These antigens should provoke a T-independent response, so will they differentiate then and there to form short-lived plasma cells? Or do they have to go to lymphoid tissue, enter a B follicle, and then differentiate? and can they differentiate into short-lived memory cells and short-lived plasma cells? Or only the latter?
Depending on the class of the antigen, B cells can be activated via different mechanisms. T-independent (TI) immune response can be induced by two types of antigens, namely TI-1 and TI-2 antigen (1).
TI-1 antigens are mostly lipopolysaccharides (1). They activate naive B cells by directly binding to the Toll like receptors expressed on the surface of B cells. Binding induce proliferation and differentiation into effector B cells, which secrete antibodies against particular antigen (2). Eventually, most of these effector B cells will mature to become large plasma cells. Most plasma cells will die within a few days, but some can survive in the bone marrow for months or years and continue to secrete antibodies into the blood (2).
TI-2 antigens include polysaccharides, glycolipids, and nucleic acids (1). They have no intrinsic B-cell-stimulating activity and activate B cells via repetitive cross-linking of membrane immunoglobulin receptors. Such activation has only been found in mature B cells, meaning that they won't activate a naive B cell (3).
(1) Cruse J, Lewis R, Wang H. Immunology Guidebook. 1st edition. Academic Press; 2004. ANTIGENS, IMMUNOGENS, VACCINES, AND IMMUNIZATION. Available from: https://www.sciencedirect.com/sdfe/pdf/download/eid/3-s2.0-B9780121983826500261/first-page-pdf
(2) Alberts B, Johnson A, Lewis J, et al. Molecular Biology of the Cell. 4th edition. New York: Garland Science; 2002. B Cells and Antibodies. Available from: https://www.ncbi.nlm.nih.gov/books/NBK26884/
(3) Janeway CA Jr, Travers P, Walport M, et al. Immunobiology: The Immune System in Health and Disease. 5th edition. New York: Garland Science; 2001. B-cell activation by armed helper T cells. Available from: https://www.ncbi.nlm.nih.gov/books/NBK27142/