Heavy Quarks on the Lattice

Lattice quantum chromodynamics provides first principles calculations for hadrons containing heavy quarks -- charm and bottom quarks. Their mass spectra, decay rates, and some hadronic matrix elements can be calculated on the lattice in a model independent manner. In this review, we introduce the effective theories that treat heavy quarks on the lattice. We summarize results on the heavy quarkonium spectrum, which verify the validity of the effective theory approach. We then discuss applications to $B$ physics, which is the main target of the lattice theory of heavy quarks. We review progress in lattice calculations of the $B$ meson decay constant, the $B$ parameter, semi-leptonic decay form factors, and other important quantities.)Comment: 38 pages, Latex, ar.sty, 7 figures. A review based on the work until February 2004. To appear in the Annual Review of Nuclear & Particle Science, Vol. 5

Phase diagram of QCD chaos in linear sigma models and holography

Measuring chaos of QCD-like theories is a challenge for formulating a novel characterization of quantum gauge theories. We define a chaos phase diagram of QCD allowing us to locate chaos in the parameter space of energy of homogeneous meson condensates and the QCD parameters such as pion/quark mass. We draw the chaos phase diagrams obtained in two ways: first, by using a linear sigma model, varying parameters of the potential, and second, by using the D4/D6 holographic QCD, varying the number of colors $N_c$ and the 't Hooft coupling constant $\lambda$. A scaling law drastically simplifies our analyses, and we discovered that the chaos originates in the maximum of the potential, and larger $N_c$ or larger $\lambda$ diminishes the chaos.Comment: 25 pages, 7 figure

GRB 100418A: a Long GRB without a Bright Supernova in a High-Metallicity Host Galaxy

We present results of a search for a supernova (SN) component associated with GRB 100418A at the redshift of 0.624. The field of GRB 100418A was observed with FOCAS on Subaru 8.2m telescope under a photometric condition (seeing 0.3"-0.4") on 2010 May 14 (UT). The date corresponds to 25.6 days after the burst trigger (15.8 days in the restframe). We did imaging observations in V, Rc, and Ic bands, and two hours of spectrophotometric observations. We got the resolved host galaxy image which elongated 1.6" (= 11 kpc) from north to south. No point source was detected on the host galaxy. The time variation of Rc-band magnitude shows that the afterglow of GRB 100418A has faded to Rc \sim > 24 without SN like rebrightening, when we compare our measurement to the reports in GCN circulars. We could not identify any SN feature such as broad emission-lines or bumps in our spectrum. Assuming the SN is fainter than the 3{\sigma} noise spectrum of our observation, we estimate the upper limit on the SN absolute magnitude MIc,obs > -17.2 in observer frame Ic-band. This magnitude is comparable to the faintest type Ic SNe. We also estimate host galaxy properties from the spectrum. The host galaxy of GRB 100418A is relatively massive (log M_{star}/M_{sun} = 9.54) compared to typical long GRB host galaxies, and has 12+log(O/H) = 8.75.Comment: 8 pages, 8 figures, accepted for publication in PASJ, changed figure 8 and related tex