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

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

Outline Anomalies in b → c τ ¯ ν Global fit results Pre- Moriond’19 and Pre- D ∗ polarization measurement 1 Post-Moriond’19 and Post- D ∗ polarization measurement 2 Observables to distinguish new physics amplitudes Summary Impact of D ∗ polarization measurement on solutions to RD - RD ∗ anomalies Suman Kumbhakar (IIT Bombay, India) May 29, 2019 2 / 20

R D − R D ∗ Puzzle ( Pre-Moriond’19 ) R D ( ∗ ) = B ( B → D ( ∗ ) τ ¯ ν ) ν ) , ( l = e , µ ) B ( B → D ( ∗ ) l ¯ = ⇒ Discrepancy was at the level of ∼ 4 σ . = ⇒ Indication of Letpon Flavor Universaity (LFU) violation R(D*) BaBar, PRL109,101802(2012) 0.5 ∆ χ 2 = 1.0 contours Belle, PRD92,072014(2015) LHCb, PRL115,111803(2015) SM Predictions Belle, PRD94,072007(2016) 0.45 Belle, PRL118,211801(2017) R(D)=0.300(8) HPQCD (2015) LHCb, FPCP2017 R(D)=0.299(11) FNAL/MILC (2015) Average R(D*)=0.252(3) S. Fajfer et al. (2012) 0.4 0.35 σ 4 σ 0.3 2 0.25 HFLAV FPCP 2017 χ 0.2 P( 2 ) = 71.6% 0.2 0.3 0.4 0.5 0.6 R(D) Impact of D ∗ polarization measurement on solutions to RD - RD ∗ anomalies Suman Kumbhakar (IIT Bombay, India) May 29, 2019 3 / 20

R D − R D ∗ World average 2019 1 Post-Moriond’19 R(D*) ∆ χ 2 = 1.0 contours HFLAV average 0.4 LHCb15 BaBar12 0.35 σ 3 LHCb18 0.3 Belle15 Belle19 0.25 Belle17 HFLAV 0.2 Average of SM predictions ± Spring 2019 R(D) = 0.299 0.003 ± R(D*) = 0.258 0.005 χ 2 P( ) = 27% 0.2 0.3 0.4 0.5 R(D) 1 https://hflav-eos.web.cern.ch/hflav-eos/semi/spring19/html/RDsDsstar/RDRDs.html Impact of D ∗ polarization measurement on solutions to RD - RD ∗ anomalies Suman Kumbhakar (IIT Bombay, India) May 29, 2019 4 / 20

R J /ψ and P τ ( D ∗ ) enter in 2017 In Sept. 2017 LHCb measured [LHCb PRL 120 (2018) no.12, 121801: c → J /ψ τ − ¯ R J /ψ = B ( B − ν ) ν ) = 0 . 71 ± 0 . 17 ± 0 . 18 c → J /ψ µ − ¯ B ( B − ⇒ 1 . 7 σ larger than the SM prediction of R SM = 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)] P τ ( D ∗ ) = Γ λ τ =1 / 2 − Γ λ τ = − 1 / 2 = − 0 . 38 ± 0 . 51 +0 . 21 − 0 . 16 Γ λ τ =1 / 2 + Γ λ τ = − 1 / 2 Though it has large errors, it is consistant with SM prediction − 0 . 497 ± 0 . 013. Impact of D ∗ polarization measurement on solutions to RD - RD ∗ anomalies Suman Kumbhakar (IIT Bombay, India) May 29, 2019 5 / 20

f L ( D ∗ ) by Belle in 2019 The D ∗ longitudinal polarization fraction is measured by Belle [arXiv:1903.03102] Γ λ D ∗ =0 f L ( D ∗ ) = = 0 . 60 ± 0 . 08 ± 0 . 04 Γ λ D ∗ =0 + Γ λ D ∗ =1 + Γ λ D ∗ = − 1 = ⇒ 1 . 7 σ larger than the SM prediction of f L ( D ∗ ) = 0 . 45 ± 0 . 04. [Alok, Dinesh, SK, UmaSankar; PRD 95 (2017) no.11, 115038] = ⇒ All measurements indicate the mechanism of b → c τ ¯ ν is not identical to that of b → c { e /µ } ¯ ν . = ⇒ New physics in b → c { e /µ } ¯ ν transition is highly disfavoured by other measurements R µ/ e and R e /µ D ∗ . [Alok, Dinesh, SK, UmaSankar; JHEP 1809 (2018) D 152] = ⇒ Take new physics in b → c τ ¯ ν transition !! Impact of D ∗ polarization measurement on solutions to RD - RD ∗ anomalies Suman Kumbhakar (IIT Bombay, India) May 29, 2019 6 / 20

New Physics operators for b → c τ ¯ ν The most general effective Hamiltonian for b → c τ ¯ ν transition at Λ = 1 TeV scale [Freytsis, Ligeti, Ruderman PRD92 (2015) no.5, 054018 ] √ � � H eff = 4 G F 2 C ( ′ , ′′ ) O ( ′ , ′′ ) � V cb O V L + √ 4 G F V cb Λ 2 i i 2 i Operator Fierz identity O V L (¯ c γ µ P L b ) (¯ τγ µ P L ν ) O V R (¯ c γ µ P R b ) (¯ τγ µ P L ν ) O S R (¯ cP R b ) (¯ τ P L ν ) O S L (¯ cP L b ) (¯ τ P L ν ) O T (¯ c σ µν P L b ) (¯ τσ µν P L ν ) O ′ (¯ τγ µ P L b ) (¯ c γ µ P L ν ) O V L V L O ′ (¯ τγ µ P R b ) (¯ c γ µ P L ν ) − 2 O S R V R − 1 O ′ (¯ τ P R b ) (¯ cP L ν ) 2 O V R S R − 1 2 O S L − 1 O ′ (¯ τ P L b ) (¯ cP L ν ) 8 O T S L − 6 O S L + 1 O ′ (¯ τσ µν P L b ) (¯ c σ µν P L ν ) 2 O T T τγ µ P L c c ) (¯ b c γ µ P L ν ) O ′′ (¯ −O V R V L τγ µ P R c c ) (¯ b c γ µ P L ν ) O ′′ (¯ − 2 O S R V R τ P R c c ) (¯ 1 b c P L ν ) O ′′ (¯ 2 O V L S R τ P L c c ) (¯ b c P L ν ) − 1 2 O S L + 1 O ′′ (¯ 8 O T S L τσ µν P L c c ) (¯ − 6 O S L − 1 b c σ µν P L ν ) O ′′ (¯ 2 O T T Impact of D ∗ polarization measurement on solutions to RD - RD ∗ anomalies Suman Kumbhakar (IIT Bombay, India) May 29, 2019 7 / 20

Fitting the data Take all data in b → c τ ¯ ν sector: (a) R D , (b) R D ∗ , (c) R J /ψ , (d) P τ and (e) f L ( D ∗ ). Define χ 2 as a function of the NP WCs: V exp + V SM � − 1 χ 2 ( C i ) � � O th ( C i ) − O exp � � � O th ( C i ) − O exp � = m mn n m , n = R D , R D ∗ ( O th ( C i ) − O exp ) 2 � + . σ 2 O R J /ψ , P τ , f L ( D ∗ ) Use MINUIT library to minimize the χ 2 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. χ 2 min falls into two disjoint ranges � 5 and � 7 . 5, whereas the χ 2 SM = 21 . 80 (After Moriond’19). We choose the NP WCs as best fit solutions which fall in the range χ 2 min � 5. Impact of D ∗ polarization measurement on solutions to RD - RD ∗ anomalies Suman Kumbhakar (IIT Bombay, India) May 29, 2019 8 / 20

Constraint from B c → τ ¯ ν Strong constraint from purely leptonic decay B c → τ ¯ ν , especially on the scalar/pseudoscalar NP. The most general expression for the branching fraction of B c → τ ¯ ν is � 2 τ τ exp � | V cb | 2 G 2 F f 2 B c m B c m 2 1 − m 2 B c τ Br ( B c → τ ¯ ν ) = m 2 8 π B c 2 � � m 2 � � B c × � 1 + C V L − C V R + m τ ( m b + m c )( C S R − C S L ) � � � � � The SM prediction is 2 . 15 × 10 − 2 . Particularly, LEP data imposes a constraint Br ( B c → τ ¯ ν ) < 0 . 1. [Akeroyd and Chen, PRD 96, no. 7, 075011 (2017)] Keep only those NP WCs which predict Br ( B c → τ ¯ ν ) < 0 . 1 and disard all others. Impact of D ∗ polarization measurement on solutions to RD - RD ∗ anomalies Suman Kumbhakar (IIT Bombay, India) 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) C V L 0 . 149 ± 0 . 032 C T 0 . 516 ± 0 . 015 C ′′ − 0 . 526 ± 0 . 102 S L ( C V L , C V R ) ( − 1 . 286 , 1 . 512) Post-Moriond’19 & D ∗ polarization: [Alok, Dinesh, SK, UmaSankar; arXiv:1903.10486] NP type Best fit value(s) C V L 0 . 104 ± 0 . 024 C ′′ − 0 . 338 ± 0 . 077 S L ( C ′′ S L , C ′′ S R ) (0 . 265 , 0 . 345) ( C V R , C S L ) ( − 0 . 139 , 0 . 249) ( C V R , C S R ) ( − 0 . 108 , 0 . 222) Additional global fit analyses after Moriond’19: 1904.09311, 1904.10432, 1905.08498, 1905.08253 etc. Impact of D ∗ polarization measurement on solutions to RD - RD ∗ anomalies Suman Kumbhakar (IIT Bombay, India) May 29, 2019 10 / 20

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

Angular observables in B → D ∗ τ ¯ ν We consider four angular observables: (a) τ polarization P τ , (b) D ∗ polarization fraction f L , (c) forward-backward asymmetry A FB and (d) longitudinal-transverse asymmetry A LT .[Sakaki, Tanaka, Watanabe; PRD 2013] Γ λ τ =1 / 2 − Γ λ τ = − 1 / 2 = , P τ Γ λ τ =1 / 2 + Γ / λ τ = − 1 / 2 Γ λ D ∗ =0 = , f L Γ λ D ∗ =0 + Γ λ D ∗ = − 1 + Γ λ D ∗ =+1 �� 1 � 0 d 2 Γ 1 � A FB = − d cos θ τ , dq 2 d cos θ τ Γ 0 − 1 � π/ 2 �� 1 � 0 � d 3 Γ d cos θ D − π/ 2 d φ 0 − dq 2 d φ d cos θ D − 1 = . A LT � π/ 2 �� 1 � 0 � d 3 Γ d cos θ D − π/ 2 d φ 0 + dq 2 d φ d cos θ D − 1 Impact of D ∗ polarization measurement on solutions to RD - RD ∗ anomalies Suman Kumbhakar (IIT Bombay, India) May 29, 2019 12 / 20