The B D ( ) & B decays, Theoretical status thereof - - PowerPoint PPT Presentation

The B → D(∗)τ ¯ ν & B → τ ¯ ν decays,

Theoretical status thereof

Marat Freytsis

University of Oregon FPCP 2016 — Caltech, June 6, 2016

Massive leptons in (semi-)leptonic B decays

unique windows into both NP and the SM via B → (X)τ ¯ ν decays

• Standard Model

◮ B → D(∗) transitions both depend on FFs whose contribution vanishes as mℓ → 0 ◮ B− → τ −¯

ν only decay sensitive to fB measurable in the near future

• New Physics

◮ NP often presumed to couple preferentially to 3rd generation ◮ A reason to persue B → Xsν¯

ν and B(s) → (X)ττ for years

[Hewitt, hep-ph/9506289; Grossman, Ligeti, Nardi, hep-ph/9510378 & hep-ph/9607473]]

• somewhere in between (focus of most of this talk)

◮ high-precision in B → Xu,cℓ¯

ν critical to extraction of |Vub|, |Vcb|

◮ ratios are great venue for tests of lepton flavor universality (LFU)

standard diclaimers: . . . general overview, but colored by my biases . . . . . . apologies to any recent work I might have missed . . .

1/ 18

Plan

• Introduction
• Precise SM predictions

◮ complimentary, CKM-parameter-free families of ratio observables for LFU sensitivity

• Quantifying NP sensitivity

◮ redundant effective operator bases for identification of UV physics

• NP descriminators

◮ more differential distributions for discrimination of scenarios

• Consequences and Conclusions

1/ 18

B− → τ −¯ ν

Pure leptonic decays

In the SM: Γ(B− → τ −¯ ν) = |Vub|2G2

F

8π f 2

Bm2 τmB

• 1 − m2

τ

m2

B

2 either measure |Vub|fB in data or use fB from lattice to extract |Vub| (e.g., latest lattice world average: fB = (190.5 ± 4.2) MeV [FLAG, 1310.8555])

• only P-odd currents contribute: 0|¯

b(γµ)γ5c |B = 0

• new pseudoscalar couplings typically proportional to fermion mass:

Γ(B− → τ −¯ ν) = |1 + rNP|2 Γ(B− → τ −¯ ν)SM = |1 + CAV + m2

BCP |2 Γ(B− → τ −¯

ν)SM

• B
• c

• e

• c

2/ 18

B− → τ −¯ ν

Eliminating |Vub| dependence

|Vub| drops out of ratio, but NP independent of lepton mass

• verall rate can still be affected/act as a bound [Hou, PRD48, 2342 (1993)]

Γ(B− → τ −¯ ν) Γ(B− → µ−¯ ν) = Γ(B− → τ −¯ ν)SM Γ(B− → µ−¯ ν)SM

• B− → µ−¯

νγ correction complicates situation – no helicity suppression an alternative: compare to helicity unsuppressed decay Rπ = τB0 τB− B(B− → τ −¯ ν) B( ¯ B0 → π+ℓ−¯ ν) = 0.73(13) from here ℓ = avg. of µ + e

[Fajfer, Kamenik, Niˇ sandˇ zi´ c, Zupan, 1206.1872]

Rπ

SM = 0.31(6) requires (improvable) decay constants and FFs from the lattice

I have nothing else to add about B− → τ −¯ ν, will now focus on b → cτ ¯ ν transitions

3/ 18

B → D(∗)τ ¯ ν

An R(X) reminder

R(X) = Γ(B → Xτ ¯ ν) Γ(B → Xℓ¯ ν)

• riginal goal: 2HDM H±
• deviation first seen at BaBar, later results from Belle and LHCb

BaBar/Belle full datasets τ → ℓν¯ ν to minimize lepton reco systematics

R(D) R(D∗) BaBar 0.440 ± 0.058 ± 0.042 0.332 ± 0.024 ± 0.018 Belle (B(had)

tag

) 0.375 ± 0.064 ± 0.026 0.293 ± 0.038 ± 0.015 Belle (B(ℓ)

tag )

0.302 ± 0.030 ± 0.011 LHCb 0.336 ± 0.027 ± 0.030

• Exp. average

0.397 ± 0.040 ± 0.028 0.316 ± 0.016 ± 0.010 SM expectation 0.300 ± 0.010 0.252 ± 0.005 Belle II, 50/ab ±0.010 ±0.005

R(D)

0.2 0.3 0.4 0.5 0.6

R(D*)

0.2 0.25 0.3 0.35 0.4 0.45 0.5

BaBar, PRL109,101802(2012) Belle, PRD92,072014(2015) LHCb, PRL115,111803(2015) Belle, arXiv:1603.06711 ) = 67%

2

χ HFAG Average, P( SM prediction

= 1.0

2

χ ∆

R(D), PRD92,054510(2015) R(D*), PRD85,094025(2012) HFAG

• Prel. Winter 2016

◮ clean SM observables: heavy quark symmetry relates FFs

Caprini, Lellouch, Neubert, hep-ph/9712417

cancellation of hadronic uncertainties, |Vcb| in ratios lattice QCD for R(D) only [MILC, 1503.07237; HPQCD, 1505.03925]

◮ R(D) — 1.9σ, R(D∗) — 3.3σ

total significance — 4.0σ largest deviation from SM right now!

• similar ratios before Belle II: LHCb: R(D)? Λb → Λ(∗)

c τ ¯

ν? BaBar/Belle: hadronic τ decays?

4/ 18

Evading unquantified systematics in SM calculations

Complementary theory predictions

• inclusive B → Xcτ ¯

ν rate bounded by known exclusive modes

[MF, Ligeti, Ruderman, 1506.08896]

◮ form-factor independent OPE-based analysis – complementary theory systematics ◮ Corrections up to O(ΛQCD/mb, α2

s)

R(Xc) = 0.223 ± 0.004

theory

B(B− → Xcℓ¯ ν) = (10.92 ± 0.16)%

inclusive ℓ data

⇒ B(B− → Xcτ ¯ ν) = (2.42 ± 0.05)%

prediction

(LEP: B(b → Xτ

+ν) = (2.41 ± 0.23)%)

• isospin-constrained fit: B( ¯

B → D∗τ ¯ ν) + B( ¯ B → Dτ ¯ ν) = (2.78 ± 0.25)%

• estimate rate to excited B(B → D∗∗τ ¯

ν) 0.2%

get conservative limit: B(B → D∗∗ℓ¯ ν)/B(B → D(∗)ℓ¯ ν) ∼ 0.3

• deviation 3σ in inclusive calculation (minimal non-perturbative inputs)

◮ complementary to SM calculation of R(D(∗)) and LEP data

5/ 18

Leveraging inclusive spectra

Precision dΓ(B → Xcτ ¯ ν)/dq2 predictions

• no measurements since LEP,

◮ papers in ‘90s used mpole

b

, no study of spectra (new data needed, in progress @ Belle)

◮ large 1/m2 OPE corrections

• we’ve been told Belle analysis in progress

3 4 5 6 7 8 9 10 11 12 0.005 0.01 0.015 0.02 0.025 q2 [GeV2] (1/Γ

0) dΓ/dq2 [GeV−2]

B → Xcτν LO NLO NLO+1/m2

b

2 0.05 0.1 0.15 0.2 0.25 0.3 1.8 2.2 2.4 2.6 Eτ [GeV] (1/Γ

0) dΓ/dEτ

[GeV−1] B → Xcτν LO NLO NLO+1/m2

b

NLO+1/m2

b+SF

1 3 4 5 6 7 8 9 10 11 12 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 q2

cut [GeV2]

• Γ(q2

cut)

B → Xcτν LO NLO NLO+1/m2

b

1 2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.8 2.2 2.4 2.6 Ecut [GeV]

• Γ(Ecut)

B → Xcτν LO NLO NLO+1/m2

b

NLO+1/m2

b+SF

[Ligeti, Tackmann, 1406.7013] 6/ 18

leveraging inclusive spectra

All τ modes. . . b → uτ ¯ ν?

• if deviation clearly established, huge motivation to study all decay modes with τ

◮ if LEP could measure B → Xcτ ¯

ν with a few × 106 B- ¯ B pairs . . .

◮ . . . “surely” Belle II can measure B → Xuτ ¯

ν with 5 × 1010 B- ¯ B pairs

• no inclusive distributions currently availible

◮ mτ = 0, mu = 0 – complications from different kinematic endpoints ◮ 1.8 GeV < Eτ < 2.9 GeV – Subtleties with shape function; match onto u jet?

[Ligeti, Luke, Tackmann, in progress]

• phase space suppression is smaller in b → u:

Γ(B → Xuτ ¯ ν) Γ(B → Xuℓ¯ ν) ≃ 0.333 Γ(B → Xcτ ¯ ν) Γ(B → Xcℓ¯ ν) ≃ 0.222

• can LHCb/Belle II measure b → uτ ¯

ν decay modes? ratios of τ/µ and/or c/u?

◮ Other exclusive modes: Λb → Λ(c)τ ¯

ν? B → πτ ¯ ν? B → ρτ ¯ ν?

7/ 18

Plan

• Introduction
• Precise SM predictions
• Quantifying NP sensitivity
• NP descriminators
• Consequences and Conclusions

7/ 18

Redundant four-fermion operator analysis

• Fits to different fermion orderings convenient to understand allowed mediator

Operator Fierz identity Allowed Current δLint OVL (¯ cγµPLb) (¯ τγµPLν) (1, 3)0 (gq ¯ qLτγµqL + gℓ¯ ℓLτγµℓL)W ′

µ

OVR (¯ cγµPRb) (¯ τγµPLν) OSR (¯ cPRb) (¯ τPLν) OSL (¯ cPLb) (¯ τPLν)

• (1, 2)1/2

(λd¯ qLdRφ + λu¯ qLuRiτ2φ† + λℓ¯ ℓLeRφ) OT (¯ cσµνPLb) (¯ τσµνPLν) O′

VL

(¯ τγµPLb) (¯ cγµPLν) ↔ OVL

• (3, 3)2/3

λ ¯ qLτγµℓLU µ O′

VR

(¯ τγµPRb) (¯ cγµPLν) ↔ −2OSR

• (3, 1)2/3

(λ ¯ qLγµℓL + ˜ λ ¯ dRγµeR)U µ O′

SR

(¯ τPRb) (¯ cPLν) ↔ − 1

2OVR

O′

SL

(¯ τPLb) (¯ cPLν) ↔ − 1

2OSL − 1 8OT

(3, 2)7/6 (λ ¯ uRℓL + ˜ λ ¯ qLiτ2eR)R O′

T

(¯ τσµνPLb) (¯ cσµνPLν) ↔ −6OSL + 1

2OT

O′′

VL

(¯ τγµPLcc) (¯ bcγµPLν) ↔ −OVR O′′

VR

(¯ τγµPRcc) (¯ bcγµPLν) ↔ −2OSR (¯ 3, 2)5/3 (λ ¯ dc

RγµℓL + ˜

λ ¯ qc

LγµeR)V µ

O′′

SR

(¯ τPRcc) (¯ bcPLν) ↔

1 2OVL

• (¯

3, 3)1/3 λ ¯ qc

Liτ2τℓLS

O′′

SL

(¯ τPLcc) (¯ bcPLν) ↔ − 1

2OSL + 1 8OT

• (¯

3, 1)1/3 (λ ¯ qc

Liτ2ℓL + ˜

λ ¯ uc

ReR)S

O′′

T

(¯ τσµνPLcc) (¯ bcσµνPLν) ↔ −6OSL − 1

2OT

◮ O parametrize all possible dim-6 contributions, O′, O′′ related by Fierzing ◮ δLint only for dim-6 gauge-inv. O’s with mediator spin ≤ 1

8/ 18

BaBar q2 spectral constraints

0.2 0.4 0.6 0.8 1 R(D) 0.2 0.4 0.6 0.8 t 0.2 0.4 0.6 0.8 1 R(D*) 0.2 0.3 0.4

[1205.5442]

5 10 50 5 10 50 : 15.1/14, p = 36.9%

2

χ a Q 5 10 50 Q 5 10 50 : 6.6/12, p = 88.4%

2

χ b

)

2

Weighted events/(0.50 GeV

5 10 50 5 10 50 : 11.0/14, p = 68.6%

2

χ x Q 5 10 50 Q 5 10 50 : 6.7/12, p = 87.6%

2

χ d

)

2

Weighted events/(0.50 GeV

5 10 50 5 10 50 : 44.5/14, p = 0.0049%

2

χ e Q 5 10 50 Q 5 10 50 : 8.1/12, p = 77.4%

2

χ f

)

2

Weighted events/(0.50 GeV

[1303.0571]

• BaBar studied q2 spectrum of at D and D∗ to observe consistency with 2HDM

◮ type-II 2HDM and SM yield equally poor fits to data ◮ other distributions can give sensitivity to, e.g., D∗, τ polarization ◮ non other disitrbutions publically availible

• no bin correlations released, we could only eyeball fits

9/ 18

Single operator fits

canonical 5 O operators non-rescalable O′ and O′′ ones

• 4
• 3
• 2
• 1

1 2 0.1 0.5 1 5 10 50 100

Ci χ2

(qq)(ll)

1σ 2σ 3σ χSM

2

CVL,CVR,CSL,CSR,CT Λ = 1 TeV

• 2
• 1

1 2 3 0.1 0.5 1 5 10 50 100

Ci χ2

(lq)(ql)

1σ 2σ 3σ χSM

2

CSL

′ ,CT ′ ,CSL ″ ,CT ″

Λ = 1 TeV

• All rates in the exact HQET limit

[W. Goldberger, hep-ph/9902311] (up to one overall typo) 10/ 18

Single operator fits

canonical 5 O operators non-rescalable O′ and O′′ ones

• 4
• 3
• 2
• 1

1 2 0.1 0.5 1 5 10 50 100

Ci χ2

(qq)(ll)

1σ 2σ 3σ χSM

2

CVL,CVR,CSL,CSR,CT Λ = 1 TeV

• 2
• 1

1 2 3 0.1 0.5 1 5 10 50 100

Ci χ2

(lq)(ql)

1σ 2σ 3σ χSM

2

CSL

′ ,CT ′ ,CSL ″ ,CT ″

Λ = 1 TeV

• All rates in the exact HQET limit

[W. Goldberger, hep-ph/9902311] (up to one overall typo) 10/ 18

Two operator fits

• 3 current mediators generate two dim-6 operators at once
• 8
• 6
• 4
• 2

2 4

• 4
• 2

2 4 6

CSR CSL

CSR v CSL

1σ, 2σ, 3σ Λ = 1 TeV

• 2
• 1

1 2

• 4
• 3
• 2
• 1

1 2

CVR

′

CV L

′

CVR

′

v CVL

′

1σ, 2σ, 3σ Λ = 1 TeV

• 8
• 6
• 4
• 2

2

• 6
• 4
• 2

2 4 6

CSR

″

CSL

″

CSR

″ v CSL ″

1σ, 2σ, 3σ Λ = 1 TeV

11/ 18

Two operator fits

• 3 current mediators generate two dim-6 operators at once
• 8
• 6
• 4
• 2

2 4

• 4
• 2

2 4 6

CSR CSL

CSR v CSL

1σ, 2σ, 3σ Λ = 1 TeV

• 2
• 1

1 2

• 4
• 3
• 2
• 1

1 2

CVR

′

CV L

′

CVR

′

v CVL

′

1σ, 2σ, 3σ Λ = 1 TeV

• 8
• 6
• 4
• 2

2

• 6
• 4
• 2

2 4 6

CSR

″

CSL

″

CSR

″ v CSL ″

1σ, 2σ, 3σ Λ = 1 TeV

Operator coefficients C′

VL = 0.24

C′

VR = 1.10

C′

VL = 0.24

C′

VR = −0.01

C′

VL = 0.96

C′

VR = 2.41 All q2 constriaints come from B → Dτ ¯ ν rate

4 6 8 10 12 0.1 0.0 0.1 0.2 0.3 0.4 q2 GeV2 1 d d q2

a b c

11/ 18

Plan

• Introduction
• Precise SM predictions
• Quantifying NP sensitivity
• NP descriminators
• Consequences and Conclusions

11/ 18

Differential observables

D∗ polarization

already saw q2 spectrum constrain fits, what about other distributions?

B D l x

y z

* D*

l

−

[Duraisamy, Datta, 1302.7031]

correlations of D∗ decay products and τ:

• D∗ polarization fraction
• AF B lepton asymmetry
• transverse asymmetries
• CP-odd asymmetries

B

0DΤ vΤ

0.2 0.1 0.0 0.1 0.2 0.05 0.00 0.05 0.10 0.15 AFB

D

AC

3

[Duraisamy, Sharma, Datta, 1405.3719]

distinguish op. fits with/without CP analytic distribution recently computed in

[Alonso, Kobach, Camalich, 1602.07671] 12/ 18

Differential observables

τ polarization

4 5 6 7 8 9 10 0.4 0.2 0.0 0.2 0.4 q 2GeV2 AFBD

Only SL ,R presents

B D 0 Τ v Τ 4 5 6 7 8 9 10 0.0 0.2 0.4 0.6 0.8 1.0 q 2GeV2 FL

D

Only SL ,R present

B D 0 Τ v Τ 4 5 6 7 8 9 10 0.5 0.0 0.5 1.0 q 2GeV2 PL

Τ

Only SL ,R present [Datta, Duraisamy, Ghosh, 1206.3760]

additional discrimination from considering τ polarization

13/ 18