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We study the tuning effect of a transverse magnetic field on the confinementof spinons in the infinite XXZ spin-1/2 chain. The spinon confinement in thismodel takes place in the gapped antiferromagnetic phase upon application of astaggered longitudinal magnetic field. The tuning transverse magnetic field hasmutually orthogonal uniform and staggered components. The energy spectra of thetwo-spinon bound states (the `mesons') in the confinement regime areanalytically calculated in this model using two different perturbative schemes.The first one applies in the extreme anisotropic (Ising) limit and employs theinverse anisotropy constant as a small parameter. The second perturbativescheme, which applies at any anisotropy in the gapped antiferromagnetic domain,exploits the integrability of the XXZ spin chain at zero magnetic field. Thesmall parameters in the second technique are the components of the transverse,and staggered longitudinal magnetic fields. It is shown, that the weaktransverse magnetic field mixes the transverse and longitudinal meson modes,and leads to an avoided crossing of their energies upon increase of itsstrength. The explicit formulas for the two-spinon contribution to thedynamical structure factors of local spin operators are obtained as well inthis model in the weak confinement regime for wave-vectors close to the pointsk = 0 and k = \pi.

Confinement of spinons in the XXZ spin-1/2 chain in presence of the transverse magnetic field