Prospects for Rare b → τ Decays

at B Factories

Karen Lingel SLAC

25 Mar 97

B Physics and CP Violation Conference, Honolulu, Hawaii

Outline:

• Theoretical introduction

• Current techniques for B → τν decays ⋆ CLEO’s “neutrino reconstruction” technique ⋆ ALEPH’s B tag + missing energy technique ⋆ L3’s missing energy + large impact parameter technique

• Proposed techniques for B → τν decays ⋆ τ → ℓνν kinematical technique ⋆ τ → ℓνν topological technique ⋆ τ → 3-prong vertex technique

B^{0}, B_{s}^{0} → τ^{+}τ^{−}

• Decays such as B → ℓ^{+}ℓ^{−} are very suppressed in the SM, but excellent place to look for FCNC.

• Standard Model:

\begin{matrix}B(B^{0} → τ^{+}τ^{−}) ∼ 10^{−8} & B(B_{s}^{0} → τ^{+}τ^{−}) ∼ 10^{−7} \\ B(B^{0} → μ^{+}μ^{−}) ∼ 10^{−10} & B(B_{s}^{0} → μ^{+}μ^{−}) ∼ 10^{−9} \\ B(B^{0} → e^{+}e^{−}) ∼ 10^{−15} & B(B_{s}^{0} → e^{+}e^{−}) ∼ 10^{−14} \end{matrix}

B → X_{s}τ^{+}τ^{−}

• Electroweak penguin or box diagram

B(B → X_{s}τ^{+}τ^{−}) ≈ 3 × 10^{−7}

B(B → X_{s}μ^{+}μ^{−}) ≈ 6 × 10^{−6}

B(B → X_{s}e^{+}e^{−}) ≈ 6 × 10^{−6}

B → τν

Γ(B^{+} → ℓ^{+}ν) = \frac{G_{F}^{2} M_{B}M_{ℓ}^{2}}{8π} (1 − \frac{M_{ℓ}^{2}}{M_{B}^{2}} ) f_{B}^{2}|V_{ub}|^{2}

• SM Predictions:

⋆ B(B^{+} → τ^{+}ν) ∼ 10^{−4} ⋆ B(B^{+} → μ^{+}ν) ∼ 10^{−7} ⋆ B(B^{+} → e^{+}ν) ∼ 10^{−12}

• Theory: f_{B} = 120 − 300 MeV.

• Use f_{B} and B^{0}B̄^{0} mixing to extract V_{td}:

\frac{Δm}{Γ} = \frac{G_{F}^{2}}{6π^{2}} |V_{td}|^{2}M_{t}^{2}F (\frac{M_{t}^{2}}{M_{W}^{2}} ) M_{B}f_{B}^{2}B_{B}η_{B} τ_{B^{0}}

B → τν at CLEO

• Events with large missing energy

• Fully reconstruct neutrinos using (E, \overrightarrow{p})_{3ν} = (E, \overrightarrow{p})_{miss} of the event.

• ΔE = E_{ℓ} + E_{3ν} − E_{beam}

• M_{B} = \sqrt{E_{beam}^{2} − (\overrightarrow{p}_{ℓ} + \overrightarrow{p}_{3ν})^{2}} • 2-dimensional fit to ΔE and M_{B}:

CLEO 1995 (PRL 75, 785).

yield = −9 ± 36

B(B^{+} → τ^{+}ν_{τ}) < 22 × 10^{−4}

B → τν at ALEPH

• Divide event into two halves

• Require detached vertex in one half (B tag)

• Look for events with large missing energy

• Suppress c, b → Xℓν background by rejecting events with identified leptons.

ALEPH 1995, PLB 343, 444. B(B^{+} → τ^{+}ν_{τ}) < 18 × 10^{−4}

B → τν at L3

• Least energetic hemisphere

• τ decay tagged by hadron or lepton ⋆ with p > 1 GeV ⋆ inconsistent with primary vertex (4σ)

• B^{+} energy and momentum given by

E_{B} = \sqrt{s} − ∑_{i≠τ tag} E_{i} \overrightarrow{P}_{B} = − ∑_{i≠τ tag} \overrightarrow{p}_{i}

• Require P_{B} > 30 GeV (reduces semileptonic background)

• In hadronic sample, require low invariant mass in cone around B direction.

L3 1996 (CERN-PPE/96-198) B(B^{+} → τ^{+}ν_{τ}) < 5.7 × 10^{−4}

Prospects at B factories

• CDF: B’s are very highly boosted ⇒ can use LEP-like techniques • Belle, BaBar: B’s are boosted, neutrinos can be inferred

• CLEO: B’s at rest, neutrinos can be inferred

Belle τ → ℓνν Kinematical Approach

(K. Namba, et al.)

• Neutrino reconstruction: P_{ν} = P_{missing}

• Require N_{ℓ} = 1, ∑ Q = 0, N_{K_{L}} = 0

• Neural Network utilizing: P_{ℓ}^{∗}, ΔE, M_{B}, N_{p}, N_{cp}

Assuming B(B → τν) = 4 × 10^{−5} and luminosity = 100 fb^{−1}

τ → eνν τ → μνν combined
Expected signal  28  40  68
Expected BB̄ background  8300  2800  11000

BaBar τ → ℓνν Topological Approach

(S. Bettarini, M. Carpinelli, M. Giorgi)

Reduce semileptonic background using topological variables:

• Signal has 2 vertices; Background has 3 vertices ⇒ more spread out along z-axis

• Lepton is closer to a vertex in background than in signal

Signal  Background  Signal  Background

χ^{2} = ∑_{i}^{n} \frac{(z_{i}− < z >)^{2}}{σ_{i}^{2}} distance between lepton and < z >

Making appropriate cuts on these sorts of variables:

• 98% background reduction

• 12% signal efficiency

CLEO τ → 3-prong Displaced Vertex Approach

(D. Cinabro)

• Select events with significant missing energy

• Find a 3-track displaced vertex

• Require rest of the event to have (E, \overrightarrow{p}) consistent with a B.

• Kinematically separate signal and b → c background using vertex mass and momentum.

• Flight distance may distinguish leftover background from b → c.

Summary

• B → τν is the most promising of the rare B → τ decays.

• Current techniques include:

⋆ CLEO neutrino reconstruction ⋆ LEP missing energy + vertex techniques

• Techniques being developed:

⋆ τ → ℓνν: not promising using kinematical variables only ⋆ τ → ℓνν: boosted B’s offer additional topological variables ⋆ τ → 3-prong: 3-prong vertex momentum and mass looks promising