Chiral and flavor SU(2) and SU(3) symmetry breaking in quantum chromodynamics (original) (raw)
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2012
In this thesis, we focus on some aspects concerning hadronic phenomena at low energy, below 1 GeV, under which the spontaneous breaking of chiral symmetry takes place. Under this scale, the spectrum of Quantum Chromodynamics reduces to an octet of light pseudo-scalar mesons (π, K and η). But because of the confinement property, QCD under 1 GeV is highly non-perturbative, it is thus not possible to describe at low energy the dynamics of these mesons in terms of gluons and quarks (in that case the three light quarks u,d, and s). Two main alternatives exist to circumvent this major obstacle: Lattice QCD and Effective Field Theories. Lattice QCD is concerned with the numerical computations of various hadronic observables, while Effective Field Theories correspond to analytical frameworks adapted to a particular energy scale. In the case of QCD at low energy, this role is devoted to Chiral Perturbation Theory (ChiPT). This theory can be built either from two quark flavours (u and d), or ...
B0d,s– mass-differences from QCD spectral sum rules
Physics Letters B, 2002
We present the first QCD spectral sum rules analysis of the SU(3) breaking parameter ξ and an improved estimate of the renormalization group invariant (RGI) bag constantBB q both entering into the B 0 d,s-B 0 d,s mass-differences. The averages of the results from the Laplace and moment sum rules to order αs are fB B B (247 ± 59) MeV and ξ ≡ fB s B Bs /fB B B (1.18 ± 0.03), in units where fπ = 130.7 MeV. Combined with the experimental data on the mass-differences ∆M d,s , one obtains the constraint on the CKM weak mixing angle |Vts/V td | 2 ≥ 20.0(1.1). Alternatively, using the weak mixing angle from the analysis of the unitarity triangle and the data on ∆M d , one predicts ∆Ms = 18.6(2.1) ps −1 in agreement with the present experimental lower bound and within the reach of Tevatron 2.
Baryon masses and flavour symmetry breaking of chiral condensates
Physics Letters B
The masses of the baryon octet and decuplet are reproduced with a (10-20)% accuracy by ratios of exponential moment QCD spectral sum rules, obeying the z (sum rule variable) stability criterion. The onset of the QCD continuum is determined by consistency with the lowest dimensional finite energy sum rule. The N-A mass splitting is mainly controlled by the size of the mixed (@aG~u) condensate. The observed masses of the strange baryons can only be reproduced if there is a large breaking of the chiral condensates (~V) and (~trG~,). This result is independent of the choice of the nucleon current.
Dimension-8 contributions to light-quark QCD sum rules
Physics Letters B, 1985
Coefficients of dimension-8 quark and gluon condensates in the operator product expansion of light-quark currents are calculated by two methods. In one method mass singularities are explicitly cancelled in four dimensions. In the other 1/~0 poles arising from dimensional regularization of mass singularities in (4-2 ~0 ) dimensions are explicitly cancelled by ultraviolet operator renormatization. The results of the two methods agree. 1. Introduction. QCD sum rules [1 ] offer the prospect of relating observable hadronic properties to condensates which reveal the non-trivial structure of the vacuum. Charmonium sum rules involving condensates with dimension d ~< 8 have been analyzed by Nikolaev and Radyushkin [2,3] at Q2 = 0 and by Reinders et al. [4] at Q2 ~ 4m 2" Nikolaev and Radyushkin found unacceptably large d = 8 corrections to their previous d = 6 analysis [5], using a factorization hypothesis to relate gluon condensates of the type (G 4) to (G2) 2. Novikov et al. [6] criticised the factorization assumption for gluonic condensates and suggested that the failure of the sum rules at Q2 = 0 might be attributed to overestimation of the {G 4) condensates. Reinders et al. [4] on the other hand found fairly insignificant changes to their previous d = 4 analysis [7] at Q2 ~ 4m 2 ' when including (G 3) and (G 4) terms estimated by factoHzation. Thi~ findingiseonsistent with ~he suggestion of Shuryak [8] that cha_maonium states may be too massive to probe the detailed vacuum structure, being sensitive only to the d = 4 condensate (G2). The situation, however, is further complicated by the lattice calculations of Makhaldiani and Miiller-Preussker [9], which suggest that (G 4) condensates may be as much as 104 times larger than those assumed by Reinders et al. [4].
Isospin-breaking quark condensates in chiral perturbation theory
We analyze the isospin-breaking corrections to quark condensates within oneloop SU(2) and SU(3) chiral perturbation theory including m u � = m d as well as electromagnetic (EM) contributions. The explicit expressions are given and several phenomenological aspects are studied. We analyze the sensitivity of recent condensate determinations to the EM low-energy constants (LEC). If the explicit chiral symmetry breaking induced by EM terms generates a ferromagnetic-like response of the vacuum, as in the case of quark masses, the increasing of the order parameter implies constraints for the EM LEC, which we check with different estimates in the literature. In addition, we extend the sum rule relating quark condensate ratios in SU(3) to include EM corrections, which are of the same order as the m u � = m d ones, and we use that sum rule to estimate the vacuum asymmetry within ChPT. We also discuss the matching conditions between the SU(2) and SU(3) LEC involved in the condensates, when both isospin-breaking sources are taken into account.
Chiral symmetry breaking and the quark model: Unification of baryon and meson constraints
Nuclear Physics B, 1977
We review the subject of chiral sytmnetry breaking and its connection with the quark model. When the light plane SU(3) charges and quark field density matrix elements are transformed back to the usual static basis it becomes clear that expectation values of chiral breaking operators, such as qXiq, do not necessarily have simple SU(3) transformation properties. Starting with the standard current quark chiral Hamiltonian H' = rnuKU + mddd + ruffs, we then use current quark light-cone distribution function concepts in combination with constraints from (i) Compton amplitude fixed poles, (ii) baryon octet and decuplet mass differences, (iii) ~rN and KN a terms, (iv) GA/GV, (v) lowenergy ~r photoproduction multipoles, (vi) Goldberger-Treiman discrepancies, (vii) meson mass ratios in PCAC and, (viii) meson mass differences to determine in = ½(m u + rod) and m s in more than four independent ways. Our results are all mutually consistent and yield the values ~z ~ mrr and ms/~Z ~ 5. In particular the independent baryon and meson sectors of the theory are completely compatible.
QCD Phase Transition with Chiral Quarks and Physical Quark Masses
Physical Review Letters, 2014
We report on the first lattice calculation of the QCD phase transition using chiral fermions at physical values of the quark masses. This calculation uses 2+1 quark flavors, spatial volumes between (4 fm) 3 and (11 fm) 3 and temperatures between 139 and 196 MeV . Each temperature was calculated using a single lattice spacing corresponding to a temporal Euclidean extent of Nt = 8. The disconnected chiral susceptibility, χ disc shows a pronounced peak whose position and height depend sensitively on the quark mass. We find no metastability in the region of the peak and a peak height which does not change when a 5 fm spatial extent is increased to 10 fm. Each result is strong evidence that the QCD "phase transition" is not first order but a continuous cross-over for mπ = 135 MeV. The peak location determines a pseudo-critical temperature Tc = 155(1)(8) MeV. Chiral SU (2)L ×SU (2)R symmetry is fully restored above 164 MeV, but anomalous U (1)A symmetry breaking is non-zero above Tc and vanishes as T is increased to 196 MeV.
The strange quark mass from flavor breaking in hadronicdecays
The strange quark mass is extracted from a finite energy sum rule (FESR) analysis of the flavorbreaking difference of light-light and light-strange quark vector-plus-axial-vector correlators, using spectral functions determined from hadronic τ decay data. We point out problems for existing FESR treatments associated with potentially slow convergence of the perturbative series for the massdependent terms in the OPE over certain parts of the FESR contour, and show how to construct alternate weight choices which not only cure this problem, but also (1) considerably improve the convergence of the integrated perturbative series, (2) strongly suppress contributions from the region of s values where the errors on the strange current spectral function are still large and (3) essentially completely remove uncertainties associated with the subtraction of longitudinal contributions to the experimental decay distributions. The result is an extraction of ms with statistical errors comparable to those associated with the current experimental uncertainties in the determination of the CKM angle, Vus. We find ms(1 GeV) = 158.6 ± 18.7 ± 16.3 ± 13.3 MeV (where the first error is statistical, the second due to that on Vus, and the third theoretical).
Chiral Imbalance in QCD and its consequences
EPJ Web of Conferences, 2016
Under extreme conditions of high temperature and/or large quark (baryon) density, the vacuum of QCD changes its properties, and deconfinement, chiral symmetry restoration as well as chiral symmetry breaking take place. These transitions (phases) are accompanied by the rapid change in the rate and nature of topological transitions connecting different topological sectors. The heavy ion collisions (HIC) program opens a possibility to study these phenomena in so-called non-Abelian Quark-gluon plasma (QGP). In these phases the currents of light quarks (vector and axial-vector) can be independently examined for right-handed (RH) and left-handed (LH) quarks. To describe such a quark matter chiral chemical potential can be introduced to quantify the presence of chirality imbalance (ChI) i.e. the difference between the average numbers of RH and LH quarks in the fireball after HIC. In this review talk we will focus our attention on the discussion of the ChI related developments in heavy ion physics at central collisions and the plans for the future experiments aimed at establishing (or falsifying) the presence of Local spacial Parity Breaking (LPB) in heavy ion data. We describe some of experimental observables in detecting the signal of LPB. A number of measurements is proposed that allow to reach a definite conclusion on the occurrence of LPB effects in non-Abelian QGP produced in central heavy ion collisions and its simulation within a number of QCD-inspired models is outlined. Based on the effective meson theory in the presence of Chern-Simons interaction it is found that the spectrum of massive vector mesons splits into three polarization components with different effective masses. Moreover a resonance broadening occurs that leads to an increase of spectral contribution to the dilepton production as compared to the vacuum state. The asymmetry in production of longitudinally and transversely polarized states of ρ and ω mesons for various values of the dilepton invariant mass can serve as a characteristic indication of the LPB in CERES, HADES, PHENIX, STAR, NA60 and ALICE experiments.