Belle II Experiment: Precision Flavor Physics

• Belle II Experiment is a high-luminosity flavor physics facility at SuperKEKB in Japan, featuring advanced accelerator and detector upgrades.
• It delivers exceptional sensitivity for rare B, D, and tau decays, enabling precise tests of the Standard Model and searches for new physics.
• Innovations like DEPFET pixel detectors and an enhanced CDC underpin Belle II’s ability to reconstruct complex decay events with excellent background control.

The Belle II experiment is a high-luminosity flavor physics facility situated at the SuperKEKB asymmetric-energy electron-positron ($e^+e^-$) collider in Tsukuba, Japan. As a next-generation upgrade to the original Belle detector and KEKB collider, Belle II is designed to record an integrated luminosity of 50 ab$^{-1}$—a dataset 50 times larger than its predecessor—at a design instantaneous luminosity of $8\times 10^{35}$ cm$^{-2}$s$^{-1}$. This combination of accelerator and detector upgrades enables world-leading sensitivity to rare processes involving $B$-mesons, $D$-mesons, and $\tau$ leptons, with a central program focused on precision tests of the Standard Model (SM) and searches for new physics via forbidden or extremely rare decays.

1. Accelerator and Detector Upgrades

Belle II operates at the SuperKEKB collider, which employs the "nano-beam" scheme to achieve an unprecedented luminosity 40 times higher than its predecessor KEKB. Key accelerator upgrades include:

• Nano-beam optics: vertical beta function, $\beta_y^*$, reduced to sub-millimeter scale,
• Higher beam currents: $I_{e^-}=3.60$ A, $I_{e^+}=2.60$ A,
• Asymmetric collision energies: 7 GeV (electron) and 4 GeV (positron) beams,
• Large crossing angle (83 mrad) to reduce parasitic collisions.

The detector features substantial advancements over Belle:

• Vertex detector: Two layers of DEPFET-based pixel detectors (PXD) and four layers of silicon strip detectors (SVD) for enhanced vertex resolution,
• Central Drift Chamber (CDC): Expanded volume and smaller drift cells for improved tracking,
• Particle Identification (PID): Aerogel RICH (ARICH) and Time-of-Propagation (TOP) systems for kaon/pion and electron/muon separation,
• Upgraded electronics across all subsystems for faster data acquisition and higher background tolerance.

These upgrades underpin Belle II's ability to reconstruct complex decay final states and control backgrounds at the requisite event rates and occupancy.

2. Collider Parameters and Data Sample

SuperKEKB is configured to maximize the production cross section for $e^+e^- \to \Upsilon(4S) \to B\bar{B}$ and $e^+e^- \to \tau^+\tau^-$. The design integrated luminosity for Belle II is:

$$\mathcal{L}_{\text{design}} = 8 \times 10^{35}~\text{cm}^{-2}~\text{s}^{-1}$$

The full dataset ($50$ ab$^{-1}$) corresponds to approximately $45 \times 10^9$ $\tau^+\tau^-$ events, enabling both high-precision SM measurements and rare decay searches dominated by systematic, rather than statistical, uncertainties.

Commissioning of SuperKEKB and partial Belle II subsystems was completed in 2018; full operation with the complete detector began in March 2019 ("Phase III run").

3. Tau Lepton Physics: Lepton Flavor and Number Violation

Belle II's large $\tau$-pair dataset establishes it as a "tau factory," allowing sensitive searches for physics beyond the Standard Model through forbidden processes:

• Lepton Flavor Violation (LFV): The Standard Model, minimally extended for neutrino masses, predicts branching ratios $\mathcal{B}(\tau \to 3\ell) \sim 10^{-54}$, making any observation of LFV an unambiguous signal of new physics (e.g., scenarios involving supersymmetry, heavy neutrinos, or other exotics).
• Lepton Number Violation (LNV): Searches for processes such as $\tau^- \to \mu^+ \pi^- \pi^-$, forbidden in the SM unless neutrinos are Majorana particles.

Experimental sensitivity for LFV channels with 50 ab$^{-1}$:

Decay Mode	Expected 90% C.L. Upper Limit (Belle II)	Current Best Limit (BaBar/Belle/LHCb)
$\tau \to 3\mu$	$<10^{-9}$	$\sim10^{-8}$–$10^{-7}$
$\tau \to \mu\gamma$	[Comparable improvement]	$10^{-8}$–$10^{-7}$

Upper limit convention:

$\mathcal{B}(\tau \to X) < \text{UL at 90\%~CL}$

Such advances will place Belle II orders of magnitude below current bounds for these forbidden decays.

4. CP Violation and Precision Tau Physics

The large cross-section for $e^+e^- \rightarrow \tau^+\tau^-$ at $\sqrt{s} = m_{\Upsilon(4S)}$ enables detailed studies of SM tau properties and CP violation:

• CP violation in tau decays: Particularly in modes such as $\tau^\pm \to K_S^0 \pi^\pm \nu_\tau$, where the decay-rate asymmetry,

$$A_\tau = \frac{ \Gamma(\tau^+\to\pi^+K^0_S\bar{\nu}_\tau) - \Gamma(\tau^-\to\pi^-K^0_S \nu_\tau) }{ \Gamma(\tau^+\to\pi^+K^0_S\bar{\nu}_\tau) + \Gamma(\tau^-\to\pi^-K^0_S \nu_\tau) }$$

has a SM prediction of $A_\tau^{\text{SM}} = (3.6 \pm 0.1)\times 10^{-3}$. BaBar's measurement, $$A_\tau^{\text{BaBar}} = (-3.6 \pm 2.3 \pm 1.1) \times 10^{-3}$$, deviates from the SM at 2.8$\sigma$.

• Prospects at Belle II: Expected statistical improvement ($\sqrt{70}$ reduction in error) will push sensitivity to the $10^{-4}$ level, testing SM predictions in tau CPV with world-leading precision.

5. Programmatic Context and Synergy

Belle II’s comprehensive tau physics program builds directly on the achievements of BaBar and Belle, which established the foundational limits and basic tau properties. The high luminosity, improved detector components, and $e^+e^-$ event environment yield low hadronic backgrounds and high event reconstruction efficiency, enhancing both SM and BSM sensitivity, especially for channels with neutrinos or other missing particles. Systematics will dominate as the statistical power surpasses previous generations by orders of magnitude.

6. Broader Physics Reach and Impact

In addition to LFV/LNV and CPV, Belle II will perform:

• Precision measurements of tau mass, lifetime, and branching fractions,
• Studies of Michel parameters in leptonic tau decays, probing Lorentz structure,
• Searches for second-class currents (SCC), e.g., $\tau^- \to \eta \pi^- \nu_\tau$, which are forbidden in the SM,
• Investigations into rare and forbidden processes with branching fractions sensitive to new charged or neutral current couplings.

With approximately 45 billion $\tau^+\tau^-$ events planned, Belle II will remain the world’s leading laboratory for tau lepton physics until a next-generation Super Tau-Charm Factory becomes operational.

7. Anticipated Legacy

Belle II’s tau sector program is expected to:

• Tighten upper limits on forbidden LFV and LNV tau decays by at least an order of magnitude over previous experiments,
• Sharpen probes of fundamental symmetries,
• Provide critical constraints for models of new physics and validate or refute hints for anomalous CP violation,
• Serve as an essential resource for flavor physics, dark sector searches, and the broader high-intensity frontier for the foreseeable future.

Summary Table: Tau Physics Sensitivity at Belle II

Physics Target	SM Prediction / Prior Limit	Belle II Sensitivity
$\tau \to \mu\gamma$, $3\mu$	$\mathcal{B}_{\rm SM}\sim10^{-54}$; prior $<10^{-8}$–$10^{-7}$	$<10^{-9}$
CPV Asymmetry ($A_\tau$)	$(3.6 \pm 0.1)\times 10^{-3}$	$\sim 10^{-4}$
Number of $\tau^+\tau^-$	n/a	$\sim 45\times 10^9$

Belle II’s data and discoveries will play a central role in constraining or discovering new particles or interactions tied to flavor physics, leptogenesis, and models beyond the Standard Model (Pérez, 2019, Villanueva, 2018).