arXiv subjects
Publications and source records attributed to Takahiro Ueda.
We introduce FORM 4.2, a new minor release of the symbolic manipulation toolkit. We demonstrate several new features, such as a new pattern matching option, new output optimization, and automatic expansion of rational functions.
The total amount of dust (or "metallicity") and the dust distribution in protoplanetary disks are crucial for planet formation. Dust grains radially drift due to gas--dust friction, and the gas is affected by the feedback from dust grains. We investigate the effects of the feedback from dust grains on the viscous evolution of the gas, taking into account the vertical dust settling. The feedback from the grains pushes the gas outward. When the grains are small and the dust-to-gas mass ratio is much smaller than unity, the radial drift velocity is reduced by the feedback effect but the gas still drifts inward. When the grains are sufficiently large or piled-up, the feedback is so effective that forces the gas flows outward. Although the dust feedback is affected by dust settling, we found that the 2D approximation reasonably reproduces the vertical averaged flux of gas and dust. We also performed the 2D two-fluid hydrodynamic simulations to examine the effect of the feedback from the grains on the evolution of the gas disk. We show that when the feedback is effective, the gas flows outward and the gas density at the region within $\sim 10\ \mbox{AU}$ is significantly depleted. As a result, the dust-to-gas mass ratio at the inner radii may significantly excess unity, providing the environment where planetesimals are easily formed via, e.g., streaming instability. We also show that a simplified 1D model well reproduces the results of the 2D two-fluid simulations, which would be useful for future studies.
Full one-loop electroweak-corrections for an $e^-e^+\rightarrow t \bar{t}$ process associated with sequential $t\rightarrow b μν_μ$ decay are discussed. At the one-loop level, the spin-polarization effects of the initial electron and positron beams are included in the total and differential cross sections. A narrow-width approximation is used to treat the top-quark production and decay while including full spin correlations between them. We observed that the radiative corrections due to the weak interaction have a large polarization dependence on both the total and differential cross sections. Therefore, experimental observables that depend on angular distributions such as the forward-backward asymmetry of the top production angle must be treated carefully including radiative corrections. We also observed that the energy distribution of bottom quarks is majorly affected by the radiative corrections.
We analytically derive the expressions for the structure of the inner region of protoplanetary disks based on the results from the recent hydrodynamical simulations. The inner part of a disk can be divided into four regions: dust-free region with gas temperature in the optically thin limit, optically thin dust halo, optically thick condensation front and the classical optically thick region in order from the inside. We derive the dust-to-gas mass ratio profile in the dust halo using the fact that partial dust condensation regulates the temperature to the dust evaporation temperature. Beyond the dust halo, there is an optically thick condensation front where all the available silicate gas condenses out. The curvature of the condensation surface is determined by the condition that the surface temperature must be nearly equal to the characteristic temperature $\sim 1200{\,\rm K}$. We derive the mid-plane temperature in the outer two regions using the two-layer approximation with the additional heating by the condensation front for the outermost region. As a result, the overall temperature profile is step-like with steep gradients at the borders between the outer three regions. The borders might act as planet traps where the inward migration of planets due to gravitational interaction with the gas disk stops. The temperature at the border between the two outermost regions coincides with the temperature needed to activate magnetorotational instability, suggesting that the inner edge of the dead zone must lie at this border. The radius of the dead-zone inner edge predicted from our solution is $\sim$ 2-3 times larger than that expected from the classical optically thick temperature.
In the Solar System, interplanetary dust particles (IDPs) originating mainly from asteroid collisions and cometary activities drift to the Earth orbit due to the Poynting-Robertson drag. We analyzed the thermal emission from IDPs that was observed by the first Japanese infrared astronomical satellite, AKARI. The observed surface brightness in the trailing direction of the Earth orbit is 3.7% greater than that in the leading direction in the $9{\rm μm}$ band and 3.0% in the $18{\rm μm}$ band. In order to reveal dust properties causing the leading-trailing surface brightness asymmetry, we numerically integrated orbits of the Sun, the Earth, and a dust particle as a restricted three-body problem including radiation from the Sun. The initial orbits of particles are determined according to the orbits of main-belt asteroids or Jupiter-family comets. The orbital trapping in mean motion resonances results in a significant leading-trailing asymmetry so that intermediate sized dust (~10-100${\rm μm}$) produces a greater asymmetry than the zodiacal light has. The leading-trailing surface brightness difference integrated over the size distribution of the asteroidal dust is obtained to be the values of 27.7% and 25.3% in the $9{\rm μm}$ and $18{\rm μm}$ bands, respectively. In contrast, the brightness difference for cometary dust is calculated as the values of 3.6% and 3.1% in the $9{\rm μm}$ and $18{\rm μm}$ bands, respectively, if the maximum dust radius is set to be $s_{\rm max} = 3000{\rm μm}$. Taking into account these values and their errors, we conclude that the contribution of asteroidal dust to the zodiacal infrared emission is less than ~10%, while cometary dust of the order of 1 mm mainly accounts for the zodiacal light in infrared.
We study the phase space distributions of gluons inside a nucleon/nucleus in the small-$x$ regime including the gluon saturation effect. This can be done by using the relation between the gluon Wigner distribution and the dipole S-matrix at small-$x$, the latter satisfies the Balitsky-Kovchegov (BK) equation. By efficiently solving the BK equation with impact parameter dependence, we compute the Wigner, Husimi and generalized TMD (GTMD) distributions in the saturation regime. We also investigate the elliptic angular dependence of these distributions which has been recently shown to be measurable in DIS experiments.
We discuss a number of FORM features that are essential in the automatic processing of very large numbers of diagrams as used in the Forcer program for 4-loop massless propagator diagrams. Most of these features are new.
We perform the leading logarithmic resummation of nonglobal logarithms for the single-hemisphere jet mass distribution in $e^+e^-$ annihilation including the finite-$N_c$ corrections. The result is compared with the previous all-order result in the large-$N_c$ limit as well as fixed-order perturbative calculations.
We compute the contribution to the total cross section for the inclusive production of a Standard Model Higgs boson induced by two quarks with different flavour in the initial state. Our calculation is exact in the Higgs boson mass and the partonic center-of-mass energy. We describe the reduction to master integrals, the construction of a canonical basis, and the solution of the corresponding differential equations. Our analytic result contains both Harmonic Polylogarithms and iterated integrals with additional letters in the alphabet.
In this paper, we show algorithms for solving the cake-cutting problem in sublinear-time. More specifically, we preassign (simple) fair portions to o(n) players in o(n)-time, and minimize the damage to the rest of the players. All currently known algorithms require Omega(n)-time, even when assigning a portion to just one player, and it is nontrivial to revise these algorithms to run in $o(n)$-time since many of the remaining players, who have not been asked any queries, may not be satisfied with the remaining cake. To challenge this problem, we begin by providing a framework for solving the cake-cutting problem in sublinear-time. Generally speaking, solving a problem in sublinear-time requires the use of approximations. However, in our framework, we introduce the concept of "eps n-victims," which means that eps n players (victims) may not get fair portions, where 0< eps =< 1 is an arbitrary constant. In our framework, an algorithm consists of the following two parts: In the first (Preassigning) part, it distributes fair portions to r < n players in o(n)-time. In the second (Completion) part, it distributes fair portions to the remaining n-r players except for the eps n victims in poly}(n)-time. There are two variations on the r players in the first part. Specifically, whether they can or cannot be designated. We will then present algorithms in this framework. In particular, an O(r/eps)-time algorithm for r =< eps n/127 undesignated players with eps n-victims, and an O~(r^2/eps)-time algorithm for r =< eps e^{sqrt{ln{n}}/{7}} designated players and eps =< 1/e with eps n-victims are presented.
An important aspect of improving perturbative predictions in high energy physics is efficiently reducing dimensionally regularised Feynman integrals through integration by parts (IBP) relations. The well-known triangle rule has been used to achieve simple reduction schemes. In this work we introduce an extensible, multi-loop version of the triangle rule, which we refer to as the diamond rule. Such a structure appears frequently in higher-loop calculations. We derive an explicit solution for the recursion, which prevents spurious poles in intermediate steps of the computations. Applications for massless propagator type diagrams at three, four, and five loops are discussed.
We review the status of the parallel versions of the computer algebra system FORM. In particular, we provide a brief overview about the historical developments, discuss the strengths of ParFORM and TFORM, and mention typical applications. Furthermore, we briefly discuss the programs FIRE and FIESTA, which have also been developed with the Collaborative Research Center/TR~9 (CRC/TR~9).
We study master integrals needed to compute the Higgs boson production cross section via gluon fusion in the infinite top quark mass limit, using a canonical form of differential equations for master integrals, recently identified by Henn, which makes their solution possible in a straightforward algebraic way. We apply the known criteria to derive such a suitable basis for all the phase space master integrals in afore mentioned process at next-to-next-to-leading order in QCD and demonstrate that the method is applicable to next-to-next-to-next-to-leading order as well by solving a non-planar topology. Furthermore, we discuss in great detail how to find an adequate basis using practical examples. Special emphasis is devoted to master integrals which are coupled by their differential equations.
We introduce the \prog{Mathematica} package \prog{MT} which can be used to compute, both analytically and numerically, convolutions involving harmonic polylogarithms, polynomials or generalized functions. As applications contributions to next-to-next-to-next-to leading order Higgs boson production and the Drell-Yan process are discussed.
In the context of inter-jet energy flow, we present the first quantitative result of the resummation of non-global logarithms at finite N_c. This is achieved by refining Weigert's approach in which the problem is reduced to the simulation of associated Langevin dynamics in the space of Wilson lines. We find that, in e+e- annihilation, the exact result is rather close to the result previously obtained in the large-N_c mean field approximation. However, we observe enormous event-by-event fluctuations in the Langevin process which may have significant consequences in hadron collisions.
We consider Higgs boson production at hadron colliders in the gluon fusion channel and compute higher order terms in the regularization parameter $ε$. In particular, the next-to-next-to-leading order cross section is evaluated including order $ε$ terms. These results are used to compute all convolutions with the splitting functions entering the next-to-next-to-next-to-leading order cross section.
It has been argued that high-multiplicity proton-proton collisions at the LHC may exhibit collective phenomena usually studied in the context of heavy-ion collisions, such as elliptic flow. We study this issue using DIPSY - a Monte Carlo event generator based on the QCD dipole model. We calculate the eccentricity of the transverse area defined by the spatial distribution of produced gluons. The resulting elliptic flow is estimated to be about 6%, comparable to the value in nucleus-nucleus collisions at RHIC and the LHC. Experimentally, elliptic flow is inferred from the azimuthal correlation between hadrons, which receives contributions from collective flow, and from various other effects referred to as "nonflow". We discuss how to identify in experiments the signal of flow in the presence of large nonflow effects.
We discuss the resummation of the large logarithmic terms appearing in the heavy quark effects on parton distribution functions inside the virtual photon. We incorporate heavy quark mass effects by changing the initial condition of the leading-order DGLAP evolution equation. In a certain kinematical limit, we recover the logarithmic terms of the next-to-leading order heavy quark effects obtained in the previous work. This method enables us to resum the large logarithmic terms due to heavy quark mass effects on the parton distributions in the virtual photon. We numerically calculate parton distributions using the formulae derived in this work, and discuss the property of the resummed heavy quark effects.