Effects of eight-quark interactions on the hadronic vacuum and mass spectra of light mesons

TLDR: In this article, a phenomenological output of eight-quark interactions considering the mass spectra of pseudoscalar and scalar mesons is derived and their equivalence to the two angle approach is derived.

About: This article is published in Annals of Physics.The article was published on 2007-09-01 and is currently open access. It has received 49 citations till now. The article focuses on the topics: Chiral symmetry breaking & Quark.

Figures

Table 2 The masses, weak decay constants of light pseudoscalars (in MeV), the singlet-octet mixing angle hp (in degrees), and the quark condensates h uui; h ssi expressed as usual by positive combinations in MeV

Table 3 The masses of the scalar nonet (in MeV), and the corresponding singlet-octet mixing angle hs (in degrees)

Fig. 2. A closer view on the effective potential V of Fig. 1c. Depending on the strength of the six-quark coupling j, with remaining parameters G, k, K fixed, the symmetric Wigner–Weyl phase of the four-quark potential (Fig. 1a) may coexist with the spontaneously broken phase induced by the presence of the ’t Hooft term. This double vacuum exists within the global stability conditions (12).

Table 1 Parameters of the model: mu, ms (MeV), G (GeV 2), K (MeV), j (GeV 5), g1, and g2 (GeV 8). We also show the corresponding values of constituent quark masses Mu and Ms (MeV)

Fig. 1. The effective potential V in the SU(3) chiral limit, as function of the quark condensate related variable h. Upper and lower panels are classifiedby the value of s ¼ N cGK2 2p2 , related to the curvature of the effective potential at the origin. Each panel shows the typical form of the potential when one adds successively to the four-quark (see a, d on the left), the six- (middle figures b, e) and eight-quark interactions (figures c, f on the right). Themetastable cases (b) and (e) are obtained in the mean field approximation VMF (the stationary phase approach leads to an unstable vacuum, without any local minimum, [17]).

Frequently asked questions

Q1. What have the authors contributed in "Effects of eight-quark interactions on the hadronic vacuum and mass spectra of light mesons" ?

This work is a follow-up of recent findings, namely ( i ) the six quark flavour determinant ’ t Hooft term destabilizes the NJL vacuum, ( ii ) the addition of a chiral invariant eight-fermion contact term renders the ground state of the theory globally stable ; ( iii ) stability constrains the values of coupling constants of the model, meaning that even in the presence of eight-quark forces the system can be unstable in a certain parameter region. In the present work the authors study a phenomenological output of eight-quark interactions considering the mass spectra of pseudoscalar and scalar mesons. The authors show that the masses of pseudoscalars are almost neutral to the eight-quark forces. 

Q2. What is the way to achieve the desired effective Lagrangian?

The bosonization of quark degrees of freedom leads then to the desirable effective Lagrangian with matter fields and a stable chiral asymmetric vacuum. 

Q3. What is the common example of a chiral perturbation theory?

A well-known example is chiral perturbation theory [1], where the Lagrangian of light pseudoscalar mesons is both a derivative and light current quark mass expansion around the asymmetric ground state which is assumed to be stable. 

Q4. What is the effect of the elimination of the field Q(x)?

After the elimination of the field Q(x) by means of its classical equation of motion, one obtains an effective mesonic Lagrangian. 

Q5. What is the main effect of the f0(600) mass?

The main effect is visible in the f0(600) mass: a further increase in g1, set (f), decreases further its mass, leaving the remaining observables almost unaffected. 

Q6. What is the effect of eight-quark interactions on the mass spectrum?

To summarize, the effect of eight-quark interactions on the mass spectrum, vacuum decay couplings, and mixing angles is relatively small as long as general properties of the QCD vacuum (the values of the quark condensates and the topological susceptibility) are correctly reproduced. 

Q7. What is the way to describe the QCD vacuum?

it is tempting to consider the intuitive picture that describes the QCD vacuum with basis on a series of multi-quark interactions reflecting several tractable features of QCD, which include aspects of chiral symmetry and of the 1/Nc expansion. 

Q8. How can one prove that V is unbounded from below?

The just mentioned controversy concerning the results obtained by the mean field method and the functional integral approach is also removed: one can prove that V ¼ VMF, i.e., the number of admissible real solutions to the stationary phase equations can be constrained to one due to eight-quark terms. 

Q9. What is the simplest way to estimate the generating functional of the theory?

The functional integral bosonization of the model exposes new shortcomings: the system of stationary phase equations used to estimate the generating functional of the theory Z, has several real solutions [17] which contribute independently, i.e., Z = Z1 + Z2 + + 

Q10. What is the direct way to study the properties of the fundamental fields of QCD?

The most direct way to study their properties is the method of effective Lagrangians written in terms of the matter fields describing mesons or baryons. 

Q11. What are the main roles of the eight-quark forces considered?

The authors view therefore the main role of eight-quark forces considered as follows: (i) they are of vital importance for the stability of the ground state built from four and sixquark interactions. 

Q12. What are the main characteristics of light pseudoscalar mesons?

In this paper the authors consider the main characteristics of light pseudoscalar mesons (JPC = 0 +): their masses and weak decay constants.