# Progress of Theoretical and Experimental Physics

Online ISSN: 2050-3911
Publications
We report a high-statistics measurement of the differential cross section of the process gamma gamma --> K^0_S K^0_S in the range 1.05 GeV <= W <= 4.00 GeV, where W is the center-of-mass energy of the colliding photons, using 972 fb^{-1} of data collected with the Belle detector at the KEKB asymmetric-energy e^+ e^- collider operated at and near the Upsilon-resonance region. The differential cross section is fit by parameterized S-, D_0-, D_2-, G_0- and G_2-wave amplitudes. In the D_2 wave, the f_2(1270), a_2(1320) and f_2'(1525) are dominant and a resonance, the f_2(2200), is also present. The f_0(1710) and possibly the f_0(2500) are seen in the S wave. The mass, total width and product of the two-photon partial decay width and decay branching fraction to the K bar{K} state Gamma_{gamma gamma}B(K bar{K}) are extracted for the f_2'(1525), f_0(1710), f_2(2200) and f_0(2500). The destructive interference between the f_2(1270) and a_2(1320) is confirmed by measuring their relative phase. The parameters of the charmonium states chi_{c0} and chi_{c2} are updated. Possible contributions from the chi_{c0}(2P) and chi_{c2}(2P) states are discussed. A new upper limit for the branching fraction of the P- and CP-violating decay channel eta_c --> K^0_S K^0_S is reported. The detailed behavior of the cross section is updated and compared with QCD-based calculations.

With the use of two kinds of boson operators, a new boson representation of the su(2)-algebra is proposed. The basic idea comes from the pseudo su(1,1)-algebra recently given by the present authors. It forms a striking contrast to the Schwinger boson representation of the su(2)-algebra which is also based on two kinds of bosons. This representation may be suitable for describing time-dependence of the system interacting with the external environment in the framework of the thermo field dynamics formalism, i.e., the phase space doubling. Further, several deformations related to the su(2)-algebra in this boson representation are discussed. On the basis of these deformed algebra, various types of time-evolution of a simple boson system are investigated.

A pseudo su(1,1)-algebra is formulated as a possible deformation of the Cooper pair in the su(2)-algebraic many-fermion system. With the aid of this algebra, it is possible to describe the behavior of individual fermions which are generated as the result of interaction with the external environment. The form presented in this paper is a generalization of a certain simple case developed recently by the authors. The basic idea follows the su(1,1) algebra in the Schwinger boson representation for treating energy transfer between the harmonic oscillator and the external environment. The Hamiltonian is given following the idea of phase space doubling in the thermo-field dynamics formalism, and the time-dependent variational method is applied to this Hamiltonian. Its trial state is constructed in the frame deformed from the BCS-Bogoliubov approach to superconductivity. Several numerical results are shown.

We report the measurement of differential cross sections for $\omega$ and $\eta'$ photoproduction from protons at backward angles ($-1.0<\cos\Theta_{C.M}^{X}<-0.8$) using linearly polarized photons at $E_{\gamma}=$$1.5-3.0$ GeV. Differential cross sections for $\omega$ mesons are larger than the predicted $u$-channel contribution in the energy range $2.0\leq\sqrt{s}\leq2.4$ GeV. The differential cross sections for $\omega$ and $\eta'$ mesons become closer to the predicted $u$-channel contribution at $\sqrt{s}>2.4$ GeV. A bump structure in the $\sqrt{s}$ dependence of the differential cross sections for $\eta'$ mesons was observed at $\sqrt{s}\sim$2.35 GeV.

We have observed a "$K^-pp$"-like structure in the $d(\pi^+,K^+)$ reaction at 1.69 GeV/$c$. In this reaction $\Lambda(1405)$ hyperon resonance is expected to be produced as a doorway to form the $K^-pp$ through the $\Lambda^*p\rightarrow K^-pp$ process. However, most of the produced $\Lambda(1405)$'s would escape from deuteron without secondary reactions. Therefore, coincidence of high-momentum ($>$ 250~MeV/$c$) proton(s) in large emission angles ($39^\circ<\theta_{lab.}<122^\circ$) was requested to enhance the signal-to-background ratio. A broad enhancement in the proton coincidence spectra are observed around the missing-mass of 2.27 GeV/$c^2$, which corresponds to the $K^-pp$ binding energy of 95 $^{+18}_{-17}$ (stat.) $^{+30}_{-21}$ (syst.) MeV and the width of 162 $^{+87}_{-45}$ (stat.) $^{+66}_{-78}$ (syst.) MeV.

We have measured an inclusive missing-mass spectrum of the $d(\pi^+, K^+)$ reaction at the pion incident momentum of 1.69 GeV/$c$ at the laboratory scattering angles between 2$^\circ$ and 16$^\circ$ with the missing-mass resolution of 2.7 MeV/$c^2$ (FWHM). In this Letter, we first try to understand the spectrum as a simple quasi-free picture based on several known elementary cross sections, considering the neutron/proton Fermi motion in deuteron. While gross spectrum structures are well understood in this picture, we have observed two distinct deviations; one peculiar enhancement at 2.13 GeV/$c^2$ is due to the $\Sigma N$ cusp, and the other notable feature is a shift of a broad bump structure, mainly originating from hyperon resonance productions of $\Lambda(1405)$ and $\Sigma(1385)^{+/0}$, by about 22.4 $\pm$ 0.6 MeV/$c^2$ toward the low-mass side.

We address a question whether the recently observed Higgs mass $M_{H} = 126$ GeV, of the order of the weak scale $M_{W}$, is calculable as a finite value in the scnenario of gauge-Higgs unification. In the scenario formulated on a flat 5-dimensional space-time, the Higgs mass is calculable, being protected under the quantum correction by gauge invariance, though the predicted Higgs mass is generally too small compared with $M_{W}$. In the 6-dimensional SU(3) model, however, a suitable orbifolding is known to lead to a mass of the order of $M_{W}$: $M_{H} = 2M_{W}$ at the tree level, which has some similarity to the corresponding prediction by the MSSM, $M_{H}$ leq (cos beta) $M_{Z}$. We demonstrate first by a general argument and secondly by explicit calculations that, even though the quantum correction to the quartic self-coupling of the Higgs field is UV-divergent, its deviation from that of $g^{2}$ is calculable, and therefore two observables, $M_{H}^{2}$ and Delta equiv $(M_{H}/2M_{W})^{2}-1$, are both calculable in the gauge-Higgs unification scenario. The implication of the precise value 126 GeV to the compactification scale and the bulk mass of the matter field in our model is also discussed.

In this paper, we analyse the hadronic decay of B to J a1(1260) in pertubative QCD approach (pQCD), where a1(1260) is a axial-vector meson and J{psi} is a vector meson.

A search for inelastic scattering of weakly interacting massive particles (WIMPs) on the isotope $^{129}$Xe was done in data taken with the single-phase liquid-xenon detector XMASS at the Kamioka Observatory. Using a restricted volume containing 41 kg of liquid xenon at the very center of our detector, we observed no significant excess of events in 165.9 live days of data. Our background reduction allowed us to derive our limits without explicitly subtracting the remaining events that are compatible with background expectations. As an example, we derive for a 50 GeV WIMP an upper limit of 3.2 pb at the 90% confidence level for its inelastic cross section on $^{129}$Xe nuclei.

We propose to use the complex-range Gaussian basis functions, {r^l e^{-(1 \pm i\omega)(r/r_n)^2}Y_{lm}(\hat{r}); r_n in a geometric progression}, in the calculation of three-body resonances with the complex-scaling method (CSM) in which use is often made of the real-range Gaussian basis functions, {r^l e^{-(r/r_n)^2}Y_{lm}(\hat{r})}, that are suitable for describing the short-distance structure and the asymptotic decaying behavior of few-body systems. The former basis set is more powerful than the latter when describing the resonant and nonresonant continuum states with highly oscillating amplitude at large scaling angles \theta. We applied the new basis functions to the CSM calculation of the 3\alpha resonances with J=0^+, 2^+ and 4^+ in 12C. The eigenvalue distribution of the complex scaled Hamiltonian becomes more precise and the maximum scaling angle becomes drastically larger (\theta_{max}=16 deg. \arrow 36 deg.) than those given by the use of the real-range Gaussians. Owing to these advantages, we were able to confirm the prediction by Kurokawa and Kato [Phys. Rev. C 71, 021301 (2005)] on the appearance of the new broad 0^+_3 state; we show it as an explicit resonance pole isolated from the 3$\alpha$ continuum.

Recent CLAS data for the pi Sigma invariant mass distributions (line-shapes) in the gamma p -> K^+ pi Sigma reaction are theoretically investigated. The line-shapes have peaks associated with the Lambda(1405) excitation. Our model consists of gauge invariant photo-production mechanisms, and the chiral unitary model that gives the rescattering amplitudes where Lambda(1405) is contained. It is found that, while the pi Sigma line-shape data in the Lambda(1405) region are successfully reproduced by our model for all the charge states, the production mechanism is not so simple that we need to introduce parameters associated with short-range dynamics to fit the data. Our detailed analysis suggests that the nonresonant background contribution is not negligible, and its sizable effect shifts the Lambda(1405) peak position by several MeV. We also analyze the data using a Breit-Wigner amplitudes instead of those from the chiral unitary model. We find that the fitted Breit-Wigner parameters are closer to the higher pole position for Lambda(1405) of the chiral unitary model. This work sets a starting point for a fuller analysis in which line-shape as well as K^+ angular distribution data are simultaneously analyzed for extracting Lambda(1405) pole(s).

We study 6d N=(2,0) theory of type SU(N) compactified on Riemann surfaces with finite area, including spheres with fewer than three punctures. The Higgs branch, whose metric is inversely proportional to the total area of the Riemann surface, is discussed in detail. We show that the zero-area limit, which gives us a genuine 4d theory, can involve a Wigner-Inonu contraction of global symmetries of the six-dimensional theory. We show how this explains why subgroups of SU(N) can appear as the gauge group in the 4d limit. As a by-product we suggest that half-BPS codimension-two defects in the six-dimensional (2,0) theory have an operator product expansion whose operator product coefficients are four-dimensional field theories.

We define supersymmetric Yang–Mills theory on an arbitrary 2D lattice (polygon decomposition) while preserving one supercharge. When a smooth Riemann surface $\Sigma _g$ with genus $g$ emerges as an appropriate continuum limit of the generic lattice, the discretized theory becomes a topologically twisted ${{\mathcal N}}=(2,2)$ supersymmetric Yang–Mills theory on $\Sigma _g$. If we adopt the usual square lattice as a special case of the discretization, our formulation is identical with Sugino's lattice model. Although the tuning of parameters is generally required while taking the continuum limit, the number of necessary parameters is at most two because of the gauge symmetry and the supersymmetry. In particular, we do not need any fine-tuning if we arrange the theory so as to possess an extra global $U(1)$ symmetry ($U(1)_{R}$ symmetry), which rotates the scalar fields.

It is known that the gauge field and its composite operators evolved by the Yang–Mills gradient flow are ultraviolet (UV) finite without any multiplicative wave function renormalization. In this paper, we prove that the gradient flow in the 2D $O(N)$ non-linear sigma model possesses a similar property: The flowed $N$-vector field and its composite operators are UV finite without multiplicative wave function renormalization. Our proof in all orders of perturbation theory uses a $(2+1)$-dimensional field theoretical representation of the gradient flow, which possesses local gauge invariance without gauge field. As an application of the UV finiteness of the gradient flow, we construct the energy–momentum tensor in the lattice formulation of the $O(N)$ non-linear sigma model that automatically restores the correct normalization and the conservation law in the continuum limit.

The gradient flow equation in the two-dimensional $O(N)$ non-linear sigma model with lattice regularization is solved in the leading order of the $1/N$ expansion. By using this solution, we analytically compute the thermal expectation value of a lattice energy--momentum tensor defined through the gradient flow. The expectation value reproduces thermodynamic quantities obtained by the standard large~$N$ method. This analysis confirms that the above lattice energy--momentum tensor restores the correct normalization automatically in the continuum limit, in a system with a non-perturbative mass gap.

We argue that 6d N=(2,0) theory on S^1 x S^3 x C_2 reduces to the 2d q-deformed Yang-Mills on C_2 at finite area, as a small extension to the result of Gadde, Rastelli, Razamat and Yan. This is done by computing the partition function on S^1 x S^3 of 4d N=2 supersymmetric non-linear sigma model on T^*G_C, which gives the propagator of the 2d Yang-Mills.

We study the parameter dependence of the internal structure of resonance states by formulating Complex two-dimensional (2D) Matrix Model, where the two dimensions represent two-levels of resonances. We calculate a critical value of the parameter at which "nature transition" with character exchange occurs between two resonance states, from the viewpoint of geometry on complex-parameter space. Such critical value is useful to know the internal structure of resonance states with variation of the parameter in the system. We apply the model to analyze the internal structure of hadrons with variation of the color number Nc from infinity to a realistic value 3. By regarding 1/Nc as the variable parameter in our model, we calculate a critical color number of nature transition between hadronic states in terms of quark-antiquark pair and mesonic molecule as exotics from the geometry on complex-Nc plane. For the large-Nc effective theory, we employ the chiral Lagrangian induced by holographic QCD with D4/D8/D8-bar multi-D brane system in the type IIA superstring theory.

The $X$(3872) formation from the $B$-decay and its decay into the two-meson state are investigated by employing a coupled-channel two-meson model with the $c{\bar c}$ state. This two-meson state consists of the $D^0{\bar D}^*{}^0$, $D^+D^{*-}$, $J/\psi\rho$, and $J/\psi\omega$ channels. The energy-dependent decay widths of the $\rho$ and $\omega$ mesons are taken into account. The interaction between $D$ and ${\bar D}^*$ mesons are taken to be consistent with a lack of the $B{\bar B}^*$ bound state. The $c{\bar c}$-$D{\bar D}^*$ coupling is taken as a parameter to fit the $X$(3872) peak energy. The coupling between the $D{\bar D}^*$ and $J/\psi\rho$ or the $D{\bar D}^*$ and $J/\psi\omega$ channels is determined with the help of a quark model. It is found that the $J/\psi\rho$ and $J/\psi\omega$ peaks appear around the $D^0{\bar D}^*{}^0$ threshold under the reasonable assumptions and that their peaks are very narrow when they appear. It is also found that the large decay width of the $\rho$ meson enhances the isospin $I=1$ component in the decay spectra in the $X$(3872) energy region. The size of the $J/\psi\pi^3$ peak we calculated is 1.29-2.38 times as large as that of the $J/\psi\pi^2$. The isospin symmetry breaking in the present model comes from the difference in the charged and neutral $D$ and $D^*$ meson masses, which seems to give a sufficiently large isospin mixing. Also, the results suggest that one can judge whether the $X$(3872) is a bound state by looking into the ratio of the partial decay width of $X$(3872) in the $D^0{\bar D}^*{}^0$ channel to that in the $J/\psi\rho$ channel. Moreover, the relative importance of the $c{\bar c}$-$D{\bar D}^*$ coupling in the $X$(3872) can be evaluated from the ratio of the transfer strength of the $D^+D^{*-}$ to that of the $D^0{\bar D}^*{}^0$ as well as from the ratio of the $J/\psi\pi^3$ peak size to that of the $J/\psi\pi^2$.

In order to understand the structure of X(3872), the $c\bar {c}$ charmonium core state that couples to the $D^0 \bar {D}^{\ast 0}$ and $D^+ D^{\ast -}$ molecular states is studied. The strengths of the couplings between the charmonium state and the hadronic molecular states are determined so as to reproduce the observed mass of X(3872). The attraction between D and $\bar {D}^{\ast }$ is determined so as to be consistent with the observed $Z_b^{\pm ,0}$(10 610) and $Z_b^{\pm ,0}$(10 650) masses. Isospin symmetry breaking is introduced by the mass differences between the neutral and charged D mesons. The structure of X(3872) that we have obtained is not just a $D^0 \bar {D}^{\ast 0}$ hadronic molecule but a charmonium–hadronic molecule hybrid state. It consists of about 6% $c\bar {c}$ charmonium, 69% isoscalar $D \bar {D}^\ast$ molecule, and 26% isovector $D \bar {D}^\ast$ molecule. This explains many of the observed properties of X(3872), such as isospin symmetry breaking, the production rate in the $p \bar {p}$ collision, the non-existence of the $\chi _{c1}(2P)$ peak predicted by the quark model, and the absence of charged X. The same picture can be applied to other heavy two-meson S-wave systems, where the states predicted by the quark model are not observed above the thresholds.

We calculate the widths of the hidden charm decay $J/\psi\omega$ of two charmonium-like states $X(3915)$ and $Z(3930)$ for $\chi_{c0}^\prime(2P)$ and $\chi_{c2}^\prime (2P)$ assignments, respectively. Our results indicate that the decay width of $Z(3930)\to J/\psi\omega$ is $2\sim 3$ orders smaller than that of $X(3915)\to J/\psi\omega$, which further explains why only one structure $X(3915)$ has been observed in the $J/\psi\omega$ invariant mass spectrum for the process $\gamma\gamma\to J/\psi\omega$.

An Abelian gauge theory with Chern-Simons term is investigated for a four-component Dirac fermion in 1+2 dimensions. The Ball-Chiu (BC) vertex function is employed to modify the rainbow-ladder approximation for the Schwinger-Dyson (SD) equation. We numerically solve the SD equation and show the gauge dependence for the resulting phase boundary for the parity and the chiral symmetry.

In contrast to the non-relativistic approaches, three-dimensional (3D) mesh calculations for the {\it relativistic} density functional theory have not been realized because of the challenges of variational collapse and fermion doubling. We overcome these difficulties by developing a novel method based on the ideas of Wilson fermion as well as the variational principle for the inverse Hamiltonian. We demonstrate the applicability of this method by applying it to $^{16}$O, $^{24}$Mg, and $^{28}$Si nuclei, providing detailed explanation on the formalism and verification of numerical implementation.

We conjecture that a new class of 3d N=2 theories are associated with a quiver Q and a mutation sequence m on it. We define the cluster partition function from the pair (Q, m), and this partition function coincides with the S^3_b partition function of the associated 3d N=2 theory T[(Q,m)]. Our formalism includes the case where 3d N=2 theories arise from the compactification of the 6d (2,0) A_{N-1} theory on a large class of 3-manifolds M, including complements of arbitrary links in S^3. In this case the quiver is defined from a 2d ideal triangulation, the mutation sequence represents an element of the mapping class group, and the 3-manifold is equipped with a canonical ideal triangulation. Our partition function coincides with that of the holomorphic part of the SL(N) Chern-Simons partition function on M; when N=2 and M is hyperbolic, the partition function reproduces the gluing conditions of ideal hyperbolic tetrahedra in the semiclassical limit.

We study N=2 supersymmetric gauge theories on squashed 3-sphere and S^1xS^2. Recent studies have shown that the partition functions in a class of N=2 theories have factorized representations in terms of vortex and anti-vortex partition functions by explicitly evaluating matrix integrals obtained by Coulomb branch localization. We directly derive this structure by performing Higgs branch localization. It turns out that more general N=2 theories have this factorization property. We also discuss the factorization of supersymmetric Wilson loop.

The coexistence of various low-lying deformed states in $^{42}$Ca and $\alpha$--$^{38}$Ar correlations in those deformed states have been investigated using deformed-basis antisymmetrized molecular dynamics. Wave functions of the low-lying states are obtained via parity and angular momentum projections and the generator coordinate method (GCM). Basis wave functions of the GCM calculation are obtained via energy variations with constraints on the quadrupole deformation parameter $\beta$ and the distance between $\alpha$ and $^{38}$Ar clusters. The rotational band built on the $J^\pi = 0_2^+$ (1.84 MeV) state as well as the $J^\pi = 0_3^+$ (3.30 MeV) state are both reproduced. The coexistence of two additional $K^\pi = 0^+$ rotational bands is predicted; one band is shown to be built on the $J^\pi = 0_3^+$ state. Members of the ground-state band and the rotational band built on the $J^\pi = 0_3^+$ state contain $\alpha$--$^{38}$Ar cluster structure components.

An exponentially large extra dimension can be naturally realized by the Casimir energy and the gaugino condensation in 5D supersymmetric theory. The model does not require any hierarchies among the 5D parameters. The key ingredient is an additional modulus other than the radion, which generically exists in 5D supergravity. SUSY is broken at the vacuum, which can be regarded as the Scherk-Schwarz SUSY breaking. We also analyze the mass spectrum and discuss some phenomenological aspects. © 2014 The Author(s) 2014. Published by Oxford University Press on behalf of the Physical Society of Japan.

Supersymmetric gauge theories in five dimensions often exhibit less symmetry than the ultraviolet fixed points from which they flow. The fixed points might have larger flavor symmetry or they might even be secretly six-dimensional theories on S^1. Here we provide a simple criterion when such symmetry enhancement in the ultraviolet should occur, by a direct study of the fermionic zero modes around one-instanton operators.

We describe a method to determine the anomaly polynomials of general 6d $\mathcal{N}=(2,0)$ and $\mathcal{N}=(1,0)$ SCFTs, in terms of the anomaly matching on their tensor branches. This method is almost purely field theoretical, and can be applied to all known 6d SCFTs. We demonstrate our method in many concrete examples, including $\mathcal{N}=(2,0)$ theories of arbitrary type and the theories on M5 branes on ALE singularities, reproducing the $N^3$ behavior. We check the results against the anomaly polynomials computed M-theoretically via the anomaly inflow.

This is a status report on our endeavor to reveal the mechanism of core-collapse supernovae (CCSNe) by large-scale numerical simulations. Multi-dimensionality of the supernova engine, general relativistic magnetohydrodynamics, energy and lepton number transport by neutrinos emitted from the forming neutron star as well as nuclear interactions there, are all believed to play crucial roles in repelling infalling matter and producing energetic explosions. These ingredients are nonlinearly coupled with one another in the dynamics of core-collapse, bounce, and shock expansion. Serious quantitative studies of CCSNe hence make extensive numerical computations mandatory. Since neutrinos are neither in thermal nor in chemical equilibrium in general, their distributions in the phase space should be computed. This is a six dimensional (6D) neutrino transport problem and quite a challenge even for those with an access to the most advanced numerical resources such as the "K computer". To tackle this problem, we have embarked on multi-front efforts. In particular we report in this paper our recent progresses in the treatments of multi-dimensional (multi-D) radiation-hydrodynamics. We are currently proceeding on two different paths to the ultimate goal; in one approach we employ an approximate but highly efficient scheme for neutrino transport and treat 3D hydrodynamics and/or general relativity rigorously; some neutrino-driven explosions will be presented and comparisons will be made between 2D and 3D models quantitatively; in the second approach, on the other hand, exact but so far Newtonian Boltzmann equations are solved in two and three spatial dimensions; we will show some demonstrative test simulations. We will also address the perspectives of exa-scale computations on the next generation supercomputers.

We propose a new next-to-minimal supersymmetric standard model (NMSSM) which is on a six-dimensional spacetime compactified on a $T^2/Z_3$ orbifold. In this model, three gauge singlet fields $N, S_1$ and $S_2$ in addition to the minimal supersymmetric standard model (MSSM) fields are introduced. These fields are localized at some fixed points except for the singlet $N$ and the gauge fields. The $\mu$ parameter is provided from the vacuum expectation value (vev) of $N$. The $F$ terms get vevs simultaneously, and the gauginos mediate the supersymmetry breaking to the MSSM sector. Both of these parameters are strongly suppressed due to the profile of $N$. Thus these parameters induced from those of the order of the so-called GUT scale can become close to the electroweak scale without unnatural fine tuning.

We study the shell and alpha cluster structures in the ground and excited states of 8Be in terms of the tensor-optimized shell model (TOSM). In TOSM, the tensor correlation is optimized in the full space of 2p2h configurations involving high-momentum components. The short-range correlation is treated with the unitary correlation operator method (UCOM). We use the effective interaction based on the bare nucleon-nucleon interaction AV8$^\prime$. The 8Be states consist of two groups of ground band states and highly excited states with the isospin T=0 and T=1. It is found that the tensor contributions of the ground band states are stronger than the highly excited states and that the kinetic energies and the central contributions of the ground band states are almost twice the 4He values. These features suggest two-alpha clustering for the ground band states in 8Be. We also estimate the correlation energy of the $\alpha$ clustering using the alpha cluster model. In the highly excited states, the calculated spectrum in TOSM reproduces the experimental level order and the relative energies of each level. This agreement suggests that those states can be interpreted as shell-like states. The level order is found to be sensitive to the presence of the tensor force in comparison with the results using the Minnesota effective interaction without the tensor force. It is also found that the tensor contributions in the T=0 states are stronger than the T=1 states, which is consistent with the state dependence of the tensor force.

In the previous paper, we have shown that $R_1\equiv\frac{\Gamma_{n \rightarrow \pi^0 + \nu^c}}{\Gamma_{p \rightarrow \pi^0 + e^c}}$ and $R_2\equiv\frac{\Gamma_{p \rightarrow K^0 + \mu^c}}{\Gamma_{p \rightarrow \pi^0 + e^c}}$ can identify the grand unification group $SU(5)$, $SO(10)$, or $E_6$ in typical anomalous $U(1)_A$ supersymmetric (SUSY) grand unified theory (GUT) in which nucleon decay via dimension-6 operators becomes dominant. When $R_1 > 0.5$ the grand unification group is not $SU(5)$, while when $R_1 > 1$ the grand unification group is $E_6$. Moreover, $R_2 > 0.3$ $E_6$ is implied. Main ambiguities come from the diagonalizing matrices for quark and lepton mass matrices in this calculation once we fix the vacuum expectation values of GUT Higgs bosons. In this paper, we calculate $R_1$ and $R_2$ in $E_6\times SU(2)_F$ SUSY GUT with anomalous $U(1)_A$ gauge symmetry, in which realistic quark and lepton masses and mixings can be obtained though the flavor symmetry $SU(2)_F$ constrains Yukawa couplings at the GUT scale. The ambiguities of Yukawa couplings are expected to be reduced. We show that the predicted region for $R_1$ and $R_2$ is more restricted than in the $E_6$ model without $SU(2)_F$ as expected. Moreover, we re-examine the previous claim for the identification of grand unification group with $100$ times more model points ($10^6$ model points), including $E_6 \times SU(2)_F$ model.

We show that the sizable $D$-term contributions to the sfermion mass spectrum can be signatures of a certain grand unified theory (GUT), $E_6\times SU(2)_F\times U(1)_A$ GUT. Note that these $D$-term contributions destroy the degeneracy of sfermion masses among different generations in this model. This is different from previous works, which have argued for the $D$-term contributions, which destroy the degeneracy of masses only between sfermions with different quantum charges, as a signature of GUT with a larger rank unification group. Such $D$-terms are strongly constrained by the flavor-changing neutral current processes if the SUSY breaking scale is the weak scale. However, in $E_6\times SU(2)_F\times U(1)_A$, a natural SUSY-type sfermion mass spectrum is obtained, and if the masses of ${{\bf{10}}}_3$ sfermions are larger than $O(1\,{\rm TeV})$ to realize the 126 GeV Higgs and the other sfermion masses are $O(10\,{\rm TeV})$, then a sizable $D$-term contribution is allowed. If these $D$-terms can be observed in future experiments, like the 100 TeV proton collider or muon collider, we may confirm the $E_6\times SU(2)_F\times U(1)_A$ GUT.

The WHOT-QCD Collaboration is pushing forward a series of lattice studies of QCD at finite temperatures and densities using improved Wilson quarks. Because Wilson-type quarks require more computational resources than the more widely adopted staggered-type quarks, various theoretical and computational techniques have to be developed and applied. In this paper, we introduce the fixed-scale approach armed with the T-integration method, the Gaussian method based on the cumulant expansion, and the histogram method combined with the reweighting technique. Adopting these methods, we have carried out the first study of finite-density QCD with Wilson-type quarks and the first calculation of the equation of state with 2+1 flavors of Wilson-type quarks. We present results of these studies and discuss perspectives towards a clarification of the properties of 2+1 flavor QCD at the physical point, at finite temperatures and densities.

It has recently been argued that atoms and molecules may become good targets of determining neutrino parameters still undetermined, if atomic/molecular process is enhanced by a new kind of coherence. We compute photon energy spectrum rate arising from coherent radiative neutrino pair emission processes of metastable excited states of I$_2$ and its iso-valent molecules, $|Av \rangle \rightarrow |Xv' \rangle + \gamma + \nu_i\nu_j$ and $|A'v \rangle \rightarrow |Xv' \rangle + \gamma + \nu_i\nu_j$ with $\gamma$ an IR photon and $\nu_{i(j)}$ $i(j)-$th neutrino mass eigenstates, and show how fundamental neutrino parameters may be determined. Energies of electronically excited states of I$_2$, including the effect of spin-orbit couplings were calculated by the multiconfigurational second order perturbation (CASPT2) method. Summation over many vibrational levels of intermediate states is fully incorporated. Unlike atomic candidate of a much larger energy difference such as Xe, I$_2$ transitions from a vibrational level $A(v=0)$ to $X(v' = 24)$ give an opportunity of determination of the mass type (Majorana vs Dirac distinction) and determination of Majorana CPV (charge-conjugation parity violating) phases, although the rate is much smaller.

We construct an action for the superconformal Chern-Simons theory with non-Abelian gauge groups in three-dimensional N=3 projective superspace. We propose a Lagrangian given by the product of the function of the tropical multiplet, that represents the N=3 vector multiplet, and the O(-1,1) multiplet. We show how the tropical multiplet is embedded into the O(-1,1) multiplet by comparing our Lagrangian with the Chern- Simons Lagrangian in the N=2 superspace. We also discuss N=4 generalization of the action.

Massless matter fields and non-Abelian gauge fields are localized on domain walls in a (4+1)-dimensional $U(N)_c$ gauge theory with $SU(N)_{L}\times SU(N)_{R}\times U(1)_{A}$ flavor symmetry. We also introduce $SU(N)_{L+R}$ flavor gauge fields and a scalar-field-dependent gauge coupling, which provides massless non-Abelian gauge fields localized on the wall. We find a chiral Lagrangian interacting minimally with the non-Abelian gauge field together with nonlinear interactions of moduli fields as the (3+1)-dimensional effective field theory up to the second order of derivatives. Our result provides a step towards a realistic model building of brane-world scenario using topological solitons.

We classify bions in the Grassmann $Gr_{N_{\rm F},N_{\rm C}}$ sigma model (including the ${\mathbb C}P^{N_{\rm F}-1}$ model) on ${\mathbb R}^{1}\times S^{1}$ with twisted boundary conditions. We formulate these models as $U(N_{\rm C})$ gauge theories with $N_{\rm F}$ flavors in the fundamental representations. These theories can be promoted to supersymmetric gauge theories and, further, can be embedded into D-brane configurations in type-II superstring theories. We focus on specific configurations composed of multiple fractional instantons, termed neutral bions and charged bions, which are identified as perturbative infrared renormalons by Ünsal and his collaborators [G. V. Dunne and M. Ünsal, J. High Energy Phys. 1211, 170 (2012); G. V. Dunne and M. Ünsal, Phys. Rev. D 87, 025015 (2013)]. We show that D-brane configurations, as well as the moduli matrix, offer a very useful tool to classify all possible bion configurations in these models. In contrast to the ${\mathbb C}P^{N_{\rm F}-1}$ model, there exist Bogomol’nyi–Prasad–Sommerfield (BPS) fractional instantons with topological charges greater than unity (of order $N_{\rm C}$) that cannot be reduced to a composite of an instanton and fractional instantons. As a consequence, we find that the Grassmann sigma model admits neutral bions made of BPS and anti-BPS fractional instantons, each of which has a topological charge greater (less) than one (minus one), that are not decomposable into an instanton–anti-instanton pair and the rest. The ${\mathbb C}P^{N_{\rm F}-1}$ model is found to have no charged bions. In contrast, we find that the Grassmann sigma model admits charged bions, for which we construct exact non-BPS solutions of the field equations.

We study the partition function of the N=6 supersymmetric U(N_1)_k x U(N_2)_{-k} Chern-Simons-matter (CSM) theory, also known as the ABJ theory. For this purpose, we first compute the partition function of the U(N_1) x U(N_2) lens space matrix model exactly. The result can be expressed as a product of q-deformed Barnes G-function and a generalization of multiple q-hypergeometric function. The ABJ partition function is then obtained from the lens space partition function by analytically continuing N_2 to -N_2. The answer is given by min(N_1,N_2)-dimensional integrals and generalizes the "mirror description" of the partition function of the ABJM theory, i.e. the N=6 supersymmetric U(N)_k x U(N)_{-k} CSM theory. Our expression correctly reproduces perturbative expansions and vanishes for |N_1-N_2|>k in line with the conjectured supersymmetry breaking, and the Seiberg duality is explicitly checked for a class of nontrivial examples.

We study supersymmetric Wilson loops in the ${\cal N} = 6$ supersymmetric $U(N_1)_k\times U(N_2)_{-k}$ Chern-Simons-matter (CSM) theory, the ABJ theory, at finite $N_1$, $N_2$ and $k$. This generalizes our previous study on the ABJ partition function. First computing the Wilson loops in the $U(N_1) \times U(N_2)$ lens space matrix model exactly, we perform an analytic continuation, $N_2$ to $-N_2$, to obtain the Wilson loops in the ABJ theory that is given in terms of a formal series and only valid in perturbation theory. Via a Sommerfeld-Watson type transform, we provide a nonperturbative completion that renders the formal series well-defined at all couplings. This is given by ${\rm min}(N_1,N_2)$-dimensional integrals that generalize the "mirror description" of the partition function of the ABJM theory. Using our results, we find the maps between the Wilson loops in the original and Seiberg dual theories and prove the duality. In our approach we can explicitly see how the perturbative and nonperturbative contributions to the Wilson loops are exchanged under the duality. The duality maps are further supported by a heuristic yet very useful argument based on the brane configuration as well as an alternative derivation based on that of Kapustin and Willett.

We consider states with large angular momentum to facilitate the study of the M-theory regime of the AdS_4/CFT_3 correspondence. We study the duality between M-theory in AdS_4xS^7/Z_k and the ABJM N=6 Chern-Simons-matter theory with gauge group U(N)xU(N) and level k, taking N large and k of order 1. In this regime the lack of an explicit formulation of M-theory in AdS_4xS^7/Z_k makes the gravity side difficult, while the CFT is strongly coupled and the planar approximation is not applicable. To overcome these difficulties, we focus on states on the gravity side with large angular momentum J>>1 and identify the dual operators in the CFT, thereby establishing the AdS/CFT dictionary in this sector. Natural approximation schemes arise on both sides thanks to the presence of the small parameter 1/J. On the AdS side, we use the matrix model of M-theory on the maximally supersymmetric pp-wave background with matrices of size J/k. A perturbative treatment of this matrix model provides a good approximation to M-theory in AdS_4xS^7/Z_k when N^{1/3}<<J<<N^{1/2}. On the CFT side, we study the theory on S^2xR with magnetic flux J/k. A Born-Oppenheimer type expansion arises naturally for large J in spite of the theory being strongly coupled. The energy spectra on the two sides agree at leading order. This provides a non-trivial test of the AdS_4/CFT_3 correspondence including near-BPS observables associated with membrane degrees of freedom, thus verifying the duality beyond the previously studied sectors corresponding to either BPS observables or the type IIA string regime.

Emission of muonium (μ^+e^-) atoms from a laser-processed aerogel surface into vacuum was studied for the first time. Laser ablation was used to create hole-like regions with diameter of about 270 μm in a triangular pattern with hole separation in the range of 300--500 μm. The emission probability for the laser-processed aerogel sample is at least eight times higher than for a uniform one.

We investigate the initial state of the inflationary universe. In our recent publications, we have shown that requesting the gauge invariance in the local observable universe guarantees the infrared (IR) regularity of loop corrections in a general single clock inflation. Following this study, in this paper, we show that choosing the Euclidean vacuum ensures the gauge invariance in the local universe and hence the IR regularity of loop corrections. It has been suggested that loop corrections to inflationary perturbations may yield secular growth, which can lead to the breakdown of the perturbative analysis in an extremely long-term inflation. The absence of secular growth has been claimed by picking up only the IR contributions, which we think is incomplete because the non-IR modes that are comparable to or smaller than the Hubble scale can potentially contribute to the secular growth. We prove the absence of secular growth without neglecting these non-IR modes to a certain order in the perturbative expansion. We also discuss how the regularity of the n-point function for the genuinely gauge-invariant variable constrains the initial states of the inflationary universe. These results apply in a fully general single-field model of inflation.

Relativistic jets in active galactic nuclei, galactic microquasars, and gamma-ray bursts are widely considered to be magnetohydrodynamically driven by black hole accretion systems, although the conversion mechanism from the Poynting into the particle kinetic energy flux is still open. Recent detailed numerical and analytical studies of global structures of steady, axisymmetric magnetohydrodynamic (MHD) flows with specific boundary conditions have not reproduced as rapid an energy conversion as required by observations. In order to find more suitable boundary conditions, we focus on the flow along a poloidal magnetic field line just inside the external boundary, without treating the transfield force balance in detail. We find some examples of the poloidal field structure and corresponding external pressure profile for an efficient and rapid energy conversion as required by observations, and that the rapid acceleration requires a rapid decrease of the external pressure above the accretion disk. We also clarify the differences between the fast magnetosonic point of the MHD flow and the sonic point of the de Laval nozzle.

The Landau–Lifshitz equation is considered as an approximation of the Abraham–Lorentz–Dirac equation. It is derived from the Abraham–Lorentz–Dirac equation by treating radiation reaction terms as a perturbation. However, while the Abraham–Lorentz–Dirac equation has pathological solutions of pre-acceleration and runaway, the Landau–Lifshitz equation and its finite higher-order extensions are free of these problems. So it seems mysterious that the properties of the solutions of these two equations are so different. In this paper we show that the problems of pre-acceleration and runaway appear when one considers a series of all-order perturbation which we call the Landau–Lifshitz series. We show that the Landau–Lifshitz series diverges in general. Hence a resummation is necessary to obtain a well-defined solution from the Landau–Lifshitz series. This resummation leads the pre-accelerating and the runaway solutions. The analysis focuses on the non-relativistic case, but we can extend the results obtained here to the relativistic case, at least in one dimension.

KEKB has completed all of the technical milestones and has offered important insights into the flavor structure of elementary particles, especially CP violation. The accelerator control system at KEKB and the injector linac was initiated by a combination of scripting languages at the operation layer and EPICS (experimental physics and industrial control system) at the equipment layer. During the project, many features were implemented to achieve extreme performance from the machine. In particular, the online linkage to the accelerator simulation played an essential role. In order to further improve the reliability and flexibility, two major concepts were additionally introduced later in the project, namely, channel access everywhere and dual-tier controls. Based on the improved control system, a virtual accelerator concept was realized, allowing the single injector linac to serve as three separate injectors to KEKB's high-energy ring, low-energy ring, and Photon Factory, respectively. These control technologies are indispensable for future particle accelerators.

We review the basic dynamics and accretion of planetesimals by showing N-body simulations. The orbits of planetesimals evolve through two-body gravitational relaxation: viscous stirring increases the random velocity and dynamical friction realizes the equiparation of the random energy. In the early stage of planetesimal accretion the growth mode of planetesimals is runaway growth where larger planetesimals grow faster than smaller ones. When a protoplanet (runaway-growing planetesimal) exceeds a critical mass the growth mode shifts to oligarchic growth where similar-sized protoplanets grow keeping a certain orbital separation. The final stage of terrestrial planet formation is collision among protoplanets known as giant impacts. We also summarize the dynamical effects of disk gas on planets and the core accretion model for formation of gas giants and discuss the diversity of planetary systems.

The Belle experiment, running at the KEKB e+e- asymmetric energy collider during the first decade of the century, achieved its original objective of measuring precisely differences between particles and anti-particles in the B system. After collecting 1000 fb-1 of data at various Upsilon resonances, Belle also obtained the many other physics results described in this article.

In the complex action theory whose path runs over not only past but also future, we study a normalized matrix element of an operator $\hat {\mathcal O}$ defined in terms of the future state at the latest time $T_B$ and the past state at the earliest time $T_A$ with a proper inner product that makes normal a given Hamiltonian that is non-normal at first. We present a theorem that states that, provided that the operator $\hat {\mathcal O}$ is $Q$-Hermitian, i.e., Hermitian with regard to the proper inner product, the normalized matrix element becomes real and time-develops under a $Q$-Hermitian Hamiltonian for the past and future states selected such that the absolute value of the transition amplitude from the past state to the future state is maximized. Furthermore, we give a possible procedure to formulate the $Q$-Hermitian Hamiltonian in terms of $Q$-Hermitian coordinate and momentum operators, and construct a conserved probability current density.

In this study we critically examine some important papers on weak measurement and weak values. We find some insufficiency and mistakes in these papers, and we demonstrate that the real parts of weak values provide the back-action to the post-selection, which is caused by weak measurement. Two examples, a counterfactual statement of Hardy's paradox and experiments that determine the average trajectory of photons passing through double slits, are investigated from our view point.

Top-cited authors
• High Energy Accelerator Research Organization
• Forschungszentrum Jülich
• University of Chicago
• Instituto Federal de Educação, Ciência e Tecnologia do Maranhão (IFMA), Brazil, São Luis