R(D) and R(D ) anomalies and their phenomenological implications. Xin-Qiang Li

Transcription

1 R(D) and R(D ) anomalies and their phenomenological implications Xin-Qiang Li Central China Normal University in collaboration with A. Pich, M. Jung, A. Celis, Y. D. Yang, X. Zhang, based on JHEP 01 (2013) 05, JHEP 08 (2016) 054, and paper to appear soon The 14th International Workshop on Tau Lepton Physics, Beijing, 2016/09/23

2 Outline R(D) and R(D ) anomalies Solution with a charged Higgs Solution with a scalar leptoquark Conclusion and Outlook 2 / 24

3 Why B physics? B-hadron decays: various final states, investigate the flavour structure in fermionic sector; [Y. Amhis et al. HFAG, ] BaBar, Belle, Tevatron, LHCb, and Belle-II: more and more precise data; to validate SM and NP flavor structures; 1.5 γ & m s m d sin 2β ε K α m d α V ub γ excluded at CL > excluded area has CL > 0.95 excluded at CL > 0.95 ε K γ excluded area has CL > m d & m s 0.5 m d α V ub α η β α η sb 0.00 β s -1.0 CKM f i t t e r EPS 15 γ ε K sol. w/ cos 2β < 0 (excl. at CL > 0.95) CKM f i t t e r EPS 15 ε K γ β s sin 2β V ud V ub + V cdv cb + V tdv tb = 0, ρ ρ sb VusV ub + VcsV cb + VtsV tb = 0 3 / 24

4 Current status of flavour anomalies While being in good agreement, NP contributions of order O(20%) to most low-energy FCNC processes are still allowed; Several intriguing deviations from the SM predictions: 2 4σ level; [T. Becher, ; Z. Ligeti, ; A. Crivellin, ] see previous talks at this workshop! While various cross-checks are still needed, some of them would be unambiguous NP signals! A unified explanation within a specific NP model? [A. Crivellin, ] 4 / 24

5 Why B D ( ) τν τ decays? Tree-level processes: mediated by W ± in SM; sensitive to tree-level NP like RH currents, charged Higgs, lepto-quarks, ; R(D ( ) ) = Br(B D( ) τν τ ) Br(B D ( ) lν l ) : uncertainties from FFs and V cb largely cancelled; [BaBar, ; Belle, talk by Shigeki Hirose; LHCb, talk by Kristof De Bruyn] R(D) SM = ± [exp.: ± ± 0.028] [D. Bigi, P. Gambino, ] R(D ) SM = ± [exp.: ± ± 0.010] [S. Fajfer et al., ] The combined WA for R(D) and R(D ) shows a 4.0σ deviation from the SM. 5 / 24

6 Why B D ( ) τν τ decays? 4.0σ R(D ( ) ) anomaly: the most significant in B physics, and motivate many studies both within the SM and in various NP models; The observed tension is model independent: exclusive already over-saturates inclusive; [M. Freytsis, Z. Ligeti, J. Ruderman, ] The data on R(D) and R(D ) imply: Br( B D τ ν) + Br( B Dτ ν) = (2.71 ± 0.18)% Including the four lightest orbitally excited D meson states: Br( B D ( ) τ ν) + Br( B D τ ν) 3% From inclusive= exclusive, 3σ tension with inclusive modes; Br( B X cτ ν) = (2.42 ± 0.05)%, Br(b Xτ + ν) = (2.41 ± 0.23)% 6 / 24

7 Possible to explain the observed R(D ( ) ) anomaly? Questions to be asked: the observed tension can or cannot be explained within the SM? explanations with QCD effects quite unlikely. how precise should we know B D ( ) FFs? LQCD improvements! [FNAL/MILC, , ; HPQCD, ] If LFU is really violated in B-meson decays, could we probe LFU violations in Λ b and B s decays? Remind: LFU in purely leptonic D (s), π, and K, hadronic τ decays already tested, and holds up to 1% level. these decays should put much stronger constraints on the NP contribution! [S. Fajfer et al., ; A. Celis et al., ] Our strategy for R(D ( ) ) anomaly: firstly perform a modelindep. analysis; then specific to some NP models [2HDM and scalar leptoquark], to see their pheno. implications; [A. Celis et al., , in preparation; Xin-Qiang Li et al., ] 7 / 24

8 Solution with a charged Higgs Solutions with a charged Higgs and pheno. implications: A. Celis, M. Jung, X. Q. Li and A. Pich, Sensitivity to charged scalars in B D ( ) τν τ and B τν τ decays, JHEP 1301 (2013) 054 [arxiv: [hep-ph]]. A. Celis, M. Jung, X. Q. Li and A. Pich, Tree-level constraints on a charged Higgs, in preparation. 8 / 24

9 The effective Lagrangian L eff : charged-scalar mediated semileptonic transitions (neglect neutrino-mass-related terms): L eff = 4G F V [ ] quq 2 d q u (g quq dl L P L + g quq dl R P R ) q d [ lp L ν l ] Processes considered: charged-scalar contributes at tree-level; Observable SM prediction Exp. Value R(D) ± ± R(D ) ± ± ± R(X c) ± ± Br(B τ ν τ ) ( ) 10 4 (1.06 ± 0.20) 10 4 Br(B 0 πτ ν τ ) (95% CL) Br(D s τ ν τ ) (4.99 ± 0.20) 10 2 (5.55 ± 0.24) 10 2 Br(D s µ ν µ) (5.13 ± 0.20) 10 3 (5.57 ± 0.24) 10 3 Br(D µ ν µ) (3.78 ± 0.16) 10 4 (3.74 ± 0.17) 10 4 Br(D τ ν τ ) (1.01 ± 0.04) (90% CL) Γ(K µ ν µ)/γ(π µ ν µ) ± ± Γ(τ Kν τ )/Γ(τ πν τ ) (6.58 ± 0.07) 10 2 (6.43 ± 0.09) 10 2 Br(τ πν)/br(π µν) (9.784 ± 0.014) 10 3 (9.713 ± 0.056) 10 3 Br(τ µν τ ν µ)/br(τ eν τ ν e) ± ± / 24

10 Strategy for the global fit CKM elements: the ones not sensitive to the charged scalar; V ud from super-allowed nuclear β decays; V cb from exclusive and inclusive semileptonic b cl ν l decays; V ub from exclusive and inclusive semileptonic b ul ν l decays. Hadronic parameters: taken from the latest FLAG, HFAG and PDG averages; [FLAG, ; PDG 2015 version; HFAG, ] Statistical analysis: choose frequentist statistics and Rfit scheme, as implemented by CKMfitter group; [Höcker et al., 2001] theo. uncertainties treated by defining allowed ranges, and within the range no contribution to χ 2, while set to infinity outside the range; theo. errors chosen conservatively and added linearly; syst. errors treated as above, while stat. errors normally. 10 / 24

11 What s new compared to A. Celis, M. Jung, X. Q. Li and A. Pich, ? Both Belle and LHCb measurements are well consistent with BaBar s, implying now 4.0σ deviation from the SM predictions; [BaBar, , ; Belle, , , , ; LHCb, ] The q 2 distributions dγ(b D ( ) τν)/dq 2 also available by Belle and BaBar, yielding additional information to distinguish NP from the SM, and different NP models from each other; [BaBar, ; Belle, ] Constraints from the inclusive semi-leptonic decay B X cτν, measured at LEP, also taken into account, providing further complementary constraints; [Freytsis, Ligeti, Ruderman, ; LEP, hep-ex/ ] Constraints from direct charged-higgs searches at the LHC now become available; [ATLAS, , , ; CMS, CMS-PAS-HIG , ; A. G. Akeroyd et al., ] combined with the LEP bound, M H ± integrate out M H ± at µ b 5 GeV, to get H eff C i O i. 80 GeV m b, one can safely 11 / 24

12 Model-independent analysis of B D ( ) τν With no assumptions on flavour structure, the only observables governed by b cτν τ : R(D), R(D ), R(X c), dγ(b D ( ) τν)/dq 2 ; δcb l (gcbl L + gcbl R )(m B m D ) 2 [scalar], m l ( m b m c) l cb (gcbl L gcbl R )m2 B [pseudo scalar] m l ( m b + m c) For real couplings: allowed parameter spaces in δ τ cb τ cb -plane; R(D ( ) ) yield four solutions (blue); dγ(b D ( ) τν)/dq 2 exclude two of them; favour the one with large τ cb (95% CL); Model-independent tension with the inclusive B X cτν τ decay reflected by small overlap regions; Conclusion: the current data can be explained simultaneously by a charged scalar, but only with both gl cbτ and gcbτ R present! 12 / 24

13 Model-independent analysis of B D ( ) τν Individual fit to R(D) and R(D ) with complex couplings: Fits including the measured q 2 spectrum and B c τ ν τ : 13 / 24

14 Cases with only g cbτ L or gcbτ R present Only gl cbτ present: possible to resolve R(D) and R(D ), but in conflict with the measured q 2 differential distributions; Dark green: fits at 95% CL; light green: at 99.7% CL; Having only a real gl cbτ as the common explanation for R(D) and R(D ) is now highly disfavoured by the q 2 differential distributions; [A. Crivellin et al., ; A. Crivellin et al., ] Only gr cbτ present: does improve the fit to R(D( ) ) compared to SM, but does not yield a good fit, when combining all data; Conclusion: charged scalar alone do can explain all the data, but only with both gl cbτ and gcbτ R added simultaneously! 14 / 24

15 Scenarios without tree-level FCNCs The model-indep. scalar-mediated charged-current interaction: L eff = 4G F V [ ] quq 2 d q u (g quq dl L P L + g quq dl R P R ) q d [ lp L ν l ] Scenarios without tree-level FCNCs: g L,R must be diagonal; [ Yukawa Alignment in the Two-Higgs-Doublet Model, A. Pich, P. Tuzon, ] L Y = 2 } v H+{ ū [V ς D M D P R ς U M U V P L ] d + νς L M L P R l g quq dl L = ς u ς l m qu m l m 2, g quq dl R = ς d ςl H ± m qd m l m 2 H ± Family-universal: ς D,U,L ς d,u,l 1, 2HDMs with NFC easily recovered; different decay modes are automatically connected; 15 / 24

16 Scenarios without tree-level FCNCs New observables involving τ: Br(B τν), Br(D d,s τν), Γ(τ Kν)/Γ(τ πν), ; Global fit using the available data with τ lepton: 95% CL dark blue: constraints from R(D ( ) ); light blue: constraints from q 2 distributions; dark yellow: the other measurements above, not depending on both couplings simultaneously; red: dashed rings excluded by D d τν and incompatible with the distributions; joined fit still remains viable: χ 2 = 62.7 for 55 dof, compared to χ 2 = 81.1 for 60 dof in SM; Conclusion: the scenario with charged-scalar interactions can explain B D ( ) τν and the remaining tree-level observables! 16 / 24

17 Solution with a scalar leptoquark Solutions with a scalar leptoquark and pheno. implications: X. Q. Li, Y. D. Yang and X. Zhang, Revisiting the one leptoquark solution to the R(D ( ) ) anomalies and its phenomenological implications, arxiv: [hep-ph]. M. Bauer and M. Neubert, Minimal Leptoquark Explanation for the R D ( ), R K, and (g 2) µ Anomalies, Phys. Rev. Lett. 116 (2016) no.14, [arxiv: [hep-ph]]. M. Freytsis, Z. Ligeti and J. T. Ruderman, Flavor models for B D ( ) τ ν, Phys. Rev. D 92 (2015) no.5, [arxiv: [hep-ph]]. 17 / 24

18 The one scalar leptoquark scenario The LQ model: one single scalar LQ with M φ 1 TeV and (3, 1, 1 3 ) added to SM; [M. Bauer and M. Neubert, ] L φ = (D µφ) D µφ M 2 φ φ 2 g hφ Φ 2 φ 2 + Q c λ L iτ 2 L φ + ū c R λr e R φ + h.c., φ interactions with fermions: rotating from the weak to the mass basis for quarks and charged leptons, to get L φ ( ) int ; L φ int = ūc L λl ul l Lφ d c L λl dν ν Lφ + ū c R λr ul l Rφ + h.c., b c (s) c b c µ µ W s s µ c (s) ( ) u µ b t µ b µ t t s Both tree- and loop-level four-fermion operators (ū i d j )( νl), (ū i u j )(l + l ) and ( d b s i d j )( νν) generated; B D ( ) τ ν τ, Bt c τ ν τ (γ), B X µ ( ) µ cτ ν τ, µ ( ) µ D 0 µ + µ, D + π + µ + µ, B X sν ν, B K ( ) ν ν, K πν ν, t (g 2) µ;,z [M. Bauer and M. Neubert, ] s µ µ t µ 18 / 24

19 LQ-mediated b cτ ν τ decays Total H eff for b cτ ν τ transitions: integrating out φ and performing the proper Fierz transformation; H eff = 4G F 2 V cb [C V (M φ ) cγ µp L b τγ µ P L ν τ + C S (M φ ) cp L b τp L ν τ 1 4 C T (M φ ) cσ µνp L b τσ µν P L ν τ ] C V, C S, C T : the WCs at the matching scale µ = M φ ; the latter two need be run down to µ b m b ; λ L bν C V (M φ ) = 1 + τ λ L cτ 4 2G F V cb Mφ 2, C S (M φ ) = C T (M φ ) = λl bν τ λ R cτ 4 2G F V cb Mφ 2 Four best-fit solutions for R(D ( ) ) along with acceptable q 2 spectra: M φ = 1 TeV; [M. Freytsis, Z. Ligeti, J. T. Ruderman, ] ( 0.35, 0.03), P A (λ L bν τ λ L cτ, λ L bν τ λ R cτ ) = (C S R, C S ( 0.96, 2.41), P B L ) = ( 5.74, 0.03), P C ( 6.34, 2.39), P D 19 / 24

20 LQ-mediated b cτ ν τ decays Solution P A : explain in a natural way three of the most striking anomalies of particle physics, while satisfying the other low-energy constraints without finetuning; [M. Bauer and M. Neubert, ] One Leptoquark to Rule Them All: A Minimal Explanation for Rn < 串 ), RK and (g-2)µ Martin Bauerαand Matthias Neubertb,c α Institut fur Theoretische Physik, Uniυ ersitat Heidelberg, Philosophenweg 16, Heidelberg, Germαny b PRISMA Cluster of Excellence & MITP, Johαnn es Gutenberg University, Mαinz, Germαny c D epαrtment of Physics & LEPP, Cornell University, Ithαcαy NY 14853, U.S.A. We show that by adding a single new scalar particle to the Standard Model, a Te V-scale leptoquark with the quantum numbers of a right-handed down quark, one can explain in a natural way three of the most striking anomalies of particle physics: the violation of lepton universality in B [(g+g decays, the enhanced B n <* )TD decay rates, and the anomalous magnetic moment of t he muon. Constraints from other precision measurements in the flavor sector can be satisfied without finet uning. Our model predicts enhanced B [((*)vd decay rates and a new-physics contribution to Bs -Bs mixing close to t he current central fit value. Question: these four best-fit solutions could be discriminated from each other using the low-energy processes mediated by the same quark-level b cτν τ transition? in addition to B D ( ) τ ν τ, we shall examine the scalar LQ effects on B c τ ν τ, B c γτ ν τ and B X cτ ν τ decays. 20 / 24

21 The purely leptonic B c τ ν τ decay The decay width with LQ-exchanged contribution: ( ) 2 Γ(Bc τ ν τ ) = G2 F 8π V cb 2 fb 2 c m 3 m 2 τ B c m 2 1 m2 τ B c m 2 B c C m 2 2 B V C c S [ m τ mb (µ b ) + m c(µ b ) ] Numerical results with the four best-fit solutions: Γ Bc, SM Γ(Bc τ ν τ ) = Γ Bc, P A 1.33 Γ Bc, P B Γ Bc, P C 1.31 Γ Bc, P D Conclusion: Clearly, P B and P D already excluded by Bc τ ν τ, because the predicted decay widths have already overshot the total width. need only consider solutions P A and P C! 21 / 24

22 Comparison between P A and P C H eff with fitted values of the effective couplings in P A and P C : [ H fit = 4G F V cb ( )] for PA cγ for P µp L b τγ µ P L ν τ C }{{} C fit V ( for PA ) for P C cp L b τp L ν τ } {{ } C S fit ( ) for PA + cσ for P µνp L b τσ µν P L ν τ C }{{} C T fit CV fit : nearly same absolute values but with opposite signs, enhance SM by 12%; CS fit and Cfit T : same (tiny) values but with opposite signs; Conclusion: it should be difficult to discriminate P A from P C ; 22 / 24

23 Some other decay modes considered: The radiative leptionic decay B c γτ ν τ : b γ b τ ντ 2.5 SM Bc c τ ντ Bc b Bc γ τ c γ d deγ PA PC c The inclusive semileptonic B X cτ ν τ decay: ντ Γ d dq RXc q d dy PC PA SM q q PC PA SM PC PA SM y The other observables in B D ( ) τν τ : q 2 distribution of R(D) and R(D ), polarizations of τ and D, and lepton forward-backward asymmetry; Conclusion: these observables are enhanced by the scalar LQ contribution, but difficult to distinguish between the two solutions P A and P C. 23 / 24

24 Conclusion and outlook R(D) and R(D ) anomalies: BaBar, Belle and LHCb results consistent with each other; The latest 2016 WA has now a 4.0σ deviation from the SM predictions (Remind: theoretical predictions are on solid footing; first NP signal?); The current data can be explained by a charged scalar, but only when both g cbτ L and g cbτ R couplings are considered simultaneously; In scenarios without tree-level FCNCs [like A2HDM: A. Celis, M. Jung, X. Q. Li and A. Pich, ]: R(D), R(D ) and the other low-energy processes can be consistently explained; however, the allowed regions are severely constrained; The current flavour anomalies can be explained by adding just one scalar leptoquark; we have discussed its effects on B(B c τ ν τ ), B(B c γτ ν τ ), R D ( )(q 2 ), db( B D ( ) τ ν τ )/dq 2, B( B X cτ ν τ ); Very interesting to study the inclusive B X cτ ν τ, and the semileptonic Λ b and B s decays, ; Thank You for Your Attention! 24 / 24