Chiral symmetry restoration at nonzero temperature in theSU ( 3 ) r × SU ( 3 )
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Abstract:
We study patterns of chiral symmetry breaking at zero temperature and its subsequent restoration at nonzero temperature within the $\mathrm{SU}{(3)}_{r}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(3)}_{l}$ linear sigma model. Gap equations for the masses of the scalar and pseudoscalar mesons and the non-strange and strange quark condensates are systematically derived in the Hartree approximation via the Cornwall-Jackiw-Tomboulis formalism. In the chiral limit, the chiral symmetry restoring transition is found to be first order, as predicted by universality arguments. Taking the experimental values for the meson masses, however, the transition is crossover. The absence of the $\mathrm{U}{(1)}_{A}$ anomaly is found to drive this transition closer to being first order. At large temperatures, the mixing angles between octet and singlet states approach ideal flavor mixing.Keywords:
Pseudoscalar meson
The ongoing and planned experimental activities with direct reference to light unflavoured pseudoscalar mesons motivate a new theoretical study regarding their properties. An overview including details on new precise calculations is presented.
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The relative magnitude of the decay constants of the pseudoscalar and vector beauty mesons poses (in contrast to the case of charmed mesons) a long-standing puzzle. We revisit this problem within the framework of our recent improvements of the QCD sum-rule formalism for relating observable properties of mesons to quantum chromodynamics and are led to conclude that the decay constants of the beauty vector mesons are undoubtedly smaller than those of their pseudoscalar counterparts.
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In the framework of the relativistic independent quark model with the QCD-motivated static potential, the masses of the ground states of pseudoscalar mesons and their radial excitations are calculated for both observed mesons and unobserved ones. The strength of the spinAspin interaction and the magnitude of the meaneld contribution are estimated for both the light and heavy 0 −+ mesons. The calculated masses are in agreement with experimental values within an accuracy of 30 ÷ 40 MeV, and the predictions are obtained for the mass values of a number of unobserved yet radial excitations of pseudoscalar mesons. ‚ · ³± I ·¥²OE¨¢¨¸E¸±µ° ³µ¤¥²¨ ´¥§ ¢¨¸¨³OI ±¢ ·±µ¢ ¸ S•-³µE¨¢¨·µ¢ ´´O³ ¸E E¨I¥¸±¨³ ¶µE¥´I¨ ²µ³ ¢OI¨¸²¥´O ³ ¸¸O µ¸´µ¢´OI ¸µ¸EµO´¨° ¶¸¥¢¤µ¸± ²O·´OI ³¥§µ´µ¢ ¨ ¨I · ¤¨ ²O´OI ¢µ§iE|¤¥´¨° ± ± ¤²O ¨§¢¥¸E´OI, E ± ¨ ¤²O ´¥¨§¢¥¸E´OI ¥Ð¥ ¸µ¸EµO´¨°. �I¥´¥´O ¢¥²¨I¨´ ¸¶¨´- ¸¶¨´µ¢µ£µ ¢§ ¨³µ¤¥°¸E¢¨O ¨ §´ I¥´¨¥ ¢±² ¤ ¸·¥¤´¥£µ ¶µ²O ¤²O ²¥£±¨I ¨ ¤²O EO|¥²OI 0 −+ -³¥§µ´µ¢. ‚OI¨¸²¥´´O¥ ³ ¸¸O ¸µ£² ¸EOE¸O ¸ O±¸¶¥·¨³¥´E ²O´O³¨ §´ I¥´¨O³¨ ¸ ¶µ£·¥I´µ¸EOO 30 ÷ 40 ŒO‚. �µ²EI¥´O E ±|¥ ¶·¥¤¸± § ´¨O §´ I¥´¨° ³ ¸¸ ¤²O · O¤ ´¥ µE±·OEOI ¶µ± · ¤¨ ²O´OI ¢µ§iE|¤¥´¨° ¶¸¥¢¤µ¸± ²O·´OI ³¥§µ´µ¢.
QCD sum rules
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The relative magnitude of the decay constants of the pseudoscalar and vector beauty mesons poses (in contrast to the case of charmed mesons) a long-standing puzzle. We revisit this problem within the framework of our recent improvements of the QCD sum-rule formalism for relating observable properties of mesons to quantum chromodynamics and are led to conclude that the decay constants of the beauty vector mesons are undoubtedly smaller than those of their pseudoscalar counterparts.
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QCD sum rules
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We study radial excitations of pseudoscalar and vector $q\overline{q}$ mesons within a chiral approach. We derive a general form for a chiral Lagrangian describing processes involving excited pseudoscalar and vector mesons. The parameters of the chiral Lagrangian are fitted using data and previous calculations in the framework of the $^{3}P_{0}$ model. Finite-width effects are examined and predictions for mesons previously not discussed are given. Available experimental data is analyzed whenever possible. Possible hints for exotic mesons and open interpretation issues are discussed.
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Pseudovector
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We study two nonets of excited vector mesons, predominantly corresponding to radially excited vector mesons with quantum numbers $n\hspace{0.08cm} ^{2S+1}L_{J}$ $=2^3S_1$ and to orbitally excited vector mesons with quantum numbers $n\hspace{0.08cm} ^{2S+1}L_{J}=1^3D_1$. We evaluate two types of decays of these mesons: into two pseudoscalar mesons and into a pseudoscalar and a ground-state vector meson. We compare the results with experimental data taken from PDG. We also make predictions for the strange-antistrange state in the $1^3D_1$ nonet denoted as $\phi(1930)$, which has not yet been discovered.
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Arguments in favor of the existence of heawy neutral pseudoscalar mesons with zero isotopoic spin are discussed. Some experiments that should help to aseertain whether these mesons exist are suggested. (auth)
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Parity (physics)
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Vector meson
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We show that the contact couplings of neutral pseudoscalar and axial mesons to the nucleon are proportional to $\Delta s$, the fraction of nucleon spin carried by the strange quark sea, and thus are strongly suppressed relative to the couplings of charged mesons to the nucleon. On the other side, recent high accuracy data on $\eta $ photoproduction at threshold reveal the need for non--negligibile $\eta NN$ vertices, while fitting $\bar N N$ phase shifts by means of effective meson exchange potentials requires a substantial presence of $f_1$ mesons there. We here advocate the idea to attribute the couplings of neutral pseudoscalar and axial vector mesons to effective triangular diagrams containig non--strange mesons and demonstrate its usefulness in describing available data.
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We study the mass spectrum of light pseudoscalar and vector mesons in the presence of an external uniform magnetic field B → B B B ρ + B
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