Roper Resonances as Vibrating Flux Tubes Between Quarks

The Roper resonances of the nucleon are described as transverse vibrations of astretched flux tube between the three quarks. The proton is modeled using currentmass quarks interacting with a confining linear flux tube potential plus thespin-dependent parts of a one-gluon exchange potential. The proton ground state hasno vibrations and the confining flux tube has the minimum length required toconnect the three quarks. The flux tube has a V or Y shape of two or threesegments, depending on the locations of the quarks. The vibrations of the fluxtube have nodes at the quarks and at the apex of the Y-shaped configuration andprovide the vibrational excitation energy to describe the proton excitations. Theamplitude of the transverse vibrations is found from a geometric analysis, anddepends on the string constant of the flux tube potential. The Roper 1. 440-GeVresonance energy is very nearly reproduced by the vibration with mode number1 acting in only one segment of the flux tube. The vibration with mode number2 in one segment of the flux tube closely reproduces the second proton excitationat 1.710 GeV. The D excited states are also well reproduced by these modes ofa vibrating flux tube.