Search for New Physics in the $B \rightarrow K \, \ell^{+} \ell^{-}$ Processes at Belle II
Alejandro Mora
February 20 - 27 of 2019

Moscow, Russia
decay-draw
Search for New Physics in the $B \rightarrow K \ell^{+} \ell^{-}$ Processes at Belle II
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The $B \rightarrow K \, \ell^{+} \ell^{-}$ decays
penguin-diagrams box-diagram
  • A flavor changing neutral current $\left(b \rightarrow s\ell^{+}\ell^{-}\right)$
  • Interplay between strong and electroweak interactions
  • Forbidden at tree level in the SM. Appears only in diagrams with one or more loops
  • $W^{\pm}$ and $t$ masses are much bigger than $B$ mass, so highly supressed ($\mathcal{B} \sim 10^{-7}$)
NP contributions can be of the same order as SM ones!
decay-rate
J. Walsh [2002] in FPCP-2002, U. Pennsylvania
  • Solid line + blue bands: SM range ($\pm$35%), Ali et al. form factors [PRD 66 (2002) 034002]
  • Dotted line: SUGRA model ($R_7 = -1.2$, $R_9 = 1.03$, $R_{10} = 1$)
  • Long-short dashed line: SUSY model ($R_7 = -0.83$, $R_9 = 0.92$, $R_{10} = 1.61$)
  • $R_i = \mathcal{C}_i/\mathcal{C}_i^{\text{SM}}$
Where to Look for New Physics

Decay rate ratios

$$R_K = \frac{\Gamma(B\rightarrow K \, \mu^{+} \, \mu^{-})}{\Gamma(B\rightarrow K \, e^{+} \, e^{-})}$$
$1 \pm \mathcal{O}(10^{-3})$ in the SM!
RK-measured
Where to Look for New Physics

Angular analysis

decay-cartoon AFB-measured
$A_{FB}^{\ell} = \frac{N_F^{\ell}-N_B^{\ell}}{N_F^{\ell}+N_B^{\ell}}$

$N_F$: Number of decays with $0 < \left|\theta_{\ell}\right| < \pi/2$

$N_B$: Number of decays with $\pi > \left|\theta_{\ell}\right| > \pi/2$

What makes the difference?

The accelerator

Campus-picture

The detector

BelleII-picture
SuperKEK-picture
Different (complementary) to the LHC:
focuses on high intensity, not energies!
CM Energy = 10.58 GeV:
Just above the $\Upsilon(4S)$ resonance mass
Cleaner events:
Both $ee$ and $\mu\mu$ channels accessible with similar efficiencies!
Aiming for a (new) world luminosity record:
$8 \times 10^{35} \text{cm}^{-2}\text{s}^{-1}$
... How?
  • Increase currents: 3.6 (2.6) A for $e^{+}$ ($e^{-}$)
  • Reduce beam sizes at IP: $10 \, \mu \text{m} \times 20 \, \text{nm}$
The nanobeam scheme
BelleII-schematics
Vertex detectors: primary and secondary vertex reconstruction ($K^0_s$)
Central tracking device: momentum measurement of charged particles
PID systems: $K/\pi$ separation. Extended to almost $4\pi$
$\gamma$ and $e$ detection: detection of Bremsstrahlung radiation and higher $\pi/e$ separation efficiency
$\mu$ detection
BelleII-firstEvent
The reconstruction process
  • particle id > 0.1
    (pid $= \mathcal{L}_{p}/\sum_i \mathcal{L}_{i}$)
  • Good track fit
    ($\chi^2 > 0.001$)
  • Near the IP
    ($d_0 < 0.5$ and $|z_0| < 2$)
  • vertex fit
  • cuts in position according to $p$
  • $0.468$ GeV $< M <$ $0.528$ GeV
  • 5.22 GeV < $m_{bc}$ < 5.29 GeV
    $m_{bc} = \sqrt{E_{\text{beam}} - \boldsymbol{p}_{B,\text{reco}}^2}$
  • -0.1 GeV < $\Delta E$ < 0.05 GeV $e$ ch.
    -0.05 GeV < $\Delta E$ < 0.05 GeV $\mu$ ch.
    $\Delta E = E_{B,\text{reco}}-E_{\text{beam}}$
$K^{\pm}$
$\ell^{\pm}$
$\pi^{\pm}$
$K_s$
$B^{\pm}$
$B^0$

$B^{\pm} \rightarrow K^{\pm} + e^{+} + e^{-}$

$B^{\pm} \rightarrow K^{\pm} + \mu^{+} + \mu^{-}$

$B^{0} \rightarrow K^{0}_S + e^{+} + e^{-}$

$B^{0} \rightarrow K^{0}_S + \mu^{+} + \mu^{-}$

Preliminary: MC efficiencies
Conclusions
  • The $B \rightarrow K \ell \ell$ constitutes an excellent probe for new physics
    • Tests contributions from different NP scenarios
    • Possible to construct observables with low systematic uncertainties
  • The Super KEK B-Factory and the Belle II experiment are the perfect environment for this searches
    • World record luminosity
    • Similar efficiencies for both electron and muon channels over the whole $q^2$ range
    • Current efficiencies similar to those from Belle, with plenty of room for improvement!

Backup

Measurements
$R_K$:
Belle: $1.03 \pm 0.19 (\text{stat}) \pm 0.06 (\text{sys})$ (full range)
[PRL 103 (2009) 171801]
BaBar: $1.00^{+0.31}_{-0.25}(\text{stat}) \pm 0.07 (\text{sys})$ (full range)
[PRD 86 (2012) 032012]
LHCb: $0.745^{+0.090}_{-0.074}(\text{stat}) \pm 0.04 (\text{sys})$ ($1 < q^2 < 6 \text{GeV}^2$)
[PRL 113 (2014) 151601]
$A_{FB}$:
Belle: $0.10 \pm 0.14 (\text{stat}) \pm 0.01 (\text{sys})$ ($B^+ \rightarrow K^+ \ell^{+} \ell^{-}$)
[PRL 96 (2006) 251801]
BaBar: $0.15^{+0.21}_{-0.23}(\text{stat}) \pm 0.08 (\text{sys})$ (all channels)
[PRD 73 (2006) 092001]
LHCb: $0.02^{+0.05}_{-0.03}(\text{stat})^{+0.02}_{-0.01}(\text{sys})$ ($B^+ \rightarrow K^+ \mu \mu$)
[JHEP 1302 (2013) 105]
Other observables
$A_{I}^{\ell} = \frac{\mathcal{B}\left(B^0 \rightarrow K^0 \ell \ell\right)-\mathcal{B}\left(B^+ \rightarrow K^+ \ell \ell\right)}{\mathcal{B}\left(B^0 \rightarrow K^0 \ell \ell\right)+\mathcal{B}\left(B^+ \rightarrow K^+ \ell \ell\right)}$
AI-measured
$A_{CP}^{\ell} = \frac{\mathcal{B}\left(\overline{B} \rightarrow \overline{K} \ell \ell\right)-\mathcal{B}\left(B \rightarrow K \ell \ell\right)}{\mathcal{B}\left(\overline{B} \rightarrow \overline{K} \ell \ell\right)+\mathcal{B}\left(B \rightarrow K \ell \ell\right)}$
ACP-measured
Effect of luminosity in $\delta R_K$
effect_lum_RdK
Similar events in Belle and LHCb
events-example-at-LHC-Belle
$B^{-} \rightarrow D^{0}\left(K^{-}\pi^{+}\right)+\tau^{-}\left(e^{-}\overline{\nu}_e\nu_{\tau}\right)+\overline{\nu}_{\tau}$
$\overline{B^{0}} \rightarrow D^{*+}\left(D^{0}\left[K^-\pi^+\right]\pi^{+}\right)+\tau^{-}\left(\mu^{-}\overline{\nu}_{\mu}\nu_{\tau}\right)+\overline{\nu}_{\tau}$
Image courtesy of T. Browder in Second international workshop "Particles, Gravitation and the Universe", 2018, Hanoi
First events topologies
event-counting
Image courtesy of T. Browder in Second international workshop "Particles, Gravitation and the Universe", 2018, Hanoi
Physics Backgrounds
Charmonium decays: $B \rightarrow K+J/\psi(\ell^{+}\ell^{-})$ and $B \rightarrow K+\psi(2S)(\ell^{+}\ell^{-})$
Solution: veto regions
  • $8.11$ GeV$^2$ $ < q^2 < 10.03$ GeV$^2$
  • $12.15$ GeV$^2$ $ < q^2 < 14.11$ GeV$^2$
  • Photo-conversion/$\pi^0$ dalitz: $0.14$ GeV $ > q$
  • $8.68$ GeV$^2$ $ < q^2 < 10.09$ GeV$^2$
  • $12.86$ GeV$^2$ $ < q^2 < 14.18$ GeV$^2$
Continuum events: $ee \rightarrow qq$
Solution: MVA classifier
Background rejected: 91.66%. Signal kept: 92.88%
(on testing dataset)
MVA specs
fastBDT
Training/testing samples with 1:1 signal to background ratio
48572 examples after reconstruction cuts (80% of data for training, 20% for testing)
18 variables
  • KSFWM (13)
  • Cosine of the angle between signal thrust and beam axis (1)
  • Cosine of the angle between signal thrust and ROE thrust (1)
  • R2 (1)
  • Magnitude of the ROE and the signal thrust axis (2)
Preliminaryy: efficiencies
Angular
In $q^2$ bins
Angular distributions
Correlations between $q^2$ and $\cos \theta_{\ell}$
Preliminary: sources of background from generic $B^0$ decays (1.2 ab$^{-1}$)