As my readers could know, I have had a paper written in collaboration with Marco Ruggieri (see here). Marco is currently working at Yukawa Institute in Kyoto (Japan). The great news is that our paper has been accepted for publication on Physical Review D. I am really happy for this very good result of a collaboration that I hope will endure. Currently, we are working on a proof of existence of the critical endpoint for QCD using the Nambu-Jona-Lasinio model. This is an open question that has serious difficulties to get an answer also for a fundamental problem encountered on the lattice: The so-called sign problem. So, a mathematical proof will make a breakthrough in the field with the possibility to be experimentally confirmed at laboratory facilities.
Marco himself proposed a novel approach to get a proof of the critical endpoint to bypass the sign problem (see here).
So, I hope to have had the chance to transmit to my readership the excitement of this line of research and how it is strongly entangled with the understanding of low-energy QCD and the more deep question of the mass gap in the Yang-Mills theory. Surely, I will keep posting on this. Just stay tuned!
Marco Frasca, & Marco Ruggieri (2011). Magnetic Susceptibility of the Quark Condensate and Polarization from
Chiral Models arXiv arXiv: 1103.1194v1
Philippe de Forcrand (2010). Simulating QCD at finite density PoS (LAT2009)010, 2009 arXiv: 1005.0539v2