Prospects for the Belle II experiment to further elucidate the KM mechanism and beyond

We present prospects for the Belle II experiment to further elucidate the KM mechanism and beyond. Recent measurements of the CKM parameter, and the radiative and electroweak penguin decays are also reported.


Introduction 1.Physics at a B factory
The main approach of flavor physics experiments is to search for evidence of new physics via quantum effects.Since all quark flavors are produced in e + e − collisions, one can study possible couplings between new particles and any quark flavor, including those of the third generation.Within the Standard Model (SM), the third generation gives rise to CP violation, as described by the Kobayashi-Maskawa (KM) mechanism.In addition to quarks, an e + e − "B factory" collider produces a very large number of tau lepton pairs, which the Belle II experiment also studies.

SuperKEKB and Belle II
SuperKEKB [1] is the only e + e − collider now running at the energy of the Υ(4S) resonance.The design goal of SuperKEKB is to achieve an instantaneous luminosity of 10 35 cm −2 s −1 .To achieve this, the accelerator runs with large beam currents and very small beam sizes at the interaction point (IP).A comparison of parameters between the previous KEKB accelerator [2] used for the Belle experiment and the SuperKEKB accelerator used for Belle II is given in Table 1.One notable difference is the beam energies, which are less asymmetric at SuperKEKB; this change significantly improves the beam lifetimes.
The Belle II detector consists of multiple components.It is designed to operate at high trigger rates and high background conditions.To achieve this, all components have been upgraded from the previous Belle detector [3], e.g., with finer segmentation and higher time resolution.As the trigger rate at the SuperKEKB design luminosity is expected to reach 30 kHz, a pipe-line readout is implemented.A new vertex detector consisting of silicon pixels and silicon strips provides excellent position resolution for decay vertices of B and D mesons.Table 1: Main parameters of KEKB and SuperKEKB colliders.
Excellent particle identification is achieved by two newly developed detectors: a quartz-based "time-of-propagation" counter, and an aerogel-based ring-imaging Cherenkov counter.
Belle II began collecting physics data in 2019.In 2020 the SuperKEKB collider exceeeded the (instantaneous) luminosity record of KEKB of 2 × 10 34 , and in 2022 it achieved a world record luminosity of 4.7×10 34 .As of the summer of 2022, the integrated luminosity had reached 427 fb −1 , which is similar to that recorded by the BABAR experiment and about half that recorded by Belle.The Belle II experiment is now concluding a long shutdown and will begin taking data again in early 2024.During this shutdown, the second layer of the silicon pixel detector was installed, and numerous other improvements were made to the detector and accelerator.

Belle II physics program
Belle (1999-2010) was constructed to confirm the KM model of CP violation.This was achieved -along with the BABAR experiment at SLAC -and resulted in the 2006 Nobel Prize in Physics being awarded to Kobayashi and Maskawa.Belle ultimately recorded almost 1 ab −1 of data.Belle II is designed to explore beyond the KM model and hopefully uncover new physics.The final dataset is expected to be ∼ 50 ab −1 .

Search for new physics in mixing
During the era of Belle and BABAR , numerous measurements of the elements of the Cabibbo-Kobayashi-Maskawa (CKM) mixing matrix were performed.These provide a precision test of the unitarity of the CKM matrix, i.e., if the internal angles of the CKM "Unitarity Triangle" summed up to less than 180 • , or if measurements of the angles determined from tree-amplitude decays and from loop-amplitude decays differed, that would indicate physics beyond the SM.Belle II will continue these measurements with much higher precision, and it is expected to yield among the most precise determinations of all three sides and all three internal angles of this triangle.
The angle ϕ 1 provided the first evidence for CP violation in the B system.This CP violation is caused by interference between a direct decay amplitude and a decay amplitude proceeding via mixing.The decay B → J/ψ K S allows one to measure the CKM angle ϕ 1 with negligible theoretical uncertainty, as the direct decay amplitude is dominated by a tree diagram and thus contains essentially a single weak phase.For this decay, there will be a time-dependent CP asymmetry between B 0 decays and B 0 decays, with an oscillation amplitude given by sin 2ϕ 1 .Decays such as B → ϕK 0 and B → η ′ K 0 should have the same weak phase and thus the same dependence upon sin 2ϕ 1 .However, they proceed via b → s penguin (loop) amplitudes and thus are sensitive to new particles propagating within internal loops.Such particles would deviate the amplitude of the time-dependent CP asymmetry from the SM prediction (sin 2ϕ 1 ).With only a small dataset, Belle II has measured sin2ϕ 1 for B → J/ψK S decays, as listed in Table 2.The result is consistent with the previous Belle measurement; the systematic uncertainties are comparable due to improvements in the detector performance [5].In particular, the addition of pixels to the silicon vertex detector improved the precision of the measurement of decay times.[6].

Experiment
Figure 1 shows the ∆t distribution of B 0 → J/ψK S and B 0 → J/ψK S decays, and the measured raw CP asymmetry, where ∆t is the difference between the decay time of the signal B → J/ψK S decay (denoted B sig ) and that of the B meson recoiling against the signal decay (denoted B tag ).The flavor of B sig (B 0 or B 0 ) is identified by the flavor of B tag .Further improvements in this measurement are expected as the integrated luminosity increases.With the full 50 ab −1 of data, the angles of the Unitarity Triangle are expected to be measured with a precision of ∼ 1 • , and the sides with a precision of 1−2%.

Flavor Changing Neutral Current processes
Flavor Changing Neutral Current (FCNC) processes are a good probe for new physics, as loop diagrams dominate such decays.There are numerous measured observables, and any deviation from the SM prediction would be interpreted as evidence for new physics.For radiative or electroweak decays, having a photon or charged leptons in the final state results in smaller theoretical uncertainties in the SM prediction.However, for exclusive decays there are still significant uncertainties due to hadronization, e.g., the process B → K * .Inclusive measurements have smaller theoretical uncertainties but experimentally are more challenging.
Belle-II has measured the branching fraction (B) for the inclusive radiative decay B → X s γ using 189 fb −1 of data [7].This decay proceeds via a b → sγ loop amplitude, and the measurement employs a "hadronic tag" in which B tag (the B meson recoiling against B sig ) is fully reconstructed.This reconstruction reduces backgrounds by orders of magnitude, but it also greatly reduces the  signal efficiency.After all selection criteria, the latter is only ∼ 0.01%.Figure 2 shows the distribution of the beam-constrained mass (M bc ) for B tag , and also the signal yield of B B events as a function of photon energy in the B sig rest frame.The observable M bc is defined as E 2 beam − p 2 tag , where E beam is the beam energy and p tag is the reconstructed momentum of B tag in the e + e − centerof-mass frame.The result, B(B → X s γ) = 3.54 ± 0.78 (stat.)± 0.83 (syst.)for E B γ > 1.8 GeV, is consistent with the SM prediction; the precision is similar to that obtained by BABAR using 210 fb −1 of data.Both measurements are dominated by systematic uncertainties.In the future, Belle II expects to reduce the overall uncertainty from 5% to 3%.The dominant systematic error in the lepton-tag method comes from a fake signal of photon due to neutral hadrons [8].
The results are: These values imply a ratio 0.83 ± 0.36, which is consistent with the theory  expectation [10].
With more data, these measurements should significantly improve.Scaling these uncertainties by luminosity, one obtains ∼ 3% precision for 50 ab −1 of data (for The electroweak penguin decay B → K ( * ) ν ν has not yet been observed.This decay is especially challenging to reconstruct as it has two neutrinos in the final state.Belle II is the only running experiment able to search for this decay.Using only 63 fb −1 of data, Belle II searched for B + → K + ν ν using a new analysis method [12].The signal K + is identified as the charged track with highest transverse momentum that satisfies particle identification criteria.All remaining tracks and energy clusters are associated with the other B meson in an event (B tag ).This results in high reconstruction efficiency but also high background levels.The latter is reduced by using a boosted decision tree classifier that is trained to identify distinctive characteristic of signal events.No signal is observed, and an upper limit on the branching fraction is obtained: This precision is similar to that obtained by Belle using 711 fb −1 of data and a hadronic tagging method.All results are summarized in Figure 4.   [13,14,15].Also shown is the SM prediction [16].

Tau physics prospects
In addition to BB events, Belle II will collect a large sample of τ + τ − events.This sample will provide a rich physics programs of high precision measurements.For example, Belle II can search for lepton flavor violation (LFV) in such modes as τ + → µ + γ, τ + → ℓ + ℓ − ℓ + (ℓ = µ, e), etc.There are more than 40 such LFV τ + decays, many of which can only be reconstructed at an e + e − experiment such as Belle II.

Dark sector prospects
Several studies of the dark sector are active at Belle II.Dark matter may interact with SM particles through various "portal" interactions.Belle II can search for dark matter having a mass in the range 100 MeV/c 2 to a few GeV/c 2 .Many decay signatures consist of only a single photon or a single track in the detector, and specialized triggers have been developed for Belle II to record such topologically unusual events.

Summary
In summary, a new e + e − collider (SuperKEKB) has been constructed and commissioned at KEK, and a new state-of-the-art detector (Belle II) has begun taking data and producing physics results.This collider is the most recent in a series that began with TRISTAN and continued with KEKB.The SuperKEKB collider has achieved a world record instantaneous luminosity of 4.7×10 34 cm −2 s −1 , and Belle II has already recorded an integrated luminosity of several hundred fb −1 , equivalent to the BABAR dataset.This is the start of a new era of measurements at a "Super B factory," with the goal of uncovering new physics beyond the SM.

Figure 2 :
Figure 2: M bc distribution for B tag candidates (left); signal yield of B B events as a function of photon energy in the B sig rest frame (right).

Table 2 :
Measurements of sin 2ϕ 1 by Belle II and Belle