We study Higgs boson production at <math><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>+</mo></msup></math> colliders at high energy. Since both initial-state particles are positively charged, there is no <math><mi>W</mi></math> boson fusion at the leading order, as it requires a <math><msup><mi>W</mi><mo>+</mo></msup><msup><mi>W</mi><mo>−</mo></msup></math> pair. However, we find that the cross section of the higher-order, <math><mi>γ</mi></math>-and <math><mi>Z</mi></math>-mediated <math><mi>W</mi></math> boson fusion process is large at high center-of-mass energies <math><msqrt><mi>s</mi></msqrt></math>, growing as <math><mo>(</mo><mi>log</mi><mi>s</mi><msup><mo>)</mo><mn>3</mn></msup></math>. This is in contrast to the <math><mi>log</mi><mi>s</mi></math> behavior of the leading-order <math><mi>W</mi></math> boson fusion. Thus, even though it is a higher-order process, the rate of Higgs boson production for 10 TeV energies at <math><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>+</mo></msup></math> colliders with polarized beams can be as high as about half of the one at <math><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math> 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 <math><mi>W</mi></math> boson in the final state also at <math><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></math> and <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> colliders.

Germany

Japan

Yu Hamada

Ryuichiro Kitano

Ryutaro Matsudo

Shohei Okawa

Ryoto Takai

Hiromasa Takaura

Lukas Treuer

Higgs boson production at <math><mrow><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> colliders

We calculate the two-loop heavy quarkonium Hamiltonian within potential-nonrelativistic-QCD effective field theory in the nonannihilation channel. This calculation represents the first nontrivial step toward determining the <math><msup><mi>N</mi><mn>4</mn></msup><mi>LO</mi></math> Hamiltonian in the weak coupling regime. The large amount of computation is systematically handled by employing the <math><mi>β</mi></math> expansion, differential equations for master integrals, and adopting a single-step matching procedure, in contrast to the conventional two-step approach.

Go Mishima

Yukinari Sumino

Two-Loop Quarkonium Hamiltonian in Nonannihilation Channel

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.

Low energy limit from high energy expansion in mass gapped theory

We determine <math><mo>|</mo><msub><mi>V</mi><mrow><mi>c</mi><mi>b</mi></mrow></msub><mo>|</mo></math> from the inclusive semileptonic decay width of the <math><mi>B</mi></math> meson with the known <math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>3</mn></mrow></msup><mi>LO</mi></mrow></math> perturbative coefficients for the first time in the <math><mover><mi>MS</mi><mo>¯</mo></mover></math> mass scheme. We make use of a recently developed method, dual-space-renormalon-subtraction method, to separate and subtract the order <math><mrow><msubsup><mrow><mi>Λ</mi></mrow><mrow><mi>QCD</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>/</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>b</mi></mrow></msub></mrow></math> infrared renormalon. This allows us to perform the analysis accurately in the <math><mover><mi>MS</mi><mo>¯</mo></mover></math> mass scheme, in which otherwise the perturbative series does not converge well up to the currently calculated perturbation order. Our result reads <math><mrow><mo>|</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>c</mi><mi>b</mi></mrow></msub><mo>|</mo><mo>=</mo><mn>0.0415</mn><mo>(</mo><msubsup><mrow><mtext> </mtext></mrow><mrow><mo>−</mo><mn>12</mn></mrow><mrow><mo>+</mo><mn>10</mn></mrow></msubsup><mo>)</mo></mrow></math>, which is consistent with the previous results based on other mass schemes and shows an independent cross-check of the current theoretical evaluation of the inclusive decay width.

Yuuki Hayashi

Inclusive <math><mrow><mo>|</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>c</mi><mi>b</mi></mrow></msub><mo>|</mo></mrow></math> determination in <math><mover><mrow><mi>MS</mi></mrow><mo>¯</mo></mover></math> mass scheme using dual-space-renormalon-subtraction method

Abstract We compute the electron g factor to the  order on the lattice in quenched quantum electrodynamics (QED). We first study finite volume (FV) corrections in various infrared regularization methods to discuss which regularization is optimal for our purpose. We find that in QED$_{L}$ the FV 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 the very large t region, t ≫ L. We adopt finite photon mass regularization to suppress FV 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 the feasibility of our calculation strategy. This study can be regarded as an intermediate step toward giving the five-loop coefficient independently of preceding studies.

Quantum electrodynamics on the lattice and numerical perturbative computation of − 2

We determine <math><mo>|</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>c</mi><mi>b</mi></mrow></msub><mo>|</mo></math> 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 <math><msub><mrow><mi>η</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>(</mo><mn>1</mn><mi>S</mi><mo>)</mo></math> and <math><mi>ϒ</mi><mo>(</mo><mn>1</mn><mi>S</mi><mo>)</mo></math> as short-distance masses and point out that there is a sizable difference of <math><mo>|</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>c</mi><mi>b</mi></mrow></msub><mo>|</mo></math> 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 <math><mi>O</mi><mo>(</mo><msubsup><mrow><mi>Λ</mi></mrow><mrow><mover><mrow><mrow><mi>MS</mi></mrow></mrow><mo>‾</mo></mover></mrow><mrow><mn>2</mn></mrow></msubsup><mo>)</mo></math> non-perturbative effects in HQET with respect to the current perturbative accuracy. Our result <math><mo>|</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>c</mi><mi>b</mi></mrow></msub><mo>|</mo><mo>=</mo><mn>0.0425</mn><mo>(</mo><mn>11</mn><mo>)</mo></math> is consistent with the PDG value determined from the inclusive decays and has a slightly larger error.

Determination of | | using N LO perturbative corrections to Γ( → ) and 1S masses

Abstract The expected measurement precisions of elastic scattering cross sections are estimated for μ$^{+}$μ$^{+}$ and μ$^{+}$e$^{−}$ colliders, which have recently been proposed as future realistic possibilities (μTRISTAN). Compared 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. For those studies, we assume the expected integrated luminosity at μTRISTAN, L$_{int}$ = 120 fb$^{−1}$ (μ$^{+}$μ$^{+}$) and 1 ab$^{−1}$ (μ$^{+}$e$^{−}$).

Taiwan

Precision And Elastic Scatterings

Abstract 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,  GeV, in a storage ring with the same size as TRISTAN (a circumference of 3 km), one can realize a collider experiment with the center-of-mass energy  GeV, which allows the production of Higgs bosons through vector boson fusion processes. We estimate the deliverable luminosity with existing accelerator technologies to be at the level of 5 × 10$^{33}$ cm$^{−2}$ s$^{−1}$, with which the collider can be a good Higgs boson factory. μ$^{+}$μ$^{+}$ colliders up to  TeV are also possible using the same storage ring. They have the capability of producing the superpartner of the muon up to TeV masses.

Mitsuhiro Yoshida

Μtristan Re-acceleration of ultra cold muon in J-PARC muon facility Nb Sn 11 T dipole for the High Luminosity LHC (CERN)

Properly separating and subtracting renormalons in the framework of the op- erator 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   <math> <mi>O</mi> <mfenced> <msubsup> <mi>Λ</mi> <mi>QCD</mi> <mn>4</mn> </msubsup> </mfenced> </math>  $$ \mathcal{O}\left({\Lambda}_{\mathrm{QCD}}^4\right) $$  renormalon from the Adler function, the   <math> <mi>O</mi> <mfenced> <msubsup> <mi>Λ</mi> <mi>QCD</mi> <mn>2</mn> </msubsup> </mfenced> </math>  $$ \mathcal{O}\left({\Lambda}_{\mathrm{QCD}}^2\right) $$  renormalon from the B → X  u  l   <math> <mover> <mi>ν</mi> <mo>¯</mo> </mover> </math>  $$ \overline{\nu} $$  decay width, and the   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (ΛQCD) and   <math> <mi>O</mi> <mfenced> <msubsup> <mi>Λ</mi> <mi>QCD</mi> <mn>2</mn> </msubsup> </mfenced> </math>  $$ \mathcal{O}\left({\Lambda}_{\mathrm{QCD}}^2\right) $$  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   <math> <mover> <mi>Λ</mi> <mo>¯</mo> </mover> </math>  $$ \overline{\Lambda} $$  FTRS = 0.495 ± 0.053 GeV and (  <math> <msubsup> <mi>μ</mi> <mi>π</mi> <mn>2</mn> </msubsup> </math>  $$ {\mu}_{\pi}^2 $$ )FTRS = −0.12 ± 0.23 GeV2 for the non-perturbative parameters of HQET. We explain the formulation and analyses in detail.

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

Abstract We theoretically clarify the functional form to be used in  extrapolation in the small flow time expansion method for the energy–momentum tensor (EMT), which facilitates lattice simulation of the EMT based on the gradient flow. We argue that in the  extrapolation analysis, lattice data should be fitted by a power function in , 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 [T. Iritani et al., Prog. Theor. Exp. Phys. 2019, 023B02 (2019)] but we obtain smaller errors due to the reduction of systematic errors.