Hard Exclusive Electroproduction of $\pi^+\pi^-$ Pairs

Hard exclusive electroproduction of $\pi^+\pi^-$ pairs off hydrogen and deuterium targets has been studied by the HERMES experiment at DESY. Legendre moments $<P_1>$ and $<P_3>$ of the angular distributions of $\pi^+$ mesons in the center-of-mass frame of the pair have been measured for the first time. Their dependence on the $\pi^+\pi^-$ invariant mass can be understood as being due to the interference between relative $P$-wave (isovector) and $S,D$-wave (isoscalar) states of the two pions. % The increase in magnitude of $<P_1>$ as Bjorken $x$ increases is interpreted in the framework of Generalized Parton Distributions as an enhancement of flavour {non-singlet} $q\bar{q}$ exchange for larger values of $x$, which leads to a sizable admixture of isoscalar and isovector pion pairs. % In addition, the interference between {$P$-wave} and {$D$-wave} states separately for transverse and longitudinal pion pairs has been studied. The data indicate that at {$\la Q^2 \ra = 3$ GeV$^2$} higher twist effects can be as large as the leading-twist longitudinal component