Meson-meson scattering in the quark model: Spin dependence and exotic channels

Abstract

We apply a quark interchange model to spin-dependent and exotic meson-meson scattering. The model includes the complete set of standard quark model forces, including OGE spin-orbit and tensor and scalar confinement spin-orbit. Scattering amplitudes derived assuming SHO and * email: barnes@bethe.phy.ornl.gov † email: nblack@nomad.phys.utk.edu ‡ email: swansone@pitt.edu 1 Coulomb plus linear plus hyperfine meson wavefunctions are compared. In I=2 ππ we find approximate agreement with the S-wave phase shift from threshold to 1.5 GeV, where we predict an extremum that is supported by the data. Near threshold we find rapid energy dependence that may reconcile theoretical estimates of small scattering lengths with experimental indications of larger ones based on extrapolation of measurements at moderate k π 2 . In PsV scattering we find that the quark-quark L·S and T forces map into L·S and T meson-meson interactions, and the P-wave L·S force is large. Finally we consider scattering in J P Cn -exotic channels, and note that some of the "Deck effect" mechanisms suggested as possible nonresonant origins of the π 1 (1400) signal are not viable in this model.

AreY(4260)andZ2+(4250)Ding1 2009Phys. Rev. D

“…Following this systematic procedure, we can convert a general T-matrix into an equivalent potential operator. In this work, we obtain the local potential by Fourier transforming the leading terms T (0) (q) of the scattering amplitude T f i , which is common in potential model [37,38]. Since the propagators are off-shell, we introduce form factor at each vertex when writing out the scattering amplitude, the usual form factor is expressed as [39,40] …”

A study of the reaction π−p→ωπ−p at 18 GeV/c: the D and S decay amplitudes for b1(1235)→ωπ

“…In a quark interchange model calculation, Barnes, Black, and Swanson [7] predict φ(D − S) = 14 deg. Our measurement, φ(D − S) = 10.54 ± (2.4) stat ± (3.9) sys deg, is consistent with their prediction.…”

Molecular states and1−+exotic mesons

“…In the limit of a large number of colours N c in QCD there are no four-quark states, but only meson-meson molecules [21]. [20,22], QCD sum rules [23], quark-antiquark pair exchange models [14,24], four-quark potential [19,25], flux-tube [26] and other [27] models, and molecular models with meson exchange [28]. We adopt the latter.…”

“…[18] and using the effective vertices, we can write down the scattering amplitude between the two constituent mesons in momentum space and convert it into configuration space by a Fourier transformation. This procedure was used to derive the effective potential between a quark and an antiquark [14]. We consider all pseudoscalar, scalar and vector meson exchanges in t-, s-and u-channel, and indicate explicit expressions for the processes that need to be included in our calculations.…”

“…So far, this scenario has only been argued to account for the E852 data, and has not been extended to the Crystal Barrel data. Also, aspects of the proposed mechanism have been challenged on theoretical grounds [11,14]. However, it has been argued that there is no need for more than one resonance in the 1.3-1.6 GeV mass region when ηπ, η ′ π and ρπ data are considered [15].…”