Impact of D polarization measurement on solutions to R D - R D - - PowerPoint PPT Presentation

Impact of D∗ polarization measurement on solutions to RD-RD∗ anomalies

Suman Kumbhakar

IIT Bombay, India

May 29, 2019 Based on arXiv:1903.10486 A K Alok, D Kumar, S Kumbhakar, S UmaSankar Updated Analysis of: JHEP 1809 (2018) 152 & Phys.Lett. B784 (2018) 16-20 Interpreting the LHC Run 2 Data and Beyond ICTP Trieste

Suman Kumbhakar (IIT Bombay, India) Impact of D∗ polarization measurement on solutions to RD -RD∗ anomalies May 29, 2019 1 / 20

Outline

Anomalies in b → cτ ¯ ν Global fit results

1

Pre-Moriond’19 and Pre-D∗ polarization measurement

2

Post-Moriond’19 and Post-D∗ polarization measurement

Observables to distinguish new physics amplitudes Summary

Suman Kumbhakar (IIT Bombay, India) Impact of D∗ polarization measurement on solutions to RD -RD∗ anomalies May 29, 2019 2 / 20

RD − RD∗ Puzzle (Pre-Moriond’19)

RD(∗) = B(B → D(∗) τ ¯ ν) B(B → D(∗) l ¯ ν) , (l = e, µ) = ⇒ Discrepancy was at the level of ∼ 4σ. = ⇒ Indication of Letpon Flavor Universaity (LFU) violation

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, PRD94,072007(2016) Belle, PRL118,211801(2017) LHCb, FPCP2017 Average SM Predictions

= 1.0 contours

2

χ ∆

R(D)=0.300(8) HPQCD (2015) R(D)=0.299(11) FNAL/MILC (2015) R(D*)=0.252(3) S. Fajfer et al. (2012)

) = 71.6%

2

χ P( σ 4 σ 2

HFLAV

FPCP 2017 Suman Kumbhakar (IIT Bombay, India) Impact of D∗ polarization measurement on solutions to RD -RD∗ anomalies May 29, 2019 3 / 20

RD − RD∗ World average 20191

Post-Moriond’19

0.2 0.3 0.4 0.5

R(D)

0.2 0.25 0.3 0.35 0.4

R(D*)

HFLAV average Average of SM predictions

= 1.0 contours

2

χ ∆

0.003 ± R(D) = 0.299 0.005 ± R(D*) = 0.258 ) = 27%

2

χ P( σ 3 LHCb15 LHCb18 Belle17 Belle19 Belle15 BaBar12

HFLAV

Spring 2019 1https://hflav-eos.web.cern.ch/hflav-eos/semi/spring19/html/RDsDsstar/RDRDs.html

Suman Kumbhakar (IIT Bombay, India) Impact of D∗ polarization measurement on solutions to RD -RD∗ anomalies May 29, 2019 4 / 20

RJ/ψ and Pτ(D∗) enter in 2017

In Sept. 2017 LHCb measured [LHCb PRL 120 (2018) no.12, 121801: RJ/ψ = B(B−

c → J/ψ τ − ¯

ν) B(B−

c → J/ψ µ− ¯

ν) = 0.71 ± 0.17 ± 0.18 = ⇒ 1.7σ larger than the SM prediction of RSM

J/ψ = 0.29.

Also a measurement of τ polarization in B → D∗τ ¯ ν decay by Belle in 2016 [Belle PRL 118, no. 21, 211801 (2017)] Pτ(D∗) = Γλτ =1/2 − Γλτ =−1/2 Γλτ =1/2 + Γλτ =−1/2 = −0.38 ± 0.51+0.21

−0.16

Though it has large errors, it is consistant with SM prediction −0.497 ± 0.013.

Suman Kumbhakar (IIT Bombay, India) Impact of D∗ polarization measurement on solutions to RD -RD∗ anomalies May 29, 2019 5 / 20

fL(D∗) by Belle in 2019

The D∗ longitudinal polarization fraction is measured by Belle [arXiv:1903.03102] fL(D∗) = ΓλD∗=0 ΓλD∗=0 + ΓλD∗=1 + ΓλD∗=−1 = 0.60 ± 0.08 ± 0.04 = ⇒ 1.7σ larger than the SM prediction of fL(D∗) = 0.45 ± 0.04. [Alok, Dinesh, SK, UmaSankar; PRD 95 (2017) no.11, 115038] = ⇒ All measurements indicate the mechanism of b → cτ ¯ ν is not identical to that

• f b → c{e/µ}¯

ν. = ⇒ New physics in b → c{e/µ}¯ ν transition is highly disfavoured by other measurements Rµ/e

D

and Re/µ

D∗ . [Alok, Dinesh, SK, UmaSankar; JHEP 1809 (2018)

152] = ⇒ Take new physics in b → cτ ¯ ν transition !!

Suman Kumbhakar (IIT Bombay, India) Impact of D∗ polarization measurement on solutions to RD -RD∗ anomalies May 29, 2019 6 / 20

New Physics operators for b → cτ ¯ ν

The most general effective Hamiltonian for b → cτ ¯ ν transition at Λ = 1 TeV scale [Freytsis, Ligeti, Ruderman PRD92 (2015) no.5, 054018 ]

Heff = 4GF √ 2 Vcb

• OVL +

√ 2 4GF VcbΛ2

• i

C (′,′′)

i

O(′,′′)

i

• Operator

Fierz identity OVL (¯ cγµPLb) (¯ τγµPLν) OVR (¯ cγµPRb) (¯ τγµPLν) OSR (¯ cPRb) (¯ τPLν) OSL (¯ cPLb) (¯ τPLν) OT (¯ cσµνPLb) (¯ τσµνPLν) O′

VL

(¯ τγµPLb) (¯ cγµPLν) OVL O′

VR

(¯ τγµPRb) (¯ cγµPLν) −2OSR O′

SR

(¯ τPRb) (¯ cPLν) − 1

2 OVR

O′

SL

(¯ τPLb) (¯ cPLν) − 1

2 OSL − 1 8 OT

O′

T

(¯ τσµνPLb) (¯ cσµνPLν) −6OSL + 1

2 OT

O′′

VL

(¯ τγµPLcc) (¯ bcγµPLν) −OVR O′′

VR

(¯ τγµPRcc) (¯ bcγµPLν) −2OSR O′′

SR

(¯ τPRcc) (¯ bcPLν)

1 2 OVL

O′′

SL

(¯ τPLcc) (¯ bcPLν) − 1

2 OSL + 1 8 OT

O′′

T

(¯ τσµνPLcc) (¯ bcσµνPLν) −6OSL − 1

2 OT

Suman Kumbhakar (IIT Bombay, India) Impact of D∗ polarization measurement on solutions to RD -RD∗ anomalies May 29, 2019 7 / 20

Fitting the data

Take all data in b → cτ ¯ ν sector: (a)RD, (b) RD∗, (c) RJ/ψ, (d) Pτ and (e) fL(D∗). Define χ2 as a function of the NP WCs: χ2(Ci) =

• m,n=RD,RD∗
• Oth(Ci) − Oexp

m

• V exp + V SM−1

mn

• Oth(Ci) − Oexp

n

+

• RJ/ψ,Pτ ,fL(D∗)

(Oth(Ci) − Oexp)2 σ2

O

. Use MINUIT library to minimize the χ2 function and get the values of NP

• WCs. We choose one operator or two (dis-)similar operators at a time to get

the strongest possible constarint. χ2

min falls into two disjoint ranges 5 and 7.5, whereas the χ2 SM = 21.80

(After Moriond’19). We choose the NP WCs as best fit solutions which fall in the range χ2

min 5.

Suman Kumbhakar (IIT Bombay, India) Impact of D∗ polarization measurement on solutions to RD -RD∗ anomalies May 29, 2019 8 / 20

Constraint from Bc → τ ¯ ν

Strong constraint from purely leptonic decay Bc → τ ¯ ν, especially on the scalar/pseudoscalar NP. The most general expression for the branching fraction of Bc → τ ¯ ν is Br(Bc → τ ¯ ν) = |Vcb|2G 2

Ff 2 BcmBcm2 ττ exp Bc

8π

• 1 − m2

τ

m2

Bc

2 ×

• 1 + CVL − CVR +

m2

Bc

mτ(mb + mc)(CSR − CSL)

• 2

The SM prediction is 2.15 × 10−2. Particularly, LEP data imposes a constraint Br(Bc → τ ¯ ν) < 0.1. [Akeroyd and Chen, PRD 96, no. 7, 075011 (2017)] Keep only those NP WCs which predict Br(Bc → τ ¯ ν) < 0.1 and disard all

• thers.

Suman Kumbhakar (IIT Bombay, India) Impact of D∗ polarization measurement on solutions to RD -RD∗ anomalies May 29, 2019 9 / 20

New Physics Solutions

Pre-Moriond’19 & D∗ polarization: [Alok, Dinesh, Jacky, SK, UmaSankar; JHEP 1809 (2018) 152] Coefficient(s) Best fit value(s) CVL 0.149 ± 0.032 CT 0.516 ± 0.015 C ′′

SL

−0.526 ± 0.102 (CVL, CVR) (−1.286, 1.512) Post-Moriond’19 & D∗ polarization: [Alok, Dinesh, SK, UmaSankar; arXiv:1903.10486] NP type Best fit value(s) CVL 0.104 ± 0.024 C ′′

SL

−0.338 ± 0.077 (C ′′

SL, C ′′ SR)

(0.265, 0.345) (CVR, CSL) (−0.139, 0.249) (CVR, CSR) (−0.108, 0.222) Additional global fit analyses after Moriond’19: 1904.09311, 1904.10432, 1905.08498, 1905.08253 etc.

Suman Kumbhakar (IIT Bombay, India) Impact of D∗ polarization measurement on solutions to RD -RD∗ anomalies May 29, 2019 10 / 20

How to distinguish these solutions ?

Suman Kumbhakar (IIT Bombay, India) Impact of D∗ polarization measurement on solutions to RD -RD∗ anomalies May 29, 2019 11 / 20

Angular observables in B → D∗τ ¯ ν

We consider four angular observables: (a) τ polarization Pτ, (b) D∗ polarization fraction fL, (c) forward-backward asymmetry AFB and (d) longitudinal-transverse asymmetry ALT.[Sakaki, Tanaka, Watanabe; PRD 2013] Pτ = Γλτ =1/2 − Γλτ =−1/2 Γλτ =1/2 + Γ/λτ =−1/2 , fL = ΓλD∗=0 ΓλD∗=0 + ΓλD∗=−1 + ΓλD∗=+1 , AFB = 1 Γ 1 −

−1

• d2Γ

dq2d cos θτ d cos θτ, ALT = π/2

−π/2 dφ

1

0 − −1

• d3Γ d cos θD

dq2dφ d cos θD

π/2

−π/2 dφ

1

0 + −1

• d3Γ d cos θD

dq2dφ d cos θD

.

Suman Kumbhakar (IIT Bombay, India) Impact of D∗ polarization measurement on solutions to RD -RD∗ anomalies May 29, 2019 12 / 20

Predictions to distinguish NP WCs

Pre-Moriond and Pre-D∗ polarization status [Alok, Dinesh, SK, UmaSankar; PLB 784 (2018) 16-20] NP type Pτ fL AFB ALT SM −0.499 ± 0.004 0.45 ± 0.04 −0.011 ± 0.007 −0.245 ± 0.003 CVL −0.499 ± 0.004 0.45 ± 0.04 −0.011 ± 0.007 −0.245 ± 0.003 CT +0.115 ± 0.013 0.14 ± 0.03 −0.114 ± 0.009 +0.110 ± 0.009 C ′′

SL

−0.485 ± 0.003 0.46 ± 0.04 −0.087 ± 0.011 −0.211 ± 0.008 (CVL, CVR) −0.499 ± 0.004 0.45 ± 0.04 −0.371 ± 0.004 +0.007 ± 0.004 If Pτ or fL can be measured with an absolute uncertainty of 0.1, then CT is either confirmed or ruled out at 3σ level. [Alok, Dinesh, SK, UmaSankar; PRD 95 (2017) no.11, 115038] If AFB or ALT can be measured with an absolute uncertainty of 0.07, then (OVL, OVR) is either confirmed or ruled out at 3σ level.

Suman Kumbhakar (IIT Bombay, India) Impact of D∗ polarization measurement on solutions to RD -RD∗ anomalies May 29, 2019 13 / 20

Distinguishing power of AFB

Pre-Moriond and Pre-D∗ polarization status [Alok, Dinesh, SK, UmaSankar; PLB 784 (2018) 16-20]

4 5 6 7 8 9 10 q 2 0.4 0.3 0.2 0.1 0.0 0.1 0.2 A FB q 2

= ⇒ AFB(q2) for OVL solution (green curve)has a zero crossing at q2 = 5.6 GeV2 whereas this crossing point occurs at q2 = 7.5 GeV2 for O′′

SL solution (blue curve).

= ⇒ AFB in the limited range 6 GeV2 < q2 < q2

max gives the result +0.1 for OVL

and +0.01 for O′′

• SL. Hence, determining the sign of AFB, for the full q2 range

and for the limited higher q2 range, provides a very useful tool for discrimination between OVL and O′′

SL solutions.

Suman Kumbhakar (IIT Bombay, India) Impact of D∗ polarization measurement on solutions to RD -RD∗ anomalies May 29, 2019 14 / 20

Predictions of angular observables

Post-Moriond & Post-D∗ polarization status [Alok, Dinesh, SK, UmaSankar; arXiv:1903.10486 ]

NP type Pτ fL AFB ALT B(Bc → τ ¯ ν) CVL −0.499 ± 0.004 0.46 ± 0.04 −0.011 ± 0.007 −0.246 ± 0.003 2.50 × 10−2 C ′′

SL

−0.493 ± 0.003 0.44 ± 0.05 −0.062 ± 0.010 −0.223 ± 0.002 1.14 × 10−6 (C ′′

SL, C ′′ SR)

−0.494 ± 0.005 0.47 ± 0.04 0.027 ± 0.008 −0.260 ± 0.003 7.93 × 10−2 (CVR, CSL) −0.526 ± 0.004 0.45 ± 0.04 −0.061 ± 0.006 −0.233 ± 0.002 2.23 × 10−3 (CVR, CSR) −0.468 ± 0.005 0.47 ± 0.04 −0.023 ± 0.006 −0.225 ± 0.003 0.12

Only (C ′′

SL, C ′′ SR) solution can be distinguished as AFB is postive for the

whole q2 range. AFB can not distinguish between C ′′

SL and (CVR, CSL). Only possiblity is

B(Bc → τ ¯ ν). For C ′′

SL, it is ∼ 10−6 and that for (CVR, CSL) is ∼ 10−3.

(CVR, CSR) solution can be distinguished only by means of B(Bc → τ ¯ ν) ∼ 10%

Suman Kumbhakar (IIT Bombay, India) Impact of D∗ polarization measurement on solutions to RD -RD∗ anomalies May 29, 2019 15 / 20

Capability of AFB

Post-Moriond and Post-D∗ polarization status [Alok, Dinesh, SK, UmaSankar; arXiv:1903.10486]

3 4 5 6 7 8 9 10 0.2 0.1 0.0 0.1 q 2 A FB q 2

(C ′′

SL, C ′′ SR) solution (blue curve) has a zero crossing at 5 GeV2.

No other solutions can be distinguished by the q2 dependence of AFB.

Suman Kumbhakar (IIT Bombay, India) Impact of D∗ polarization measurement on solutions to RD -RD∗ anomalies May 29, 2019 16 / 20

Summary

Pre-Moriond and Pre-D∗ polarization: 4 NP solutions, each with different Lorentz structure. Post-Moriond and Post-D∗ polarization: 5 NP solutions, The tensor solution is now ruled out at the level of 5σ by D∗ polarization measurement. Discrimanting 5 solutions: Although AFB and B(Bc → τ ¯ ν) are useful to discriminate, but measuring these are challenging. Need to find other observables to distinguish all solutions uniquely. Thank You !!

Suman Kumbhakar (IIT Bombay, India) Impact of D∗ polarization measurement on solutions to RD -RD∗ anomalies May 29, 2019 17 / 20

Backup Slides

Suman Kumbhakar (IIT Bombay, India) Impact of D∗ polarization measurement on solutions to RD -RD∗ anomalies May 29, 2019 18 / 20

B → D∗τ ¯ ν

We can describe the decay by defining 3 angles θτ, θD and φ in the D∗ rest frame which are shown in figure θD the angle between B and D where D meson comes from D∗ decay. θτ the angle between τ and B. φ the angle between D∗ decay plane and plane defined by lepton momenta. Out of these 3 angle it is possible to measure θD from the same data used by BaBar and Belle to determine RD∗. Other 2 angles have not been measured because so far τ lepton has not been measured in any of the experiments which measure RD/RD∗.

Suman Kumbhakar (IIT Bombay, India) Impact of D∗ polarization measurement on solutions to RD -RD∗ anomalies May 29, 2019 19 / 20

4-Fold Distribution for B → D∗τ ¯ ν

The four-fold distribution for the decay can be obtained using helicity formalism i.e. d4Γ dq2d cos θτd cos θDdφ = NF ×

• cos2 θD(I 0

1 + I 0 2 cos 2θτ + I 0 3 cos θτ) + sin2 θD

(I T

1 + I T 2 cos 2θτ + I T 3 cos θτ + I T 4 sin2 θτ cos 2φ + I T 5

sin2 θτ sin 2φ) + sin 2θD(I 0T

1

sin 2θτ cos φ + I 0T

2

sin 2θτ sin φ + I 0T

3

sin θτ sin φ)

• where the normalization factor NF = 3G 2

F|pD∗||Vcb|2βτ

211π3m2

B

Br(D∗ → Dπ) Here βµ =

• 1 − m2

τ

q2 2 and |pD∗| is the D∗ momentum in the B-meson rest frame, |pD∗| = λ1/2 m2

B, m2 D∗, q2

/2mB with λ(a, b, c) = a2 + b2 + c2 − 2(ab + bc + ca). The twelve angular coefficients I’s depend on couplings, kinematics variables and form factors.

Suman Kumbhakar (IIT Bombay, India) Impact of D∗ polarization measurement on solutions to RD -RD∗ anomalies May 29, 2019 20 / 20