B 0 D ( ) Analyzing New Physics in the decays Chien-Thang - PowerPoint PPT Presentation

Introduction Hadronic Matrix Elements and Form Factors Covariant Confined Quark Model Decay distribution and experimental constraints Analyzing New B 0 → D ( ∗ ) τ − ¯ Analyzing New Physics in the decays ¯ ν τ Chien-Thang Tran a , b , ∗ , M. A. Ivanov b , and J. G. K¨ orner c a) Moscow Institute of Physics and Technology b) Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna c) PRISMA Cluster of Excellence, Institut f¨ ur Physik, J.G.-Universit¨ at, Mainz, Germany ∗ ) ctt@theor.jinr.ru Gatchina, HSQCD-2016

Introduction Hadronic Matrix Elements and Form Factors Covariant Confined Quark Model Decay distribution and experimental constraints Analyzing New Content Introduction Hadronic Matrix Elements and Form Factors Covariant Confined Quark Model Decay distribution and experimental constraints Analyzing New Physics

Introduction Hadronic Matrix Elements and Form Factors Covariant Confined Quark Model Decay distribution and experimental constraints Analyzing New Experimental Status • Ratios of branching fractions B 0 → D ( ∗ ) τ − ¯ B 0 → D ( ∗ ) µ − ¯ R(D ( ∗ ) ) ≡ B (¯ ν τ ) / B (¯ ν µ ) • Experiments R(D ∗ ) | BABAR = 0 . 332 ± 0 . 030 , R(D) | BABAR = 0 . 440 ± 0 . 072 , R(D ∗ ) | BELLE = 0 . 293 ± 0 . 041 , R(D) | BELLE = 0 . 375 ± 0 . 069 , R(D ∗ ) | LHCb = 0 . 336 ± 0 . 040 , (statistical and systematic uncertainties combined in quadrature) • Average ratios R(D ∗ ) | expt = 0 . 322 ± 0 . 022 , R(D) | expt = 0 . 391 ± 0 . 050 , HFAG 2015 • SM expectations R(D ∗ ) | SM = 0 . 252 ± 0 . 003 , R(D) | SM = 0 . 297 ± 0 . 017 , Fajfer et al. 2012, Kamenik et al. 2008 → SM excess: 1 . 9 σ and 3 . 2 σ , respectively;

Introduction Hadronic Matrix Elements and Form Factors Covariant Confined Quark Model Decay distribution and experimental constraints Analyzing New Theoretical attempts to explain the excess 1) Specific NP models: two-Higgs-doublet models (2HDMs), Minimal Supersymmetric Standard Model (MSSM), Leptoquark models, etc. W. S. Hou, Enhanced charged Higgs boson effects in B → τ ¯ ν τ , • B → µ ¯ ν µ and b → τ ¯ ν τ + X , Phys. Rev. D 48 , 2342 (1993). • Y. Sakaki, M. Tanaka, A. Tayduganov and R. Watanabe, Testing leptoquark models in ¯ B → D ( ∗ ) τ ¯ ν , Phys. Rev. D 88 , no. 9, 094012 (2013). A. Crivellin, C. Greub and A. Kokulu, Explaining B → D τν , B → D ∗ τν • and B → τν in a 2HDM of type III, Phys. Rev. D 86 , 054014 (2012). • L. Calibbi, A. Crivellin and T. Ota, Effective field theory approach to b → s ℓℓ ( ′ ) , B → K ( ∗ ) ν ¯ ν and B → D ( ∗ ) τν with third generation couplings, Phys. Rev. Lett. 115 , 181801 (2015). A. Crivellin, J. Heeck and P. Stoffer, A perturbed lepton-specific • two-Higgs-doublet model facing experimental hints for physics beyond the Standard Model, Phys. Rev. Lett. 116 , no. 8, 081801 (2016). • M. Bauer and M. Neubert, One Leptoquark to Rule Them All: A Minimal Explanation for R D ( ∗ ) , R K and (g − 2) µ , Phys. Rev. Lett. 116 , no. 14, 141802 (2016). • S. Fajfer and N. Koˇ snik, Vector leptoquark resolution of R K and R D ( ∗ ) puzzles, Phys. Lett. B 755 , 270 (2016).

Introduction Hadronic Matrix Elements and Form Factors Covariant Confined Quark Model Decay distribution and experimental constraints Analyzing New Theoretical attempts to explain the excess 2) Model-independent approach: general SM+NP effective Hamiltonian for b → c ℓν is imposed A. Datta, M. Duraisamy, and D. Ghosh, Diagnosing New Physics in • b → c τ ν τ decays in the light of the recent BaBar result, Phys. Rev. D 86 , 034027 (2012). • S. Fajfer, J. F. Kamenik, I. Nisandzic, and J. Zupan, Implications of lepton flavor universality violations in B-Decays, Phys. Rev. Lett. 109 , 161801 (2012). • S. Fajfer, J. F. Kamenik, and I. Nisandzic, On the B → D ∗ τ ¯ ν τ sensitivity to New Physics, Phys. Rev. D 85 , 094025 (2012). • M. Duraisamy and A. Datta, The Full B → D ∗ τ − ¯ ν τ Angular Distribution and CP violating Triple Products, JHEP 1309 , 059 (2013). • M. Duraisamy, P. Sharma and A. Datta, Azimuthal B → D ∗ τ − ¯ ν τ angular distribution with tensor operators, Phys. Rev. D 90 , no. 7, 074013 (2014). • M. Tanaka and R. Watanabe, New physics in the weak interaction of B → D ( ∗ ) τ ¯ ¯ ν , Phys. Rev. D 87 , 034028 (2013). • P. Biancofiore, P. Colangelo, and F. De Fazio, On the anomalous enhancement observed in B → D ( ∗ ) τ ¯ ν τ decays, Phys. Rev. D 87 , 074010 (2013). • S. Bhattacharya, S. Nandi and S. K. Patra, Optimal-observable analysis of possible new physics in B → D ( ∗ ) τν τ , Phys. Rev. D 93 , no. 3, 034011 (2016).

Introduction Hadronic Matrix Elements and Form Factors Covariant Confined Quark Model Decay distribution and experimental constraints Analyzing New Effective Hamiltonian Effective Hamiltonian for the quark-level transition b → c τ − ¯ ν τ √ H eff = 2 2G F V cb [(1 + V L ) O V L + V R O V R + S L O S L + S R O S R + T L O T L ] , where the four-Fermi operators are written as c γ µ P L b) (¯ O V L = (¯ τγ µ P L ν τ ) , c γ µ P R b) (¯ O V R = (¯ τγ µ P L ν τ ) , O S L = (¯ cP L b) (¯ τ P L ν τ ) , O S R = (¯ cP R b) (¯ τ P L ν τ ) , c σ µν P L b) (¯ O T L = (¯ τσ µν P L ν τ ) . Here, σ µν = i [ γ µ , γ ν ] / 2, P L , R = (1 ∓ γ 5 ) / 2 are the left and right projection operators, and V L , R , S L , R , and T L are the complex Wilson coefficients governing the NP contributions. In the SM one has V L , R = S L , R = T L = 0. We assume that NP only affects leptons of the third generation.

Introduction Hadronic Matrix Elements and Form Factors Covariant Confined Quark Model Decay distribution and experimental constraints Analyzing New Matrix element B 0 → D ( ∗ ) τ ¯ The invariant matrix element of ¯ ν τ can be written as � G F V cb (1 + V R + V L ) � D ( ∗ ) | ¯ c γ µ b | ¯ B 0 � ¯ τγ µ (1 − γ 5 ) ν τ M = √ 2 +(V R − V L ) � D ( ∗ ) | ¯ c γ µ γ 5 b | ¯ B 0 � ¯ τγ µ (1 − γ 5 ) ν τ +(S R + S L ) � D ( ∗ ) | ¯ cb | ¯ B 0 � ¯ τ (1 − γ 5 ) ν τ +(S R − S L ) � D ( ∗ ) | ¯ c γ 5 b | ¯ B 0 � ¯ τ (1 − γ 5 ) ν τ � +T L � D ( ∗ ) | ¯ c σ µν (1 − γ 5 )b | ¯ B 0 � ¯ τσ µν (1 − γ 5 ) ν τ . Note that the axial and pseudoscalar hadronic currents do not contribute B 0 → D transition, while the scalar hadronic current does not to the ¯ B 0 → D ∗ transition. contribute to the ¯

Introduction Hadronic Matrix Elements and Form Factors Covariant Confined Quark Model Decay distribution and experimental constraints Analyzing New Form factors Hadronic matrix elements are parametrized by a set of form factors: F + (q 2 )P µ + F − (q 2 )q µ , c γ µ b | ¯ B 0 (p 1 ) � � D(p 2 ) | ¯ = cb | ¯ B 0 (p 1 ) � (m 1 + m 2 )F S (q 2 ) , � D(p 2 ) | ¯ = � P µ q ν − P ν q µ + i ε µν Pq � iF T (q 2 ) c σ µν (1 − γ 5 )b | ¯ B 0 (p 1 ) � � D(p 2 ) | ¯ = , m 1 + m 2 B 0 → D transition, and for the ¯ c γ µ (1 ∓ γ 5 )b | ¯ B 0 (p 1 ) � � D ∗ (p 2 ) | ¯ � � ǫ † ∓ g µα PqA 0 (q 2 ) ± P µ P α A + (q 2 ) ± q µ P α A − (q 2 ) + i ε µα Pq V(q 2 ) 2 α = , m 1 + m 2 � D ∗ (p 2 ) | ¯ c γ 5 b | ¯ B 0 (p 1 ) � = ǫ † 2 α P α G S (q 2 ) , � � P µ g να − P ν g µα + i ε P µνα � c σ µν (1 − γ 5 )b | ¯ B 0 (p 1 ) � = − i ǫ † G T 1 (q 2 ) � D ∗ (p 2 ) | ¯ 2 α + (q µ g να − q ν g µα + i ε q µνα ) G T 2 (q 2 ) � P µ q ν − P ν q µ + i ε Pq µν � � G T 0 (q 2 ) P α + , (m 1 + m 2 ) 2 B 0 → D ∗ transition. Here, P = p 1 + p 2 , q = p 1 − p 2 , and ǫ 2 is the for the ¯ polarization vector of the D ∗ meson so that ǫ † 2 · p 2 = 0. The particles are on their mass shells: p 2 1 = m 2 1 = m 2 B and p 2 2 = m 2 2 = m 2 D ( ∗ ) .

Introduction Hadronic Matrix Elements and Form Factors Covariant Confined Quark Model Decay distribution and experimental constraints Analyzing New Covariant Confined Quark Model in a nutshell G. V. Efimov, M. A. Ivanov, V. E. Lyubovitskij, J. G. K¨ orner, P. Santorelli,. . . • Main assumption: hadrons interact via quark exchange only • Interaction Lagrangian L int = g H · H(x) · J H (x) • Quark current � � q a f 1 (x 1 ) Γ H q a J H (x) = dx 1 dx 2 F H (x; x 1 , x 2 ) · ¯ f 2 (x 2 ) • Vertex Function F H (x; x 1 , x 2 ) = δ (x − w 1 x 1 − w 2 x 2 ) Φ H ((x 1 − x 2 ) 2 ) where w i = m q i / (m q 1 + m q 2 ) Translational invariant: F H (x + c; x 1 + c , x 2 + c) = F H (x; x 1 , x 2 ) • Nonlocal Gaussian-type vertex functions with fall-off behavior in Euclidean space to temper high energy divergence of quark loops � dx e ikx Φ H (x 2 ) = e k 2 / Λ 2 Φ H ( − k 2 ) = � H where Λ H characterizes the meson size.

Introduction Hadronic Matrix Elements and Form Factors Covariant Confined Quark Model Decay distribution and experimental constraints Analyzing New Covariant Confined Quark Model in a nutshell • Compositeness condition Z H = 0 Salam 1962; Weinberg 1963 Z H – wave function renormalization constant of the meson H. Z 1 / 2 = < H bare | H dressed > = 0 H • Z H = 1 − ˜ H ) = 0 where ˜ Π ′ (m 2 Π(p 2 ) is the meson mass operator. q 2 p p H H q 1 ¯ � dk Π P (p) = 3g 2 Φ 2 � P ( − k 2 )tr[S 1 (k+w 1 p) γ 5 S 2 (k − w 2 p) γ 5 ] P (2 π ) 4 i � V [g µν − p µ p ν dk Π V (p) = g 2 Φ 2 � V ( − k 2 )tr [S 1 (k + w 1 p) γ µ S 2 (k − w 2 p) γ ν ] ] p 2 (2 π ) 4 i