The Hagedorn temperature , T H , is the temperature in theoretical physics where hadronic matter (i.e. ordinary matter) is no longer stable, and must either "evaporate" or convert into quark matter ; as such, it can be thought of as the " boiling point " of hadronic matter. It was discovered by Rolf Hagedorn . The Hagedorn temperature exists because the amount of energy available is high enough that matter particle ( quark – antiquark ) pairs can be spontaneously pulled from vacuum. Thus, naively considered, a system at Hagedorn temperature can accommodate as much energy as one can put in, because the formed quarks provide new degrees of freedom, and thus the Hagedorn temperature would be an impassable absolute hot. However, if this phase is viewed as quarks instead, it becomes apparent that the matter has transformed into quark matter , which can be further heated.
47-673: This article is about the surname Hagedorn. For the temperature in theoretical physics, see Hagedorn temperature . For the hormone, see NPH insulin . Hagedorn is a surname of German language origin, meaning "hawthorn". Notable people with the surname include: Bettina Hagedorn (born 1955), German politician Bob Hagedorn , US Democratic legislator from Colorado Brian Hagedorn , Wisconsin Judge Britt Hagedorn , German model and talk show host Edward Hagedorn (artist) (1902–1982), American artist Edward S. Hagedorn , mayor of
94-609: A branching fraction of 0.999877, is a leptonic decay into a muon and a muon neutrino : π + ⟶ μ + + ν μ π − ⟶ μ − + ν ¯ μ {\displaystyle {\begin{aligned}\pi ^{+}&\longrightarrow \mu ^{+}+\nu _{\mu }\\[2pt]\pi ^{-}&\longrightarrow \mu ^{-}+{\overline {\nu }}_{\mu }\end{aligned}}} The second most common decay mode of
141-643: A meson . Pions are the lightest mesons and, more generally, the lightest hadrons . They are unstable, with the charged pions π and π decaying after a mean lifetime of 26.033 nanoseconds ( 2.6033 × 10 seconds), and the neutral pion π decaying after a much shorter lifetime of 85 attoseconds ( 8.5 × 10 seconds). Charged pions most often decay into muons and muon neutrinos , while neutral pions generally decay into gamma rays . The exchange of virtual pions, along with vector , rho and omega mesons , provides an explanation for
188-528: A finite contribution from energy levels that accumulate at the ionization energy. The states that cause the divergence are spatially big, since the electrons are very far from the protons. The divergence indicates that at a low temperature hydrogen–antihydrogen will not be produced, rather proton/antiproton and electron/antielectron. The Hagedorn temperature is only a maximum temperature in the physically unrealistic case of exponentially many species with energy E and finite size. The concept of exponential growth in
235-708: A number of research institutions, including the Los Alamos National Laboratory 's Meson Physics Facility, which treated 228 patients between 1974 and 1981 in New Mexico , and the TRIUMF laboratory in Vancouver, British Columbia . In the standard understanding of the strong force interaction as defined by quantum chromodynamics , pions are loosely portrayed as Goldstone bosons of spontaneously broken chiral symmetry . That explains why
282-457: A photon and an electron - positron pair in the final state: π 0 ⟶ γ + e − + e + {\displaystyle \pi ^{0}\longrightarrow \gamma +{\rm {e^{-}+e^{+}}}} The third largest established decay mode ( BR 2e2 e = 3.34 × 10 ) is the double-Dalitz decay, with both photons undergoing internal conversion which leads to further suppression of
329-680: A pion, with a branching fraction of 0.000123, is also a leptonic decay into an electron and the corresponding electron antineutrino . This "electronic mode" was discovered at CERN in 1958: π + ⟶ e + + ν e π − ⟶ e − + ν ¯ e {\displaystyle {\begin{aligned}\pi ^{+}&\longrightarrow {\rm {e}}^{+}+\nu _{e}\\[2pt]\pi ^{-}&\longrightarrow {\rm {e}}^{-}+{\overline {\nu }}_{e}\end{aligned}}} The suppression of
376-484: A separate Hagedorn temperature can be defined for strings rather than hadrons. This temperature is extremely high (10 K) and thus of mainly theoretical interest. The Hagedorn temperature was discovered by German physicist Rolf Hagedorn in the 1960s while working at CERN. His work on the statistical bootstrap model of hadron production showed that because increases in energy in a system will cause new particles to be produced, an increase of collision energy will increase
423-441: Is a spin effect known as helicity suppression. Its mechanism is as follows: The negative pion has spin zero; therefore the lepton and the antineutrino must be emitted with opposite spins (and opposite linear momenta) to preserve net zero spin (and conserve linear momentum). However, because the weak interaction is sensitive only to the left chirality component of fields, the antineutrino has always left chirality, which means it
470-404: Is a prominent quantity in many sub-fields of particle physics, such as chiral perturbation theory . This rate is parametrized by the pion decay constant ( f π ), related to the wave function overlap of the quark and antiquark, which is about 130 MeV . The π meson has a mass of 135.0 MeV/ c and a mean lifetime of 8.5 × 10 s . It decays via
517-528: Is called the Yukawa interaction . The nearly identical masses of π and π indicate that there must be a symmetry at play: this symmetry is called the SU(2) flavour symmetry or isospin . The reason that there are three pions, π , π and π , is that these are understood to belong to the triplet representation or
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#1732779629905564-791: Is different from Wikidata All set index articles Hagedorn temperature The Hagedorn temperature, T H , is about 150 MeV/ k B or about 1.7 × 10 K , little above the mass–energy of the lightest hadrons, the pion . Matter at Hagedorn temperature or above will spew out fireballs of new particles, which can again produce new fireballs, and the ejected particles can then be detected by particle detectors. This quark matter may have been detected in heavy-ion collisions at SPS and LHC in CERN (France and Switzerland) and at RHIC in Brookhaven National Laboratory (USA). In string theory ,
611-569: Is forbidden by the C-symmetry of the electromagnetic interaction: The intrinsic C-parity of the π is +1, while the C-parity of a system of n photons is (−1) . The second largest π decay mode ( BR γ e e = 0.01174 ) is the Dalitz decay (named after Richard Dalitz ), which is a two-photon decay with an internal photon conversion resulting
658-402: Is its own antiparticle. Together, the pions form a triplet of isospin . Each pion has overall isospin ( I = 1 ) and third-component isospin equal to its charge ( I z = +1, 0, −1 ). The π mesons have a mass of 139.6 MeV/ c and a mean lifetime of 2.6033 × 10 s . They decay due to the weak interaction . The primary decay mode of a pion, with
705-492: Is often known as the GMOR relation and it explicitly shows that M π = 0 {\displaystyle M_{\pi }=0} in the massless quark limit. The same result also follows from Light-front holography . Empirically, since the light quarks actually have minuscule nonzero masses, the pions also have nonzero rest masses . However, those masses are almost an order of magnitude smaller than that of
752-448: Is right-handed, since for massless anti-particles the helicity is opposite to the chirality. This implies that the lepton must be emitted with spin in the direction of its linear momentum (i.e., also right-handed). If, however, leptons were massless, they would only interact with the pion in the left-handed form (because for massless particles helicity is the same as chirality) and this decay mode would be prohibited. Therefore, suppression of
799-400: The π , and these are the antiparticles of one another. The neutral pion π is a combination of an up quark with an anti-up quark, or a down quark with an anti-down quark. The two combinations have identical quantum numbers , and hence they are only found in superpositions . The lowest-energy superposition of these is the π , which
846-587: The Boltzmann constant . Because of the divergence, people may come to the incorrect conclusion that it is impossible to have temperatures above the Hagedorn temperature, which would make it the absolute hot temperature, because it would require an infinite amount of energy . In equations: This line of reasoning was well known to be false even to Hagedorn. The partition function for creation of hydrogen–antihydrogen pairs diverges even more rapidly, because it gets
893-549: The University of California 's cyclotron in Berkeley, California , by bombarding carbon atoms with high-speed alpha particles . Further advanced theoretical work was carried out by Riazuddin , who in 1959 used the dispersion relation for Compton scattering of virtual photons on pions to analyze their charge radius. Since the neutral pion is not electrically charged , it is more difficult to detect and observe than
940-419: The adjoint representation 3 of SU(2). By contrast, the up and down quarks transform according to the fundamental representation 2 of SU(2), whereas the anti-quarks transform according to the conjugate representation 2* . With the addition of the strange quark , the pions participate in a larger, SU(3), flavour symmetry, in the adjoint representation, 8 , of SU(3). The other members of this octet are
987-510: The cosmic microwave background , through the Greisen–Zatsepin–Kuzmin limit . Theoretical work by Hideki Yukawa in 1935 had predicted the existence of mesons as the carrier particles of the strong nuclear force . From the range of the strong nuclear force (inferred from the radius of the atomic nucleus ), Yukawa predicted the existence of a particle having a mass of about 100 MeV/ c . Initially after its discovery in 1936,
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#17327796299051034-544: The electromagnetic force , which explains why its mean lifetime is much smaller than that of the charged pion (which can only decay via the weak force ). The dominant π decay mode, with a branching ratio of BR γγ = 0.98823 , is into two photons : π 0 ⟶ 2 γ {\displaystyle \pi ^{0}\longrightarrow 2\ \gamma } The decay π → 3 γ (as well as decays into any odd number of photons)
1081-542: The gelatin-silver process were placed for long periods of time in sites located at high-altitude mountains, first at Pic du Midi de Bigorre in the Pyrenees , and later at Chacaltaya in the Andes Mountains , where the plates were struck by cosmic rays. After development, the photographic plates were inspected under a microscope by a team of about a dozen women. Marietta Kurz was the first person to detect
1128-477: The muon (initially called the "mu meson") was thought to be this particle, since it has a mass of 106 MeV/ c . However, later experiments showed that the muon did not participate in the strong nuclear interaction. In modern terminology, this makes the muon a lepton , and not a meson. However, some communities of astrophysicists continue to call the muon a "mu-meson". The pions, which turned out to be examples of Yukawa's proposed mesons, were discovered later:
1175-467: The residual strong force between nucleons . Pions are not produced in radioactive decay , but commonly are in high-energy collisions between hadrons . Pions also result from some matter–antimatter annihilation events. All types of pions are also produced in natural processes when high-energy cosmic-ray protons and other hadronic cosmic-ray components interact with matter in Earth's atmosphere. In 2013,
1222-445: The surname Hagedorn . If an internal link intending to refer to a specific person led you to this page, you may wish to change that link by adding the person's given name (s) to the link. Retrieved from " https://en.wikipedia.org/w/index.php?title=Hagedorn&oldid=1132631932 " Categories : Surnames German-language surnames Hidden categories: Articles with short description Short description
1269-972: The Miracle-Gro company Jessica Hagedorn , Filipino playwright, novelist, poet and musician living in New York Jim Hagedorn (1962–2022), American politician, member of the United States House of Representatives John Hagedorn , US associate professor of criminal justice Karl Hagedorn (1889–1969) , German-born painter, naturalised British Karl Hagedorn (1922–2005) , German-American painter Katherine Hagedorn (1961–2013), American academic Mary Hagedorn , US marine biologist Rolf Hagedorn , German physicist who spent most of his career at CERN in Geneva , Switzerland Tom Hagedorn (born 1943), US politician [REDACTED] Surname list This page lists people with
1316-490: The charged pions are. Neutral pions do not leave tracks in photographic emulsions or Wilson cloud chambers . The existence of the neutral pion was inferred from observing its decay products from cosmic rays , a so-called "soft component" of slow electrons with photons. The π was identified definitively at the University of California's cyclotron in 1949 by observing its decay into two photons. Later in
1363-551: The charged pions in 1947, and the neutral pion in 1950. In 1947, the first true mesons, the charged pions, were found by the collaboration led by Cecil Powell at the University of Bristol , in England. The discovery article had four authors: César Lattes , Giuseppe Occhialini , Hugh Muirhead and Powell. Since the advent of particle accelerators had not yet come, high-energy subatomic particles were only obtainable from atmospheric cosmic rays . Photographic emulsions based on
1410-660: The city Puerto Princesa in the Philippines Eric E. Hagedorn , American politician Erwin Hagedorn (1952–1972), German serial killer Friedrich Hagedorn , 19th-century German watercolorist Friedrich von Hagedorn , early 18th-century German poet Gregor Hagedorn (born 1965), German botanist Hans Christian Hagedorn , Danish biologist and pharmacologist with focus on insulin research Hermann Hagedorn (1882–1964), American author, poet and biographer Hermann Hagedorn (poet) (1884–1951), German poet Horace Hagedorn , American businessman and co-founder of
1457-423: The detection of characteristic gamma rays originating from the decay of neutral pions in two supernova remnants has shown that pions are produced copiously after supernovas, most probably in conjunction with production of high-energy protons that are detected on Earth as cosmic rays. The pion also plays a crucial role in cosmology, by imposing an upper limit on the energies of cosmic rays surviving collisions with
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1504-414: The electron decay channel comes from the fact that the electron's mass is much smaller than the muon's. The electron is relatively massless compared with the muon, and thus the electronic mode is greatly suppressed relative to the muonic one, virtually prohibited. Although this explanation suggests that parity violation is causing the helicity suppression, the fundamental reason lies in the vector-nature of
1551-790: The electronic decay mode with respect to the muonic one is given approximately (up to a few percent effect of the radiative corrections) by the ratio of the half-widths of the pion–electron and the pion–muon decay reactions, R π = ( m e m μ ) 2 ( m π 2 − m e 2 m π 2 − m μ 2 ) 2 = 1.283 × 10 − 4 {\displaystyle R_{\pi }=\left({\frac {m_{e}}{m_{\mu }}}\right)^{2}\left({\frac {m_{\pi }^{2}-m_{e}^{2}}{m_{\pi }^{2}-m_{\mu }^{2}}}\right)^{2}=1.283\times 10^{-4}} and
1598-471: The entropy of the system rather than the temperature, and "the temperature becomes stuck at a limiting value". Hagedorn temperature is the temperature T H above which the partition sum diverges in a system with exponential growth in the density of states. where β = 1 / k B T {\displaystyle \beta =1/k_{\text{B}}T} , k B {\displaystyle k_{\text{B}}} being
1645-439: The four kaons and the eta meson . Pions are pseudoscalars under a parity transformation. Pion currents thus couple to the axial vector current and so participate in the chiral anomaly . Pions, which are mesons with zero spin , are composed of first- generation quarks . In the quark model , an up quark and an anti- down quark make up a π , whereas a down quark and an anti- up quark make up
1692-442: The interaction which dictates a different handedness for the neutrino and the charged lepton. Thus, even a parity conserving interaction would yield the same suppression. Measurements of the above ratio have been considered for decades to be a test of lepton universality . Experimentally, this ratio is 1.233(2) × 10 . Beyond the purely leptonic decays of pions, some structure-dependent radiative leptonic decays (that is, decay to
1739-469: The masses of the three kinds of pions are considerably less than that of the other mesons, such as the scalar or vector mesons. If their current quarks were massless particles, it could make the chiral symmetry exact and thus the Goldstone theorem would dictate that all pions have a zero mass. In fact, it was shown by Gell-Mann, Oakes and Renner (GMOR) that the square of the pion mass is proportional to
1786-473: The nucleons, roughly m π ≈ v m q f π ≈ m q {\displaystyle m_{\pi }\approx {\tfrac {\sqrt {vm_{q}}}{f_{\pi }}}\approx {\sqrt {m_{q}}}} 45 MeV, where m q are the relevant current-quark masses in MeV, around 5−10 MeV. The pion is one of the particles that mediate
1833-411: The number of states was originally proposed in the context of condensed matter physics . It was incorporated into high-energy physics in the early 1970s by Steven Frautschi and Hagedorn. In hadronic physics, the Hagedorn temperature is the deconfinement temperature. In string theory , it indicates a phase transition: the transition at which very long strings are copiously produced. It is controlled by
1880-663: The rate: π 0 ⟶ 2 e − + 2 e + {\displaystyle \pi ^{0}\longrightarrow {\rm {2\ e^{-}+2\ e^{+}}}} The fourth largest established decay mode is the loop-induced and therefore suppressed (and additionally helicity -suppressed) leptonic decay mode ( BR e e = 6.46 × 10 ): π 0 ⟶ e − + e + {\displaystyle \pi ^{0}\longrightarrow {\rm {e^{-}+e^{+}}}} The neutral pion has also been observed to decay into positronium with
1927-462: The reach of current, or even foreseeable technology. Pion In particle physics , a pion ( / ˈ p aɪ . ɒ n / , PIE -on ) or pi meson , denoted with the Greek letter pi ( π ), is any of three subatomic particles : π , π , and π . Each pion consists of a quark and an antiquark and is therefore
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1974-459: The residual strong interaction between a pair of nucleons . This interaction is attractive: it pulls the nucleons together. Written in a non-relativistic form, it is called the Yukawa potential . The pion, being spinless, has kinematics described by the Klein–Gordon equation . In the terms of quantum field theory , the effective field theory Lagrangian describing the pion-nucleon interaction
2021-454: The same year, they were also observed in cosmic-ray balloon experiments at Bristol University. ... Yukawa choose the letter π because of its resemblance to the Kanji character for 介 [ kai ], which means "to mediate". Due to the concept that the meson works as a strong force mediator particle between hadrons. The use of pions in medical radiation therapy, such as for cancer, was explored at
2068-583: The size of the string tension, which is smaller than the Planck scale by some power of the coupling constant. By adjusting the tension to be small compared to the Planck scale, the Hagedorn transition can be much less than the Planck temperature . Traditional grand unified string models place this in the magnitude of 10 K , two orders of magnitude smaller than the Planck temperature. Such temperatures have not been reached in any experiment and are far beyond
2115-677: The sum of the quark masses times the quark condensate : M π 2 = ( m u + m d ) B + O ( m 2 ) , {\displaystyle M_{\pi }^{2}=(m_{u}+m_{d})B+{\mathcal {O}}(m^{2}),} with B the quark condensate: B = | ⟨ 0 | u ¯ u | 0 ⟩ f π 2 | m q → 0 {\displaystyle B=\left\vert {\frac {\rm {\langle 0\vert {\bar {u}}u\vert 0\rangle }}{f_{\pi }^{2}}}\right\vert _{m_{q}\to 0}} This
2162-435: The unusual "double meson" tracks, characteristic for a pion decaying into a muon , but they were too close to the edge of the photographic emulsion and deemed incomplete. A few days later, Irene Roberts observed the tracks left by pion decay that appeared in the discovery paper. Both women are credited in the figure captions in the article. In 1948, Lattes , Eugene Gardner , and their team first artificially produced pions at
2209-891: The usual leptons plus a gamma ray) have also been observed. Also observed, for charged pions only, is the very rare "pion beta decay " (with branching fraction of about 10 ) into a neutral pion, an electron and an electron antineutrino (or for positive pions, a neutral pion, a positron, and electron neutrino). π + ⟶ π 0 + e + + ν e π − ⟶ π 0 + e − + ν ¯ e {\displaystyle {\begin{aligned}\pi ^{+}&\longrightarrow \pi ^{0}+{\rm {e}}^{+}+\nu _{e}\\[2pt]\pi ^{-}&\longrightarrow \pi ^{0}+{\rm {e}}^{-}+{\overline {\nu }}_{e}\end{aligned}}} The rate at which pions decay
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