Puzzles in B Decays Alakabha Datta University of Mississippi April - PowerPoint PPT Presentation

Puzzles in B Decays Alakabha Datta University of Mississippi April 21, 2017 WIN 2017, Irvine Alakabha Datta ( UMiss ) April 21, 2017 1 / 42 Puzzles in B Decays

Outline of Talk In recent times there have been some anomalies in B decays that indi- cate lepton non-universal new physics. These are in semileptonic b → c τ ¯ ν τ transitions: R D ( ∗ ) puzzle. These are in semileptonic b → s ℓ + ℓ − ( l = µ, e ) transitions: P ′ 5 and R K , R K ( ∗ ) puzzles. BR of b → s µ + µ − modes are lower. Alakabha Datta ( UMiss ) April 21, 2017 2 / 42 Puzzles in B Decays

Outline of Talk Recently, LHCb announced LUV in measurement of R K ( ∗ ) I will focus on simultaneous explanation of the R D ( ∗ ) and R K , R K ( ∗ ) anomalies. Recent work shows how future measurements can distinguish among the models. Light new physics: GeV scale or 10-100 MeV mediators. Alakabha Datta ( UMiss ) April 21, 2017 3 / 42 Puzzles in B Decays

R D ( ∗ ) puzzle − − − b / − W / W ’ H − V cb 0 B c (*) D G F � � � D ( ∗ ) ( p ′ ) | ¯ c γ µ (1 − γ 5 ) b | ¯ √ A SM = V cb B ( p ) � τγ µ (1 − γ 5 ) ν τ ¯ 2 B ( ¯ R ( D ∗ ) ≡ B ( ¯ B → D + τ − ¯ B → D ∗ + τ − ¯ ν τ ) ν τ ) R ( D ) ≡ ν ℓ ) . B ( ¯ B ( ¯ B → D + ℓ − ¯ B → D ∗ + ℓ − ¯ ν ℓ ) Alakabha Datta ( UMiss ) April 21, 2017 4 / 42 Puzzles in B Decays

Experiments: R D ( ∗ ) puzzle Recently, the BaBar, Belle and LHCb have reported the following measurements : B ( ¯ B → D + τ − ¯ ν τ ) R ( D ) ≡ ν ℓ ) = 0 . 440 ± 0 . 058 ± 0 . 042 , B ( ¯ B → D + ℓ − ¯ B ( ¯ B → D ∗ + τ − ¯ ν τ ) R ( D ∗ ) ≡ ν ℓ ) = 0 . 332 ± 0 . 024 ± 0 . 018 . (1) B ( ¯ B → D ∗ + ℓ − ¯ Belle R ( D ) ≡ 0 . 375 ± 0 . 064 ± 0 . 026 , R ( D ∗ ) ≡ 0 . 293 ± 0 . 038 ± 0 . 015 , 0 . 302 ± 0 . 030 ± 0 . 011 . (2) LHCb R ( D ∗ ) ≡ 0 . 336 ± 0 . 027 ± 0 . 030 . R ( D ∗ ) ≡ 0 . 306 ± 0 . 016 ± 0 . 010 . (3) Alakabha Datta ( UMiss ) April 21, 2017 5 / 42 Puzzles in B Decays

Average HFAG R ( D ) ≡ 0 . 397 ± 0 . 040 ± 0 . 028 R ( D ∗ ) ≡ 0 . 316 ± 0 . 016 ± 0 . 010 . (4) Theory R ( D ) ≡ 0 . 299 ± 0 . 011( FNAL / MILC ) , 0 . 300 ± 0 . 008( HPQCD ) ≡ 0 . 299 ± 0 . 003( arXiv : 1703 . 05330) R ( D ∗ ) ≡ 0 . 257 ± 0 . 003( arXiv : 1703 . 05330) . (5) R ( D ∗ ) is 3.3 σ from SM. R ( D ) is 1.9 σ from SM. Combined with co-relations is 4 σ deviation. Alakabha Datta ( UMiss ) April 21, 2017 6 / 42 Puzzles in B Decays

¯ B → D ( ∗ ) ℓ − ¯ ν ℓ In the ratios R ( D ( ∗ ) ) the form factors effects (largely) cancel, V cb cancels and experimental systematic effects cancel. The SM has a flavor symmetry SU (3) Q × SU (3) U × SU (3) D × SU (3) L × SU (3) E in the absence of Yukawa interactions. W couples universally to all lepton generations. The results imply lepton non-universal interactions. Alakabha Datta ( UMiss ) April 21, 2017 7 / 42 Puzzles in B Decays

Model independent NP analysis (See for example: Datta, Duraisamy, Ghosh) Effective Hamiltonian for b → cl − ¯ ν l with Non-SM couplings. The NP has to be LUV. 4 G F V cb � c γ µ P L b ] [¯ l γ µ P L ν l ] + V R [¯ c γ µ P R b ] [¯ H eff = √ (1 + V L ) [¯ l γ µ P L ν l ] 2 � cP L b ] [¯ cP R b ] [¯ c σ µν P L b ] [¯ + S L [¯ lP L ν l ] + S R [¯ lP L ν l ] + T L [¯ l σ µν P L ν l ] The NP can be probed via distributions and other related decays. Alakabha Datta ( UMiss ) April 21, 2017 8 / 42 Puzzles in B Decays

B → D ( ∗ ) τν τ in SM + NP, Helicity Amplitudes Decay Distribution described by Helicity Amplitudes 1 � ( m 2 B − m 2 D ∗ − q 2 )( m B + m D ∗ ) A 1 ( q 2 ) H 0 = � q 2 2 m D ∗ − 4 m 2 B | p D ∗ | 2 � m B + m D ∗ A 2 ( q 2 ) (1 − g A ) , √ 2( m B + m D ∗ ) A 1 ( q 2 )(1 − g A ) , H � = √ 2 2 m B V ( q 2 ) H ⊥ = − ( m B + m D ∗ ) | p D ∗ | (1 + g V ) , 2 m B | p D ∗ | A 0 ( q 2 ) H t = (1 − g A ) , � q 2 − 2 m B | p D ∗ | A 0 ( q 2 ) H P = ( m b ( µ ) + m c ( µ )) g P . Alakabha Datta ( UMiss ) April 21, 2017 9 / 42 Puzzles in B Decays

B → D ( ∗ ) τν τ in SM The helicity amplitudes and consequently the NP couplings can be extracted from an angular distribution and compared with models. l D y x W D* * l z B Distribution includes CPV terms which are clean probes of NP without form factor issues. If we observe τ decay then we can measure τ polarization and CPV. Alakabha Datta ( UMiss ) April 21, 2017 10 / 42 Puzzles in B Decays

Other Decays NP can be constrained from other decays have the same quark tran- sition as R D ( ∗ ) : B c → τ − ¯ ν τ ( Alonso, Grinstein, Camalich) , B c → J /ψτ − ¯ ν τ , b → τν X (LEP), Λ b → Λ c τ ¯ ν τ . Measurements in Λ b → Λ c τ ¯ ν τ can further constrain the NP parameter space. (Datta:2017aue, Shivashankara:2015cta). B [Λ b → Λ c τ ¯ ν τ ] R (Λ c ) = B [Λ b → Λ c ℓ ¯ ν ℓ ] R (Λ c ) SM + NP R Ratio = . Λ c R (Λ c ) SM Λ b → Λ c form factors are calculated from lattice QCD (Datta:2017aue, Detmold:2015aaa). Alakabha Datta ( UMiss ) April 21, 2017 11 / 42 Puzzles in B Decays

R Ratio = 1 . 3 ± 3 × 0 . 05 Λ c Only g P present Only g s present 4 1.0 2 0.5 Im [ g P ] Im [ g s ] 0 0.0 - 0.5 - 2 - 1.0 - 4 - 1.5 - 1.0 - 0.5 0.0 0.5 - 4 - 2 0 2 Re [ g s ] Re [ g P ] Only g L present Only g R present Only g T present 1.5 3 3 1.0 2 2 1 1 0.5 Im [ g L ] Im [ g R ] Im [ g T ] 0 0 0.0 - 1 - 1 - 0.5 - 2 - 2 - 1.0 - 3 - 3 - 1.5 - 4 - 3 - 2 - 1 0 1 2 - 2 - 1 0 1 2 3 4 - 2.5 - 2.0 - 1.5 - 1.0 - 0.5 0.0 0.5 Alakabha Datta ( UMiss ) April 21, 2017 12 / 42 Puzzles in B Decays Re [ g L ] Re [ g R ] Re [ g T ]

Interesting Facts R ( D ) exp R Ratio = = 1 . 30 ± 0 . 17 , D R ( D ) SM R ( D ∗ ) exp R Ratio = = 1 . 25 ± 0 . 08 . D ∗ R ( D ∗ ) SM If NP is just V − A then ≡ R expt ≡ R expt = | 1 + V L | 2 = R ratio R ratio D D ∗ . D D ∗ R SM R SM D D ∗ In this case the distributions are just scaling of the SM distributions. Alakabha Datta ( UMiss ) April 21, 2017 13 / 42 Puzzles in B Decays

b → s µ + µ − Anomaly − α G F H eff ( b → s ℓ ¯ V tb V ∗ � ¯ � s L γ µ b L ) � √ ℓ ) = C 9 (¯ ℓγ µ ℓ ts 2 π s L γ µ b L ) � ¯ ℓγ µ γ 5 ℓ �� + C 10 (¯ , − α G F V tb V ∗ s L γ µ b L ) νγ µ (1 − γ 5 ) ν � � H eff ( b → s ν ¯ ν ) = √ ts C L (¯ ¯ , 2 π e H eff ( b → s γ ∗ ) s σ µν ( m s P L + m b P R ) b ] F µν = 16 π 2 [¯ C 7 Alakabha Datta ( UMiss ) April 21, 2017 14 / 42 Puzzles in B Decays

Some Facts At the m b scale C 9 ∼ − C 10 = 4 . 2 while C 7 ∼ 0 . 3 and so semileptonic operators usually dominate. NP contribution from C 7 is not LUV. Low q 2 region is clean. Factorization results hold and Form Factors can satisfy certain symmetry relations(SCET). For very low q 2 the photon pole may dominates over the semileptonic operators. b → s ℓ + ℓ − can come from charm resonance. b → sJ /ψ ( → ℓℓ ). So charm resonance region is cut out from measurement. Alakabha Datta ( UMiss ) April 21, 2017 15 / 42 Puzzles in B Decays

P ′ 5 in B 0 d → K ∗ µ + µ − d 4 (Γ + ¯ 1 Γ) d (Γ + ¯ Γ) / d q 2 d q 2 d � Ω 9 � 4 (1 − F L ) sin 2 θ k + F L cos 2 θ k 3 = 32 π 4 (1 − F L ) sin 2 θ k cos 2 θ l + 1 − F L cos 2 θ k cos 2 θ l + S 3 sin 2 θ k sin 2 θ l cos 2 φ + S 4 sin 2 θ k sin 2 θ l cos φ + S 5 sin 2 θ k sin θ l cos φ 3 A FB sin 2 θ k cos θ l + S 7 sin 2 θ k sin θ l sin φ + 4 + S 8 sin 2 θ k sin 2 θ l sin φ + S 9 sin 2 θ k sin 2 θ l sin 2 φ � . (6) Alakabha Datta ( UMiss ) April 21, 2017 16 / 42 Puzzles in B Decays

Optimal observables. When E K is large, small q 2 , in leading order in SCET these observables are free from form factors. Corrections are ∼ O ( 1 E K ). m 2 B + m 2 K ( ∗ ) − q 2 E K ( ∗ ) = E K ( ∗ ) ∼ m B , 2 m B when q 2 small. 2 S 3 (1 − F L ) = A (2) P 1 = T , P 2 = 2 A FB (1 − F L ) , 3 − S 9 P 3 = (1 − F L ) , (7) S 4 , 5 , 8 P ′ 4 , 5 , 8 = , � F L (1 − F L ) S 7 P ′ 6 = . � F L (1 − F L ) Alakabha Datta ( UMiss ) April 21, 2017 17 / 42 Puzzles in B Decays

LHC 0 . 6 SM (ABSZ/flavio) SM (ABSZ/flavio) 0 . 75 LHCb LHCb 0 . 4 � P 1 � ( B 0 → K ∗ 0 µ + µ − ) 4 � ( B 0 → K ∗ 0 µ + µ − ) CMS 0 . 50 ATLAS ATLAS 0 . 2 0 . 25 0 . 0 0 . 00 − 0 . 2 − 0 . 25 − 0 . 4 − 0 . 50 � P ′ − 0 . 6 − 0 . 75 − 0 . 8 − 1 . 00 0 5 10 15 0 5 10 15 q 2 [GeV 2 ] q 2 [GeV 2 ] SM (ABSZ/flavio) 0 . 6 LHCb 5 � ( B 0 → K ∗ 0 µ + µ − ) 0 . 4 ATLAS CMS 0 . 2 0 . 0 − 0 . 2 − 0 . 4 − 0 . 6 � P ′ − 0 . 8 − 1 . 0 0 5 10 15 q 2 [GeV 2 ] Alakabha Datta ( UMiss ) April 21, 2017 18 / 42 Puzzles in B Decays

NP Explanation Effective theory :Fits to NP semileptonic operators. Perform a model-independent analysis of ¯ s ℓ + ℓ − , considering NP b → ¯ ℓ O ′ ℓ ), where O and O ′ span all Lorentz s O b )(¯ operators of the form (¯ structures ( Descotes-Genon, Matias, Virto, arXiv:1307.5683 ). NP in ∆ C 9 µ Can come from Z ′ models or Leptoquark Models. Can be induced by four quark operators. Alakabha Datta ( UMiss ) April 21, 2017 19 / 42 Puzzles in B Decays