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Koji Hashimoto | Osaka univ. | Japan

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Learning lattice.

Yesterday, I spent a whole day to learn a part of history of lattice QCD and brand-new results of baryon spectroscopy in lattice QCD simulations. My colleagues who are specialists of the lattice study kindly explained all of what I asked them.

The motivation came from two parts. The first one was the seminar of the day before yesterday, on a new result on a phase structure of QCD, with use of strong coupling expansion of lattice QCD. It was so interesting and I wanted to know how much this kind of strong coupling expansion makes sense in study, and my friend explained me also its histrical perspective. It was truely instructive for me, because I am not familiar with the lattice QCD and I am lack of the sense.

The second motivation just came eventually when I talked about my recent results on holographic QCD to my colleagues in RIKEN. What we computed in our paper is a baryon mass shift due to the change of the quark mass, in QCD. We used gauge/string duality to compute this, in the large Nc limit and large ‘t Hooft coupling limit. Anyway we got some number for the shift, our result is the shift delta M for nucleon is about 4 times pion mass squared. I told this story to my colleague, and he eventually answered that he has been involved with a Japanese lattice QCD collaboration and submitted a paper very recently, on this nucleon mass shift! And the result of this lattice QCD which has 158 MeV for the pion mass which is the closest ever in 2+1 dynamiical unquenched QCD, is in fact, 4 times pion mass squared! I was so surprised that this new technology of holographic QCD is really successful, although I don’t know why it is so successful, since we are working in large Nc and large ‘tHooft coupling expansion…..

He told me some references and I read those hep-lat papers, and I found another coincidence : We predicted that the mass shift for Delta excitation is the same as that of the nucleon, and in one paper of lattice QCD, they computed it and showed that it is again 4 times pion mass squared! So our prediction for the Delta is again confirmed. It was so exciting. Wow. Sring theory really helps real physics (in this case, hadron physics), in some sense.

I hope in the near future there appear some lattice results on the mass shift for the Roper and N(1440) S11 excitations fit with heavy baryon chiral perturbation theory. We, string theorists,  have predictions!

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