Covariant confinement model for the calculation of the properties of scalar mesons

Abstract

We continue our studies of a relativistic quark model that features chiral symmetry, covariance, and confinement. In this work we apply our model to the study of scalar-isoscalar mesons. Several of the parameters of the model have been determined in our earlier work, so that only two new parameters are needed for our analysis. We find a good fit to the spectrum of the f 0 mesons, if we add a glueball with energy of about 1700 MeV. In this model we are rather close to ''ideal mixing,'' with the f 0 (980) having the largest ss mixture of 10%. The f 0 (1370) is the nodeless ss state, while the f 0 (1500) is a nn ϭ(uū ϩdd )/& state with a single node. ͓The presence of that node accounts for the small width of the f 0 (1500).͔ The next state is a nn state with two nodes at 1843 MeV. Thus, we identify the f 0 (1770) as the state with the largest glueball component. It was found that the vacuum polarization functions that describe coupling to the two-meson and other continuum meson channels play an important role in achieving a good fit to the experimentally determined spectrum. In this work we use a Gaussian regulator in all our calculations of meson decay amplitudes. In the first part of our study we multiply the Gaussian regulator by a P 2 -dependent factor that was chosen so as to modify the threshold behavior of our polarization functions. With that factor in place, we can study the spectrum of f 0 states without introducing the imaginary parts of the polarization functions that describe decay to the twomeson continuum. When we do introduce the imaginary parts, we use the vacuum polarization functions with unmodified threshold behavior. The use of the P 2 -dependent factor helps to clarify the nature of the f 0 (400-1200), which is seen, in part, to have its origin as a rather complex threshold effect associated with the rapid increase of the amplitudes for decay to the and KK channels. ͓For a full understanding of the f 0 (400-1200) one needs to also consider the role of t-channel exchange.͔ The model used in this work is based upon weak quarkonium-glueball coupling. However, the four-pion decay of the f 0 (1370) and the f 0 (1500) suggests that these states may be strongly mixed with the glueball, which may have a large four-pion decay width. It is also possible that mixing of these states with the f 0 (980) may be important for understanding the four-pion decay widths. We provide a short discussion of quarkonium-glueball mixing in a schematic model. There is not enough information presently available to treat that problem in an unambiguous manner.

Erratum: Comparing the Higgs sector of electroweak theory with the scalar sector of low energy QCD [Phys. Rev. D68, 013008 (2003)]

“…(27) effectively replaces the tree level denominator (m 2 σb − s) by the magnitude of the quantity in Eq. (17), which defines the physical pole position in the complex s plane and which we used to identify the physical Higgs mass.…”

“…(27) for the divergence at s = m 2 σb with that of the conventional Breit Wigner prescription used for example in [68,69], given in Eq. (12) with Γ = Γ tree .…”

Description of deconfinement at finite matter density in a generalized Nambu–Jona-Lasinio model

“…We may consider the relation given in an early work on scalar mesons [27]. In the case of the f 0 (980) we presented a discussion of such terms as they affect the energy predicted for the f 0 (980) in Ref.…”

Branching ratio andCPasymmetry ofBs→K0*(1430)ρZhang1 2010Phys. Rev. D

“…Along with many scalar mesons found in experiments, more and more efforts have been made to study the scalar meson spectrum theoretically [1][2][3][4][5][6][7]. Today, it is still a difficult but interesting topic.…”