arXiv subjects

Hiromasa Takaura

Publications and source records attributed to Hiromasa Takaura.

At least 19 recordsLinked to original sources

arXiv2026

Beyond thresholds: reconstructing UV physics from IR expansions

We show that ultraviolet information can be extracted from low-energy expansion coefficients, assuming analyticity and the absence of massless singularities. By reorganizing the low-energy expansion through an inverse Laplace transform and a controlled coarse-graining procedure, we make ultraviolet behavior accessible beyond the cutoff of the effective field theory. In particular, we determine the sign of the beta function and the associated dynamical scale directly from the low-energy expansion of a physical observable below the mass thresholds in QED and QCD-like theories.

hep-th↗

arXiv2025

Gradient-flowed operator product expansion without IR renormalons

A long-standing problem concerns the question how to consistently combine perturbative expansions in QCD with power corrections in the context of the operator product expansion (OPE), since the former exhibit ambiguities due to infrared renormalons, which are of the same order as the power corrections. We propose to use the gradient flow time $1/\sqrt{t}$ as a factorization scale and to express the OPE in terms of IR renormalon-free subtracted perturbative expansions and unambiguous matrix elements of gradient-flow regularized local operators. We show on the example of the Adler function and its leading power correction from the gluon condensate that this method dramatically improves the convergence of the perturbative expansion. We employ lattice data on the action density to estimate the gradient-flowed gluon condensate, and obtain the Adler function with non-perturbative accuracy and significantly reduced theoretical uncertainty, enlarging the predictivity at low $Q^2$. When applied to the hadronic decay width of the tau lepton, the method resolves the long-standing discrepancy between the fixed-order and contour-improved approach in favour of the fixed-order treatment.

hep-ph↗

arXiv2025

A new approach to quark mass determination using the gradient flow

We propose a new method to determine quark masses using ratios of the vacuum-expectation values (VEVs) of flowed quark bilinear operators. They can be expressed as functions of the flow time $t$ and the ${\overline {\rm MS}}$ quark mass $\overline{m}$, which can then be determined by matching with the corresponding lattice results. Motivated by this, we evaluate these VEVs perturbatively through next-to-leading order in the strong coupling. We provide the results as expansions in the limits of small and large $\overline{m}^2 t$. To this end, we develop a new expansion technique based on the Laplace transform. Additionally, we present numerical results with the exact mass dependence over a wide range of $\overline{m}^2t$. We discuss the expected perturbative precision for the mass determination based on our next-to-leading order perturbative calculations, and possible non-perturbative corrections.

hep-lat↗

arXiv2025

Higgs boson production at $μ^+ μ^+$ colliders

We study Higgs boson production at $μ^+ μ^+$ colliders at high energy. Since both initial-state particles are positively charged, there is no $W$ boson fusion at the leading order, as it requires a $W^+ W^-$ pair. However, we find that the cross section of the higher-order, $γ$- and $Z$-mediated $W$ boson fusion process is large at high center-of-mass energies $\sqrt s$, growing as $(\log s)^3$. This is in contrast to the $\log s$ behavior of the leading-order $W$ boson fusion. Thus, even though it is a higher-order process, the rate of Higgs boson production for 10 TeV energies at $μ^+ μ^+$ colliders with polarized beams can be as high as about half of the one at $μ^+ μ^-$ colliders, assuming the same integrated luminosity. To calculate the cross section of this process accurately, we carefully treat the collinear emission of the photon in the intermediate state. The thereby obtained large cross section furthermore shows the significance of Higgs production with an extra $W$ boson in the final state also at $μ^+ μ^-$ and $e^+ e^-$ colliders.

hep-ph↗

arXiv2024

Determining the Quark Mass with the Gradient Flow

We propose a new method to determine the quark mass by using bilinear operators of the flowed quark field defined within the gradient-flow formalism. This method enables the quark mass determination through a comparison of perturbative calculations with lattice data. The gauge-invariant nature of the observable should allow clear control over perturbative errors. At the same time, the gradient flow suppresses the noise in the lattice measurements of the observable, which simply consists of one-point functions. Concerning the perturbative input in this framework, we study the mass dependence of the flowed quark condensate $\langle \barχ(t,x) χ(t,x) \rangle$ at the two-loop level. For this purpose, we develop a novel approach for expanding massive gradient-flow integrals in the limit of small and large $(m^2t)$. We also present a fully numerical result which includes the full mass dependence.

hep-lat↗

arXiv2024

Two-loop Quarkonium Hamiltonian in Non-annihilation Channel

We calculate the two-loop heavy quarkonium Hamiltonian within potential-NRQCD effective field theory in the non-annihilation channel. This calculation represents the first non-trivial step towards determining the N$^4$LO Hamiltonian in the weak coupling regime. The large amount of computation is systematically handled by employing the $β$ expansion, differential equations for master integrals, and adopting a single-step matching procedure, in contrast to the conventional two-step approach.

hep-ph↗

arXiv2024

Low energy limit from high energy expansion in mass gapped theory

We present a method to extract the low energy behavior of physical observables from their high energy expansions, systematically calculable via the operator product expansion (OPE), in asymptotically free and mass-gapped theories. By applying the inverse Laplace transform to correlation functions, their analytic structure is modified such that low-energy information connects with high energy expansions. Furthermore, this transformation alleviates the renormalon problem, enabling a more straightforward application of the OPE compared to the OPE before the transformation. We demonstrate that the low energy limit of correlation functions can be accurately extracted using the OPE in the two dimensional $O(N)$ nonlinear $σ$ model, serving as a first testing ground.

hep-th↗

arXiv2023

Inclusive $|V_{cb}|$ determination in $\overline{\mathrm{MS}}$ mass scheme using dual-space-renormalon-subtraction method

We determine $|V_{cb}|$ from the inclusive semileptonic decay width of the $B$ meson with the known N$^3$LO perturbative coefficients for the first time in the $\overline{\mathrm{MS}}$ mass scheme. We make use of a recently developed method, dual-space-renormalon-subtraction (DSRS) method, to separate and subtract the order $Λ_{\rm QCD}^2/m_b$ infrared renormalon. This allows us to perform the analysis accurately in the $\overline{\mathrm{MS}}$ mass scheme, in which otherwise the perturbative series does not converge well up to the currently calculated perturbation order. Our result reads $|V_{cb}|=0.0415\,(^{+10}_{-12})$, which is consistent with the previous results based on other mass schemes and showing an independent cross check of the current theoretical evaluation of the inclusive decay width.

hep-ph↗

arXiv2023

QED on the lattice and numerical perturbative computation of $g-2$

We compute the electron $g$ factor to the $\mathcal{O}(α^5)$ order on the lattice in quenched QED. We first study finite volume corrections in various IR regularization methods to discuss which regularization is optimal for our purpose. We find that in QED$_L$ the finite volume correction to the effective mass can have different parametric dependences depending on the size of Euclidean time $t$ and match the `naive on-shell result' only at very large $t$ region, $t \gg L$. We adopt finite photon mass regularization to suppress finite volume effects exponentially and also discuss our strategy for selecting simulation parameters and the order of extrapolations to efficiently obtain the $g$ factor. We perform lattice simulation using small lattices to test feasibility of our calculation strategy. This study can be regarded as an intermediate step toward giving the five-loop coefficient independently of the preceding studies.

hep-lat↗

arXiv2023

Gradient-flow renormalon subtraction and the hadronic tau decay series

The inconsistency between the fixed-order (FO) and contour-improved (CI) representation of the QCD corrections to the inclusive hadronic tau decay width limits the precision to which the strong coupling can be determined from this process. It has recently been shown that subtracting the infrared renormalon divergence related to the gluon condensate resolves the discrepancy. Here we suggest to employ the gradient flow to define gauge-invariant regularized operators and to use the corresponding condensates in the operator product expansion. The associated rearrangement of the perturbative series results in automatic renormalon subtraction without the need to determine explicitly the Stokes constants that normalize the divergent asymptotic series. Applying this method to the gluon condensate, we find that the CI series is modified and now agrees with the (unmodified) FO series. This conclusively demonstrates the preference for the fixed-order approach, as has been advocated long ago.

hep-ph↗

arXiv2023

Renormalon Subtraction in OPE by Dual Space Approach: Nonlinear Sigma Model and QCD

It is becoming more important to subtract renormalons efficiently from perturbative calculations, in order to achieve high precision QCD calculations. We propose a new framework ``Dual Space Approach" for renormalon separation, which enables subtraction of multiple renormalons simultaneously. Using a dual transform which suppresses infrared renormalons, we derive a one-parameter integral representation of a general observable. We investigate systematically how renormalons emerge and get canceled in the entire operator product expansion (OPE) of an observable, by applying the expansion-by-regions (EBR) method to this one-parameter integral expression. In particular we investigate in detail OPEs in a solvable model, the 2-dimensional $O(N)$ nonlinear $σ$ model, by the dual space approach. A nontrivial mechanism of renormalon cancellation in this model can be understood from an integration identity on which the EBR method is founded. We demonstrate that the dual space approach can be useful by a simulation study imitating the QCD case. Application of this method to QCD calculations is also discussed.

hep-ph↗

arXiv2022

Determination of HQET nonperturbative matrix elements with renormalon subtraction using Fourier transform

As higher order perturbative series are available, it is becoming necessary to include nonperturbative effects in QCD calculations using the OPE. In order to systematically determine nonperturbative effects and to incorporate them into theoretical calculations, the renormalon problem should be resolved. We use a renormalon subtraction method utilizing Fourier transform to determine nonperturbative matrix elements of HQET, $\barΛ$ and $μ_π^2$. This is the first determination performed with subtraction of the $u=1$ renormalon.

hep-ph↗

arXiv2022

Precision $μ^+μ^+$ and $μ^+e^-$ elastic scatterings

Expected precisions of measurements of the elastic scattering cross sections are estimated for $μ^+ μ^+$ and $μ^+ e^-$ colliders, which are recently proposed as future realistic possibilities ($μ$TRISTAN). Comparing with contributions from possible new physics represented by higher dimensional operators, we find that the measurements at a TeV energy $μ^+μ^+$ collider can probe the scale of new physics up to $O(100)$~TeV. A $μ^+ e^-$ collider for the Higgs boson factory can also improve the electroweak precision test.

hep-ph↗

arXiv2022

$μ$TRISTAN

The ultra-cold muon technology developed for the muon $g-2$ experiment at J-PARC provides a low emittance $μ^+$ beam which can be accelerated and used for realistic collider experiments. We consider the possibility of new collider experiments by accelerating the $μ^+$ beam up to 1 TeV. Allowing the $μ^+$ beam to collide with a high intensity $e^-$ beam at the TRISTAN energy, $E_{e^-}= 30$ GeV, in the storage ring with the same size as TRISTAN (the circumference of 3 km), one can realize a collider experiment with the center-of-mass energy $\sqrt s = 346$ GeV, which allows productions of the Higgs bosons through the vector boson fusion processes. We estimate the deliverable luminosity with existing accelerator technologies to be at the level of $5 \times 10^{33}$ cm$^{-2}$ s$^{-1}$, with which the collider can be a good Higgs boson factory. The $μ^+ μ^+$ colliders up to $\sqrt s = 2$ TeV are also possible by using the same storage ring. They have a capability of producing the superpartner of the muon up to TeV masses.

hep-ph↗

arXiv2022

Determination of $|V_{cb}|$ using N$^3$LO perturbative corrections to $Γ(B \to X_c \ell ν)$ and 1S masses

We determine $|V_{cb}|$ using the third-order perturbative series for the inclusive semileptonic $B$ decay width and for the masses of the bottomonium 1S states. We use the masses of $η_b(1S)$ and $Υ(1S)$ as short-distance masses and point out that there is a sizable difference of $|V_{cb}|$ between the two 1S mass schemes. This is the dominant error of our determination and stems from insufficiency to describe theoretically the observed mass splitting of the bottomonium 1S states. We also study the significance of the $\mathcal{O}(Λ_{\overline{\rm MS}}^2)$ non-perturbative effects in HQET with respect to the current perturbative accuracy. Our result $|V_{cb}|=0.0425 (11)$ is consistent with the PDG value determined from the inclusive decays and has a slightly larger error.

hep-ph↗

arXiv2021

Renormalon subtraction in OPE using Fourier transform: Formulation and application to various observables

Properly separating and subtracting renormalons in the framework of the operator product expansion (OPE) is a way to realize high precision computation of QCD effects in high energy physics. We propose a new method (FTRS method), which enables to subtract multiple renormalons simultaneously from a general observable. It utilizes a property of Fourier transform, and the leading Wilson coefficient is written in a one-parameter integral form whose integrand has suppressed (or vanishing) renormalons. The renormalon subtraction scheme coincides with the usual principal-value prescription at large orders. We perform test analyses and subtract the ${\cal O}(Λ_{\rm QCD}^4)$ renormalon from the Adler function, the ${\cal O}(Λ_{\rm QCD}^2)$ renormalon from the $B\to X_ul\barν$ decay width, and the ${\cal O}(Λ_{\rm QCD})$ and ${\cal O}(Λ_{\rm QCD}^2)$ renormalons from the $B,\,D$ meson masses. The analyses show good consistency with theoretical expectations, such as improved convergence and scale dependence. In particular we obtain $\barΛ_{\rm FTRS}=0.495\pm0.053~\text{GeV}$ and$ (μ_π^2)_{\rm FTRS}=-0.12\pm 0.23~\text{GeV}^2$ for the non-perturbative parameters of HQET. We explain the formulation and analyses in detail.

hep-ph↗

arXiv2021

Renormalons in static QCD potential: review and some updates

We give a brief review of the current understanding of renormalons of the static QCD potential in coordinate and momentum spaces. We also reconsider estimate of the normalization constant of the $u=3/2$ renormalon and propose a new way to improve the estimate.

hep-ph↗

arXiv2021

$t \to 0$ extrapolation function in SF$t$X method for the energy-momentum tensor

We theoretically clarify the functional form to be used in $t \to 0$ extrapolation in the small flow time expansion (SF$t$X) method for the energy-momentum tensor (EMT), which facilitates lattice simulation of the EMT based on the gradient flow. We argue that in the $t \to 0$ extrapolation analysis, lattice data should be fitted by a power function in $g(μ(t))$, the flow time dependent running coupling, where the power is determined by the perturbation order we consider. From actual lattice data, we confirm the validity of the extrapolation function. Using the new extrapolation function, we present updated lattice results for thermodynamics quantities in quenched QCD; our results are consistent with the previous study [arXiv:1812.06444] but we obtain smaller errors due to reduction of systematic errors.

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