CP Violation in B Physics Puzzles, Opportunities at LHCb,

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1 CP Violation in B Physics Puzzles, Opportunities at LHCb, Matthias Neubert Matthias Neubert Institut für Physik (THEP) Johannes Gutenberg-Universität Mainz CPT@ICTP, Trieste, July

2 Flavor Puzzles in B Physics and LHCb Capabilities New Physics CP phase in B s mixing sin2β from tree vs. penguins CP violation in B πk decays Matthias Neubert CPT@ICTP, Trieste, July

3 New physics in B s mixing? Main information from flavor-tagged analysis of mixing-induced CP violation in B s J/ψ φ decay Combined probability regions for φ s =2β s and ΔΓ s 2β s SM =0.04 CDF (Dec. 2007) D0 (Feb. 2008) Matthias Neubert CPT@ICTP, Trieste, July

4 New physics in B s mixing? Combined analysis (UTfit collab., March 2008): Δm s A SL s A SL µµ τ(b s ) {φ s,δγ s } (CDF) (D0) (CDF, D0) (ALEPH, DELPHI, (CDF, D0) OPAL, CDF, D0) some bayesian magic Matthias Neubert CPT@ICTP, Trieste, July

5 New physics in B s mixing? 3.7σ evidence for a non-standard CP phase! Matthias Neubert CPT@ICTP, Trieste, July

6 New physics in B s mixing? Model-independent parameterization: If confirmed with more data, this would be clear evidence for NP! see also: Lenz, Nierste (2006) Matthias Neubert CPT@ICTP, Trieste, July

7 New physics in B s mixing? Capabilities of LHCb: Luminosity 0.5 fb -1 (~2009) 2 fb -1 (~2010) 10 fb -1 (~2013) σ(2β s ) Precision: 2β s SM = times better than this bar! Matthias Neubert CPT@ICTP, Trieste, July

8 New physics in rare B decays (I)? CP violation in interference of mixing and decays in neutral B decays into CP eigenstates Time-dependent CP asymmetry provides direct access to angles of the unitarity triangle: B 0 B 0 f Consider modes with φ A = 0 and compare results for sin2β from tree- and loop-dominated processes Grossman, Worah (1996) Matthias Neubert CPT@ICTP, Trieste, July

9 (sin2β) tree vs. (sin2β) penguin theor. corrections increase deviations Beneke, MN (2003) Matthias Neubert Trieste, July

10 (sin2β) tree vs. (sin2β) penguin Present accuracy: σ(sin2β φks ) = 0.17 LHCb capability with 10 fb -1 : σ(sin2β φks ) = 0.10 Super-B factory! Matthias Neubert CPT@ICTP, Trieste, July

11 (sin2β s ) tree vs. (sin2β s ) penguin But LHCb can do analogous test using B s decays Compare sin2β s values extracted from B s J/ψ φ vs. B s φφ B s b W s c c s J/ψ φ B s b W t,c,u g,z s s s s φ φ Luminosity σ(2β s φφ ) 2 fb -1 (~2010) fb -1 (~2013) β s φφ,sm =0 Matthias Neubert CPT@ICTP, Trieste, July

12 New physics in rare B decays (II)? Belle and Babar observe large difference in direct CP asymmetries between B ± K ± π 0 and B 0 K ± π -+ decays (Belle paper in Nature, March 2008): this large deviation in direct CP violation between charged and neutral B meson decays could be an indication of new sources of CP violation World-average experimental data: A CP (B - K - π 0 ) = ± A CP (B 0 K - π + ) = ± LHCb capability: σ(a CP (B 0 K - π + )) = with 10 fb -1 Matthias Neubert CPT@ICTP, Trieste, July

13 New physics in rare B decays (II)? Interference of tree and penguin amplitudes: s K - W b u u B 0 V π + ub ~ e -iγ d W t,c,u b g,z d s K u - u B 0 π + Matthias Neubert CPT@ICTP, Trieste, July

14 Amplitude interference: A πk puzzle? 2 A(B - K - π 0 ) = P - (T + C) e -iγ + P EW A(B 0 K - π + ) = P - T e -iγ QCD predictions (model independent): P EW = f real (m t /m W ) (T + C) U-spin symmetry and Fierz relations Fleischer (1996); MN, Rosner (1998) arg(c/t) = O[α s (m b ), Λ QCD /m b ] QCD factorization, SCET Beneke, Buchalla, MN, Sachrajda ( ) Bauer, Rothstein, Stewart (2005) CP asymmetries predicted to have same sign! (and similar magnitude) test of theoretical assumptions requires Super-B factory Matthias Neubert CPT@ICTP, Trieste, July

15 If any of these effects are real Hints at O(1) new physics effects in mixing amplitudes and rare decay amplitude Requires large, O(1) new CP-violating phases Curious what s in my belly?? Check at ATLAS/CMS! Not a Minimal Flavor Violation scenario! Matthias Neubert CPT@ICTP, Trieste, July

16 Flavor physics in the Randall-Sundrum Model with: Uli Haisch and Martin Bauer, Sandro Casagrande, Florian Goertz, Leonard Gründer, Torsten Pfoh Matthias Neubert Trieste, July

17 Warped extra dimensions (RS) [Randall, Sundrum 1999] Appealing solution to hierarchy problem: huge separation between weak and Planck scale generated by exponential warp factor in AdS 5 generic in flux compactifications of string theory Matthias Neubert CPT@ICTP, Trieste, July

18 Warped extra dimensions (RS) Placing matter and gauge fields in the bulk provides new perspective on flavor problem: localization of fermionic zero modes near UV brane leads to exponentially small Yukawas explains huge hierarchies in fermion spectrum: best theory of flavor to date! nontrivial overlap with gauge bosons gives rise to rich structure of flavor-violating effects [Burdman 2003; Agashe, Perez, Soni 2004] UV IR [Grossman, MN 1999; (Higgs) Gherghetta, Pomarol 2000; Huber, Shafi 2000] Matthias Neubert Trieste, July

19 Flavor in RS Already many studies in literature, in particular: Huber, Shafi 1999; Huber 2003 Burdman 2003 Agashe, Perez, Soni 2004 Agashe, Papucci, Perez, Pirjol 2005 Davidson, Isidori, Uhlig 2007 Csaki, Falkowski, Weiler 2008 Here: first complete study of all tree-level processes some important effects neglected so far (not captured by zero-mode approximation) Matthias Neubert Trieste, July

20 Warp factor: Notations and parameters ε = e -krπ L = - ln(ε) 37 Variable along extra dimension: t = ε e -kr φ KK scale: M KK = kε = O(TeV) M g M KK Fermion c i parameters: c Qi = m Qi /k, c qi = -m qi /k t=ε SM Higgs t=1 Matthias Neubert CPT@ICTP, Trieste, July

21 Bulk fermions KK decomposition (up-quark sector): expansion coefficients (3-comp. vectors for each n) exact mass eigenstates normalization: C n (φ) and S n (φ) are even/odd solutions to the bulk equations of motion Grossman, MN (1999) Gherghetta, Pomarol (2000) Matthias Neubert CPT@ICTP, Trieste, July

22 Bulk fermions Exact field equations with Yukawa couplings are incompatible with orthonormality relations for fermion profiles Generalized relations: extra terms are O(v/M KK ) for KK modes, but O(1) for light SM particles! M KK = kε = O(TeV) ε = e -krπ Matthias Neubert CPT@ICTP, Trieste, July

23 Zero-mode approximation (ZMA) Used in all previous work on flavor in RS Amounts to keeping leading terms in x n =m n /M KK in profiles for light SM fermions: with: ε = e -krπ L = - ln(ε) 37 (ZMA) t = ε e -kr φ exponentially small if c < -1/2 Grossman, MN (1999) Important finding: S n (φ) profiles cannot always be neglected, but give rise to some leading effects Matthias Neubert CPT@ICTP, Trieste, July

24 Scaling relations Effective Yukawa matrices (in ZMA): diagonal natural to assume that Y q are anarchical matrices flavor hierarchies explained by fact that F(c Q,q ) profiles are exponentially small and hierarchical ( Froggatt-Nielsen mechanism) Froggatt, Nielsen (1979) Huber, Shafi (2000) Relations for quark masses and CKM parameters: Matthias Neubert CPT@ICTP, Trieste, July

25 Gauge interactions with SM fermions Couplings of light weak gauge bosons flavor violation from modification of gauge-boson profiles due to EWSB on IR brane L = - ln(ε) 37 Z 0, W ± t = ε e -kr φ nontrivial φ dependence Csaki, Ehrlich, Terning (2002) flavor violation from non-orthonormality of fermion profiles (mixing between SU(2) L doublets and singlets) Matthias Neubert CPT@ICTP, Trieste, July

26 Gauge interactions with SM fermions Couplings of KK gauge bosons: flavor violation from nontrivial profiles dominant contributions from KK gluons g (n),γ (n),z (n),w (n) Burdman (2003); Agashe, Perez, Soni (2004) Both cases: Fact that flavor-violating effects live near IR brane implies suppression ~ F(c i ) F(c j ) RS-GIM mechanism! Agashe, Perez, Soni (2004); Agashe, Papucci, Perez, Pirjol (2005) Matthias Neubert CPT@ICTP, Trieste, July

27 Summing over KK modes Sum over KK gluons and photons: g (n),z (n), Sum over Z, W and KK excitations: L = - ln(ε) 37 ΔF=2 processes (dominated by KK gluons) ΔF=1 processes (dominated by Z boson) Matthias Neubert CPT@ICTP, Trieste, July

28 Overlap integrals Flavor-violating effects described by matrices omitted by previous authors! and corresponding matrices Δ q, Δ q, δ q in righthanded sector Matthias Neubert CPT@ICTP, Trieste, July

29 Overlap integrals Hermitian matrices in flavor space CP violation possible with N 2 generations! Scaling relations: but effects enhanced by M KK2 /m Z 2! parametrically of same order! Matthias Neubert CPT@ICTP, Trieste, July

30 Applications Matthias Neubert Trieste, July

31 Generic diagrams: Tree-level FCNCs g (n) Z, Z (n) γ (n) dominant for ΔF=2 processes dominant for ΔF=1 processes always small likely to give largest flavor-violating effects consider b s+qq for example analogous results hold for b d and s d FCNCs, and for decays of the type b s+l + l -, b s+νν no tree-level contribution to b sγ dipole operator! Matthias Neubert CPT@ICTP, Trieste, July

32 b s+qq Effective weak Hamiltonian: list RS contributions to Wilson coefficients of QCD and electroweak penguin operators Q 3,,10 analogous expressions for coefficients of oppositechirality operators Matthias Neubert CPT@ICTP, Trieste, July

33 Wilson coefficients: b s+qq sources: g, γ, Z Matthias Neubert CPT@ICTP, Trieste, July

34 b s+qq phenomenology Electroweak penguin effects in rare hadronic decays such as B πk or B φk are naturally O( 1) compared with SM and can introduce new, large CP-violating phases Potentially relevant for B πk puzzle and sin2β extractions from penguin modes Similarly, potentially large effects in B X s l + l - and B K * µ + µ - decay Matthias Neubert CPT@ICTP, Trieste, July

35 Neutral meson mixing Effective weak Hamiltonian: Coefficients in RS (examples): gluon contribution agrees with: [Csaki, Falkowski, Weiler 2008] for CP violation in K mixing (ε K ), KK gluon contribution to C 4 is by far dominant Matthias Neubert CPT@ICTP, Trieste, July

36 Neutral meson mixing Presence of tree-level FCNCs mediated by vector bosons potentially disastrous Recent analysis finds typical bound M KK >10 TeV (KK gluon mass >21 TeV) Reason is enhancement of <Q 4 > matrix element from RG evolution and chiral factor ~(m K /m s ) 2 In RS model: [Bona et al. (UTfit) 2007] [Csaki, Falkowski, Weiler 2008] [Burdman 2003; Agashe, Perez, Soni 2004] only second term included in early papers Matthias Neubert CPT@ICTP, Trieste, July

37 Neutral meson mixing Generic results for ε K : [ ] Matthias Neubert CPT@ICTP, Trieste, July

38 Possible ways out: Neutral meson mixing accidental smallness of relevant Yukawa couplings, requires ~1-5% fine-tuning (not so bad ) make L significantly smaller (little RS models); e.g., UV scale at 1000 TeV lowers bound to M KK >4 TeV [Davoudiasl, Perez, Soni 2008] impose bulk flavor symmetry to get hierarchical Yukawas (Y d ~1) [Cacciapaglia et al. 2007; Fitzpatrick, Perez, Randall 2007] Matthias Neubert CPT@ICTP, Trieste, July

39 Neutral meson mixing More alternatives: i) increase Yukawa couplings to O(10) while keeping effective Yukawas unchanged (quark masses and CKM matrix unaffected), thus lowering KK scale to O(1 TeV): ii) impose equality of c i parameters in righthanded down sector ( principle of minimal flavor protection ): c d1 =c d2 =c d3 [Santiago 2008] Matthias Neubert CPT@ICTP, Trieste, July

40 Neutral meson mixing Either solution leaves large, irremovable effects in ΔF=1 processes and B d,s mixing Preliminary scan: similar effects in B s mixing o φ Matthias Neubert CPT@ICTP, Trieste, July

41 Summary (I) Existing puzzles in flavor physics point to new physics that is not of MFV type! LHCb experiment offers significant reach to explore this physics Capability to definitively settle question of new CP phases in B s mixing, and shed light on possible new physics effects in rare B s and B d decays Matthias Neubert CPT@ICTP, Trieste, July

42 Summary (II) Randall-Sundrum models offer viable solution to the gauge and fermion hierarchy problems (attractive alternative to supersymmetry) Rich structure of flavor-violating interactions in gauge couplings to fermions (generically not MFV) ΔF=1 FCNC processes dominated by Z exchange ΔF=2 FCNC processes dominated by KK gluon exchange Effects naturally of O(1) in modes where deviations from SM are allowed/indicated by the data, while small in other modes (e.g., B X s γ) More results to come soon! Matthias Neubert CPT@ICTP, Trieste, July