Laboratory of Mathematical Sciences, TAKIZAWA

1. Theoretical hadron physics
2. Experimental hadron physics (Belle and Belle II collaborateons)

(1) Meson structure

Using the three-flavor version of the Nmbu-Jona- Lasinio model, we have studied theproperties of the low-lying nonet scalar, pseudoscal;ar, vector and axial-vector mesons.We have especially focused on the effects of the U_A(1) anomaly.

(2) Radiative eta decays

We have studied the eta -> gamma gamma, eta -> gamma mu^- mu^+, eta -> pi^0gamma gamma decays using the three-flavor Nambu-Jona- Lasinio model that includesthe 't Hooft instanton induced interaction. We have found that the eta-meson mass, theeta -> gamma gamma, eta -> gamma mu^- mu^+, eta -> pi^0 gamma gamma decaywidths are in good agreement with the experimental values when the U_A(1) breaking isstrong.

(3) Radiative eta decays

We have studied the eta -> gamma gamma, eta -> gamma mu^- mu^+, eta -> pi^0gamma gamma decays using the three-flavor Nambu-Jona- Lasinio model that includesthe 't Hooft instanton induced interaction. We have found that the eta-meson mass, theeta -> gamma gamma, eta -> gamma mu^- mu^+, eta -> pi^0 gamma gamma decaywidths are in good agreement with the experimental values when the U_A(1) breaking isstrong.

(4) Improved ladder QCD

We have studied the finite quark mass effects of the low-energy QCD using the improvedladder Schwinger-Dyson and Bethe-Salpeter equations which are derived in the mannerconsistent with the vector and axial-vector Ward-Takahashi identities. We have explicitlyshown that the partial conservation of axial-vector current relation holds. Reasonablevalues of the pion mass, the pion decay constant and the quark condensate are obtainedwith a rather large Lambda_QCD. Our results suggest that chiral perturbation isapplicable up to the strange quark mass region.

(5) Eta and eta’ mesic nuclei

We have discussed theoretically the possibility of observing the bound state of the etaand eta' mesons in nuclei. We have applied the NJL model to study the eta and eta'meson properties at finite density and calculate the formation cross sections of the etaand eta' bound states with the Green function method for (gamma, p) reaction. We haveconcluded that we can expect to observe resonance peaks in (gamma, p) spectra for theformation of meson bound states and we can deduce new information on eta and eta'properties at finite density.

(6) Improved ladder QCD

We have studied the finite quark mass effects of the low-energy QCD using the improvedladder Schwinger-Dyson and Bethe-Salpeter equations which are derived in the mannerconsistent with the vector and axial-vector Ward-Takahashi identities. We have explicitlyshown that the partial conservation of axial-vector current relation holds. Reasonablevalues of the pion mass, the pion decay constant and the quark condensate are obtainedwith a rather large Lambda_QCD. Our results suggest that chiral perturbation isapplicable up to the strange quark mass region.

(7) Structure of the X(3872)

In order to understand the structure of the X(3872), the cc^bar charmonium core state whichcouples to the D 0 D^{*0 bar} and D + D^*- molecular states is studied. The strengths of thecouplings between the charmonium state and the hadronic molecular states aredetermined so as to reproduce the observed mass of the the X(3872). The attractionbetween D and D^{* bar} is determined so as to be consistent with the observed Z_b (10610)and Z_b (10650) masses. The isospin symmetry breaking is introduced by the massdifferences of the neutral and the charged D mesons. The structure of the X(3872) wehave obtained is not just a D 0 D^{*0 bar} hadronic molecule but the charmonium-hadronicmolecule hybrid state. It consists of about 6% cc ba charmonium, 69% isoscalar D and D^{* bar}molecule and 26% isovector D and D^{* bar} molecule. This explains many of the observedproperties of the X$(3872), such as the isospin symmetry breaking, the production rate inthe pp ^bar collision, a lack of the existence of the chi_c1 (2P) peak predicted by the quarkmodel, and the absence of the charged X. We further study the effctes of the J/psi rhoand J/psi omega channels with the rho and omega decay widths.

(8) Hadron physics at Belle and Belle II experiments

I belong to the Belle and Belle II collaborations as a member of Nuclear PhysicsConsortium (NPC). We are analyzing Belle data and studies of the hadron properties areon going. As for Belle II experiment, the physics data taking will be started at the end of2018. Our group is now constructing the Central Drift Chamber (CDC). I am a member ofthe Belle II outreach team and taking care of the Belle II Japanese Facebook/Twittersites.

Direct problems

Many kinds of inverse problems have been studied in science and engineering. The Laplaceequation is a famous governing equation of many physical phenomena as well as a mathematicallybasic equation. We consider the Cauchy problem of the Laplace equation. This is a well knowninverse boundary value problem, where for given boundary data as a priori information on a partof the boundary of a domain, we identify unknown boundary value on the rest of the boundary.This problem can be regarded as mathematical models of inverse problem of electrocardiographyin medical science as well as the defect identification for the corrosion of a blast furnace bythermal observations.

We consider a problem with noisy Cauchy data, since the Cauchy data usually contain noisesdue to observation errors. In past years, some researchers have numerically solved the Cauchyproblem by various methods. However, to our knowledge, their methods, which are the finitedifference method or the spectral collocation method in multiple-precision arithmetic, cannotsuccessfully solve a problem whose exact solution has singular points outside the computationaldomain. We use the method of fundamental solutions (MFS) to directly discretize the Cauchyproblem of the Laplace equation. The Cauchy problem is an ill-posed problem, that is, the solutiondoes not depend continuously on the given boundary data. Namely, a small noise contained in thegiven Cauchy data has a possibility to affect sensitively on the accuracy of the solution.Consequently, we use the Tikhonov regularization to avoid the sensitivity and to obtain a stableregularized solution. The regularized solution depends on a regularization parameter. Then, we usethe L-curve suggested by Hansen for determining a suitable regularization parameter to obtain abetter regularized solution. We numerically indicate that a suitable regularized solution obtainedby the L-curve is optimal in the sense that the error between the regularized solution and the exactone is minimized. We respectively show the accuracy and the optimal regularization parameteragainst a noise level. We also mention influence of the total numbers of the source and thecollocation points, which are used in the MFS, on accuracy. Based on our numerical experiments,it is concluded that the numerical method proposed in the study is effective for a problem whosesolution has singular points outside the computational domain. No multiple-precision arithmetic isrequired to obtain a good solution. It is noteworthy that such kind of problems can alsosuccessfully be solved. Moreover, the method is applicable for solving a problem in a complicateddomain with the Cauchy data that contains large noises even with a noise level of 10%.