arXiv subjects

F. Meier

Publications and source records attributed to F. Meier.

At least 19 recordsLinked to original sources

arXiv2025

Search for lepton-flavor-violating tau decays to $\ell\alpha$ at Belle

We report a search for the lepton-flavor-violating decays $\tau^{\pm}\to\ell^{\pm}\alpha$~($\ell=e,\mu$), where $\alpha$ is an undetected spin-0 particle, such as an axion-like particle using $736\times10^{6}$ tau lepton pairs collected by the Belle detector at the KEKB asymmetric-energy $e^{+}e^{-}$ collider. We find no evidence of signal and obtain the most stringent upper limits on the branching fractions at 95\% confidence level: $\mathcal{B}(\tau^{\pm}\rightarrow e^{\pm}\alpha)$ $<$ $(0.4$--$6.4)\times10^{-4}$ and $\mathcal{B}(\tau^{\pm}\rightarrow \mu^{\pm}\alpha)$ $<$ $(0.2$--$3.5)\times10^{-4}$ at 95\% confidence level for an $\alpha$ mass in the range $0.0\leq m_{\alpha}\leq 1.6$~GeV/$c^{2}$.

hep-ex↗

arXiv2025

Design and Commissioning of Readout Electronics for a $K_L^0$ and $\mu$ Detector at the Belle II Experiment

The K-long and muon detector (KLM) constitutes the outer-most volume of the Belle II spectrometer at the interaction region of the SuperKEKB collider in Tsukuba, Japan. The KLM detector was partially upgraded since the Belle experiment by replacing many of its resistive-plate chambers with scintillators containing wavelength-shifting fibers and instrumenting it with silicon photomultipliers. We describe the readout electronics, firmware, and software created to control and acquire data from the scintillators and resistive-plate chambers.

hep-ex↗

arXiv2024

Search for $h_b(2P)\to\gamma\chi_{bJ}(1P)$ at $\sqrt{s} = 10.860$ GeV

In the bottomonium sector, the hindered magnetic dipole (M1) transitions between P-wave states $h_b(2P) \rightarrow \chi_{bJ}(1P) \gamma$, $J=0, \, 1, \, 2$, are expected to be severely suppressed according to the Relativized Quark Model, due to the spin flip of the $b$ quark. Nevertheless, a recent model following the coupled-channel approach predicts the corresponding branching fractions to be enhanced by orders of magnitude. In this Letter, we report the first search for such transitions. We find no significant signals and set upper limits at 90% CL on the corresponding branching fractions: $\mathcal{B}[h_b(2P)\to\gamma\chi_{b0}(1P)] < 2.7 \times 10^{-1}$, $\mathcal{B}[h_b(2P)\to\gamma\chi_{b1}(1P)] < 5.4 \times 10^{-3}$ and $\mathcal{B}[h_b(2P)\to\gamma\chi_{b2}(1P)] < 1.3 \times 10^{-2}$. These values help to constrain the parameters of the coupled-channel models. The results are obtained using a $121.4 \, fb^{-1}$ data sample taken around $\sqrt{s}= 10.860 \, GeV$ with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider.

hep-ex↗

arXiv2024

Evidence of $h_{b}(\text{2P}) \to \Upsilon(\text{1S})\eta$ decay and search for $h_{b}(\text{1P,2P}) \to \Upsilon(\text{1S})\pi^0$ with the Belle detector

We report the first evidence for the $h_{b}(\text{2P}) \to \Upsilon(\text{1S})\eta$ transition with a significance of $3.5$ standard deviations. The decay branching fraction is measured to be $\mathcal{B}[h_{b}(\text{2P}) \to \Upsilon(\text{1S})\eta]=(7.1 ~^{+3.7} _{-3.2}\pm 0.8)\times10^{-3}$, which is noticeably smaller than expected. We also set upper limits on $\pi^0$ transitions of $\mathcal{B}[h_{b}(\text{2P}) \to \Upsilon(\text{1S})\pi^0] < 1.8\times10^{-3}$, and $\mathcal{B}[h_{b}(\text{1P})\to \Upsilon(\text{1S})\pi^0] < 1.8\times10^{-3}$, at the $90\%$ confidence level. These results are obtained with a $131.4$~fb$^{-1}$ data sample collected near the $\Upsilon(\text{5S})$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider.

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arXiv2024

Search for charmed baryons in the $\Lambda_c^+\eta$ system and measurement of the branching fractions of $\Lambda_c(2880)^+$ and $\Lambda_c(2940)^+$ decaying to $\Lambda_c^+\eta$ and $pD^0$ relative to $\Sigma_c(2455)\pi$

We search for excited charmed baryons in the $\Lambda_c^+\eta$ system using a data sample corresponding to an integrated luminosity of 980 $\rm fb^{-1}$. The data were collected by the Belle detector at the KEKB $e^{+}$$e^{-}$ asymmetric-energy collider. No significant signals are found in the $\Lambda_c^+\eta$ mass spectrum, including the known $\Lambda_c(2880)^+$ and $\Lambda_c(2940)^+$. Clear $\Lambda_c(2880)^+$ and $\Lambda_c(2940)^+$ signals are observed in the $pD^0$ mass spectrum. We set upper limits at 90\% credibility level on ratios of branching fractions of $\Lambda_c(2880)^+$ and $\Lambda_c(2940)^+$ decaying to $\Lambda_c^+\eta$ relative to $\Sigma_c(2455)\pi$ of $<0.13$ for the $\Lambda_c(2880)^+$ and $<1.11$ for the $\Lambda_c(2940)^+$. We measure ratios of branching fractions of $\Lambda_c(2880)^+$ and $\Lambda_c(2940)^+$ decaying to $pD^0$ relative to $\Sigma_c(2455)\pi$ of $0.75 \pm 0.03(\text{stat.}) \pm 0.07(\text{syst.})$ for the $\Lambda_c(2880)^+$ and $3.59 \pm 0.21(\text{stat.}) \pm 0.56(\text{syst.})$ for the $\Lambda_c(2940)^+$.

hep-ex↗

arXiv2024

Search for Two-Body $B$ Meson Decays to $\Lambda^{0}$ and $\Omega^{(*)0}_{c}$

We report the results of the first search for Standard Model and baryon-number-violating two-body decays of the neutral $B$ mesons to $\Lambda^{0}$ and $\Omega^{(*)0}_c$ using 711~${\rm fb^{-1}}$ of data collected at the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider. We observe no evidence of signal from any such decays and set 95\% confidence-level upper limits on the products of $B^0$ and $\bar{B}^0$ branching fractions for these two-body decays with $\mathcal{B}(\Omega_{c}^{0} \to \pi^+ \Omega^-)$ in the range between 9.5~$\times 10^{-8}$ and 31.2~$\times 10^{-8}$.

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arXiv2024

Search for Baryon-Number-Violating Processes in $B^-$ Decays to the $\bar{\Xi}_{c}^{0} \bar{\Lambda}_{c}^{-}$ Final State

We report the results of the first search for $B^-$ decays to the $\bar{\Xi}_{c}^{0} \bar{\Lambda}_{c}^{-}$ final state using 711~${\rm fb^{-1}}$ of data collected at the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider. The results are interpreted in terms of both direct baryon-number-violating $B^-$ decay and $\Xi_{c}^{0}-\bar{\Xi}_{c}^{0}$ oscillations which follow the Standard Model decay $B^- \to \Xi_{c}^{0} \bar{\Lambda}_{c}^{-}$. We observe no evidence for baryon number violation and set the 95\% confidence-level upper limits on the ratio of baryon-number-violating and Standard Model branching fractions ${\mathcal{B}(B^- \rightarrow \bar{\Xi}_{c}^{0} \bar{\Lambda}_{c}^{-})}/{\mathcal{B}(B^- \rightarrow \Xi_{c}^{0} \bar{\Lambda}_{c}^{-})}$ to be $< 2.7\%$ and on the $\Xi_{c}^{0} - \bar{\Xi}_{c}^{0}$ oscillation angular frequency $\omega$ to be $< 0.76\ \mathrm{ps}^{-1}$ (equivalent to $\tau_{\rm mix} > 1.3$~ps).

hep-ex↗

arXiv2023

Search for the decay $B_s^0\to J/\psi\pi^0$ at Belle experiment

We have analyzed 121.4 fb$^{-1}$ of data collected at the $\Upsilon(5S)$ resonance by the Belle experiment using the KEKB asymmetric-energy $e^+e^-$ collider to search for the decay $B_s^0\to J/\psi\pi^0$. We observe no signal and report an upper limit on the branching fraction $\mathcal{B}(B_s^0\to J/\psi\pi^0)$ of $1.21\times 10^{-5}$ at 90\% confidence level. This result is the most stringent, improving the previous bound by two orders of magnitude.

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arXiv2023

Measurement of the Ratio of Partial Branching Fractions of Inclusive $\overline{B} \to X_u \ell \overline{\nu}$ to $\overline{B} \to X_{c} \ell \overline{\nu}$ and the Ratio of their Spectra with Hadronic Tagging

We present a measurement of the ratio of partial branching fractions of the semi-leptonic inclusive decays, $\overline{B} \to X_{u} \ell \overline{\nu}$ to $\overline{B} \to X_{c} \ell \overline{\nu}$, where $\ell = (e, \mu)$, using the full Belle sample of $772 \times 10^{6}$ $B \kern 0.18em\overline{\kern -0.18em B}$ pairs collected at the $\Upsilon(4S)$ resonance. The ratio is measured via a two-dimensional fit to the squared four-momentum transfer to the lepton pair, and the charged lepton energy in the $B$ meson rest frame, where the latter must be larger than $1$ Ge\kern -0.1em V, covering approximately $86\%$ and $78\%$ of the $\overline{B} \to X_{u} \ell \overline{\nu}$ and $\overline{B} \to X_{c} \ell \overline{\nu}$ phase space, respectively. We find $\Delta \mathcal{B}(\overline{B} \to X_{u} \ell \overline{\nu})/ \Delta \mathcal{B}(\overline{B} \to X_{c} \ell \overline{\nu}) = (1.99 \pm 0.17_{\rm stat} \pm 0.16_{\rm syst}) \times 10^{-2}$ where the uncertainties are statistical and systematic, respectively. In addition, we report the partial branching fractions separately for charged and neutral $B$ meson decays, and for electron and muon decay channels. We place a limit on isospin breaking in $\overline{B} \to X_{u} \ell \overline{\nu}$ decays, and find no indication of lepton flavor universality violation in either the charmed or charmless mode. Furthermore, we unfold the $\overline{B} \to X_{u} \ell \overline{\nu}$ and $\overline{B} \to X_{c} \ell \overline{\nu}$ yields and report the differential ratio in lepton energy and four-momentum transfer squared.

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arXiv2023

Measurement of Angular Coefficients of $\bar{B} \to D^* \ell \bar{\nu}_\ell$: Implications for $|V_{cb}|$ and Tests of Lepton Flavor Universality

We measure the complete set of angular coefficients $J_i$ for exclusive $\bar{B} \to D^* \ell \bar{\nu}_\ell$ decays ($\ell = e, \mu$). Our analysis uses the full $711\,\mathrm{fb}^{-1}$ Belle data set with hadronic tag-side reconstruction. The results allow us to extract the form factors describing the $B \to D^*$ transition and the Cabibbo-Kobayashi-Maskawa matrix element $|V_{\rm cb}|$. Using recent lattice QCD calculations for the hadronic form factors, we find $|V_{\rm cb}| = (41.0 \pm 0.7) \times 10^3 $ using the BGL parameterization, compatible with determinations from inclusive semileptonic decays. We search for lepton flavor universality violation as a function of the hadronic recoil parameter $w$, and investigate the differences of the electron and muon angular distributions. We find no deviation from Standard Model expectations.

hep-ex↗

arXiv2023

Search for baryon and lepton number violating decays $\boldsymbol{D \rightarrow p\ell}$

We search for the baryon and lepton number violating charm decays, $D \rightarrow p\ell$, where $D$ is either a $D^0$ or a $\overline{D}^0$ and $\ell$ is a muon or an electron, using a data sample of $921\,\mathrm{fb}^{-1}$ collected by the Belle detector at the KEKB asymmetric energy $e^{+}e^{-}$ collider. In the absence of significant signals, we set upper limits on the branching fractions in the range $(5 - 8) \times 10^{-7}$ at a 90\% confidence level, depending on the decay mode.

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arXiv2023

Photon Reconstruction in the Belle II Calorimeter Using Graph Neural Networks

We present the study of a fuzzy clustering algorithm for the Belle II electromagnetic calorimeter using Graph Neural Networks. We use a realistic detector simulation including simulated beam backgrounds and focus on the reconstruction of both isolated and overlapping photons. We find significant improvements of the energy resolution compared to the currently used reconstruction algorithm for both isolated and overlapping photons of more than 30% for photons with energies E < 0.5 GeV and high levels of beam backgrounds. Overall, the GNN reconstruction improves the resolution and reduces the tails of the reconstructed energy distribution and therefore is a promising option for the upcoming high luminosity running of Belle II.

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arXiv2023

Measured and projected beam backgrounds in the Belle II experiment at the SuperKEKB collider

The Belle II experiment at the SuperKEKB electron-positron collider aims to collect an unprecedented data set of $50~{\rm ab}^{-1}$ to study $CP$-violation in the $B$-meson system and to search for Physics beyond the Standard Model. SuperKEKB is already the world's highest-luminosity collider. In order to collect the planned data set within approximately one decade, the target is to reach a peak luminosity of $\rm 6 \times 10^{35}~cm^{-2}s^{-1}$ by further increasing the beam currents and reducing the beam size at the interaction point by squeezing the betatron function down to $\beta^{*}_{\rm y}=\rm 0.3~mm$. To ensure detector longevity and maintain good reconstruction performance, beam backgrounds must remain well controlled. We report on current background rates in Belle II and compare these against simulation. We find that a number of recent refinements have significantly improved the background simulation accuracy. Finally, we estimate the safety margins going forward. We predict that backgrounds should remain high but acceptable until a luminosity of at least $\rm 2.8 \times 10^{35}~cm^{-2}s^{-1}$ is reached for $\beta^{*}_{\rm y}=\rm 0.6~mm$. At this point, the most vulnerable Belle II detectors, the Time-of-Propagation (TOP) particle identification system and the Central Drift Chamber (CDC), have predicted background hit rates from single-beam and luminosity backgrounds that add up to approximately half of the maximum acceptable rates.

hep-ex↗

arXiv2022

First observation of $B\!\to \bar{D}_1(\to\bar{D}\pi^+\pi^-)\ell^+\nu_\ell$ and measurement of the $B\!\to \bar{D}^{()}\pi\ell^+\nu_\ell$ and $B\!\to \bar{D}^{()}\pi^+\pi^-\ell^+\nu_\ell$ branching fractions with hadronic tagging at Belle

We report measurements of the ratios of branching fractions for $B \to \bar{D}^{(*)}\pi\ell^+\nu_\ell$ and $B \to \bar{D}^{(*)}\pi^+\pi^-\ell^+\nu_\ell$ relative to $B \to \bar{D}^*\ell^+\nu_\ell$ decays with $\ell = e, \mu$. These results are obtained from a data sample that contains $772 \times 10^6 B\bar{B}$ pairs collected near the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric energy $e^+e^-$ collider. Fully reconstructing both $B$ mesons in the event, we obtain \begin{align*} \frac{B(B^0 \to \bar{D}^0\pi^-\ell^+\nu_\ell)}{B(B^0 \to D^{*-}\ell^+\nu_\ell)} &= (7.24\pm0.36\pm0.12)\%\ ,\\ \frac{B(B^+ \to D^-\pi^+\ell^+\nu_\ell)}{B(B^+ \to \bar{D}^{*0}\ell^+\nu_\ell)} &= (6.78\pm0.24\pm0.15)\%\ ,\\ \frac{B(B^0 \to \bar{D}^{*0}\pi^-\ell^+\nu_\ell)}{B(B^0 \to D^{*-}\ell^+\nu_\ell)} &= (11.10\pm0.48\pm0.20)\%\ ,\\ \frac{B(B^+ \to D^{*-}\pi^+\ell^+\nu_\ell)}{B(B^+ \to \bar{D}^{*0}\ell^+\nu_\ell)} &= (9.50\pm0.33\pm0.27)\%\ ,\\ \frac{B(B^0 \to D^-\pi^+\pi^-\ell^+\nu_\ell)}{B(B^0 \to D^{*-}\ell^+\nu_\ell)} &= (2.91\pm0.37\pm0.25)\%\ ,\\ \frac{B(B^+ \to \bar{D}^0\pi^+\pi^-\ell^+\nu_\ell)}{B(B^+ \to \bar{D}^{*0}\ell^+\nu_\ell)} &= (3.10\pm0.26\pm0.21)\%\ ,\\ \frac{B(B^0 \to D^{*-}\pi^+\pi^-\ell^+\nu_\ell)}{B(B^0 \to D^{*-}\ell^+\nu_\ell)} &= (1.03\pm0.43\pm0.18)\%\ ,\\ \frac{B(B^+ \to \bar{D}^{*0}\pi^+\pi^-\ell^+\nu_\ell)}{B(B^+ \to \bar{D}^{*0}\ell^+\nu_\ell)} &= (1.25\pm0.27\pm0.15)\%\ , \end{align*} where the uncertainties are statistical and systematic, respectively. The invariant mass spectra of the $D\pi$, $D^*\pi$, and $D\pi\pi$ systems are studied. Branching fraction products are extracted, among them the first observations of $B(B^0 \to D_1^-\ell^+\nu_\ell) \times B(D_1^- \to D^-\pi^+\pi^-) = (0.102\pm0.013\pm0.009)\%$ and $B(B^+ \to \bar{D}_1^0\ell^+\nu_\ell) \times B(\bar{D}_1^0 \to \bar{D}^0\pi^+\pi^-) = (0.105\pm0.011\pm0.008)\%$.

hep-ex↗

arXiv2022

Measurements of branching fractions of $\Lambda_c^+ \to \Sigma^+ \eta$ and $\Lambda_c^+ \to \Sigma^+ \eta'$ and asymmetry parameters of $\Lambda_c^+ \to \Sigma^+ \pi^0$, $\Lambda_c^+ \to \Sigma^+ \eta$, and $\Lambda_c^+ \to \Sigma^+ \eta'$

We report a study of $\Lambda_c^+ \to \Sigma^+ \pi^0$, $\Lambda_c^+ \to \Sigma^+ \eta$, and $\Lambda_c^+ \to \Sigma^+ \eta'$ using the data sample corresponding to an integrated luminosity of 980 $\rm fb^{-1}$ collected with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. The branching fractions relative to $\Lambda_c^+ \to \Sigma^+ \pi^0$ are measured as: $\mathcal{B}_{\Lambda_c^+ \to \Sigma^+ \eta}/\mathcal{B}_{\Lambda_c^+ \to \Sigma^+ \pi^0}=0.25 \pm 0.03 \pm 0.01$ and $\mathcal{B}_{\Lambda_c^+ \to \Sigma^+ \eta'}/\mathcal{B}_{\Lambda_c^+ \to \Sigma^+ \pi^0}=0.33 \pm 0.06 \pm 0.02$. Using $\mathcal{B}_{\Lambda_c^+ \to \Sigma^+ \pi^0}=(1.25 \pm 0.10)\%$, we obtain $\mathcal{B}_{\Lambda_c^+ \to \Sigma^+ \eta}=(3.14 \pm 0.35 \pm 0.11 \pm 0.25)\times10^{-3}$ and $\mathcal{B}_{\Lambda_c^+ \to \Sigma^+ \eta'}=(4.16 \pm 0.75 \pm 0.21 \pm 0.33)\times10^{-3}$. Here the uncertainties are statistical, systematic, and from $\mathcal{B}_{\Lambda_c^+ \to \Sigma^+ \pi^0}$, respectively. The ratio of the branching fraction of $\Lambda_c^+ \to \Sigma^+ \eta'$ with respect to that of $\Lambda_c^+ \to \Sigma^+ \eta$ is measured to be $\mathcal{B}_{\Lambda_c^+ \to \Sigma^+ \eta'}/\mathcal{B}_{\Lambda_c^+ \to \Sigma^+ \eta}=1.34 \pm 0.28 \pm 0.06$. We update the asymmetry parameter of $\Lambda_c^+ \to \Sigma^+ \pi^0$, $\alpha_{\Sigma^+ \pi^0} = -0.48 \pm 0.02 \pm 0.02$, with a considerably improved precision. The asymmetry parameters of $\Lambda_c^+ \to \Sigma^+ \eta$ and $\Lambda_c^+ \to \Sigma^+ \eta'$ are measured to be $\alpha_{\Sigma^+ \eta} = -0.99 \pm 0.03 \pm 0.05$ and $\alpha_{\Sigma^+ \eta'} = -0.46 \pm 0.06 \pm 0.03$ for the first time.

hep-ex↗

arXiv2022

Observation of $\Omega(2012)^- \to \Xi(1530)\bar{K}$ and measurement of the effective couplings of $\Omega(2012)^-$ to $\Xi(1530)\bar{K}$ and $\Xi\bar{K}$

Using $\Upsilon(1S)$, $\Upsilon(2S)$, and $\Upsilon(3S)$ data collected by the Belle detector, we discover a new three-body decay, $\Omega(2012)^-\to\Xi(1530)\bar K\to\Xi\pi\bar K$, with a significance of 5.2~$\sigma$. The mass of the $\Omega(2012)^-$ is $(2012.5\pm0.7\pm0.5)$ MeV and its effective couplings to $\Xi(1530)\bar{K}$ and $\Xi\bar{K}$ are $(39^{+31}_{-39}\pm9)\times10^{-2}$ and $(1.7\pm0.3\pm0.3)\times10^{-2}$, where the first uncertainties are statistical and the second are systematic. The ratio of the branching fraction for the three-body decay to that for the two-body decay to $\Xi\bar{K}$ is $0.99\pm0.26\pm0.06$, assuming isospin symmetry.

hep-ex↗

arXiv2022

Measurement of the branching fraction of $\Xi_{c}^{0}\to \Lambda_{c}^{+}\pi^{-}$ at Belle

Based on a data sample of 983 fb$^{-1}$ collected with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider, we present the study of the heavy-flavor-conserving decay $\Xi_{c}^{0}\to \Lambda_{c}^{+}\pi^{-}$ with $\Lambda_{c}^{+}$ reconstructed via its $pK^{-} \pi^{+}$ decay mode. The branching fraction ratio $\mathcal{B}(\Xi_{c}^{0}\to \Lambda_{c}^{+}\pi^{-})/\mathcal{B}(\Xi_{c}^{0}\to \Xi^{-}\pi^{+})$ is measured to be $0.38 \pm 0.04 \pm 0.04$. Combing with the world average value of $\mathcal{B}(\Xi_{c}^{0}\to \Xi^{-}\pi^{+})$, the branching fraction $\mathcal{B}(\Xi_{c}^{0}\to \Lambda_{c}^{+}\pi^{-})$ is deduced to be $(0.54 \pm 0.05 \pm 0.05 \pm 0.12)\%$. Here, the uncertainties above are statistical, systematic, and from $\mathcal{B}(\Xi_c^{0} \to \Xi^{-}\pi^{+})$, respectively.

hep-ex↗

arXiv2022

Snowmass 2021 White Paper on Upgrading SuperKEKB with a Polarized Electron Beam: Discovery Potential and Proposed Implementation

Upgrading the SuperKEKB electron-positron collider with polarized electron beams opens a new program of precision physics at a center-of-mass energy of 10.58 GeV. This white paper describes the physics potential of this `Chiral Belle' program. It includes projections for precision measurements of $\sin^2\theta_W$ that can be obtained from independent left-right asymmetry measurements of $e^+e^-$ transitions to pairs of electrons, muons, taus, charm and b-quarks. The $\sin^2\theta_W$ precision obtainable at SuperKEKB will match that of the LEP/SLC world average, but at the centre-of-mass energy of 10.58 GeV. Measurements of the couplings for muons, charm, and $b$-quarks will be substantially improved and the existing $3\sigma$ discrepancy between the SLC $A_{LR}$ and LEP $A_{FB}^b$ measurements will be addressed. Precision measurements of neutral current universality will be more than an order of magnitude more precise than currently available. As the energy scale is well away from the $Z^0$-pole, the precision measurements will have sensitivity to the presence of a parity-violating dark sector gauge boson, $Z_{\rm dark}$. The program also enables the measurement of the anomalous magnetic moment $g-2$ form factor of the $\tau$ to be made at an unprecedented level of precision. A precision of $10^{-5}$ level is accessible with 40~ab$^{-1}$ and with more data it would start to approach the $10^{-6}$ level. This technique would provide the most precise information from the third generation about potential new physics explanations of the muon $g-2$ $4\sigma$ anomaly. Additional $\tau$ and QCD physics programs enabled or enhanced with having polarized electron beams are also discussed in this White Paper. This paper includes a summary of the path forward in R&D and next steps required to implement this upgrade and access its exciting discovery potential.

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