Probing New Physics Through B s Mixing Patricia Ball IPPP, Durham Moriond EW, Mar 12 2007
Phenomenology of B s Mixing B 0 = (b s) and B 0 = (s b) with definite flavour content, but not mass eigenstates Mixing! mixing induces mass and width mixing matrices M s ab, Γs ab M s 12 is loop-induced: sensitive to new physics! observables: M s = 2 M s 12, φ s = arg( M s 12 /Γs 12 ) arg M s 12 CP asymmetry in B s J/ψφ Γ s = 2 Γ s 12 cos φ s semileptonic CP asymmetry A s SL = N( B 0 s l + X) N(B 0 s l X) N( B 0 s l + X) + N(B 0 s l X) = Γ s M s tan φ s p.1
Experimental status of B s Observables M s = (17.77 ± 0.10 ± 0.07) ps 1 (CDF) (2006!) Γ s = (0.17 ± 0.09 ± 0.02) ps 1 (D0) (2007!) A s SL = 0.001 ± 0.0090 (D0) (2007)! φ s = 0.70 +0.47 0.39 from As SL and B s J/ψφ (D0) (2007)! For LHCb, expect (van Hunen CKM06) sensitivity σ φs = 0.04 rad @ 0.5 fb 1, σ φs = 0.02 rad @ 2 fb 1 first results promised for 2008 p.2
M s in the SM M SM 12 = = G2 F M 2 W 12π 2 M B s ˆη B ˆBBs f 2 B s (V tsv tb ) 2 S 0 (x t ) S 0 (x t = m 2 t /MW 2 ) = 2.35 ± 0.06: Inami-Lim function ˆη B = 0.552: NLO QCD correction (Buras/Jamin/Weiss 90) ˆB Bs fb 2 s Bs 0 ( sb) V A ( sb) V A B s 0 : hadronic matrix element, from lattice V tsv tb : from tree-level processes p.3
Status of Input Parameters ˆB Bs f Bs = (0.281 ± 0.021) GeV (HPQCD 06, unquenched, N f = 2 + 1 staggered light quarks) ˆB Bs f Bs = (0.245 ± 0.021 0.002 +0.003 ) GeV (JLQCD 03, unquenched, N f = 2 Wilson light quarks) V tsv tb = (41.3 ± 0.7) 10 3 SM predictions: M s JLQCD = (16.1 ± 2.8) ps 1, M s HPQCD = (21.3 ± 3.2) ps 1 recall CDF result: (17.77 ± 0.12) ps 1 p.4
New Physics Models with impact on M s SUSY: gluino-squark loops (Ball hep-ph/0604249) SUSY: Higgs penguins at large tan β (Freitas hep-ph/0702267) SUSY GUT (Dutta hep-ph/0607147) SUSY: R-parity violation (Xiang-Dong hep-ph/0609269) tree-level: Z with flavour-non-diagonal couplings (Baek hep-ph/0607113) warped extra dimension (Chang hep-ph/0607313) littlest Higgs model (Buras hep-ph/0605214) p.5
Generic Parametrisation of New Physics new physics can significantly affect M s 12, but not Γs 12 : tree-dominated model-independent parametrisation of NP effects in terms of only two real parameters Lines of ρ s =const.: M s 12 = M s,sm 12 (1 + κ s e iσ s ) κ s > 0: NP amplitude σ s : new CP-violating phase Deviation from SM measured by ρ s M s M SM s κq 2.5 1.5 0.5 2 1 0 100 200 300 σ q [deg] = (1 + 2κ s cos σ s + κ 2 s) 1/2 p.6
Constraints from M SM s Recall: two unquenched calculations available: JLQCD: N f = 2 Wilson fermions + NRQCD heavy fermions HPQCD: N f = 2 + 1 staggered light + NRQCD heavy fermions 1σ constraints from JLQCD: 2.5 2 1.5 from HPQCD: 2.5 2 1.5 κs 1 κs 1 0.5 0.5 0 100 200 300 σ s [deg] 0 100 200 300 σ s [deg] M s exp compatible... not compatible with SM (at 1σ) p.7
Constraints from M SM s Conclusions: M s th not yet known accurately enough to exclude even M s,np 12 M s,sm 12 (i.e. κ s < 1) improved predictions expected in due course thanks to recent breakthrough in lattice algorithms to reduce the cost of simulations of light quark masses for Wilson fermions (Del Debbio, Lüscher 06) timescale? Current uncertainty of M s th 14%. Sachrajda quoted 1-2% for 2015 (LHCb upgrade workshop Jan 2007) also use alternative constraints φ s p.8
Constraints from φ s φ s = arg M s 12 = φsm s + φ NP s with φ SM s = 2λ 2 R b sin γ 2 lines of ρ s =const.: lines of φ NP s =const.: 2.5 2 2.5 2 κq 1.5 1 0.5 κq 1.5 0.5 1 0 100 200 300 σ q [deg] 0 100 200 300 σ q [deg] Observables sensitive to φ s : CP asymmetries in B s J/ψφ (and related), Γ s, A s SL p.9
Status of φ s φ s from b ccs decays, e.g. B s J/ψφ: Γ(t) e Γ st { cosh Γ st 2 η f cos φ s sinh Γ st 2 } + η f qd sin φ s sin( M s t) η f : CP eigenvalue of final state (±1), q = +1( 1) if tagged as B s ( B s ) at production, q = 0 if untagged, D: tagging dilution factor Untagged events: cos φ s and Γ s from 2nd term: Tevatron 2007 (up to discrete ambuities, φ s φ s, Γ s Γ s ; theory-indep.): D0: Γ s = (0.17 ± 0.09 ± 0.02) ps 1, φ s = 0.79 ± 0.56 +0.14 0.01 Tagged events: sin φ s from 3rd term: LHCb 200x (up to dilution factor D, to be determined from control channels, and discrete ambiguity φ s π φ s ; theory-indep. ) p.10
Status of φ s φ s from flavour-specific (vulgo: semileptonic) CP-asymmetry a s fs, e.g. A s SL = N( B 0 s l + X) N(B 0 s l X) N( B 0 s l + X) + N(B 0 s l X) = Γ s M s tan φ s Also measurement of dimuon charge asymmetry: (D0 06) A µµ SL = N(b b µ + µ + X) N(b b µ µ X) N(b b µ + µ + X) + N(b b µ µ X) = ( 0.92±0.44±0.32) 10 2 contains contributions from B d and B s, but not B u, Λ b etc. D0 translates both into A s SL = ( 0.64 ± 1.01) 10 2. Using the constraint from A s SL in the analysis of B s J/ψφ: D0: Γ s = (0.13 ± 0.09)ps 1, φ s = 0.70 +0.47 0.39 p.11
Theory Predictions for Γ s and A s SL Γ = 2 Γ s 12 cos φ s with Γ s 12 = G2 F m2 b 24πM Bs (V csv cb ) 2 [ C 1 O s 1 + C 2 O s 2 + δ 1/mb ] Lenz/Nierste hep-ph/0612167 improve upon Beneke et al. hep-ph/9808385 by switching to a different operator basis (reduced sensitivity to power-suppressed contributions): Γ s = (0.088 ± 0.017) ps 1, A s SL = (2.06 ± 0.57) 10 5 Using theory predictions for the B d contribution to A µµ data from the B factories), and the D0 data for B s J/ψφ, LN find sin φ s = 0.77 ± 0.04(th) ± 0.34(exp): φ s 0 at 2σ SL (instead of exp. p.12
Combined Constraint on κ s, σ s Using D0 combined result: 1σ constraints from JLQCD: 2.5 2.5 from HPQCD: 2. 2. 1.5 1.5 1. 1. 0.5 0.5 0. 50. 100. 150. 200. 250. 300. 350. 0. 50. 100. 150. 200. 250. 300. 350. M s,np 12 M s,sm 12 still allowed σ s < 180 disfavoured p.13
Constraints on Specific NP Models: Z assume absence of Z Z mixing, i.e. flavour-diagonal Z couplings assume flavour non-diagonal Z couplings only to q L constrain ρ L exp(iφ L ) (g M Z )/(gm Z )B L sb with BL sb being sz b coupling κ s < 1.2 ρ L < 1.3 10 3 can translate this into bound on Z mass: ( ) g B L sb 3.0 TeV g < M Z very strong constraint! V ts p.14
MSSM (in MIA) MSSM (box diagram) contributions from charged Higgs, neutralinos, photinos, gluinos and charginos for B s mixing, only gluino contributions relevant full NLO Wilson coefficients available (Ciuchini hep-ph/0606197) also from double Higgs penguins, which are however only relevant for large tan β 1 ) Im ( δ d 23 LL 0.5 0-0.5 Constraints on (δ23 d ) LL insertion using JLQCD lattice data. Open lines: constraints from φ s. -1-1 -0.5 0 0.5 1 ) Re ( δ d 23 LL p.15
Summary new physics in B s mixing can be described, in a model-independent way, by 2 real parameters constraints from M s not very strong, despite excellent experimental accuracy: large hadronic (lattice) uncertainties 14% more decisive constraints from NP mixing phase present constraints on φ s from A s SL and untagged B s J/ψφ (Tevatron) not very strong, although slight hint at NP (2σ acc. to Lenz/Nierste) expect much more precise constraints on/measurement of φ s from LHCb: σ φs = 0.04 with 0.5 fb 1 : 1st year of running together with improved lattice calculations, the B s system will prove a powerful tool to constrain/find NP p.16