Higgs boson

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Higgs boson (H)

classification
Elementary particle
boson
properties
electric charge neutral
Dimensions approx. 2.23 · 10 −25  kg
Resting energy 125.10 ± 0.14  GeV
Spin 0
average lifespan approx. 10 −22  s
Interactions weak
gravitation
according to the Higgs mechanism with all particles with mass

The Higgs boson or Higgs particle is an elementary particle named after the British physicist Peter Higgs from the Standard Model of elementary particle physics . It is electrically neutral , has spin 0 and decays after a very short time.

The Higgs particle belongs to the Higgs mechanism , a theory proposed as early as the 1960s, according to which all elementary particles (for example the electron) except for the Higgs boson only acquire their mass through interaction with the omnipresent Higgs field .

For the experimental proof of the Higgs boson and the determination of its mass, particle accelerators with sufficient energy and luminosity are necessary, which is why the proof was not successful for several decades. It was only in July 2012 that the CERN accelerator center announced the detection of a particle at the Large Hadron Collider that could be the Higgs boson. After the assumption was confirmed by analyzing further data, the experimental confirmation was considered so advanced that François Englert and Peter Higgs were awarded the 2013 Nobel Prize in Physics for the theoretical development of the Higgs mechanism . The internationally coordinated evaluation of the resulting measurement data will continue for years in Template: future / in 5 yearsorder to further test the whole picture and refine it if necessary.

Higgs particle in the standard model

Simulation of the decay of a Higgs particle on the CMS detector

The building blocks of the standard model of particle physics can be divided into four groups: the quarks (the basic building blocks of atomic nuclei), the leptons (e.g. the electron ), the gauge bosons (which mediate the interactions between particles) and the Higgs field .

In physics, the second quantization eliminates the clear contrast between particles and waves ; a particle is represented as an excited state of the corresponding quantum field . Accordingly, the Higgs boson corresponds to a quantum mechanical excitation of the Higgs field, which manifests itself as a detectable particle.

Expressed figuratively, the Higgs field corresponds to a violin or guitar string , as a vibratory system with basic state and vibrations. In this image, the Higgs boson corresponds to the vibration pattern of the string by certain energy supply in characteristic vibration was moved and encouraged it. This can be heard on a string as a tone of a certain pitch. Exactly this “making the string vibrate” only happens during collisions in high-energy particle accelerators due to the very high energies required . With the proof of the Higgs boson, the proof for the underlying Higgs field was also provided.

Higgs mechanism

The main reason that the Higgs boson is so important for particle physics is that its existence is predicted by the Higgs mechanism, an integral part of the Standard Model.

The basic for the standard model gauge theory requires mathematical reasons that the gauge bosons, which produce the interactions between other particles themselves are particles without mass. This is really the case with the gauge boson of the electromagnetic interaction , the photon , and with the gauge bosons of the strong interaction , the gluons , but not with the gauge bosons of the weak interaction , the W and Z bosons . These have a relatively large mass, which causes the short range that makes the "weak interaction" appear so weak in relation to the electromagnetic interaction.

The Higgs mechanism shows that the massless W and Z bosons in the original equation of the theory can appear in all further equations like particles with a certain mass. To do this, you have to let them interact with another physical field , the Higgs field specially introduced for this purpose. The elementary excitations of the Higgs field are the Higgs bosons. The Higgs mechanism makes it possible to set up a basic gauge theory in which the electromagnetic and weak interaction are unified to form an electroweak interaction . Their interaction with the Higgs field also explains the masses of the fermionic elementary particles (quarks and leptons).

The mass of the elementary particles, a property previously considered to be original, is thus interpreted as the result of a new type of interaction. Only the origin of the Higgs mass itself eludes this interpretation; it remains unexplained.

Experimental evidence

According to the results so far, the Higgs boson has a very large mass of about 125 GeV / c 2 in comparison with most other elementary particles  - this corresponds to about two iron atoms (for comparison: the Z boson has a mass of 91 GeV / c 2 , the muon 106 MeV / c 2 , the electron 511 keV / c 2 , the electron neutrino less than 2.2 eV / c 2 ).

Large particle accelerators are used to generate the center of gravity energy required for generation . Because of its short lifespan of around 10 −22  s, the Higgs boson decays practically at the point of origin into other elementary particles, preferably those with the greatest possible mass. In the experiments, these decay products and their properties are measured and the measured values ​​are compared with computer simulations of the experiment with and without the Higgs boson. In particular, one searches through the possible combinations of decay products to see whether a certain invariant mass occurs more frequently than would be expected on the basis of known other reactions.

Since statistical fluctuations can also simulate such a signal, the discovery of a new particle is generally only spoken of when the coincidence required an average of 3.5 million or more attempts to (coincidentally!) Bring about such a significant event ( one speaks of a significance of at least 5 σ). This corresponds roughly to the frequency of receiving “tails” 22 times when tossing a fair two-sided coin 22 times.

Higgs boson and the cause of mass

In simplified representations, the Higgs boson is often shown across the board as the cause of mass. This is wrong or imprecise for several reasons:

  • On the one hand there is the Higgs field, which is present everywhere with the same strength and has an interaction with the elementary particles of the Standard Model, through which they behave as if they had a certain, unchangeable mass; the photons and gluons are excluded because they have no interaction with the Higgs field.
  • Furthermore, the mass of the Higgs boson itself is not explained from an interaction with the Higgs field, but is assumed in the standard model as a prerequisite for making the Higgs mechanism possible in the first place.
  • The mass values ​​of the particles resulting from the Higgs field only contribute approx. 1% to the weighable mass of the usual matter , because this is based on the equivalence of mass and energy on all interactions between its components. Therefore, over 99% of the weighable mass comes from the strong bond between the quarks in the nucleons of the atomic nuclei. The masses of the quarks and electrons generated by the Higgs field only contribute the remaining 1%.

history

Developing the theory

Peter Higgs (2009)

In 1964, Peter Higgs and two research teams - on the one hand François Englert and Robert Brout , on the other hand Gerald Guralnik , Carl R. Hagen and TWB Kibble  - independently and approximately simultaneously developed the same formal mechanism through which initially massless elementary particles interact with a background field (the " Higgs field ") become massive. Although all three papers appeared one after the other in the same issue of the journal Physical Review Letters , with Englert and Brout having submitted their manuscript a little earlier, so that their publication was placed before that of the other authors, the field and its particle (the field quantum ) were named after Higgs alone. He was the only one who had spoken explicitly of a new particle.

The Higgs mechanism was originally developed in analogy to solid state physics and was only formulated for Abelian gauge theories . After it was transferred to non- Abelian gauge theories ( Yang-Mills theories ) by TWB Kibble in 1967 , the mechanism could be applied to the weak interaction. This led to the prediction of the - experimentally confirmed in 1983 - large masses of the W and Z bosons responsible for the weak interaction .

In two independent works, Steven Weinberg in 1967 and Abdus Salam in 1968 applied the Higgs mechanism to the electroweak theory of Sheldon Lee Glashow and thus created the standard model of particle physics, for which all three received the 1979 Nobel Prize in Physics .

The term “God Particle”, which is used in popular representations, but only rarely in serious science, comes from the publishing house in which Nobel Prize winner Leon Max Lederman wanted to publish his book The goddamn particle (“The goddamn particle”) . The publisher forced him to copy the title in The God Particle: If the Universe Is the Answer, What Is the Question? ("The god particle: If the universe is the answer, what is the question?") To change.

Peter Higgs himself rejects the term God Particle because it could hurt religious people.

Experimental search

overview

  • Creation and decay processes (selection)

  • Two gluons each generate a top / antitop quark pair that combine to form a Higgs boson

  • Two quarks emit W or Z bosons that combine to form a Higgs boson

  • The decay of a Higgs boson into two photons

  • The decay of a Higgs boson into four electrically charged leptons

In the form of Feynman diagrams , the above figures show two mechanisms on the left that contribute to the production of a Higgs boson at the LHC . Two possible decay paths (“ decay channels ”) for Higgs bosons are shown on the right. The decay of a Higgs boson into two photons means that in an accelerator experiment, compared to a model without a Higgs boson, more photon pairs with a center of mass energy or invariant mass equal to the mass of the Higgs boson are generated. Since the Higgs boson itself does not interact with photons, the decay must take place via intermediate electrically charged particles (in the diagram above via a charged fermion ). The decay of a Higgs boson into four electrically charged leptons by means of intermediate Z bosons, together with the decay into two photons, is one of the most important discovery channels for the Higgs boson. Through a systematic combined search for these decays, clear indications of the existence of a corresponding particle could be found on two independent detectors of the LHC. The local significance here is 5.9 σ, which largely rules out an error in the discovery.

Results

Since many special properties of such an electroweak interaction have been experimentally confirmed very well, the standard model with a Higgs particle is considered plausible. As early as 1977, the theoretical maximum mass of the Higgs particle was estimated by Lee, Quigg and Thacker with a TeV / c 2 .

After experiments with other particles, the mass of the Higgs boson, if it exists, should be at most 200 GeV / c 2 . (For comparison: proton and neutron each have around 1 GeV / c 2. ) If no Higgs particle had been found in this area, some theories predicted a Higgs multiplet that could also be realized at higher energies.

As early as 2003, data evaluations at the LEP at CERN were able to determine 114.4 GeV / c 2 as the lower limit for the mass.

In addition, measurements of the CDF and D0 experiments (2010) on the Tevatron by Fermilab excluded the range of 156–175 GeV / c 2 .

In December 2011 and February 2012, preliminary reports of the experiments at the LHC of CERN were published, according to which the existence of a Standard Model Higgs boson in various mass ranges could be ruled out with high confidence levels. Here, data from 2011 of particle collisions at a center-of-mass energy of approximately 7 TeV were evaluated. According to these results, the mass of the Higgs boson, if it exists, is in the range of 116 to 130 GeV / c 2 ( ATLAS ) or 115 to 127 GeV / c 2 ( CMS ).

The first signs of the existence of the particle could be obtained. A mass of 124 to 126 GeV / c 2 with a local significance of over 3 σ was measured in these detections . However, at least 5 σ are required for recognition as a scientific discovery in particle physics. In July, a further analysis of the 2011 data by ATLAS revealed a local significance of 2.9 σ at approximately 126 GeV / c 2 .

The CDF and DØ groups of the now decommissioned Tevatron also provided new data evaluations in March and July 2012 that contained possible indications of the Higgs boson in the 115–135 GeV / c 2 range , with a significance of 2.9 σ.

On July 4, 2012, the LHC experiments ATLAS and CMS published results, according to which a particle with a mass of 125–127 GeV / c 2 was found. In addition, data from 2012 from particle collisions at a center-of-mass energy of approximately 8 TeV were evaluated. The local significance reached 5 σ in both experiments, whereby the inclusion of additional channels in CMS slightly reduced the statistical significance of the given value (4.9 σ). The masses of the new particle were found to be ∼126.5 GeV / c 2 (ATLAS) and 125.3 ± 0.6 GeV / c 2 (CMS).

On July 31, 2012, ATLAS improved the data analysis by including a further channel and thus increased the significance to 5.9 σ with a mass of 126 ± 0.4 (stat) ± 0.4 (sys) GeV / c 2 . CMS also increased the significance to 5 σ at a mass of 125.3 ± 0.4 (stat) ± 0.5 (sys) GeV / c 2 .

To ensure that the particle found is actually the Higgs boson of the Standard Model, additional data had to be obtained and evaluated. In particular, it had to be investigated for the particle found, with which frequencies the various possible combinations of other particles into which it decays occur. A specific prediction applies to the Higgs boson: the probability of generating a particle during decay increases proportionally to the square of the particle's mass. In November 2012 the ATLAS and CMS cooperation published results on five different decay channels (decay into (1) two gamma quanta, (2) four electrons or muons, (3) two electrons / muons and two neutrinos, (4) two leptons or (5) two bottom quarks). They do not contradict the predictions of the Standard Model, but were still fraught with areas of uncertainty that were too great to be conclusively confirmed.

In March 2013, ATLAS and CMS presented new analyzes that confirm that the new particle fits the predictions for the Higgs boson, measurements in 2015 and 2016 also confirmed this.

In July 2018 it was announced that the long sought-after decay of the Higgs boson into two bottom quarks was detected at CERN (Atlas Collaboration, CMS). The separation of the bottom quarks from the decays of the Higgs boson from the background noise (formation of bottom quarks from other sources) was made possible by advances in data analysis with machine learning. The decay was detected to be greater than five standard deviations from analyzing the data over several years at 7, 8 and 13 TeV collision energies. When the Higgs boson was discovered in 2012, less frequent decay channels such as decay into two photons had been observed, and the coupling of the Higgs boson to the heaviest fermions ( tau lepton , top quark ) had already been observed. The preliminary data on the decay rate are consistent with the Standard Model. The observation is seen as a success for the understanding of Higgs physics that has now been achieved and is cited as a support for the planned upgrade of the LHC to the high-luminosity LHC.

Higgs bosons outside the Standard Model

Supersymmetry

In the minimal supersymmetric standard model (MSSM), an extension of the standard model for supersymmetry , there are five Higgs bosons, three “neutral” and two “charged” (the terms “neutral” and “charged” are as in the electroweak gauge theory Are defined):

Higgs bosons in the MSSM
contained in ... Dimensions Electric charge Symmetry property
neutral loaded
Standard model
(Higgs boson) 		rel. light - scalar
MSSM heavy
- pseudoscalar

The A particle is odd in terms of CP symmetry , i.e. i.e., it is a pseudoscalar , while the h and H bosons are CP-even ( scalars ). In addition, the A particle does not couple to the three gauge bosons W + , W - or Z.

Depending on the benchmark scenario used, the h boson has a theoretically permissible mass of a maximum of 133 GeV / c 2 and is therefore particularly similar to the Higgs boson of the standard model.

In addition to these five Higgs bosons, five more, so-called Higgsinos, are postulated as super partners in this model .

Compound particles

The idea that the Higgs boson is not an elementary but a composite particle is e.g. B. treated in Technicolor theories . Here it is assumed that a new strong interaction exists and that the Higgs boson is a bond state of this interaction. In 2013, Danish and Belgian scientists found that the previous measurements were also compatible with Technicolor.

Another approach to explaining the particle masses as an alternative to the Higgs mechanism is based on the assumption that the particles, quarks and leptons previously assumed to be fundamental and punctiform , are also composed of "haplons" and their mass is the equivalent of the interaction between the haplons. In this picture, the particle newly discovered at CERN is also a boson made up of haplons.

Documentaries

literature

  • Gordon Kane: The Higgs particle. The secret of the crowd . In: Spectrum of Science . No. 2 , 2006, ISSN  0170-2971 , p. 36-43 .
  • John F. Gunion, Sally Dawson, Howard E. Haber: The Higgs Hunter's Guide . Perseus Publ., Cambridge Mass 2000, ISBN 0-7382-0305-X .
  • Walter Greiner : gauge theory of weak interaction . Thun, Frankfurt am Main 1995, ISBN 3-8171-1427-3 , pp. 133 ff .
  • Karl Jakobs, Chris Seez: The Higgs Boson discovery . In: Scholarpedia . tape 10 , no. 9 , 2015, p. 32413 , doi : 10.4249 / scholarpedia.32413 .

Web links

Commons : Higgs Boson  - collection of images, videos and audio files
Wiktionary: Higgs boson  - explanations of meanings, word origins, synonyms, translations

References and comments

  1. ↑ M. Tanabashi et al. (Particle Data Group): 2019 Review of Particle Physics. H 0 mass. In: pdgLive.lbl.gov.
  2. ↑ a b CERN experiments observe particle consistent with long-sought Higgs boson . Press release from CERN. July 4, 2012. Retrieved October 15, 2012.
  3. ↑ a b New results indicate that particle discovered at CERN is a Higgs boson . Press release from CERN. March 14, 2013. Retrieved March 14, 2013.
  4. ^ Nobelprize.org: The Nobel Prize in Physics 2013. Retrieved October 8, 2013.
  5. ↑ An example of the upcoming discussions, which have not been overtaken by the previous reference, can be found in the announcement of a public “panel of experts” that took place in mid-February 2013 as part of the AAAS meeting.
  6. ↑ M. Strassler: The Standard Model Higgs. In: "Of Particular Significance" (blog). December 13, 2011, accessed July 15, 2012 .
  7. ↑ Contribution by David Spiegelhalter on the numerical value 1: 3.5 million as a reaction to an incorrect representation in a Nature article on the Higgs particle search . The enormously large number 3.5 million is the reciprocal of the very small number p mentioned below ; 5.0 σ corresponds to p = 2.8 × 10 −7 .
  8. ↑ PW Higgs: Broken symmetries, massless particles and gauge fields . In: Phys. Lett. . 12, 1964, p. 132. doi : 10.1016 / 0031-9163 (64) 91136-9 .
  9. ↑ PW Higgs: Broken symmetries and the masses of gauge bosons . In: Phys. Rev. Lett. . 13, 1964, p. 508. doi : 10.1103 / PhysRevLett.13.508 .
  10. ^ F. Englert, R. Brout: Broken symmetry and the mass of gauge vector mesons . In: Phys. Rev. Lett. . 13, 1964, p. 321. doi : 10.1103 / PhysRevLett.13.321 .
  11. ↑ GS Guralnik, CR Hagen, TWB Kibble: Global conservation laws and massless particles . In: Phys. Rev. Lett. . 13, 1964, p. 585. doi : 10.1103 / PhysRevLett.13.585 .
  12. ↑ In the so-called Abelian groups , it is assumed that - as with the multiplication of two real numbers - when two group elements a or b are executed one after the other, the sequence does not matter, a × b = b × a. This does not apply to non-Abelian groups.
  13. ^ TWB Kibble: Symmetry breaking in non-Abelian gauge theories . In: Phys. Rev. . 155, 1967, p. 1554. doi : 10.1103 / PhysRev.155.1554 .
  14. ^ S. Weinberg: A model of leptons . In: Phys. Rev. Lett. . 19, 1967, p. 1264. doi : 10.1103 / PhysRevLett.19.1264 .
  15. ^ A. Salam: Weak and electromagnetic interactions . In: Proc. Nobel Symp . 8, 1968, pp. 367-377.
  16. ^ SL Glashow: Partial symmetries of weak interactions . In: Nucl. Phys. . 22, 1961, p. 579. doi : 10.1016 / 0029-5582 (61) 90469-2 .
  17. ↑ Higgs Boson: Hope for the God Particle. At: Spiegel online . December 7, 2011.
  18. ↑ LHC particle accelerator: Why is the Higgs boson also called "God Particle"? At: Zeit online . April 7, 2010. Page 2/2 in In the barrage of the big bangs.
  19. ^ The God Particle. (PDF). P. 2.
  20. ^ Anything but the God particle . The Guardian. May 29, 2009. Retrieved July 6, 2012.
  21. ↑ James Randerson: Father of the 'God Particle' . In: The Guardian , June 30, 2008. 
  22. ↑ Interview: The man behind the 'God particle'. In: New Scientist . September 13, 2008, pp. 44-45.
  23. ↑ 5.9 σ corresponds to a so-called p- value of ~ 10 −9 (see a footnote above); 5.0 σ has a p-value of 2.8 × 10  −7 .
  24. ↑ A very suggestive plot over ten mass decades, for the entire range from 110 to 150 GeV / c 2 , can be found in an article by Markus Schumacher and Christian Weiser: Higgs or not Higgs boson? Physik Journal 11 (8/9), 2012, pp. 18–20, Fig. 2. Note on this figure: However, the extremely deep “troughs” observed with both detectors for the mass of the new particle also have a width that cannot be neglected (ie it does not make sense to give the mass of the new particle extremely sharply; in addition, a value for the inaccuracy of the mass determination is necessary).
  25. ^ LEP Working Group For Higgs Boson Searches: Search for the Standard Model Higgs boson at LEP . In: Physics Letters B . 565, 2003, pp. 61-75. arxiv : hep-ex / 0306033 . doi : 10.1016 / S0370-2693 (03) 00614-2 .
  26. ↑ Fermilab experiments narrow allowed mass range for Higgs boson . Fermilab. July 26, 2010. Retrieved April 28, 2012.
  27. ↑ The CDF & D0 Collaborations: Combined CDF and D0 Upper Limits on Standard Model Higgs Boson Production with up to 8.6 fb-1 of Data . In: EPS 2011 Conference Proceedings . 2011. arxiv : 1107.5518 .
  28. ↑ ATLAS Collaboration: Combined search for the Standard Model Higgs boson using up to 4.9 fb-1 of pp collision data at √s = 7 TeV with the ATLAS detector at the LHC . In: Physics Letters B . 710, No. 1, 2012, pp. 49-66. arxiv : 1202.1408 . doi : 10.1016 / j.physletb.2012.02.044 .
  29. ↑ CMS Collaboration: Combined results of searches for the standard model Higgs boson in pp collisions at √s = 7 TeV . In: Physics Letters B . 710, No. 1, 2012, pp. 26-48. arxiv : 1202.1488 . doi : 10.1016 / j.physletb.2012.02.064 .
  30. ↑ ATLAS and CMS experiments submit Higgs search papers . CERN press release. February 7, 2012. Retrieved December 2, 2015.
  31. ↑ C. Soap: CERN's gamble shows perils, rewards of playing the odds . In: Science . 289, No. 5488, 2000, pp. 2260-2262. doi : 10.1126 / science.289.5488.2260 .
  32. ↑ ATLAS Collaboration: Combined search for the Standard Model Higgs boson in pp collisions at √s = 7 TeV with the ATLAS detector . In: Physical Review D . 86, No. 3, 2012, p. 032003. arxiv : 1207.0319 . doi : 10.1103 / PhysRevD.86.032003 .
  33. ↑ Tevatron scientists announce their final results on the Higgs particle . Fermilab press room. July 2, 2012. Retrieved July 2, 2012.
  34. ↑ The CDF & D0 Collaborations: Updated Combination of CDF and D0 Searches for Standard Model Higgs Boson Production with up to 10.0 fb-1 of Data . July 3, 2012, arxiv : 1207.0449 .
  35. ↑ Latest Results from ATLAS Higgs Search . ATLAS. July 4, 2012. Retrieved August 28, 2017.
  36. ^ ATLAS collaboration: Observation of an Excess of Events in the Search for the Standard Model Higgs boson with the ATLAS detector at the LHC . In: ATLAS-CONF-2012-093 . 2012.
  37. ↑ Observation of a New Particle with a Mass of 125 GeV . CMS. July 4, 2012. Retrieved July 4, 2012.
  38. ^ CMS collaboration: Observation of a new boson with a mass near 125 GeV . In: CMS-PAS-HIG-12-020 . 2012.
  39. ^ ATLAS collaboration: Observation of a New Particle in the Search for the Standard Model Higgs Boson with the ATLAS Detector at the LHC . In: Physics Letters B . 716, No. 1, 2012, pp. 1-29. arxiv : 1207.7214 . doi : 10.1016 / j.physletb.2012.08.020 .
  40. ^ CMS collaboration: Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC . In: Physics Letters B . 716, No. 1, 2012, pp. 30-61. arxiv : 1207.7235 . doi : 10.1016 / j.physletb.2012.08.021 .
  41. ^ The ATLAS collaboration: Higgs Property Measurement with the ATLAS Detector . 2012 ( cern.ch [accessed on February 6, 2020]).
  42. ↑ Graphic preparation of the results.
  43. ↑ ATLAS collaboration: Combined measurements of the Higgs boson production and decay rates in H → ZZ ∗ → 4ℓ and H → γγ final states using pp collision data at √s = 13 TeV in the ATLAS experiment . August 8, 2016.
  44. ↑ CMS collaboration: Updated measurements of Higgs boson production in the diphoton decay channel at √s = 13 TeV in pp collisions at CMS. . 5th August 2016.
  45. ↑ CMS collaboration: Measurements of properties of the Higgs boson and search for an additional resonance in the four-lepton final state at √s = 13 TeV . 5th August 2016.
  46. ↑ Researchers observe for the first time the decay of Higgs particles into bottom quarks. Spiegel Online, August 28, 2018.
  47. ^ Long-sought decay of Higgs boson observed. Atlas Experiment, August 2018.
  48. ↑ David Eriksson: H ± W ∓ production at the LHC. High Energy Physics, Uppsala University, IKP seminar, October 6, 2006 ( PDF; 2.5 MB. ( Memento from June 10, 2007 in the Internet Archive )).
  49. ↑ Janusz Rosiek: Complete Set of Feynman Rules for the MSSM - incl. Erratum. November 6, 1995, KA-TP-8-1995, arxiv : hep-ph / 9511250 , doi: 10.1103 / PhysRevD.41.3464 .
  50. ↑ Particle Physics. Higgs doesn't have to be Higgs. In: Golem.de. Retrieved August 24, 2016 .
  51. ↑ The Technicolor Higgs in the light of LHC data . September 9, 2013, arxiv : 1309.2097v1 .
  52. ↑ Harald Fritzsch : Composite Weak Bosons at the Large Hadron Collider . arxiv : 1307.6400 .