Connections between chiral Lagrangians and QCD sum-rules

Abstract

It is shown how a chiral Lagrangian framework can be used to derive relationships connecting quark-level QCD correlation functions to mesonic-level two-point functions. Crucial ingredients of this connection are scale factor matrices relating each distinct quark-level substructure (e.g., quarkantiquark, four-quark) to its mesonic counterpart. The scale factors and mixing angles are combined into a projection matrix to obtain the physical (hadronic) projection of the QCD correlation function matrix. Such relationships provide a powerful bridge between chiral Lagrangians and QCD sum-rules that are particularly effective in studies of the substructure of light scalar mesons with multiple complicated resonance shapes and substantial underlying mixings. The validity of these connections is demonstrated for the example of the isotriplet a0(980)-a0(1450) system, resulting in an unambiguous determination of the scale factors from the combined inputs of QCD sum-rules and chiral Lagrangians. These scale factors lead to a remarkable agreement between the quark condensates in QCD and the mesonic vacuum expectation values that induce spontaneous chiral symmetry breaking in chiral Lagrangians. This concrete example shows a clear sensitivity to the underlying a0-system mixing angle, illustrating the value of this methodology in extensions to more complicated mesonic systems.Scalars are the Higgs bosons of QCD and induce spontaneous chiral symmetry breaking and their internal structure holds key information about nonperturbative QCD. However, understanding the light scalar sector of QCD has turned out to be considerably more challenging than other sectors [1][2][3]. Particularly the investigation of the quark substructure of scalar mesons continues to pose various complications, mostly stemming from the underlying mixings among different quark and glue components. On the one hand, the experimental data on light scalars, which originate from various lowenergy decays and scatterings, seems to be less certain than other better understood channels such as vectors or pseudoscalars, while on the other hand, the theoretical foundation for understanding scalars faces challenges within the quark model. The theoretical challenges include describing the light and inverted scalar mass spectrum below 1 GeV, which finds a fundamental explanation in terms of four-quark states described by the MIT bag model [4], as well as describing the existing deviations from a quark-antiquark substructure of scalar states above 1 GeV, which finds a natural explanation in an underlying mixing among scalars below and above 1 GeV [5] (other works on mixing include Refs. [6][7][8][9][10][11][12][13]). QCD sum-rules also find evidence of an inverted spectrum for four-quark states [14][15][16].Such mixing patterns and global relations are far from the focus of chiral perturbation theory [17][18][19][20][21] which aims to probe the near-threshold region in a systematic way. * fariboa@sunyit.edu †

Constraint on the light quark mass mq from QCD sum rules in the I=0 scalar channel

“…The agreement between our result m q (2 GeV) = 4.7 +0.8 −0.7 MeV, the PDG value, and QCDSR determinations in the pion channel provide a consistent framework connecting QCD and low-energy hadronic physics (see also Ref. [40]). Furthermore, this agreement in the quark mass determinations confirms the validity of our improved Monte-Carlo based QCD sum rules, which has previously been systematically examined in the ρ meson channel in Ref.…”

Algebraic vacuum limits of QCD condensates from in-medium projections of Lorentz tensors

“…QCD sum rules (QSRs) have turned out to be a suitable tool in this respect [8][9][10][11][12][13]. That method provides testable predictions for spectral properties of mesons and baryons in vacuum (see [14][15][16][17][18][19][20][21][22][23][24][25] for recent studies) and in a medium [26][27][28][29][30][31][32][33][34][35]; even exotic states can be dealt with [36][37][38][39][40][41]. Moreover, QSRs also allow for more general discussions w. r. t. dynamical chiral symmetry breaking (DχSB) and its restoration in the medium [42][43][44][45][46][47][48][49][50][51].…”

Universal scale factors relating mesonic fields and quark operators

“…In Refs. [3,4] we demonstrated how a linkage between two existing frameworks, QCD sum-rules [5,6] (that significantly connect fundamental QCD to hadronic physics through duality relations) and chiral Lagrangians (which are appropriately designed in terms of the hadron fields and can be conveniently used to describe low-energy data) can provide an approximation of such a bridge. This linkage occurs through scale-factor matrices relating mesonic fields of chiral Lagrangians to quark-level structures of QCD sum-rules.…”

“…This linkage occurs through scale-factor matrices relating mesonic fields of chiral Lagrangians to quark-level structures of QCD sum-rules. Specifically, the scale factors were first determined for the isovector scalar sector [3,4] by connecting the QCD sum-rules to the chiral Lagrangian described by the generalized linear sigma model [7]. However, chiral symmetry requires that the scale factors must be universal for all members of the chiral nonets.…”

“…The exact relationship between the composite fields of quarks representing a mesonic state (which requires a mass dimension of three or higher), and that of a single mesonic field (of mass dimension one) is not known. We have assumed [3,4] that this relationship is of a simple form where the underlying composite fields of quarks inside a scalar meson are linearly proportional to the meson field. If this as-sumption is a good approximation to the exact relationship between the meson fields and their underlying quark fields, then the scale factor adjusting the mass dimensions should reflect certain characteristics of the meson.…”