Renormalization-group analysis of dynamical symmetry breaking in QCD

Chang, Lay Nam; Chang, Ngee-Pong

doi:10.1103/physrevd.29.312

Cited by 28 publications

(16 citation statements)

References 30 publications

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“…This solution also appears when using an improved renormalization group approach in QCD, associated to a finite quark condensate [36], and it minimizes the vacuum energy as long as > n 5 f [37]. Moreover, this specific solution is the only one consistent with Regge-pole like solutions [28].…”

mentioning

confidence: 99%

Limit on the pion distribution amplitude

Luna¹,

Natale²

2014

J. Phys. G: Nucl. Part. Phys.

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The pion distribution amplitude (DA) can be related to the fundamental QCD Greenʼs functions as a function of the quark self-energy and the quark-pion vertex, which in turn are associated with the pion wave function through the Bethe-Salpeter equation. Considering the extreme hard asymptotic behavior in momentum space allowed for a pseudoscalar wave function, which is limited by its normalization condition, we compute the pion DA and its second moment. From the resulting amplitude, representing the field theoretical upper limit on the DA behavior, we calculate the photon-pion transition form factor πγγ F Q ( ) * 2 . The resulting upper limit on the pion transition form factor is compared with existing data published by CLEO, BaBar and Belle Collaborations.Keywords: non-perturbative QCD, pion distribution amplitude, hadron physics (Some figures may appear in colour only in the online journal)A few years ago new data were published [1,2] for the γ γ π → * 0 process, where one of the photons is far off mass shell (large Q 2 ) and the other one is near mass shell ( ≈ Q 0 2 ). These measurements of the photon-pion transition form factor πγγ F Q ( ) * 2 , taken in the single-taggede e e e 0 reaction, were performed in a wide range of momentum transfer squared (4-40) GeV 2 ). At sufficiently high Q 2 it is expected that the standard factorization approach can be applied [3][4][5] (for a review, see [6]). The amplitude for this process at high virtuality has the form As a consequence of these experiments there were many theoretical papers speculating why the data should (or not) obey the BL limit [9][10][11][12][13][14][15][16][17][18][19]. The first attempt to explain the BaBar result can be found in [20]. Among these there were proposals claiming that the pion distribution amplitude should be modified [9][10][11]16], leading to a broader or flatter distribution in the place of the asymptotic form φas [21]. A flat DA would be consistent with the BaBar data, although a field theoretical support for such possibility is still missing. Some papers claim that other transition form factors of heavier mesons are compatible among themselves and with the saturation required by factorization theorems obtained from pQCD [13,22]. However, for heavier mesons than the pion the DA may be more peaked away from the end points [12]. A common statement in all papers is the need for more data to settle this problem.Meanwhile, the pion transition form factor is the most sensitive physical quantity to observe a non-perturbative contribution to the DA. Other quantities, for instance, like the pion form factor, may already contain a hard scattering amplitude at leading order with a soft behavior, due to the effect of extra coupling constants or gluon propagators [23]. This means that they do not lead to such a simple integral over a DA as the one shown by equation (1). As claimed in [24], we may assume that at present there is no definite conclusion on which is the asymptotic form of the pion DA, and it is possible that in the futur...

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mentioning

confidence: 99%

Limit on the pion distribution amplitude

Luna¹,

Natale²

2014

J. Phys. G: Nucl. Part. Phys.

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“…It was noted in [21] that the absence of a conventional mass term led to broken PT symmetry and so it is natural, at the perturbative level, to consider a massive theory. Moreover one approach to dynamical mass generation [28] is to consider a theory with a mass which is then determined self-consistently through a gap equation [29].…”

Section: The Yukawa Modelmentioning

confidence: 99%

“…At the end of the calculation of the two-point one-particle-irreducible (1PI) functions for the scalar and the fermion, we set M 2 = ∆M 2 and ∆m = m [29]. The renormalised two point 1PI functions for the fermion and scalar are assumed to behave like…”

Section: Dynamical Mass Generationmentioning

confidence: 99%

PT symmetric fermionic field theories with axions: Renormalization and dynamical mass generation

Mavromatos,

Sarkar,

Soto

2021

Preprint

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We consider the renormalisation properties of non-Hermitian Yukawa theories involving a pseudoscalar (axion) field. More generally these models provide simple paradigms for the study of the quantum behaviour of non-Hermitian (but PT -symmetric) fermionic models as higher dimensional field theories. The flow between of PT -symmetric and Hermitian fixed points under the renormalisation group flows is examined.

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“…In that spirit, then, there is no question about the higher-order correc-1 tions to the NJL gap equation. y T = x + % ( I n $ -y g ) = O In 1984, we [22] applied the N J L formulation of the selfconsistent generation of mass to the renormalizable QCD. If M is the effective quark mass at zero four momentum, and a solution that is now genuinely independent of p .…”

Section: Gap Equationmentioning

confidence: 99%

Nambu-Goldstone bosons and dynamical symmetry breaking in QCD at high temperatures

Chang

1992

Phys. Rev. D

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We report on the renormalization-group study of the low-energy effective potential in QCD. We derive the dynamically induced linear a model (DSM), whose self-couplings are not free parameters but are determined in terms of the running coupling of the underlying QCD. In this DSM, the a meson is not a fundamental field, but a genuine quark-antiquark 0+ bound state, while the .~r is the quark-antiquark 0-bound state. We show the masslessness of the 7~ at zero temperature, so that the .~r is a true Nambu-Goldstone boson coupled to zero-temperature chirality. At high temperatures, the 7~ remains massless. Thus the zero-temperature chirality is not restored at high temperatures. The apparent chiral symmetry operative at high temperatures is thus to be distinguished from that at T = 0. Comparison is made with the situation in the BCS and other theories where symmetry restoration does indeed take place.

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Renormalization-group analysis of dynamical symmetry breaking in QCD

Cited by 28 publications

References 30 publications

Limit on the pion distribution amplitude

Limit on the pion distribution amplitude

PT symmetric fermionic field theories with axions: Renormalization and dynamical mass generation

Nambu-Goldstone bosons and dynamical symmetry breaking in QCD at high temperatures

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