Shaikh Saad Based on: arXiv:2004.07880 (Saad, A. Thapa) : - PowerPoint PPT Presentation

Radiative Neutrino Mass Models and ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) Anomalies Shaikh Saad Based on: arXiv:2004.07880 (Saad, A. Thapa) : arXiv:2005.04352 (Saad) Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 1 / 45

Outline Muon anomalous magnetic moment: ∆ a µ Flavor anomalies: R K ( ∗ ) , R D ( ∗ ) Neutrino mass Proposals (Model-I, Model-II) Summary *Talk intended for the graduate students, faculties may find it trivial Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 2 / 45

( g − 2) µ Dirac’s relativistic wave equation formulation: 1928 Muon magnetic moment: � 2 m µ � e M = g µ S Land´ e g-factor: g µ = 2 Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 3 / 45

( g − 2) µ Quantum loop corrections: g µ � = 2 Bethe (1947) did before Schwinger (1948), but in non-relativistic framework Anomalous magnetic moment: a µ = g µ − 2 2 Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 4 / 45

( g − 2) µ a exp − a SM ≡ ∆ a µ = (274 ± 73) × 10 − 11 ∼ 3 . 7 σ µ µ Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 5 / 45

R K ( ∗ ) b → s : Neutral current process ∗ µ + µ − ) R K = Γ( B → K µ + µ − ) R K ∗ = Γ( B → K Γ( B → Ke + e − ) , . ∗ e + e − ) Γ( B → K R SM R SM = 1 . 0003 ± 0 . 0001 , K ∗ = 1 . 00 ± 0 . 01 K Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 6 / 45

R K ( ∗ ) Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 7 / 45

R K ( ∗ ) LHCb, arXiv:1903.09252 − 0 . 054 − 0 . 014 , 1 . 1 GeV 2 < q 2 < 6 . 0 GeV 2 R exp = 0 . 846 +0 . 06+0 . 016 K Belle, arXiv:1904.02440 � − 0 . 21 ± 0 . 10 , 0 . 1 GeV 2 < q 2 < 8 . 0 GeV 2 0 . 90 +0 . 27 R exp K ∗ = − 0 . 32 ± 0 . 10 , 15 GeV 2 < q 2 < 19 GeV 2 1 . 18 +0 . 52 LHCb, arXiv:1705.05802 − 0 . 070 ± 0 . 024 , 0 . 045 GeV 2 < q 2 < 1 . 1 GeV 2 � 0 . 660 +0 . 110 R exp K ∗ = − 0 . 069 ± 0 . 047 , 1 . 1 GeV 2 < q 2 < 6 . 0 GeV 2 0 . 685 +0 . 113 Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 8 / 45

R K ( ∗ ) R K ∼ 2 . 5 σ ∼ 2 . 5 σ (LHCb) R K ∗ ′ ′ Angular observables: P 4 , P 5 B s → µµ (ATLAS, CMS, LHCb) and more ... Combined: ∼ 4 . 5 σ Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 9 / 45

R D ( ∗ ) b → c : Charged current process R D = Γ( B → D τν ) R D ∗ = Γ( B → D ∗ τν ) Γ( B → D ℓν ) , Γ( B → D ∗ ℓν ) R SM R SM = 0 . 299 ± 0 . 003 , D ∗ = 0 . 258 ± 0 . 005 D Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 10 / 45

R D ( ∗ ) Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 11 / 45

R D ( ∗ ) Global average: (Belle, BaBar, LHCb) R exp R exp = 0 . 334 ± 0 . 031 , D ∗ = 0 . 297 ± 0 . 015 D R D , R D ∗ ∼ 3 σ R J /ψ , f D ∗ L , P 8 τ and more ... Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 12 / 45

Neutrino Mass In SM, neutrino mass = 0 Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 13 / 45

Synopsis SM cannot explain neutrino oscillation data Long-standing tension in ( g − 2) µ Large deviations in flavor ratios Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 14 / 45

Solution? ✗ Standard Model ✓ Physics Beyond the Standard Model Can all these be related? Combined explanations? ✓ Scalar Leptoquarks ➸ Which Leptoquarks? Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 15 / 45

LQ Solution: ( g − 2) µ ✓ S 1 ∼ (3 , 1 , 1 / 3) γ q i φ 1 / 3 ℓ ℓ γ φ 1 / 3 q i ℓ ℓ ∆ a µ ≃ − 3 m t m µ � 7 6 + 2 � y L 32 y R 3 log[ x t ] . 32 M 2 8 π 2 1 R 2 ∼ (3 , 2 , 7 / 6) ✓ Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 16 / 45

LQ Solution: Flavor anomalies arXiv:1808.08179 ✗ Single LQ Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 17 / 45

Two possibilities ✓ R 2 ∼ (3 , 2 , 7 / 6) + S 3 ∼ (3 , 3 , 1 / 3) : Model-I S 1 ∼ (3 , 1 , 1 / 3) + S 3 ∼ (3 , 3 , 1 / 3) : Model-II ✓ Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 18 / 45

Model-I R 2 ∼ (3 , 2 , 7 / 6) + S 3 ∼ (3 , 3 , 1 / 3) Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 19 / 45

R K ( ∗ ) Wolfgang S 3 ∼ (3 , 3 , 1 / 3) C µµ = − C µµ 10 = − 0 . 53 arXiv:1903.10434 9 Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 20 / 45

R K ( ∗ ) S 3 ∼ (3 , 3 , 1 / 3) � � � = − 4 G F C ij ,ℓℓ ′ O ij ,ℓℓ ′ H dd ℓℓ √ V tj V ∗ + h . c ., eff ti X X 2 X =9 , 10 = α = α O ij ,ℓℓ ′ , O ij ,ℓℓ ′ d i γ µ P L d j d i γ µ P L d j � � � ℓγ µ ℓ ′ � � � � ℓγ µ γ 5 ℓ ′ � . 9 10 4 π 4 π � ∗ v 2 y S � y S π C ℓℓ ′ = − C ℓℓ ′ b ℓ ′ s ℓ 10 = . 9 M 2 V tb V ∗ α em ts 3 C µµ = − C µµ 10 = − 0 . 53 arXiv:1903.10434 9 Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 21 / 45

R D ( ∗ ) R 2 ∼ (3 , 2 , 7 / 6) = 4 G F H du ℓν � C fi � ℓ L γ µ ν Li � ( c L γ µ b L ) + C fi � � √ V cb ℓ Rf ν Lj ( c R b L ) eff V S 2 ℓ Rf σ µν ν Li + C fi � � � ( c R σ µν b L ) + T y L cj ( y R ˆ b τ ) ∗ C j S ( µ = m R ) = 4 C j √ T ( µ = m R ) = . 2 m 2 4 R G F V cb C S = 4 C T Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 22 / 45

μ R D ( ∗ ) R 2 ∼ (3 , 2 , 7 / 6) : C S = 4 C T 0.6 μ = m R 1.0 C S = 4 C T 0.4 0.5 0.2 μ = m R τ ] C S = 4 C T Im [ C S C S 0.0 0.0 - 0.2 - 0.5 - 0.4 - 1.0 - 0.6 - 0.6 - 0.4 - 0.2 0.0 0.2 0.4 - 0.6 - 0.4 - 0.2 0.0 0.2 0.4 0.6 e Re [ C S τ ] C S Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 23 / 45

Model-II S 1 ∼ (3 , 1 , 1 / 3) + S 3 ∼ (3 , 3 , 1 / 3) Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 24 / 45

R D ( ∗ ) S 3 ∼ (3 , 3 , 1 / 3) + S 1 ∼ (3 , 1 , 1 / 3) = 4 G F H du ℓν C fi ℓ L γ µ ν Li ( c L γ µ b L ) + C fi � � � � � √ V cb ℓ Rf ν Lj ( c R b L ) eff V S 2 + C fi � ℓ Rf σ µν ν Li � � ( c R σ µν b L ) + T y R � ∗ � y L T = − v 2 bi C fi S = − 4 C fi cf , M 2 4 V cb 1 � V ∗ y L � ∗ V ∗ y S � ∗ � y L � − y S � v 2 bi bi C fi cf cf V = . M 2 M 2 4 V cb 1 3 C S = − 4 C T Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 25 / 45

Neutrino mass? ✗ R 2 ∼ (3 , 2 , 7 / 6) + S 3 ∼ (3 , 3 , 1 / 3) : Model-I S 1 ∼ (3 , 1 , 1 / 3) + S 3 ∼ (3 , 3 , 1 / 3) : Model-II ✗ Minimal choice: single scalar Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 26 / 45

Model-I: Neutrino mass R 2 ∼ (3 , 2 , 7 / 6) + S 3 ∼ (3 , 3 , 1 / 3) + χ 1 ∼ (3 , 1 , 2 / 3) � H 0 � � H 0 � � H 0 � χ 2 / 3 R 2 / 3 S − 2 / 3 ν L u L ν L u R arXiv: 1907.09498 µλ v 3 1 M ν � ( y L ) ∗ ki m u � k ( V ∗ y ) kj + ( i ↔ j ) ij = m 0 ; m 0 ≈ M 2 1 M 2 16 π 2 2 Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 27 / 45

Model-I: Combined explanations TX-I :       0 0 0 0 0 0 0 0 0 y R =  , y L =  , y =  . 0 0 0 ∗ ∗ ∗ ∗ ∗ ∗    0 0 ∗ 0 0 ∗ 0 ∗ 0 TX-II :       0 0 0 0 0 0 0 0 0 y R =  , y L =  , y =  . 0 0 0 ∗ ∗ ∗ 0 ∗ ∗    0 0 ∗ 0 0 ∗ ∗ ∗ 0 Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 28 / 45

Model-I Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 29 / 45

LHC bounds LHC (ATLAS, CMS) Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 30 / 45

Model-I: BM-TX-I M 2 = 1 . 2 TeV, M 3 = 2 . 5 TeV   0 0 0 y R =  , 0 0 0  0 0 1 . 09527 i   0 0 0 y L =  , 4 . 0503 × 10 − 3 − 2 . 1393 × 10 − 2 1 . 2243  − 4 . 9097 × 10 − 4 0 0   0 0 0  , − 4 . 5241 × 10 − 4 − 7 . 7187 × 10 − 3 − 4 . 6354 × 10 − 4 y =  6 . 8578 × 10 − 1 0 0 m 0 = 1 . 297 × 10 − 8 . Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 31 / 45

Model-I: BM fits Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 32 / 45

Model-I 10 - 12 10 - 13 CR ( μ -> e ) 10 - 14 10 - 15 10 - 16 TX - I 10 - 17 - 0.60 - 0.55 - 0.50 - 0.45 C 9 =- C 10 Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 33 / 45

Model-I 10 - 12 10 - 13 CR ( μ -> e ) 10 - 14 10 - 15 10 - 16 10 - 17 TX - I 10 - 14 10 - 12 10 - 10 10 - 8 Br ( τ -> μγ ) Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 34 / 45

Model-I 0.34 60 % 0.32 R D * 0.30 30 % 0.28 10 % 0.26 TX - I 0.30 0.32 0.34 0.36 0.38 0.40 R D Br ( B c → τν )% Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 35 / 45

Model-II: Neutrino mass S 1 ∼ (3 , 1 , 1 / 3) + S 3 ∼ (3 , 3 , 1 / 3) + ω ∼ (6 , 1 , 2 / 3) φ 1 / 3 φ 1 / 3 ω 2 / 3 ν L d L d R d R d L ν L Babu, Leung 2001 � M 2 1 1 � ij = 24 µ p y p lk I p kk y p I p DQ M ν li m d ll y ω lk m d kj ; lk = I 256 π 4 M 2 M 2 p p Saad ( g − 2) µ , R K ( ∗ ) , R D ( ∗ ) , M ν 36 / 45