arXiv subjects

Yukinari Sumino

Publications and source records attributed to Yukinari Sumino.

At least 19 recordsLinked to original sources

arXiv2026

Two-loop quarkonium Hamiltonian in annihilation channel

We calculate the two-loop quarkonium Hamiltonian in the annihilation channel within the framework of potential-NRQCD effective field theory. The result agrees with the previous calculation of the corresponding four-quark operator in NRQCD for SU(N) color gauge group. We further obtain an expression with a more general color structure applicable to other gauge groups. Combined with the recently calculated two-loop Hamiltonian in the non-annihilation channel, this completes the full two-loop quarkonium Hamiltonian.

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arXiv2025

Method to measure quarkonium wave function using $B_c$ decay

We propose a method that enables a direct experimental probe of the quarkonium wave function defined in potential nonrelativistic QCD (pNRQCD) using the three-body decay of the $B_c$ meson. We show that the momentum distribution of the spectator $c$-quark in the partonic decay is proportional to the absolute square of the momentum-space wave function of the $B_c$ state. It would provide, for the first time, an experimentally accessible probe of the quarkonium wave function.

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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.

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arXiv2024

Two-loop $O(ε)$ term of $1/(mr^2)$ heavy quarkonium potential

As a straightforward application of the recently calculated two-loop heavy quarkonium Hamiltonian, we evaluate the two-loop $O(ε)$ term of the $1/(mr^2)$ heavy quarkonium potential. Compared to a previous calculation we find a small difference in the coefficient of the maximally non-abelian color factor $C_F C_A^2 $. We further examine this coefficient carefully.

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arXiv2024

On order $Λ_{\rm QCD}^2/m$ renormalons in quarkonium system

For the heavy quarkonium system we examine ${\cal O}(Λ_{\rm QCD}^2/m)$ renormalons, which are expected to be included in the perturbative series of the pole mass and $1/(mr^2)$ interquark potential. We find indications of existence and cancellation of these renormalons, from examinations of stability and convergence properties of the perturbative series and their resummations, as well as by comparison with the known properties of the ${\cal O}(Λ_{\rm QCD})$ renormalons.

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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.

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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.

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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.

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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.

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arXiv2021

New method for renormalon subtraction using Fourier transform

To improve accuracy in calculating QCD effects, we propose a method for renormalon subtraction in the context of the operator-product expansion. The method enables subtracting renormalons of various powers in $Λ_{\rm QCD}$ efficiently and simultaneously from single-scale observables. We apply it to different observables and examine consistency with theoretical expectations.

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arXiv2020

On renormalons of static QCD potential at $u=1/2$ and $3/2$

We investigate the $u=1/2$ [$\mathcal{O}(Λ_{\rm QCD})$] and $u=3/2$ [$\mathcal{O}(Λ_{\rm QCD}^3)$] renormalons in the static QCD potential in position space and momentum space using the OPE of the potential-NRQCD effective field theory. This is an old problem and we provide a formal formulation to analyze it. In particular we present detailed examinations of the $u=3/2$ renormalons. We clarify how the $u=3/2$ renormalon is suppressed in the momentum-space potential in relation with the Wilson coefficient $V_A(r)$. We also point out that it is not straightforward to subtract the IR renormalon and IR divergences simultaneously in the multipole expansion. Numerical analyses are given, which clarify the current status of our knowledge on the perturbative series. The analysis gives a positive reasoning to the method for subtracting renormalons used in recent $α_s(M_Z)$ determination from the QCD potential.

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arXiv2019

Perturbative static quark potential in Maximal Abelian gauge

We calculate the static quark potential for an SU(N) gauge theory in the Maximal Abelian gauge as well as its Abelian projection up to two loops in perturbation theory. We discuss its renormalization properties. The result is compared with a recent lattice result at $r \lesssim 0.5$ fm.

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arXiv2019

UV contributions to energy of a static quark-antiquark pair in large $β_0$ approximation

The total energy of a static quark-antiquark pair $E_{\rm tot}(r)=2m_{\rm pole}+V_{\rm QCD}(r)$ is known to be predictable up to ${\cal O}(Λ_{\rm QCD}^3 r^2)$ and ${\cal O}(\frac{Λ_{\rm QCD}^3}{\overline{m}^2})$ renormalon uncertainties in the large-$β_0$ approximation, after canceling ${\cal O}(Λ_{\rm QCD})$ renormalons. We compute the predictable part (genuine UV part) in terms of the $\overline{\rm MS}$ mass $\overline{m}$, extending a recently-proposed method which conforms with OPE. In particular the $r$-independent part is determined. The result would help understanding the nature of $E_{\rm tot}(r)$ in the context of OPE with renormalon subtraction.

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arXiv2019

Determination of $α_s$ from static QCD potential: OPE with renormalon subtraction and lattice QCD

We determine the strong coupling constant $α_s$ from the static QCD potential by matching a theoretical calculation with a lattice QCD computation. We employ a new theoretical formulation based on the operator product expansion, in which renormalons are subtracted from the leading Wilson coefficient. We remove not only the leading renormalon uncertainty of $\mathcal{O}(Λ_{\rm QCD})$ but also the first $r$-dependent uncertainty of $\mathcal{O}(Λ_{\rm QCD}^3 r^2)$. The theoretical prediction for the potential turns out to be valid at the static color charge distance $Λ_{\rm \overline{MS}} r \lesssim 0.8$ ($r \lesssim 0.4$ fm), which is significantly larger than ordinary perturbation theory. With lattice data down to $Λ_{\rm \overline{MS}} r \sim 0.09$ ($r \sim 0.05$ fm), we perform the matching in a wide region of $r$, which has been difficult in previous determinations of $α_s$ from the potential. Our final result is $α_s(M_Z^2) = 0.1179^{+0.0015}_{-0.0014}$ with 1.3 % accuracy. The dominant uncertainty comes from higher order corrections to the perturbative prediction and can be straightforwardly reduced by simulating finer lattices.

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arXiv2019

Determination of $α_s$ from static QCD potential with renormalon subtraction

We determine the strong coupling constant $α_s(M_Z)$ from the static QCD potential by matching a lattice result and a theoretical calculation. We use a new theoretical framework based on operator product expansion (OPE), where renormalons are subtracted from the leading Wilson coefficient. We find that our OPE prediction can explain the lattice data at $Λ_{\rm QCD} r \lesssim 0.8$. This allows us to use a larger window in matching, which leads to a more reliable determination. We obtain $α_s(M_Z)=0.1179^{+0.0015}_{-0.0014}$.

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arXiv2018

Probing Higgs self-coupling of a classically scale invariant model in $e^+e^- \to Zhh$: Evaluation at physical point

A classically scale invariant extension of the standard model predicts large anomalous Higgs self-interactions. We compute missing contributions in previous studies for probing the Higgs triple coupling of a minimal model using the process $e^+e^- \to Zhh$. Employing a proper order counting, we compute the total and differential cross sections at the leading order, which incorporate the one-loop corrections between zero external momenta and their physical values. Discovery/exclusion potential of a future $e^+e^-$ collider for this model is estimated. We also find a unique feature in the momentum dependence of the Higgs triple vertex for this class of models.

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arXiv2017

Subtracting IR Renormalons from Wilson Coefficients: Uniqueness and power dependences on $Λ_\mathrm{QCD}$

In the context of OPE and using the large-$β_0$ approximation, we propose a method to define Wilson coefficients free from uncertainties due to IR renormalons. We first introduce a general observable $X(Q^2)$ with an explicit IR cutoff, and then we extract a genuine UV contribution $X_\mathrm{UV}$ as a cutoff-independent part. $X_\mathrm{UV}$ includes power corrections $\sim (Λ_\mathrm{QCD}^2/Q^2)^n$ which are independent of renormalons. Using the integration-by-regions method, we observe that $X_\mathrm{UV}$ coincides with the leading Wilson coefficient in OPE and also clarify that the power corrections originate from UV region. We examine scheme dependence of $X_\mathrm{UV}$ and single out a specific scheme favorable in terms of analytical properties. Our method would be optimal with respect to systematicity, analyticity and stability. We test our formulation with the examples of the Adler function, QCD force between $Q \bar{Q}$, and $R$-ratio in $e^{+} e^{-}$ collision.

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arXiv2017

Determination of $m_c$ and $m_b$ from quarkonium 1S energy levels in perturbative QCD

We update determination of the $\overline{\rm MS}$ masses of the charm and bottom quarks, from comparisons of the masses of the charmonium and bottomonium $1S$ states with their perturbative predictions up to next-to-next-to-next-to-leading order in $\varepsilon$ expansion and using the $\overline{\rm MS}$ masses. Effects of non-zero charm-quark mass in the bottomonium masses are incorporated up to next-to-next-to-leading order. We obtain $\overline m_c=1246\pm 2 (d_3) \pm 4 (α_s) \pm 23 (\text{h.o.} )~{\rm MeV} $ and $\overline m_b=4197\pm 2 (d_3) \pm 6 (α_s) \pm 20 (\text{h.o.} )\pm 5 (m_c)~ {\rm MeV} $, which agree with the current Particle Data Group values.

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