})^{-1/2} \simeq 246.22 \; \textrm{GeV}</math><ref>
 +
{{cite journal
 +
|last=Plehn |first=T.
 +
|last2=Rauch |first2=M.
 +
|year=2005
 +
|title=Quartic Higgs coupling at hadron colliders
 +
|journal=[[Physical Review D]]
 +
|volume=72 |pages=053008
 +
|arxiv=hep-ph/0507321
 +
|bibcode=2005PhRvD..72e3008P
 +
|doi = 10.1103/PhysRevD.72.053008 }}</ref>
  
 
==References==
 
==References==
{{Reflist}}
+
{{Reflist|2}}
  
 
{{Four-fermion interactions}}
 
{{Four-fermion interactions}}
Line 73: Line 158:
 
[[Category:Particle physics]]
 
[[Category:Particle physics]]
 
[[Category:Quantum field theory]]
 
[[Category:Quantum field theory]]
 
+
[[Category:Enrico Fermi|Interaction]]
 
 
{{Quantum-stub}}
 
 
 
[[ar:تفاعل فيرمي]]
 
[[de:Fermi-Wechselwirkung]]
 
[[pl:Teoria Fermiego]]
 

Latest revision as of 23:40, 9 September 2014

Template:Distinguish

[[Image:Beta-minus Decay.svg|thumb|360px|Template:SubatomicParticle decay in an atomic nucleus (the accompanying antineutrino is omitted).
The inset shows beta decay of a free neutron.
In both processes, the intermediate emission of a virtual [[W boson|Template:SubatomicParticle boson]] (which then decays to electron and antineutrino) is not shown.]]In particle physics, Fermi's interaction (also the Fermi Theory of Beta Decay) is an explanation of the beta decay, proposed by Enrico Fermi in 1933.[1][2][3][4] The theory posits four fermions directly interacting with one another, at one vertex.
For example, this interaction explains beta decay of a neutron by direct coupling of a neutron with:

  1. an electron,
  2. an antineutrino and
  3. a proton.[5]

Fermi first introduced this coupling in his description of beta decay in 1933.[6] The Fermi interaction was the precursor to the theory for the weak interaction where the interaction between the proton-neutron and electron-antineutrino is mediated by a virtual W- boson.

History of initial rejection and later publication

Fermi first submitted his "tentative" theory of beta decay to the famous science journal Nature, which rejected it for being "too speculative." Nature later admitted the rejection to be one of the great editorial blunders in its history. Fermi then submitted the paper to Italian and German publications, which accepted and published it in 1933 in those languages, but it did not appear at the time in a primary publication in English (Nature finally belatedly republished Fermi's report on beta decay in English on January 16, 1939).

Fermi found the initial rejection of the paper so troubling that he decided to take some time off from theoretical physics, and do only experimental physics. This would lead shortly to his famous work with activation of nuclei with slow neutrons.

The nature of the interaction

The interaction could also explain muon decay via a coupling of a muon, electron-antineutrino, muon-neutrino and electron, with the same fundamental strength of the interaction. This hypothesis was put forward by Gershtein and Zeldovich and is known as the Conserved Vector Current hypothesis.[7]

Fermi's four-fermion theory describes the weak interaction remarkably well. Unfortunately, the calculated cross-section grows as the square of the energy , making it unlikely that the theory is valid at energies much higher than about 100 GeV. The solution is to replace the four-fermion contact interaction by a more complete theory (UV completion)—an exchange of a W or Z boson as explained in the electroweak theory.

In the original theory, Fermi assumed that the form of interaction is a contact coupling of two vector currents. Subsequently, it was pointed out by Lee and Yang that nothing prevented the appearance of an axial, parity violating current, and this was confirmed by experiments carried out by Chien-Shiung Wu.[8][9]

MuonFermiDecay.gif 
Fermi's interaction showing the 4-point fermion vector current, coupled under Fermi's Coupling Constant GF. Fermi's Theory was the first theoretical effort in describing nuclear decay rates for Beta-Decay.

The inclusion of Parity violation in Fermi's interaction was done by George Gamow and Edward Teller in the so-called Gamow-Teller Transitions which described Fermi's interaction in terms of Parity violating "allowed" decays and Parity conserving "superallowed" decays in terms of anti-parallel and parallel electron and neutrino spin states respectively. Before the advent of the electroweak theory and the Standard Model, George Sudarshan and Robert Marshak, and also independently Richard Feynman and Murray Gell-Mann, were able to determine the correct tensor structure (vector minus axial vector, VA) of the four-fermion interaction.

Fermi constant

The strength of Fermi's interaction is given by the Fermi coupling constant GF. The most precise experimental determination of the Fermi constant comes from measurements of the muon lifetime, which is inversely proportional to the square of GF (when neglecting the muon mass against the mass of the W boson).[10] In modern terms:[6]

Here Template:Mvar is the coupling constant of the weak interaction, and mW is the mass of the W boson which mediates the decay in question.

In the Standard Model, Fermi's constant is related to the Higgs vacuum expectation value [11]

References

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  5. {{#invoke:citation/CS1|citation |CitationClass=book }}
  6. 6.0 6.1 {{#invoke:citation/CS1|citation |CitationClass=book }}
  7. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
  8. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
  9. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
  10. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
  11. {{#invoke:Citation/CS1|citation |CitationClass=journal }}

Template:Four-fermion interactions