A family of mesons lies on a Regge trajectory of slope

PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Beyond the Standard Model · Beyond the Standard Model

Symmetry and Flavour, Ch The relativistic string: action, light-cone quantisation, spectrum and D-branes

Problem

\alpha' = 0.80\,\mathrm{GeV^{-2}}

. Model them as rotating open strings, so that

T_0 = 1/2\pi\alpha'

. A static open string with this tension has length

\ell = 1.2\,\mathrm{fm}

; it is straight and at rest, with each end held fixed. ((a)) Find

T_0

\mathrm{GeV^2}

, and say by how many per cent it differs from the quark-potential tension

\kappa \approx 0.18\,\mathrm{GeV^2}

. ((b)) Use the Nambu-Goto action evaluated on the static configuration to find the energy stored in the string, in

\mathrm{GeV}

and in joules. ((c)) Express the tension

T_0

as a force in newtons.