arXiv subjects

Kaoru Hagiwara

Publications and source records attributed to Kaoru Hagiwara.

At least 19 recordsLinked to original sources

arXiv2026

Multi-channel phase space with Feynman-diagram-gauge amplitudes

Multi-channel phase space with a single Feynman diagram enhancement is a powerful tool for high-energy physics event generation if a diagram with a singular propagator dominates the total scattering amplitude at the corresponding singular kinematical region, and when the interference among amplitudes is not larger than the square of each amplitude. These conditions are satisfied in the Feynman-diagram-gauge amplitudes for both unbroken (QED and QCD) and broken (EW) gauge theories. We illustrate the usefulness of this method in lepton collider processes that are challenging to accurately simulate at very high energies, i.e., $ l\bar{l} \to ν_l \barν_l t\bar{t} H $, $ l \barν_l t\bar{b} H $, and $ l \bar{l} t\bar{t} H $, in the SMEFT with a complex top-Yukawa coupling. The total cross sections of the latter two processes contain lepton-mass singularities arising from $t$-channel photon-exchange diagrams. To address this issue, we develop a phase-space parametrization that accurately generates the distributions of forward-emitted charged leptons. We modify the \HELAS\ library to evaluate helicity amplitudes in the singular region so that vertices at very small invariant momentum square of order $m_e^2$ can be accurately evaluated even at multi-TeV energies.

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arXiv2026

Prospects for toponium formation at the LHC in the single-lepton mode

We investigate the formation of toponium in the single-leptonic final state at the LHC. Our study builds on our recently proposed framework that incorporates the associated non-perturbative effects into Monte Carlo simulations through the Green's function of the non-relativistic QCD Hamiltonian and the re-weighting of hard-scattering matrix elements. This allows us to perform a phenomenological analysis that demonstrates that a statistically significant excess from toponium formation could already be accessible in Run~2 data. Moreover, our results highlight observables that provide handles for signal characterisation and establish the single-leptonic channel as a competitive and complementary avenue for the ongoing exploration of toponium signatures at colliders.

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arXiv2025

Simulating toponium formation signals at the LHC

We present a method to simulate toponium formation events at the LHC using the Green's function of non-relativistic QCD in the Coulomb gauge, which governs the momentum distribution of top quarks in the presence of the QCD potential. This Green's function can be employed to re-weight any matrix elements relevant for $t\bar{t}$ production and decay processes where a colour-singlet top-antitop pair is produced in the $S$-wave at threshold. As an example, we study the formation of $η_t$ toponium states in the gluon fusion channel at the LHC, combining the re-weighted matrix elements with parton showering.

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arXiv2024

One-loop QCD amplitudes in the Feynman-Diagram gauge

Scattering amplitudes for the massless QCD process, $q\bar{q}\to q^\prime\bar{q}^\prime$, are calculated in the one-loop order in the Feynman-Diagram (FD) gauge, where gluons are quantized on the light cone with opposite direction of the three-momenta. We find non-decoupling of the Faddeev-Popov ghosts and non-conventional UV singularities in dimensional regularization. The known QCD amplitudes with asymptotic freedom are reproduced only after summing propagator and vertex corrections. By quantizing gluons in the Feynman gauge on the FD gauge background, we obtain the one-loop improved FD gauge amplitudes.

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arXiv2024

Automatic generation of helicity amplitudes in Feynman-Diagram gauge

We develop a method to calculate helicity amplitudes of an arbitrary tree-level process in Feynman-Diagram (FD) gauge for an arbitrary gauge model with MadGraph5_aMC@NLO. We start from the 't Hooft-Feynman gauge Lagrangian in FeynRules and generate scattering amplitudes by identifying the Goldstone boson as the $5^{\rm th}$ component of each weak boson. All the vertices of the 5-component weak bosons are then created automatically by assembling the relevant weak boson and Goldstone boson vertices in the Feynman gauge. The 5-component weak boson vertices are then connected by the $5\times5$ matrix propagator in the FD gauge. As a demonstration of the method we calculate the cross section for the process $μ^-μ^+\toν_μ\barν_μt\bar{t}H$ with complex top Yukawa coupling, which can be obtained by adding a gauge invariant dimension-6 operator to the Standard Model (SM) Lagrangian. The FD gauge and the unitary (U) gauge amplitudes give exactly the same cross section, and subtle gauge theory cancellation among diagrams in the U gauge at high energies is absent in the FD gauge, as has been observed for various SM processes. In addition, we find that the total cross sections at high energies are dominated by a single, or a set of non-vanishing Feynman amplitudes with the higher dimensional vertices in the FD gauge.

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arXiv2023

Helicity amplitudes in light-cone and Feynman-diagram gauges

Recently proposed Feynman-diagram (FD) gauge propagator for massless and massive gauge bosons is obtained from a light-cone (LC) gauge propagator, by choosing the gauge vector along the opposite direction of the gauge boson three-momentum. We implement a general LC gauge propagator for all the gauge bosons of the Standard Model (SM) in the HELicity Amplitude Subroutines (HELAS) codes, such that all the SM helicity amplitudes can be evaluated at the tree level in the LC gauge by using MadGraph. We confirm that our numerical codes produce physical helicity amplitudes which are consistent among all gauge choices. We then study interference patterns among Feynman amplitudes, for a few $2\to3$ scattering processes in QED and QCD, and the process $γγ\to W^+W^-$ followed by the $W^\pm$ decays. We find that in a generic LC gauge, where all the gauge boson propagators share a common gauge vector, we cannot remove the off-shell current components which grow with their energy systematically from all the Feynman amplitudes in $2\to3$ processes. On the other hand, the $5\times5$ LC gauge propagator for the weak bosons removes components which grow with energy due to the longitudinal polarization mode of the external bi-fermion currents, and hence can give $2\to2$ weak boson scattering amplitudes which are free from subtle cancellation at high energies. The particular choice of the FD gauge vector has advantages over generic LC gauge, not only because all the terms which grow with energy of off-shell and on-shell currents are removed systematically from all the diagrams, but also because no artificial gauge vector direction dependence of individual amplitudes appears.

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arXiv2023

CP-violating top-Higgs coupling in SMEFT

The total cross section of the process $μ^- μ^+ \to ν_μ\barν_μt \bar{t} H$ has strong dependence on the CP phase $ξ$ of the top Yukawa coupling, where the ratio of $ξ=π$ and $ξ= 0$ (SM) grows to 670 at $\sqrt{s}$ = 30 TeV, 3400 at 100 TeV. We study the cause of the strong energy dependence and identify its origin as the $(E/m_W^{})^2$ growth of the weak boson fusion sub-amplitudes, $W_L^- W_L^+ \to t \bar{t} H$, with the two $W$s are longitudinally polarized. We repeat the study in the SMEFT framework where EW gauge invariance is manifest and find that the highest energy cross section is reduced to a quarter of the complex top Yukawa model result, with the same energy power. By applying the Goldstone boson (GB) equivalence theorem, we identify the origin of this strong energy growth of the SMEFT amplitudes as associated with the dimension-6 $π^- π^+ ttH$ vertex, where $π^\pm$ denotes the GB of $W^\pm$. We obtain the unitarity bound on the coefficient of the SMEFT operator by studying all $2\to2$ and $2\to3$ cross sections in the $J=0$ channel.

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arXiv2023

Helicity amplitudes without gauge cancellation for electroweak processes

In the 5-component representation of weak bosons, the first four components make a Lorentz four vector, representing the transverse and longitudinal polarizations excluding the scalar component of the weak bosons, whereas its fifth component corresponds to the Goldstone boson. We obtain the $5\times 5$ component propagators of off-shell weak bosons, proposed previously and named after the Goldstone boson equivalence theorem, by starting from the unitary-gauge representation of the tree-level scattering amplitudes, and by applying the BRST (Becchi--Rouet--Stora--Tyutin) identities to the two sub-amplitudes connected by each off-shell weak-boson line. By replacing all weak boson vertices with those among the off-shell 5-component wavefunctions, we arrive at the expression of the electroweak scattering amplitudes, where the magnitude of each Feynman amplitude has the correct on-shell limits for all internal propagators, and hence with no artificial gauge cancellation among diagrams. Although our derivation is limited to the tree-level only, it allows us to study the properties of each Feynman amplitude separately, and then learn how they interfere in the full amplitudes. We implement the 5-component weak boson propagators and their vertices in the numerical helicity amplitude calculation code HELAS (Helicity Amplitude Subroutines), so that an automatic amplitude generation program such as MadGraph can generate the scattering amplitudes without gauge cancellation. We present results for several high-energy scattering processes where subtle gauge-theory cancellation among diagrams takes place in all the other known approaches.

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arXiv2023

Long-lived Higgsino pairs decaying within the LHC detectors

Pair-produced long-lived lightest Higgsinos decaying within a few meters in the LHC detectors are considered. The relatively light nearly-pure Higgsino states object of this study are those of a supersymmetric minimal model with gauge-mediated supersymmetry breaking and heavy sfermions and gauginos. The heavier Higgsinos decay instantly into the lightest one, with very little activities. Hence, all pair-produced Higgsinos end up as a pair of the lightest neutral Higgsinos, possibly long lived and decaying into the gravitino and either the Higgs or the Z boson. If they decay inside the detectors, these bosons deposit huge energies in the calorimeters. The cross section $σ_2$ ($σ_1$) for the events with two (at least one) decaying-in-flight lightest Higgsinos is examined. The combination $(σ_1)^2/σ_2$ is found to be almost insensitive to the lightest Higgsino lifetime, thereby providing a good variable to measure its mass. The ratio $σ_1/σ_2$, instead, mildly dependent on its mass, can give good information on its lifetime. It is argued that the lightest Higgsinos in the events are rather slow, as the very relativistic ones escape away. Thus, the initial state radiations tend to be soft and a trigger system appropriate for such events is necessary to detect them.

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arXiv2021

Signatures of toponium formation in LHC run 2 data

We study reported deviations between observations and theoretical predictions associated with the production of a pair of di-leptonically decaying top quarks at the LHC, and we examine the possibility that they reflect a signal of toponium formation. We investigate the production by gluon fusion of a color-singlet spin-0 toponium $η_t$ bound state of a top and anti-top quark, that then decays di-leptonically ($gg\toη_t \to \bar\ell \ell b \bar{b} ν\barν$). We find strong correlations favoring the production of di-lepton systems featuring a small angular separation in azimuth and a small invariant mass. Although toponium production only contributes to 0.8% of the total top-quark pair-production cross section at the 13 TeV LHC, there is a possibility that it can account for observed excesses in the narrow edges of phase space. We propose a method to discover toponium formation by `reconstructing' both its top and anti-top quark constituents in the di-lepton channel.

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arXiv2020

QED and QCD helicity amplitudes in parton-shower gauge

We introduce photon and gluon propagators in which the scalar polarization component is subtracted systematically by making use of the BRST invariance of the off-shell vector boson created from physical on-shell states. The propagator has the light-cone gauge form, where the spacial component of the gauge vector points along the negative of the off-shell vector boson momentum. We call the gauge as parton-shower gauge, since in collinear configurations the absolute value squared of each Feynman amplitude reproduces all the singular behaviors of the corresponding parton shower in this gauge. We introduce new HELAS codes that can be used to calculate the tree-level helicity amplitudes of arbitrary QED and QCD processes by using MadGraph. The absence of subtle gauge cancellation among Feynman amplitudes allows numerical codes to evaluate singular behaviors accurately, and helps us gaining physical insights on interference patterns.

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arXiv2020

Determining Strong Phase of $a_1$ Meson Decay Amplitude using $W \to ντ(\to νa_1(\toπ^\mp π^\mp π^\pm))$ Process

To measure the helicity of a spin-1 meson from the triple vector product of the three-momenta of its decay products, one needs information about the strong phase of the decay amplitude. In this paper, taking $a_1(1260)$ meson as an example, we present a method to extract information about the strong phase from the triple vector product of the pion momenta in $W \to ντ(\to νa_1(\toπ^\mp π^\mp π^\pm))$ process, where the $a_1$ helicity is known a priori from electroweak theory. This process is advantageous in that highly-boosted $a_1^-$ mesons from $τ_L^-$ decays have nearly maximal helicity asymmetry and thus most reflect the strong phase. We revisit the theoretical calculation of the $a_1$ meson helicity in $W \to ντ(\to νa_1)$ process. We formulate the differential decay rate of polarized $a_1$ mesons in a manner convenient for the study of the $a_1$ meson helicity asymmetry. Finally, we present the method for extracting information about the strong phase, and assess its feasibility at the LHC.

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arXiv2020

Probing the top Yukawa coupling at the LHC via associated production of single top and Higgs

We study Higgs boson production associated with single top or anti-top via $t$-channel weak boson exchange at the LHC. The process is an ideal probe of the top quark Yukawa coupling, because we can measure the relative phase of $htt$ and $hWW$ couplings, thanks to the significant interference between the two amplitudes. By choosing the emitted $W$ momentum along the polar axis in the $th\,(\bar{t}h)$ rest frame, we obtain the helicity amplitudes for all the contributing subprocesses analytically, with possible CP phase of the Yukawa coupling. We study the azimuthal asymmetry between the $W$ emission and the $Wb\,(\bar{b})\to t(\bar{t})\,h$ scattering planes, as well as several $t$ and $\bar{t}$ polarization asymmetries as a signal of CP violating phase in the $htt$ coupling. Both the azimuthal asymmetry and the polarization perpendicular to the scattering plane are found to have the opposite sign between the top and anti-top events. We identify the origin of the sign of asymmetries, and propose the possibility of direct CP violation test in $pp$ collisions by comparing the top and anti-top polarization at the LHC.

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arXiv2018

Probing the Higgs Yukawa coupling to the top-quark at the LHC via single top + Higgs production

The conjoined production at the LHC of single top and Higgs boson via $t$-channel weak boson exchange is ideal to probe the top-quark Yukawa coupling, due to a delicate cancellation between the amplitudes with the $htt$ and the $hWW$ couplings. We find that the top quark is produced with $100\%$ polarization in the leading order, and its quantum state is determined by the spin-vector direction in the $t$-quark rest frame. We relate the spin direction to the four-momenta of the top, Higgs and a jet in the helicity amplitude framework. We identify a polarization asymmetry that is sensitive to CP violation, even after partial integration over the forward jet momentum. This CP violating asymmetry may be observed at the LHC via the component of the top-quark polarization that is perpendicular to the $th$ scattering plane.

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arXiv2018

Closing in on the chargino contribution to the muon g-2 in the MSSM: current LHC constraints

We revisit the current LHC constraints on the electroweak-ino sector parameters in the minimal supersymmetric standard model (MSSM) that are relevant to explaining the $(g-2)_μ$ anomaly via the dominant chargino and muon sneutrino loop. Since the LHC bounds on electroweak-inos become weaker if they decay via an intermediate stau or a tau sneutrino instead of the first two generation sleptons, we perform a detailed analysis of the scenario with a bino as the lightest supersymmetric particle (LSP) and a light stau as the next-to-lightest one (NLSP). Even in this scenario, the chargino sector parameters in the MSSM that can account for the $(g-2)_μ$ anomaly within $1 σ$ are already found to be significantly constrained by the 8 TeV LHC and the available subset of the 13 TeV LHC limits. We also estimate the current LHC exclusions in the left-smuon (and/or left-selectron) NLSP scenario from multilepton searches, and further combine the constraints from the multi-tau and multi-lepton channels for a mass spectrum in which all three generations of sleptons are lighter than the chargino. In the latter two cases, small corners of the $1 σ$ favoured region for $(g-2)_μ$ are still allowed at present.

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arXiv2018

Probing the CP properties of top Yukawa coupling at an $e^+e^-$ collider

We study consequences of CP violation in the $ht\bar{t}$ Yukawa coupling through the process $e^+e^- \to$ $h(125)t\bar{t}$. The helicity amplitudes are calculated in the $t\bar{t}$ rest frame, where the initial $e^+e^-$ current and the final Higgs boson have the same three-momentum. CP-violating asymmetries appear not only in the azimuthal angle between the $e^+e^-$ plane and the $t\bar{t}$ plane about the Higgs momentum direction, but also in the correlated decay angular distributions of $t$ and $\bar{t}$. Complete description of the production and decay angular distributions are obtained analytically, including both leptonic and hadronic decays of $t$ and $\bar{t}$. We study the ultimate sensitivity to the CP-violating $ht\bar{t}$ coupling at a few center-of-mass energies. Our analysis shows that the possibility of discovering CP violating $ht\bar{t}$ coupling improves significantly by studying $t\bar{t}$ decay angular correlations, and more importantly, by increasing its energy upgrade target from $\sqrt{s} = 500$ GeV to 550 GeV.

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arXiv2017

Probing CP violation in $h\to τ^{-}τ^{+}$ at the LHC

We propose a novel method to reconstruct event by event the full kinematics of the cascade decay process, $h \to τ^+τ^- \to (π^+ \barν) (π^- ν)$, which allows us to measure the $τ^+τ^-$ spin correlation, a measure of the CP property of the Higgs boson. By noting that the $τ^{\pm}$ momenta lie on the plane spanned by the accurately measured impact parameter and momentum vectors of charged pions, we can obtain the most likely momenta of the two missing neutrinos by using the probability distribution functions of the $\met$ vector and the location of the primary vertex. A simple detector level simulation shows an excellent agreement between the reconstructed and the true kinematics, both in the $τ^+τ^-$ and the $π^+π^-$ rest frames. The method can be tested in $Z \to τ^+τ^-$ events, which should exhibit no correlation.

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arXiv2017

Revisiting T2KK and T2KO physics potential and $ν_μ$ - $\barν_μ$ beam ratio

We revisit the sensitivity study of the Tokai-to-Kamioka-and-Korea (T2KK) and Tokai-to-Kamioka-and-Oki (T2KO) proposals where a water Cerenkov detector with the 100 kton fiducial volume is placed in Korea ($L = 1000$ km) and Oki island ($L = 653$ km) in Japan, respectively, in addition to the Super-Kamiokande for determination of the neutrino mass hierarchy and leptonic CP phase ($δ_{CP}$). We systematically study the running ratio of the $ν_μ$ and $\barν_μ$ focusing beams with dedicated background estimation for the $ν_e$ appearance and $ν_μ$ disappearance signals, especially improving treatment of the neutral current $π^0$ backgrounds. Using a $ν_μ$ - $\barν_μ$ beam ratio between 3 : 2 and 2.5 : 2.5 (in unit of $10^{21}$POT with the proton energy of 40 GeV), the mass hierarchy determination with the median sensitivity of 3 - 5 $σ$ by the T2KK and 1 - 4 $σ$ by the T2KO experiment are expected when $\sin^2θ_{23} = 0.5$, depending on the mass hierarchy pattern and CP phase. These sensitivities are enhanced (reduced) by $30\%$ - $40\%$ in $Δχ^2$ when $\sin^2θ_{23} = 0.6\, (0.4)$. The CP phase is measured with the uncertainty of $20^\circ$ - $50^\circ$ by the T2KK and T2KO using the $ν_μ$ - $\barν_μ$ focusing beam ratio between 3.5 : 1.5 and 1.5 : 3.5. These findings indicate that inclusion of the $\barν_μ$ focusing beam improves the sensitivities of the T2KK and T2KO experiments to both the mass hierarchy determination and leptonic CP phase measurement simultaneously with the preferred beam ratio being between 3 : 2 - 2.5 : 2.5 ($\times 10^{21}$POT).

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