Quark Mixing at BABAR

Transcription

1 Title Klaus R. Schubert, TU Dresen 27 October 2008, B-Factory Symposium in recognition of the achievements of PEP-II an BABAR Quark Mixing at BABAR Quark Mixing in the St. Moel: Origin of observe CP Violation Manifestations: K 0, D 0, B 0 Oscillations an CKM Hirarchy of Weak Decays L max (DORIS-2) /cm 2 /s 20. L max (DORIS-1978) BABAR Contributions to B 0 an D 0 Oscillations an to Determinations of V us, V cb, V ub, (V ts ), V t Deviations from the CKM Description of Quark Mixing? 9 Nov 2007 K. R. Schubert (TU Dresen), ARGUS Fest at DESY 1

2 Without Quark Mixing No CP Violation *) Example: Discovery of Direct CPV in B K + π -, K - π + PRL 93(2004) M BB, 1600 Kπ Decays. N(K + ) > N(K - ) B 0 K + π - B 0 K - π + (N + -N - )/(N + +N - ) = 0.13 with 4.2 σ from 0 First CPV Observation without any Time Info. Explanation: CPV is an interference *) of two ecay contributions; here b W V ub V us ʉ s u b V tb W t V ts g s ʉ u A slightly ifferent view on the 2n graph: b 1 t W U <<1 U =αt +βc +γu *) in the Stanar Moel g s ʉ u K. R. Schubert (TU Dresen), B-Factory Symposium at SLAC 2

3 Quark Mixing in the St. Moel Quarks (, s, b) (u, c,t) couple to both W an H fiels. Without H, perfect symmetry between an also between u 1 u 2 u 3. Most general H Rotation in - (u-) space i H j u i u j qhq couplings: iagonalizes C (C u ) C ij C u ij u Gauge couplings uw require oublets il. Rotations rotate the oublets il an either iagonalize C or C u. The ifference between the two is V: The 3x3 unitary If V* V, q mixing ul ul u R u R matrix V has 4 violates CP. L L R R parameters, e.g. Only at T m = h cl cl c V R c = V * R sl sl V us, V cb, V ub, s R s R q get masses. Im(V ub V u V c V cb ) tl tl * * tr tr bl bl CPT requires: b R b V = V R KM V CKM (1973, 1987) One of the first manifestations of quark mixing was K 0 K 0 mixing. But... K. R. Schubert (TU Dresen), B-Factory Symposium at SLAC 3

4 BABAR Publications on Quark Mixing From 19 Mar 2001 to 20 Oct 2008 BABAR has publishe 349 Journal papers on physics results 165 in Phys. Rev. Letters V CKM 184 in Phys. Rev. D 53 of them on Quark Mixing topics (15%) 7 on D 0 D 0 Mixing 8 on B 0 B 0 Mixing 13 on V cb topics 18 on V ub topics 4 on V ts topics 3 on V t topics Main obligations: Check if V CKM is unitary an etermine its 4 parameters K. R. Schubert (TU Dresen), B-Factory Symposium at SLAC 4

5 q/p 1 in all four systems All four M h an M l are CP eigenstates D 0 D 0 Mixing All meson systems which are allowe to mix are now observe to mix: K K 0 K 0 S L 1956, χ = 0.498, ΔΓ, Δm B 0 B Bh Bl 1987, χ = 0.19, Δm B s B s Bsh Bsl 2006, χ = 0.499, Δm, ΔΓ ( 0 with1.5σ), D 0 D 0 0 D 0 D 2007, χ ( 0 with 9 σ), Δm,ΔΓ ( 0 with 2σ) Common Mixing Phenomenology: 0 + K 0 - M M h l -i( m+δm / 2) t ( Γ / 2+ΔΓ / 4) t ( t) = ( p M + q M) e -i( m Δm / 2) t ( Γ / 2 ΔΓ / 4) t () t = ( p M q M) e Three inepenent x = Δm/Γ, y = ΔΓ/2Γ χ = (x 2 +y 2 )/(2+2x 2 ) pairs ofproperties: K 0 L = - = h heavy & light B s L = - (1.5σ) =? Long- & Shortliving D 0 L = - (4σ)= l (2σ) CP = +1 & CP = -1 B 0 L =? =? K. R. Schubert (TU Dresen), B-Factory Symposium at SLAC 5

6 D 0 D 0 Mixing: y an x 2 + y 2 in D 0 D 0 K + π - N + K π 2 2 -Γt x + y ( t) = N + K π (0) e RD + RD y Γt + t 4 2 ( Γ ) x' cosδ = y' sinδ sinδ x cosδ y PRL 98(2007) /fb best fit, 3.9σ from no mixing ata - nomix fit mix fit - nomix fit best point in phys. region no mixing CDF PRL100(2008) /fb x 2 = (-0.12±0.35)10-3, y = (8.5±7.6)10-3, 3.8σ K. R. Schubert (TU Dresen), B-Factory Symposium at SLAC 6

7 D 0 D 0 Mixing: y in τ(kk,ππ,kπ) PRD 78(2008)011105(R) 384/fb τ 1 KK e + e - D* + X, D* + D 0 π +, D 0 K - K +,π - π +,K - π y = = y = (1.24 ± 0.39 ± 0.13) 10-2 ( ) τ ( ππ) τ ( Kπ) 3 σ PRL 98(2007) /fb y = (1.31± 0.32 ± 0.25) σ HFAG Aug/08 average (together with others): (1.07 ± 0.26) σ K. R. Schubert (TU Dresen), B-Factory Symposium at SLAC 7

8 x 2 + y 2 in D 0 D 0 K + l - Å, K + π - π 0,K + π - π + π - K + l - Å χ = (x 2 + y 2 +7 )/2 = (0.4-6) /fb PRD 76(2007) K + l - Å (1.3 ± 2.2 ± 2.0) /fb PRD 77(2008) K + π - π x 10-4 with 3.2σ 384/fb arxiv: PRL K + π - π + π - (1.9 ±1.6) /fb hep-ex/ (2006) x an y from D 0 K 0 Sπ + π - Dalitz Plot Analysis x= (0.80± 0.29± y = (0.33± 0.24± )10 )10 2σ from no mixing /fb PRL 99(2007) K. R. Schubert (TU Dresen), B-Factory Symposium at SLAC 8

9 D 0 D 0 Mixing: Summary D 0 (t) K + π - (y,x 2 ) (0,0) with 4 σ τ(k + K -,π + π - )/τ(k - π + ) y 0 with 3.2 an 3 σ D 0 (t) K 0 S π + π - Dalitz Plot (x,y) (0,0) with 2 σ HFAG average August 2008: x = (10.1 ± 2.4) 10-3, y = (7.3 ± 1.8) 10-3 χ = (x 2 +y 2 )/2 = (0.77 ± 0.25)10-4 of all prouce D 0 ecay as D 0, χ 0 with 9.8 σ. No CPV(D 0 ) observe. St. Moel Expectation: c ʉ W s s W u c c ʉ s s u K + K - u c negligible χ 10-4 K. R. Schubert (TU Dresen), B-Factory Symposium at SLAC 9

10 1,5 B 0 (full.rec) - CPtag: A 1 0,5 0-0, Δt -1,5 81/fb ΔΓ/2Γ <0.04 B 0 B 0 Mixing l ± l ± 14 Apr 2000 PDG 2008 uses 3 BABAR results on Δm: A Bastei (D) /fb l ± - l ±, A = (N +- -N ±± )/(N +- +N ±± ) 2/fb /fb B 0 (full.rec) - CPtag, /fb B 0 D*lν(part.rec) - l ± PRD 73(2006) Present PDG Mean Δm=(0.507± 0.005)/ps ominate by BABAR 06 + BELLE 05 ΔΓ/2Γ=0 =0,05 =0,1 PRD 70(2004) A 0 0,05 l ± l ± 27 Jul 2000 Osaka (J) 8/fb 0, ll Δm= (0.507± 0.015± 0.022)/ps K. R. Schubert (TU Dresen), B-Factory Symposium at SLAC 10

11 B 0 B 0 Mixing; CP, T an CPT St. Moel b Expectation: W t u ʉ ŧ W LQCD 2007 : f 2 = (223 ± 8 ± 16) 2 MeV 2 B B B V tb V t = (8.1 ± 0.6) 10-3 b Δm = G 2 2 F mb f B BBη B 6π 2 ΔΓ/ 2Γ , 2 2 2, 2 Vt Vtb f m mt W q p 1 = o 10 3 Search for CP an T Violation in Mixing: PRL 96(2006) N ++ N in ilepton events measures the CP- an 211/fb N ++ + N T-violating asymmetry B 0 B 0 / B 0 B 0 q/p - 1 = (-0.8 ± 2.7 ± 1.9) 10-3, PDG 08: (1.8 ± 1.8) 10-3 with D0 & Belle 2006 CPT Test in B 0 B 0 Mixing: same paper N + N + ( Δt > 0) N ( Δt < 0) ( Δt > 0) + N + ( Δt < 0) measures the CPT-violating asymmetry B 0 B 0 / B 0 B 0. Results: z δ m δ Γ ( 3.5 ± 1.9 ± 1.0) 10 3 δ = = + i = + i 7.0 ± 3.6 ± Δm 2Δm ps ΔΓ {δ from Charpak & Gourin 1967} K. R. Schubert (TU Dresen), B-Factory Symposium at SLAC 11 + ( ) 3

12 V us τ τ Contributions from our 580 M τ-lepton pairs; exclusively an inclusively 1 1 V us V u W - W - ʉ s ν τ ʉ ν τ K - π - f K /f π = ± LQCD 2008, Follana+al 1or 3K+X 2 Γs u V + δ ( m ) us s = Γu 2 Vu 0or2K+X δ from Gamiz+al /fb ± π - K - Γ ( τ Kν ) Γ( τ πν ) = ( 6.53 ± 0.06 ± 0.09) 10 2 K. R. Schubert (TU Dresen), B-Factory Symposium at SLAC 12

13 b W - t V cb t = V tb t + V cb c + V ub u, coherent at time of W emission, ecoherent at time of meson formation: Γ(B c+x) ~ V cb 2, Γ(B t+x) = 0, Γ(B u+x) ~ V ub 2 Rate measurements allow etermination of V cb, Smallest influence of the strong interaction: Best-stuie reconstructe moe: B 0 D *+ l - Å BF ~ 5%, str.int.contr. ~ 10% if Γ/q 2 at q 2 max: l B D Å PRD 77(2008) Full reconstruction of the ecay with D *+ (K - π + ) D π + slow an cosθ B,D*l Latest result: p r B θ 79/fb r p D * + K. R. Schubert (TU Dresen), B-Factory Symposium at SLAC 13 p r l p r ν b W - Å e c B 0 D +,D *+

14 V cb continue F(1) V cb Full information on B 0 D *+ l - Å is in the rate 4 Γ/q 2 χ cosθ l cosθ V. Integration over the angles with fitte parameter values R 1,R 2 gives Γ/q 2 q 2 max Slope ρ 2 ρ 2 = 1.19 ± 0.05 ± 0.03 F(1) V cb = (34.4 ± 0.3 ± 1.1) 10-3 Ba agreement Look for new approaches: q 2 min ρ 2 BABAR D* fit 08 BABAR D* 0 rec. 08 BABAR D* + rec. 08 PRL100(2008) D *0 (K - π + ) D π 0 slow B - D *0 l - Å 205/fb ρ 2 = 1.16 ± 0.06 ± 0.08 F(1) V cb = (35.9 ± 0.6 ± 1.4) 10-3 arxiv: B (D 0,D ± ) l - Å 207/fb p D,p l,θ B,Dl fit ρ 2 = 1.21 ± 0.02 ± 0.07 F(1) V cb = (35.7 ± 0.2 ± 1.2) 10-3 HFAG +LQCD: V cb D* = (38.5 ±0.7±1.0)10-3 HFAG +LQCD: V cb D = (39.2 ± 1.6 ± 0.9) 10-3 My average: V cb excl = (38.6 ± 0.6 ± 1.0)10-3 K. R. Schubert (TU Dresen), B-Factory Symposium at SLAC 14

15 V cb (inclusive) N e PRD69(2004) /fb Momentum spectrum of electrons in BB e + νx e - ÅX events BF(B e + νx, E e >0.6 GeV/c) p* e [GeV/c] =(10.36 ± 0.06 ± 0.23)%, 0.98 X c X u Γ + B e ν, = Xc Ee > Emin V 2 f ,,, cb HQE E min; mb, mc, μπ μ G ρ D ρ LS HQE = effective QCD with expansion in Λ QCD /m b The shape of the spectrum, with more precision its moments <E ek >, k=1,2,3 for 5 ifferent E min, etermine the parameters m b... ρ LS3 an therewith V cb an the extrapolate BF for E min =0. The HQE fit in the kinetic scheme in PRL93(2004) inclues moments <m Xk >,k=1...4 of the mass spectrum of the X c system for 8 ifferent E min. The 2004 BABAR+HQE fit fins V cb incl = (41.4±0.4±0.7) The creibility is emonstrate by the quality of the overconstraining fit: K. R. Schubert (TU Dresen), B-Factory Symposium at SLAC 15

16 more V cb inclusive V cb incl (BABAR 2004) = (41.4±0.4±0.7)10-3 V cb incl (HFAG 2008) = (41.7±0.4±0.6)10-3 incl. CLEO,BELLE,DELPHI an moments from B X s γ V cb excl (HFAG+LQCD) = (38.6 ± 0.6 ± 1.0)10-3 Inclusive ±1.7%, exclusive ± 3.0%. Tension between the two is 2.3 σ. K. R. Schubert (TU Dresen), B-Factory Symposium at SLAC 16

17 V ub Since 1990 (ARGUS, CLEO) V ub /V cb 0.1, i.e. N(B u+x)/n(b c+x) 0.02, Rate measurements for eterminations of V ub have bg/signal 50. Cleanest ways: exclusive an inclusive semileptonic ecays V ub 1 W - l - Å 2 3 Γ 2 G p = V F 2 ub q 24π 3 2 f 2 + q b u f + (q 2 ) from LQCD π - for large q 2 3 papers on πl ν: from LCSR for small q 2 3 Γ B X u lν Integrate p 2 2 X l q m u X over optimize regions of the lepton momentum, q 2 (lå),an the mass of X u π ( ) PRL98(2007) /fb π+ l ν untagge, i.e. BB X + π + l ν BF = ±11%, V ub = ±15% PRL97(2006) /fb tagge, BB (D(*) l ν or ha.rec)+(π +,π 0 ) l ν BF = ±15%, V ub = ±15% newest (π +,π 0 ) l ν tagge with D (*) l ν PRL101(2008) paper: 348/fb BF ±12%, V ub = ±15% K. R. Schubert (TU Dresen), B-Factory Symposium at SLAC 17

18 V ub (2) from the untagge π + l ν analysis: Inclusive V ub Measurements I choose 3 BABAR analyses. V ub extraction is one with very refine HQE methos. Expansion converges poorely in the limite p l q 2 m X bg-minimizing regions. Non-perturbative shape functions neee; leaing parameters now taken from HQE(B X c lå) results. - Cut on p l only - Cut on p l an q 2 - Cuts on m X ; m X an q 2 ; P + = E X -p X ) K. R. Schubert (TU Dresen), B-Factory Symposium at SLAC 18

19 V ub inclusive First: p l only, p e > 2.0 GeV/c, f u =0.25 PRD73(2006) (80+10)/fb DlÅ an D*lÅ moele, continuum from ata, p miss > 0.5 GeV/c ΔBF(p e > 2.0), V ub (BLNP,HFAG-08) = ±9%, stable with p e cut variations. 2n: p l an q 2 PRL95(2005) (81+10)/fb p e > 2.1 GeV/c an s max h (p e,q 2 ) < m 2 D with p ν = 0.8 p miss if 0 < E miss -p miss < 0.8 GeV/c V ub (BLNP,HFAG)= ±11% 3r: m X, q 2 an E X -p X 347/fb PRL100(2008) BB B reco (η=0.4%) + X u lå p l >1 GeV/c, D*lÅ veto, K veto 3 regions: m X <1.55; E X -p X <0.66; M x <1.7GeV an q 2 >8GeV V ub (BLNP)=4.1±9%, 4.4 ±10%, 3.8±10% K. R. Schubert (TU Dresen), B-Factory Symposium at SLAC 19

20 V ub an V cb Summary HFAG averages all incl.v ub results separately for BNLP, DGE, GGOU, ADFR. Errors ± 7%, sprea ± 5% V ub incl = ±9% From B πl ν V ub excl = ± 15% Δ < 1σ BABAR&BELLE : σ( V ub ) ± 30% ±9% Recalling V cb : V cb excl = ±3.0% With V ub, V c, V us (mainly Kl3, but τ is coming), an V t (Δm ofb 0,B s ), the unitarity of the CKM matrix shows that CP is violate: Conclusion from only CP-symmetric observations. [two solutions; CPV (ε K, β, γ) shows Im(V u V ub * V cb V c *) > 0.] V cb incl = ± 1.7% Δ = 2.3σ σ( V cb ) ± 5% ±2% K. R. Schubert (TU Dresen), B-Factory Symposium at SLAC 20

21 V ts in Decays B 0,+ K* 0,+ γ arxiv: /fb Moes K + π -, K S π 0, K + π 0, K S π + b V tb W γ V ts s K + π ev. K S π ev. Precision of formfactor calculation not sufficient for V tb V ts,this may change! b s γ PRD 72(2005) Σ of 4 K* + 34 other moes BF 100 MeV 82/fb V ts not goal of the 3 analyses; here only for completeness: PRL 97(2006) /fb BB γx, π 0 -η-veto, lepton tagging PRL 77(2008) /fb B reco tags smaller but cleaner event sample. BF compatible, but σ(bf) 3 times larger. WA(PDG 08): BF(b s γ)=(35.6±2.5)10-5 K. R. Schubert (TU Dresen), B-Factory Symposium at SLAC 21

22 V t in Decays b ʉ V tb W γ V t B + ρ + γ B 0 ρ 0 γ ʉ B 0 ωγ π + π σ π + π σ π + π - π σ arxiv: /fb Combine significance 6.5 σ ρ + π + π 0 ρ 0 π + π - ω π + π - π 0 BF(combine) = (1.63 ± ± 0.16)10-6 V t /V ts = ± ± in agreement but not competitive with V t /V ts = ± ± from Δm(B 0 )/Δm(B s ) an LQCD. (this topic really belongs into S. Playfer s talk) K. R. Schubert (TU Dresen), B-Factory Symposium at SLAC 22

23 Summary No eviation from the CKM escription of quark mixing has been observe. Precision of the agreement between V us, V cb, V ub, V tb V t, V t /V ts, the phases of the invariant quartets V u V ub * V tb V t *, V t V tb * V cb V c *, V u V ub * V cb V c *, an V u, V c, V cs, V ts V tb is impressive. CKMfitter 2008: V us = ± , V cb = ±, V ub = ± , Im(V ub V u * V c V cb * 0.2 ) = + (2.8 ± ) Why is precision important? FutureTheory may reuce # of St.M. parameters (when preparing this talk, I encountere only one 4σ iscrepancy, the rate of τ Kν isagrees with that of K μν an lepton universality.) K. R. Schubert (TU Dresen), B-Factory Symposium at SLAC 23

24 Honours One spin-½ quartet (p,n,λ,ζ) + H,W 2 L-oublets, 4 R-singlets no CPV 2 L-oublets, 1 R-., 2 R-s. CPV one new scalar fiel CPV PRL 10 (1963) 531 J = cos S S μ θ μ μ θ = from Γ(K μν)/γ(π μν) ( V + A) Δ = 0 + sin θ ( V + A) Δ = 1 (1960)... V CKM V GLCHGWSBIMKM We are very prou of the prize aware to KM. K. R. Schubert (TU Dresen), B-Factory Symposium at SLAC 24