Tucumán is connected to Buenos Aires (via La Banda/Santiago del Estero and Rosario) daily from beautiful Estación Mitre. Expect long delays, poor visibility, ordinary food and questionable cleanliness. As the trip is so cheap it books up well in advance.
At the time of research, trains were leaving Buenos Aires’ Retiro station seven times a day on the 15- to 18-hour journey. From Tucumán, trains leave twice daily for Buenos Aires. The trip costs AR$74/130 in 1st class/Pullman class (reclinable seats). There's a bar/restaurant on board.