e(+)e(-) -> pi(+)pi(-)pi(+)pi(-), K+K-pi(+)pi(-), and K+K-K+K- cross sections at center-of-mass energies 0.5-4.5 GeV measured with initial-state radiation RID A-8798-2012 RID C-2728-2008 RID C-5223-2009 RID C-5719-2008 RID D-1055-2009 RID A-2675-2009

We study the process e(+)e- -> pi(+)pi(-)pi(+)pi(-) gamma, with a hard photon radiated from the initial state. About 60 000 fully reconstructed events have been selected from 89 fb(-1) of BABAR data. The invariant mass of the hadronic final state defines the effective e(+)e(-) e(+)e(-) center-of-mass energy, so that these data can be compared with the corresponding direct e(+)e(-) measurements. From the 4 pi -mass spectrum, the cross section for the process e(+)e(-) -> pi(+)pi(-)pi(+)pi(-) is measured for center-of-mass energies from 0.6 to 4.5 GeV. The uncertainty in the cross section measurement is typically 5%. We also measure the cross sections for the final states K+K- pi(+)pi(-) and K+K-K+K-. We observe the J/psi in all three finial states and measure the corresponding branching fractions. We search for X(3872) in J/psi(-> mu(+)mu(-))pi(+)pi(-) and obtain an upper limit on the product of the e(+)e(-) width of the X(3872) and the branching fraction for X(3872) -> J/psi pi(+)pi(-).