Quark (physics)

A proton consisting of two up quarks and one down quark

In the standard model of particle physics, quarks ([ kwɔrk s], [ kwɑːk s] or [ kwɑrk s]) are the elementary components ( elementary particles ) of which hadrons (e.g. the atomic nucleus building blocks protons and neutrons ) consist.

Elementary particles of the Standard Model

 Quarks	 Exchange particles
 Leptons	 Higgs boson

They have the spin quantum number ¹ ⁄ ₂ and are therefore fermions . Together with the leptons and the gauge bosons , they are now considered to be the fundamental building blocks from which all matter is built. Thus, there are baryons (eg. As the proton ) of three quark, mesons (eg. As the Pion ) each composed of a quark and an anti-quark.

The quark concept was from Caltech - physicist Murray Gell-Mann published. He received the 1969 Nobel Prize in Physics for structuring the hadronic "particle zoo" using quarks . Independently of this, George Zweig developed a similar model at CERN , the fundamental building blocks of which he called "aces". The Swiss physicist André Petermann also postulated the existence of quarks in 1963. His manuscript was not published until 1965 and his contribution was forgotten.

The classification of the then known hadrons with the special unitary group SU (3) was also proposed independently by Juval Ne'eman in 1962.

The experimental investigation of quarks through deep inelastic electron-nucleon scattering began in the late 1960s. References to the existence and properties of the quarks were found in the structure functions , whereby the point constituents of the hadrons were only called partons at that time .

The fact that no free quarks have yet been observed is one of the greatest unsolved problems in particle physics. This phenomenon, known as confinement, is one of the Millennium problems (see Yang-Mills theory ). While there is strong evidence that the strong interaction theory , quantum chromodynamics (QCD) , leads to such entrapment of quarks, rigorous mathematical proof is still pending.

introduction

Feynman diagram of a deep inelastic scattering of a lepton (l) on a hadron (h)
The virtual photon (γ ^* ) knocks a quark (q) out of the hadron. The experimental evidence of such scattering events shows that protons are composed of other particles.

With the triumphant advance of atomistic theory in the 19th century, the atoms were viewed as these building blocks and initially, as the name testifies to this, considered indivisible. In Rutherford's atomic model it was shown that the atom is composed of an atomic nucleus and shell electrons . The nuclear physics then showed the structure of the atomic nucleus of protons and neutrons . With the five elementary particles protons, neutrons, electrons, muons and neutrinos , a seemingly complete picture of the structure of matter was achieved in the 1930s .

But the detection of ever new mesons and baryons , first in cosmic radiation, later with particle accelerators , which eventually led to the joking expression "particle zoo", was an impetus to look for more fundamental particles from which the hadrons , i.e. H. Mesons and baryons. The other motivation was measurements of the form factor of the more stable hadrons, which clearly demonstrated spatial expansion, while electrons and muons prove to be point-shaped up to the limits of measurability.

properties

For all quarks there is an antiparticle with an opposite electrical charge. These antiparticles are called antiquarks. Only the first generation quarks form nucleons and thus normal matter. The components of the atomic nucleus, the protons and neutrons , are made up of down quarks and up quarks.

In contrast to leptons , quarks are subject to all basic forces of physics :

• Strong interaction
• Weak interaction
• Electromagnetic interaction
• Gravity

Color charge

→ Main article : Color charge

Quarks carry a color charge and therefore participate in the strong interaction. This color charge can assume the three values red , green and blue . If three quarks with one of these three values ​​each enter into a bond state , then the resulting object is colorless. The color charge has nothing to do with the colors known from everyday life. Antiquarks carry the color charge anti-red , anti-green or anti- blue .

The confinement hypothesis states that only colorless bond states can exist in isolation. This assumption was made after individual quarks could never be observed in isolation. They are always bound in hadrons. In the case of baryons , they are integrated as combinations of three quarks. There are three antiquarks for antibaryons. Mesons , on the other hand, consist of a quark and an antiquark. Four quarks and one anti-quark form a penta quark and two quarks with two antiquarks form a tetra quark . Theoretically, other colorless bonding states could also exist.

With computer simulations one can show that between two static quarks (pair generation is suppressed) a potential develops, which increases linearly with the distance. This is explained by the fact that the exchange particles of the strong interaction, the gluons , which themselves carry a color charge (a color-anti-color combination), bind to form a strand, the energy of which increases with length. Separating one color-charged particle from the rest would therefore require extremely high energy. A separation of the quarks from the gluons is therefore only possible under certain conditions and for a very short time.

The exact mechanisms of how this strand is formed are related to the interaction of the gluons with one another or the interaction of the gluons with vacuum fluctuations and are the subject of current research. There are various scenarios for how this strand can be formed, but a unified picture has not yet established itself.

As part of the thermodynamics of QCD , a state is predicted for quarks in which the quarks behave like quasi-free particles, the quark-gluon plasma .

Electric charge

→ Main article : Electric charge

The electric charge of the quarks is either - ¹ ⁄ ₃ or + ² ⁄ _{3 of} the elementary charge . Since only colorless bond states are allowed to exist in isolation, only bond states of such (anti-) quark combinations - (anti-) baryons - or quark-anti-quark combinations - meson - that have integer charges are permitted. Experimentally (e.g. Millikan's experiment ) there is no evidence of broken charges on isolated particles. The third-number charges of the quarks bound in hadrons can be clearly deduced from scattering experiments .

Quark flavors

In the standard model of elementary particle physics, the down quark, the up quark, the electron and the electron neutrino belong to the first generation of particles. The six quarks, together with the leptons and the gauge bosons, are the basic building blocks of matter .

The following six different types of quark are also known as quark flavors (American English flavor ).

generation ration	Surname	sym bol	Charge ( s )	Flavor - quantum numbers	hyper- charge	Mass ( MeV )
1	Up	u	+ 2 ⁄ 3	I z = + 1 ⁄ 2	+ 1 ⁄ 3	000002.16 ${\displaystyle _{-0,26}^{+0,49}}$
	Down	d	- 1 ⁄ 3	I z = - 1 ⁄ 2	+ 1 ⁄ 3	000004.67 ${\displaystyle _{-0,17}^{+0,48}}$
2	Charm	c	+ 2 ⁄ 3	C = +1	+ 4 ⁄ 3	001270 ± 20
	Strange	s	- 1 ⁄ 3	S = −1	- 2 ⁄ 3	000093 ${\displaystyle _{-5}^{+11}}$
3	Top	t	+ 2 ⁄ 3	T = +1	+ 4 ⁄ 3	172900 ± 400
	Bottom	b	- 1 ⁄ 3	B ' = −1	- 2 ⁄ 3	004180 ${\displaystyle _{-20}^{+30}}$

The quantum numbers of top and bottom quarks are also known as truth and beauty, respectively .

Up type

Up , charm and top quark (dark fields) and their antiparticles, charge number + ² ⁄ ₃ , with the antiparticles the opposite sign

Down type

Down , strange and bottom quark (bright fields) and their antiparticles, charge number - ¹ ⁄ ₃ , with the antiparticles the opposite sign

light quarks

Up , down and strange quarks are collectively referred to as that.

The allocation of the masses is not clear. In this context, a distinction is made between constituent quarks (“effective” quarks in hadrons) and current quarks (“naked” quarks). The masses given here are those of the current quarks. Since quarks never appear alone, but always in groups, conclusions about the individual components can only be made from the mass of the group.

The natural mass eigen- states of the quarks q are not identical to the eigen-states of the weak interaction q ' . Nicola Cabibbo showed how the physical down quark d can be described as a mixture of the weak down quark d ' and the weak strange quark s' . The mixture is parameterized using the so-called Cabibbo angle . This formalism was expanded to a mixture of the weak eigenstates of down, strange and bottom quark to the physical eigenstates. Instead of a single one, this now requires four parameters that describe a 3 × 3 matrix, the so-called Cabibbo-Kobayashi-Maskawa matrix .

Up-Quark

Up is English for (up) above . This name refers to one of the physical quantities that are assigned to quarks: the isospin . The isospin corresponds in its mathematical description to an angular momentum (spin) with the quantum number ¹ ⁄ ₂ and, like this, can be oriented in two "directions", up or down (these directions have nothing to do with spatial directions). It was proposed by Heisenberg to represent the two core components proton and neutron as different states of one and the same particle, the nucleon . This was motivated by the fact that protons and neutrons behave in exactly the same way from the perspective of nuclear forces. In the constituent quark picture, the isospin of the nucleons is a direct consequence of the isospin of the participating up and down quarks.

The up quark has an electrical charge of + ² ⁄ ₃  e.

Down quark

Down is English for downwards . The down quark corresponds to the other setting of the isospin : down . It has an electrical charge of - ¹ ⁄ ₃  e, an isospin of - ¹ ⁄ ₂ and a mass of 5 MeV.

Charm quark

The charm quark belongs to the second family of quarks and is thus the counterpart of the strange quark. The charm quark corresponds to the Charm - quantum number C, which takes the value +1 for the charm quark. The charm quark was predicted in 1970, and in 1974 it was artificially created in an experiment for the first time. The mass is significantly larger than that of the three light quarks.

In particle detectors , hadrons with charm quarks can be recognized by their relatively long lifespan of around 10 ⁻¹²  seconds. This is due to the fact that the charm quarks can only decay into strange quarks or down quarks via the weak interaction .

The charm quark, for example, is part of the D mesons and the J / ψ meson .

Strange curd

After using the quark model based on up- and down-quark, the structure of some baryons such as B. could not explain des , des and des , Gell-Mann introduced a new quark in order to be able to explain these particles with the help of the quark model. He called this "strange" quark strange quark. ${\displaystyle \Sigma ^{+}}$ ${\displaystyle \Sigma ^{-}}$ ${\displaystyle \Sigma ^{0}}$

The eccentricity (engl .: strangeness ) of its particle is opposite and equal to the number of Strange quark contained. A single strange quark therefore has the oddity −1.

Particles that contain the strange quark are also called strange particles ( Strangelet or strange matter ). Among the mesons, these include B. the kaons and the Phi resonance and among the baryons the hyperons .

Top curd

The top quark (also called truth quark) is the heaviest quark and the partner of the bottom quark. Since its lifespan is only 4.2 · 10 ⁻²⁵  seconds, it cannot form any hadronic bond states in nature ( hadronization only takes place after approx. 10 ⁻²³  s). In contrast to all other quarks, the top quark decays well before the time it takes to form hadrons. There are therefore neither mesons nor baryons which contain a top quark.

Another special feature is its large mass, which is on the order of a gold atom. Due to the immense amount of energy required to generate it, it could only be proven experimentally 18 years after his partner in 1995 (by CDF at the Fermi National Accelerator Laboratory ), although it was theoretically postulated as early as 1977 with the discovery of the bottom quark.

The flavor quantum number assigned to the top quark is the topness T (also truth ), the top quark has T = +1.

Bottom curd

The bottom quark (also called beauty quark) forms the third generation of particles in the standard model with the top quark, the tauon and the tauon neutrino . The first particle to contain a bottom quark was discovered in 1977 at the Fermi National Accelerator Laboratory .

The bottom quark is part of the so-called B mesons and the Υ meson .

The flavor quantum number assigned to it is bottomness B '(also beauty ), the bottom quark has B' = −1.

history

The idea of ​​quarks was developed independently in the early 1960s by André Petermann , Murray Gell-Mann and George Zweig . This scheme grouped the particles with a certain isospin and certain strangeness according to a unitary symmetry, which was derived from the current algebra . Today, this global SU (3) - flavor symmetry (not to be confused with the gauge symmetry of QCD ) as part of the approximately valid chiral symmetry of QCD known.

In this scheme, the lightest mesons (spin 0) and baryons (spin  ¹ ⁄ ₂ ) are grouped in octets of flavor symmetry. A classification of the spin ³ ⁄ ₂ baryons forms a decuplet, which led to the prediction of a new elementary particle, the Ω ^- . With the discovery of the Ω ^- in 1964, the Quark model was widely accepted.

Gell-Mann called this scheme the Eightfold Way , an allusion to the eightfold path of Buddhism because of the octets of the model. He also coined the name Quark, which he took from the phrase "Three quarks for Muster Mark" from James Joyce 's novel Finnegans Wake . Joyce, on the other hand, had heard the word while traveling through Germany in Freiburg , when market women offered their dairy products at a farmers' market. Gell-Mann originally wanted to publish it in the American Physical Review Letters , but his essay on quarks was rejected there as too speculative. He then turned in 1964 to Leon van Hove , who put him in competition with Phys. Rev. Lett. founded European Physics Letters after he initially advised Gell-Mann against it. Zweig (originally a student of Gell-Mann, who at that time had no more contact with him) developed the concept at the same time at CERN, where he was staying as a post-doctoral student from the USA and where Leon van Hove was research director. When Leon van Hove insisted that Zweig publish in the European Physics Letters, Zweig, who was only a visiting scientist and was funded by US agencies, refused. Van Hove was angry about this and blocked or obstructed publications by Zweig and even the presentation of his ideas in a seminar at CERN. In the end it stayed with a CERN preprint from Zweig (dated 1964).

At first, the existence of quarks could not be confirmed experimentally.

From the analysis of certain properties in high-energy reactions of hadrons , Richard Feynman postulated a substructure of hadrons, the partons, in 1969 . A scaling of the deep inelastic scattering cross-sections, which James Bjorken derived from the current algebra, could also be explained by the Partons. When the Bjorken scale was demonstrated in 1969 by the experiments of Jerome I. Friedman , Henry W. Kendall, and Richard E. Taylor ( Nobel Prize in Physics 1990), it was clear that partons and quarks could be the same. With the proof of the asymptotic freedom of the QCD in 1973 by David Gross , Frank Wilczek and David Politzer (Nobel Prize in Physics 2004), this idea was further established.

The charm quark was postulated in 1970 by Sheldon Glashow , John Iliopoulos and Luciano Maiani ( GIM mechanism ) in order to prevent previously unobserved flavor changes in disintegration due to the weak interaction (so-called “flavor-changing neutral currents”); otherwise, such flavor changes would occur in the standard model . This was confirmed in 1974 with the discovery of the J / ψ meson , which consists of a charm quark and its antiquark.

The existence of a third generation of quarks was predicted in 1973 by Makoto Kobayashi and Toshihide Maskawa (Nobel Prize in Physics 2008). They found that the CP violation by neutral kaons cannot be explained with the Standard Model with two Quark generations. The bottom quark and the top quark were discovered at Fermilab in 1977 and 1995.

Current research focus

The mass of the top quark

A collaboration between scientists at Fermilab (Illinois / USA) only succeeded in 2004 in determining the mass of the top quark with good accuracy and thus enabling a better prediction of the mass of the Higgs boson predicted by the standard model, but still undiscovered .

Quarks cannot usually be observed individually by experiment: They always appear in combinations of several quarks (see below) and can only be detected indirectly using certain transformations. The top quark is an exception as it decays before it could form hadrons. It was not until 1995 that two working groups at Fermilab were able to independently announce the detection of top quarks that had formed there as quark-antiquark pairs in proton - antiproton collisions. After an extremely short 10 ⁻²⁴ seconds, the ^{pair of} particles we are looking for decays into W bosons and lighter quarks, the latter being almost always bottom quarks . Only these then bind other quarks to themselves, a process called hadronization . This results in jets . The mass of the top quark can be determined by a precise analysis of the energy and momentum balance of these decays. The evaluation of such complex events in the CDF experiment and DØ experiment ( i.e. D-Zero ) in 1995 resulted in a high mass of more than 170 GeV / c², considerably heavier than the other quarks; however, the measurement uncertainty at that time was 10%. Later measurements reached an uncertainty of less than 0.5%.

The extremely large mass of the top quark suggests that it is fundamentally different from the five lighter quarks. On the basis of a precise measurement of its mass, statements about the mass of the Higgs boson can be obtained and compared with the direct measurement of the Higgs mass. This particle, which was predicted in 1964 by the English physicist Peter Higgs , interacts with other elementary particles and thereby gives them their mass. It completes the standard model . The value for the mass of this Higgs particle could be determined by the two experiments ATLAS and CMS at the LHC at CERN and is about 125 GeV / c².

The large mass of the top quark also makes its decays a fertile field for the search for new particles, such as the particles of supersymmetry , a possible extension of the Standard Model. With the production of top quark pairs at higher collision energies, the question of whether the quarks are really structureless, fundamental particles can perhaps also be answered. New results on the top quark therefore come primarily from the LHC, which went into operation at the beginning of September 2008. There two proton beams with an energy of up to 6.5 TeV per proton are brought to collision.

Confinement

→ Main article : Confinement

The theoretical explanation of the confinement problem is one of the great challenges of theoretical particle physics. Various models have been developed which have been investigated theoretically in recent years. One possibility is the formation of a gluon condensate, which can then contain non-trivial topological objects (chromo-magnetic monopoles , center vortices, dyons), another idea is to explain confinement by instantons , i.e. tunnel processes. In recent years, individual Greens functions of the QCD have also been investigated using various methods. The gluon propagator is of particular interest here ; different methods provide different results for its behavior in the infrared range. This problem was and is heavily discussed and is currently (January 2011) not yet completely resolved. The infrared behavior of the gluon propagator provides indications of the validity of various confinement scenarios.

QCD phase diagram

Another research focus in recent years, on a theoretical level, is the behavior of quarks at finite temperatures and densities. It is known from experiments that a new phase occurs at extremely high densities, the quark-gluon plasma . The theoretical description of this state and the description of the phase transition is of great theoretical interest. On the one hand, the quarks are quasi-free, so the confinement hypothesis no longer applies and one speaks of a confinement-deconfinement transition. The chiral symmetry is also restored at high temperatures and densities (except for the explicit refraction by the current quark masses ). A connection between these two phase transitions is considered very likely and the transition temperatures for both transitions apparently match. How exactly the relationship exists, what order the phase transition is and whether the transition temperatures may not be different in certain areas, as predicted by some researchers, has not yet been finally solved and will probably only be answered by experimental measurements .

See also : quantum chromodynamics

See also

• Valence quark , sea quark , current quark

literature

• Harald Fritzsch: Quarks - the primary substance of our world. Piper, Munich 2006, ISBN 978-3-492-24624-8 .
• Hans G. Dosch: Beyond the nanoworld - leptons, quarks and gauge bosons. Springer, Berlin 2005, ISBN 3-540-22889-6 .
• Maurice Jacob : The quark structure of matter. World Scientific, Singapore 1992, ISBN 981-02-0962-2 .
• David Blaschke: Heavy quark physics. Springer, Berlin 2004, ISBN 978-3-540-21921-7 .

Web links

Commons : Quark  album with pictures, videos and audio files

• What are quarks? from the alpha-Centauri television series(approx. 15 minutes). First broadcast on Aug 18, 2004.
• Harald Fritzsch : The Problem of Mass for Quarks and Leptons - Lecture on March 22, 2000 at the Kavli Institute for Theoretical Physics (lecture documents / audio recording; English)
• The Particle Adventure . (Good introduction to the world of quarks)
• The "birth" of the quarks . Uni Erlangen (fundamentals of particle physics, well explained)
• What are quarks?
• How do you pronounce “Quark” correctly?
• Particle Data Group

References and footnotes

1. ↑ M. Gell-Mann: A Schematic Model of Baryons and Mesons in Phys. Lett. 8, 1964, 214-215, doi: 10.1016 / S0031-9163 (64) 92001-3 .
2. ↑ G. Zweig: An SU (3) Model for Strong Interaction Symmetry and Its Breaking I + II . 1964, CERN preprint CERN-TH-401
3. ↑ Vladimir A. Petrov: Half a Century with Quarks . In: 30th International Workshop on High Energy Physics: Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects. (IHEP 2014) . 2014, doi : 10.1142 / 9789814689304_0027 , arxiv : 1412.8681 .
4. ^ Confinement problem. Clay Mathematics Institute
5. ↑ Jeff Green Site: Introduction to the confinement problem . 1st edition. Springer, Berlin 2011, ISBN 978-3-642-14381-6 .
6. ↑ R. Alkofer, J. Green Site: Quark Confinement: The Hard Problem of HadronPhysics . In: Journal of Physics . G, no. 34 , 2007, doi : 10.1088 / 0954-3899 / 34/7 / S02 , arxiv : hep-ph / 0610365 .
7. ^ Christof Gattringer, Christian B. Lang: Quantum Chromodynamics on the Lattice: An Introductory Presentation . 1st edition. Springer, 2009, ISBN 978-3-642-01849-7 .
8. ↑ R. Alkofer, J. Green Site: Quark Confinement: The Hard Problem of HadronPhysics . In: Journal of Physics . G, no. 34 , 2007, doi : 10.1088 / 0954-3899 / 34/7 / S02 , arxiv : hep-ph / 0610365 .
9. ↑ In particle physics , calculations are often made in natural units , with masses being given in the energy unit electron volts (eV) using Einstein's relation E = mc ² . 1 MeV / c ² corresponds to a mass of approx. 1.8 · 10 ⁻³⁰  kg.
10. ↑ The masses of the quarks come from the following source: M. Tanabashi et al .: 2019 Review of Particle Physics, Quarks Summary Tables. (PDF; 46 kB) In: Phys. Rev. D 98, 2018, p. 030001 and 2019 update. Particle Data Group, accessed June 10, 2019 .  The quark masses are given in the MS-quer scheme.
11. ↑ K. Nakamura et al. ( Particle Data Group ): PDGLive Particle Summary Quarks (u, d, s, c, b, t, b ', t', Free). (PDF; 40 kB) Particle Data Group , 2010, accessed on January 2, 2011 (English). 
12. ↑ Harald Fritzsch : The absolutely unchangeable. The final riddles of physics . 2007, ISBN 978-3-492-24985-0 , p. 99.
13. ^ John Moffat , Cracking the Quantum Code of the Universe, Oxford University Press, 2014, p. 7. Based on a communication from Gell-Mann to Moffat.
14. ↑ Interview with George Zweig , CERN 2014
15. ^ DJ Gross, Frank Wilczek: Ultraviolet Behavior of Nonabelian Gauge Theories . In: Phys. Rev. Lett. tape 30 , 1973, p. 1343-1346 , doi : 10.1103 / PhysRevLett.30.1343 .
16. ^ H. David Politzer: Reliable Perturbative Results for Strong Interactions? In: Phys. Rev. Lett. tape 30 , 1973, p. 1346-1349 , doi : 10.1103 / PhysRevLett.30.1346 .
17. ↑ E598 Collaboration (JJ Aubert et al.): Experimental Observation of a Heavy Particle J . In: Phys. Rev. Lett. tape 33 , 1974, pp. 1404-1406 , doi : 10.1103 / PhysRevLett.33.1404 .
18. ↑ SLAC-SP-017 Collaboration (JE Augustin et al.): Discovery of a Narrow Resonance in e + e Annhilation . In: Phys. Ref. Lett. tape 33 , 1974, pp. 1406-1408 , doi : 10.1103 / PhysRevLett.33.1406 ( slac-pub-1504 ). slac-pub-1504 ( Memento of the original from March 10, 2007 in the Internet Archive ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice.  
19. ^ Makoto Kobayashi, Toshihide Maskawa: CP Violation in the Renormalizable Theory of Weak Interaction . In: Prog. Theor. Phys. tape 49 , no. 2 , 1973, p. 652-657 , doi : 10.1143 / PTP.49.652 .
20. ↑ CDF Collaboration (F. Abe et al.): Observation of Top Quark Production in p p Collisions . In: Phys. Rev. Lett. tape 74 , 1995, pp. 2626–2631 , doi : 10.1103 / PhysRevLett.74.2626 , arxiv : hep-ex / 9503002 .
21. ↑ KA Olive et al. (Particle Data Group): pdg.lbl.gov (PDF) 2014.
22. ↑ F. Abe et al. ( CDF Collaboration ): Observation of Top Quark Production in Antiproton Proton Collisions with the Collider Detector at Fermilab . In: Physical Review Letters . Vol. 74, No. 14 , 1995, pp. 2626–2631 , doi : 10.1103 / PhysRevLett.74.2626 , PMID 10057978 , bibcode : 1995PhRvL..74.2626A (English).
23. ↑ S. Abachi et al. ( DØ Collaboration ): Search for High Mass Top Quark Production in Proton Antiproton Collisions at s  = 1.8 TeV . In: Physical Review Letters . Vol. 74, No. 13 , 1995, pp. 2422-2426 , doi : 10.1103 / PhysRevLett.74.2422 , bibcode : 1995PhRvL..74.2422A (English).
24. ↑ Collaborations by ATLAS, CDF, CMS, D0: First combination of Tevatron and LHC measurements of the top-quark mass arxiv : 1403.4427 , as of March 2014.
25. ↑ CMS collaboration: Measurement of the top quark mass using proton-proton data at sqrt (s) = 7 and 8 TeV. arxiv : 1509.04044
26. ↑ ATLAS collaboration: Measurement of the top quark mass in the → dilepton channel from √s = 8 TeV ATLAS data ${\displaystyle t{\bar {t}}}$ , arxiv : 1606.02179
27. ↑ C. Fischer, A. Maas, J. Pawlowski: On the Infrared Behavior of Landau Gauge Yang-Mills Theory . In: Annals of Physics . tape 324 , Issue 11, November 2009, p. 2408-2437 , doi : 10.1016 / j.aop.2009.07.009 (American English).