Edit: I read the paper and it just speaks of humoral immunity. Wikipedia:
> Humoral immunity is the aspect of immunity that is mediated by macromolecules found in extracellular fluids such as secreted antibodies, complement proteins, and certain antimicrobial peptides.
Antibodies I'll get to below. Complement proteins and antimicrobial peptides links go to articles saying they're part of the innate immune system (covid protection is done by the adaptive immune system if I understand it correctly). So antibodies is the relevant part:
> Together with B and T cells, antibodies comprise the most important part of the adaptive immune system. They occur in two forms: one that is attached to a B cell, and the other, a soluble form, that is unattached and found in extracellular fluids such as blood plasma. Initially, all antibodies are of the first form, attached to the surface of a B cell – these are then referred to as B-cell receptors (BCR). After an antigen binds to a BCR, the B cell activates to proliferate and differentiate into either plasma cells, which secrete soluble antibodies with the same paratope, or memory B cells, which survive in the body to enable long-lasting immunity to the antigen.
So B cells (well, some but not all) are responsible for long-term immunity, distinct from antibody levels. An antibody (further up the article) is a Y-shaped cell with receptors on the tips which it uses to bind to and thereby tag pathogens for other parts of the immune system to deal with or to neutralize it directly.
So it doesn't sound to me like the paper talks about how long vaccination has an effect, just how long the Y-shaped receptors are in the blood for. This is the so-manyth research I've seen looking at antibodies rather than memory cells. I'd be curious why, but either way it's an incomplete way of looking at protection.