The B → D(∗)τ ν & B → τ ν decays,Theoretical status thereof

Marat FreytsisUniversity 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 ModelI B → D(∗) transitions both depend on FFs whose contribution vanishes as m` → 0I B− → τ−ν only decay sensitive to fB measurable in the near future

• New PhysicsI NP often presumed to couple preferentially to 3rd generationI A reason to persue B → Xsνν 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)I high-precision in B → Xu,c`ν critical to extraction of |Vub|, |Vcb|I 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 predictionsI complimentary, CKM-parameter-free families of ratio observables for LFU sensitivity

• Quantifying NP sensitivityI redundant effective operator bases for identification of UV physics

• NP descriminatorsI more differential distributions for discrimination of scenarios

• Consequences and Conclusions

1/ 18

B− → τ−νPure leptonic decays

In the SM:

Γ(B− → τ−ν) =|Vub|2G2

F

8πf2Bm

2τmB

(1− m2

τ

m2B

)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〉 6= 0

• new pseudoscalar couplings typically proportional to fermion mass:

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

= |1 + CAV +m2BCP |2 Γ(B− → τ−ν)SM

b

�

�

�

�

B

�

c

b

e

�

�

e

B

0

D

+

�

�

c

b

B

0

d

D

+

u

d d

d d

u

2/ 18

B− → τ−νEliminating |Vub| dependence

|Vub| drops out of ratio, but NP independent of lepton massoverall 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+`−ν)= 0.73(13) from here ` = avg. of µ+ e

[Fajfer, Kamenik, Nisandzic, Zupan, 1206.1872]

RπSM = 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 νAn R(X) reminder

R(X) =Γ(B → Xτν)

Γ(B → X`ν)

original goal: 2HDM H±

• deviation first seen at BaBar, later results from Belle and LHCbBaBar/Belle full datasets τ → `νν 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(`)tag ) 0.302± 0.030± 0.011

LHCb 0.336± 0.027± 0.030Exp. average 0.397± 0.040± 0.028 0.316± 0.016± 0.010

SM expectation 0.300± 0.010 0.252± 0.005Belle 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

0.5BaBar, PRL109,101802(2012)Belle, PRD92,072014(2015)LHCb, PRL115,111803(2015)Belle, arXiv:1603.06711

) = 67%2χHFAG Average, P(SM prediction

= 1.02χ∆

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

HFAGPrel. Winter 2016

I clean SM observables: heavy quark symmetry relates FFsCaprini, Lellouch, Neubert, hep-ph/9712417

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

I R(D) — 1.9σ, R(D∗) — 3.3σtotal 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 calculationsComplementary theory predictions

• inclusive B → Xcτ ν rate bounded by known exclusive modes[MF, Ligeti, Ruderman, 1506.08896]

I form-factor independent OPE-based analysis – complementary theory systematicsI Corrections up to O(ΛQCD/mb, α

2s)

R(Xc) = 0.223± 0.004 theory

B(B− → Xc`ν) = (10.92± 0.16)% inclusive ` 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 → Dτν) = (2.78± 0.25)%

• estimate rate to excited B(B → D∗∗τ ν) & 0.2%get conservative limit: B(B → D∗∗`ν)/B(B → D(∗)`ν) ∼ 0.3

• deviation & 3σ in inclusive calculation (minimal non-perturbative inputs)I complementary to SM calculation of R(D(∗)) and LEP data

5/ 18

Leveraging inclusive spectraPrecision dΓ(B → Xcτ ν)/dq2 predictions

• no measurements since LEP,

I papers in ‘90s used mpoleb , no study of spectra (new data needed, in progress @ Belle)

I large 1/m2 OPE corrections

• we’ve been told Belle analysis in progress

0

3 4 5 6 7 8 9 10 11 12

0.005

0.01

0.015

0.02

0.025

q2 [GeV2]

(1/Γ0)dΓ/dq2

[GeV

−2] B → Xcτν

LONLONLO+1/m2

b0

2

0.05

0.1

0.15

0.2

0.25

0.3

1.8 2.2 2.4 2.6

Eτ [GeV]

(1/Γ0)dΓ/dE

τ[G

eV

−1] B → Xcτν

LO

NLONLO+1/m2

b

NLO+1/m2b+SF

0

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

q2cut [GeV2]

Γ(q

2 cut)

B → Xcτν

LO

NLONLO+1/m2

b

0

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(E

cut)

B → Xcτν

LO

NLONLO+1/m2

b

NLO+1/m2b+SF

[Ligeti, Tackmann, 1406.7013]

6/ 18

leveraging inclusive spectraAll τ modes. . . b→ uτν?

• if deviation clearly established, huge motivation to study all decay modes with τI if LEP could measure B → Xcτ ν with a few× 106 B-B pairs . . .I . . . “surely” Belle II can measure B → Xuτ ν with 5× 1010 B-B pairs

• no inclusive distributions currently availibleI mτ 6= 0,mu = 0 – complications from different kinematic endpointsI 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 → Xu`ν)' 0.333

Γ(B → Xcτ ν)

Γ(B → Xc`ν)' 0.222

• can LHCb/Belle II measure b→ uτν decay modes? ratios of τ/µ and/or c/u?I Other exclusive modes: Λb → Λ(c)τ ν? B → πτν? 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) (τ γµPLν) (1,3)0 (gq qLτγµqL + g` ¯Lτγ

µ`L)W ′µOVR (cγµPRb) (τ γµPLν)OSR (cPRb) (τPLν)OSL (cPLb) (τPLν)

⟩(1,2)1/2 (λdqLdRφ+ λuqLuRiτ2φ

† + λ` ¯LeRφ)

OT (cσµνPLb) (τσµνPLν)

O′VL(τ γµPLb) (cγµPLν) ↔ OVL

⟨(3,3)2/3 λ qLτγµ`LU

µ

O′VR(τ γµPRb) (cγµPLν) ↔ −2OSR

⟩(3,1)2/3 (λ qLγµ`L + λ dRγµeR)Uµ

O′SR(τPRb) (cPLν) ↔ − 1

2OVR

O′SL(τPLb) (cPLν) ↔ − 1

2OSL − 1

8OT (3,2)7/6 (λ uR`L + λ qLiτ2eR)R

O′T (τσµνPLb) (cσµνPLν) ↔ −6OSL + 12OT

O′′VL(τ γµPLc

c) (bcγµPLν) ↔ −OVR

O′′VR(τ γµPRc

c) (bcγµPLν) ↔ −2OSR (3,2)5/3 (λ dcRγµ`L + λ qcLγµeR)V µ

O′′SR(τPRc

c) (bcPLν) ↔ 12OVL

⟨(3,3)1/3 λ qcLiτ2τ `LS

O′′SL(τPLc

c) (bcPLν) ↔ − 12OSL + 1

8OT

⟩(3,1)1/3 (λ qcLiτ2`L + λ ucReR)S

O′′T (τσµνPLcc) (bcσµνPLν) ↔ −6OSL − 1

2OT

I O parametrize all possible dim-6 contributions, O′, O′′ related by Fierzing

I δLint only for dim-6 gauge-inv. O’s with mediator spin ≤ 1

8/ 18

BaBar q2 spectral constraints

0 0.2 0.4 0.6 0.8 1

R(D

)

0.2

0.4

0.6

0.8

t0 0.2 0.4 0.6 0.8 1

R(D

*)

0.2

0.3

0.4

[1205.5442]

5 10

0

50

5 10

0

50

: 15.1/14, p = 36.9%2χ a

Q5 10

0

50

Q5 10

0

50

: 6.6/12, p = 88.4%2χ b

)2W

eigh

ted

even

ts/(

0.50

GeV

5 10

0

50

5 10

0

50

: 11.0/14, p = 68.6%2χ x

Q5 10

0

50

Q5 10

0

50

: 6.7/12, p = 87.6%2χ d

)2W

eigh

ted

even

ts/(

0.50

GeV

5 10

0

50

5 10

0

50

: 44.5/14, p = 0.0049%2χ e

Q5 10

0

50

Q5 10

0

50

: 8.1/12, p = 77.4%2χ f

)2W

eigh

ted

even

ts/(

0.50

GeV

[1303.0571]

• BaBar studied q2 spectrum of at D and D∗ to observe consistency with 2HDMI type-II 2HDM and SM yield equally poor fits to dataI other distributions can give sensitivity to, e.g., D∗, τ polarizationI 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 0 1 20.1

0.51

510

50100

Ci

χ2

(qq)(ll)

1σ

2σ

3σχSM

2

CVL,CVR,CSL,CSR,CTΛ = 1 TeV

-2 -1 0 1 2 30.1

0.51

510

50100

Ci

χ2

(lq)(ql)

1σ

2σ

3σχSM

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 0 1 20.1

0.51

510

50100

Ci

χ2

(qq)(ll)

1σ

2σ

3σχSM

2

CVL,CVR,CSL,CSR,CTΛ = 1 TeV

-2 -1 0 1 2 30.1

0.51

510

50100

Ci

χ2

(lq)(ql)

1σ

2σ

3σχSM

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 0 2 4

-4

-2

0

2

4

6

CSR

CS

L

CSR v CSL

1σ, 2σ, 3σ

Λ = 1 TeV

-2 -1 0 1 2-4

-3

-2

-1

0

1

2

CVR

′

CV

L

′

CVR

′ v CVL

′

1σ, 2σ, 3σ

Λ = 1 TeV

-8 -6 -4 -2 0 2-6

-4

-2

0

2

4

6

CSR

″

CS

L

″

CSR

″ v CSL

″

1σ, 2σ, 3σ

Λ = 1 TeV

Operator coefficientsC′VL

= 0.24 C′VR= 1.10

C′VL= 0.24 C′VR

= −0.01C′VL

= 0.96 C′VR= 2.41

All q2 constriaints come from B → Dτν rate

4 6 8 10 12

-0.1

0.0

0.1

0.2

0.3

0.4

q2 � GeV2

I1�G

MdG

�dq

2

a

b

c

11/ 18

Two operator fits

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

-8 -6 -4 -2 0 2 4

-4

-2

0

2

4

6

CSR

CS

L

CSR v CSL

1σ, 2σ, 3σ

Λ = 1 TeV

-2 -1 0 1 2-4

-3

-2

-1

0

1

2

CVR

′

CV

L

′

CVR

′ v CVL

′

1σ, 2σ, 3σ

Λ = 1 TeV

-8 -6 -4 -2 0 2-6

-4

-2

0

2

4

6

CSR

″

CS

L

″

CSR

″ v CSL

″

1σ, 2σ, 3σ

Λ = 1 TeV

Operator coefficientsC′VL

= 0.24 C′VR= 1.10

C′VL= 0.24 C′VR

= −0.01C′VL

= 0.96 C′VR= 2.41

All q2 constriaints come from B → Dτν rate

4 6 8 10 12

-0.1

0.0

0.1

0.2

0.3

0.4

q2 � GeV2

I1�G

MdG

�dq

2a

b

c

11/ 18

Plan

• Introduction

• Precise SM predictions

• Quantifying NP sensitivity

• NP descriminators

• Consequences and Conclusions

11/ 18

Differential observablesD∗ polarization

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

B

D

l

xy

z

*D*l

−

[Duraisamy, Datta, 1302.7031]

correlations of D∗ decay products and τ :

• D∗ polarization fraction

• AFB lepton asymmetry

• transverse asymmetries

• CP -odd asymmetries

B0®D*+Τ vΤ

-0.2 -0.1 0.0 0.1 0.2-0.05

0.00

0.05

0.10

0.15

<AFBD*>

<A

CH3L >

[Duraisamy, Sharma, Datta, 1405.3719]

distinguish op. fits with/without CP

analytic distribution recently computedin

[Alonso, Kobach, Camalich, 1602.07671]

12/ 18

Differential observablesτ polarization

4 5 6 7 8 9 10

-0.4

-0.2

0.0

0.2

0.4

q 2 @GeV2 D

@A

FBD

D*

Only SL , R presents

B -®D 0 *Τ-v Τ

4 5 6 7 8 9 100.0

0.2

0.4

0.6

0.8

1.0

q 2 @GeV2 D

FLD*

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 2 @GeV2 D

PL*Τ

Only SL , R present

[Datta, Duraisamy, Ghosh, 1206.3760]

additional discrimination from considering τ polarization

13/ 18

Differential observablesCP observables in B → Dτν

z

x

y

z′

x′

y

!pB = !pD

!Q2

!p1

!p2

θ1

φ1

ρ orρ′

!pν1+ !pν2 [q rest frame]

[Q2 rest frame]

θV

π−

π0

z

x

y

z′

x′

y

!pB = !pD

!Q3

!p1

!P23

θ1

φ1

a1

!pν1+ !pν2 [q rest frame]

[Q3 rest frame]

θV

π+

!p2 !p3

π−π−

4 6 8 10-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

q2@GeV2D

A3

Hq2L@

GeV

-2

D

CS =

i

C S=

-i

CT = - i

CT= i

[Hagiwara, Nojiri, Sakaki, 1403.5892]

multi-prong hadronic τ decays allow forCP -sensitive observables in B → Dτνas well

14/ 18

Plan

• Introduction

• Precise SM predictions

• Quantifying NP sensitivity

• NP descriminators

• Consequences and Conclusions

14/ 18

Some wilder ideasSuppress, don’t enhance

[MF, Ligeti, Ruderman, in progress]

• (to my knowledge) all NP explanations enhance the τ mode compared to the SM

• deviation in ratio of decay rates – suppress the e and µ modes instead?I operator fits at smaller Wilson coefficients comperable in both cases

• e and µ modes used for CKM matrix element extraction

V(exp)cb ∼ 0.9V

(SM)cb , V

(exp)ub ∼ 0.9V

(SM)ub (1)

• strongest constraint is from εK

|εK | =G2Fm

2WmKf

2K

6√

2π2∆mK

BKκε|Vcb|2λ2η[|Vcb|2(1− ρ)ηttS0(xt) + ηctS0(xc, xt)− ηccxc

]I current central values are in tension with such modelsI reduced tension with R(D(∗)) if CKM fits moved off central values

— shifts to both within present uncertainties can lead to a self-consistent story

• current CKM limits on Vub have killed BSM scenarios before, e.g. flavored GUTsI should some of these be revisited?

15/ 18

Some wilder ideasB → D(∗)eν vs. B → D(∗)µν

• How well is the difference of the e and µ rates constrained?

Parameters De sample Dµ sample combined result

ρ2D 1.23± 0.05± 0.08 1.13± 0.07± 0.09 1.16± 0.04± 0.08ρ2D∗ 1.23± 0.02± 0.07 1.24± 0.03± 0.07 1.33± 0.04± 0.09B(D0`ν)(%) 2.38± 0.03± 0.14 2.26± 0.04± 0.16 2.32± 0.03± 0.013B(D∗0`ν)(%) 5.45± 0.03± 0.22 5.27± 0.04± 0.37 5.48± 0.04± 0.02

χ2/n.d.f. (probability) 422/470 (0.94) 494/467 (0.19) 2.2/4 (0.71)

[BaBar, 0809.0828]

• Individual rates appear to be systematics limited

• We assumed e/µ universality, not a necessityI Reaching 1% level on ratio might be possible (but tough) even at Belle III 10% e/µ non-universality still seems possible (despite what the PDG claims)

— Simultaneous explaination of B(B → Kµ+µ−)/B(B → Ke+e−) challenging

16/ 18

Signals both high and low (energy)

• LHC: (mostly) simple modifications of existing searchesI extensions of t/b searches to higher prod. cross sections

I searches for tτ resonances, mixed bτ tν decay channels

I t→ bτ ν,cτ+τ− non-resonant decays

I on-shell t-channel states pp collisions

I Enhanced h→ τ+τ− rate (model dependent)

• Low energy probes:I more B → D(∗)τ ν kinematic distributions,

cross checks w/ inclusive deacys

I look at ratios themselves differentially: dR(D(∗))/dq2

I Improve bounds on B(B → K(∗)νν)

I B(D → πνν) ∼ 10−5 possible (BES III?), enhanced B(D → µ+µ−)

I B(Bs → τ+τ−) ∼ 10−3 possible

17/ 18

Conclusions

• Precise SM predictionsI complimentary, CKM-parameter-free families of ratio observables for LFU sensitivity

• Quantifying NP sensitivityI redundant effective operator bases for identification of UV physics

• NP descriminatorsI more differential distributions for discrimination of scenarios

• Consequences and ConclusionsI no CKM or loop suppression in SM contribution

=⇒ not how NP was “supposed to” show upmaybe OK to think about some crazier ideas? (YMMV)

I if it persists, robust ways of characterizing the excess existI looking forward to more data

18/ 18

Thank you!

18/ 18