Roper resonances as vibrating flux tubes between quarks

The Roper resonances of the nucleon are described as transverse vibrations of a stretched flux tube between the three quarks. The proton is modeled us ing current mass quarks interacting with a confining linear flux tube poten tial plus the spin-dependent parts of a one-gluon exchange potential. The p roton ground state has no vibrations and the confining flux tube has the mi nimum length required to connect the three quarks. The flu?: tube has a V o r Y shape of two or three segments, depending on the locations of the quark s. The vibrations of the flux tube have nodes at the quarks and at the apex of the Y-shaped configuration and provide the vibrational excitation energ y to describe the proton excitations. The amplitude of the transverse vibra tions is found from a geometric analysis, and depends on the string constan t of the flux tube potential. The Roper 1.440-GeV resonance energy is very nearly reproduced by the vibration with mode number 1 acting in only one se gment of the flux tube. The vibration with mode number 2 in one segment of the flux tube closely reproduces the second proton excitation at 1.710 GeV. The Delta excited states are also well reproduced by these modes of a vibr ating flux tube.