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B . Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

A l 3 ( r -i h ). l. 1- l 2 /2. - l. 1- l 2 /2. A l 2. -A l 2. A l 3 (1- r -i h ). 1. h. r. Measurements of CKM Elements and Unitarity Triangle. B. Golob, Belle Collaboration University of Ljubljana. Aim: constraints on CKM matrix consistency between data/SM. V ud V us V ub

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B . Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

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  1. Al3(r-ih) l 1-l2/2 -l 1-l2/2 Al2 -Al2 Al3(1-r-ih) 1 h r Measurements of CKM Elements and Unitarity Triangle B. Golob, Belle Collaboration University of Ljubljana Aim: constraints on CKM matrix consistency between data/SM Vud Vus Vub Vcd Vcs Vcb Vtd Vts Vtb • Cabbibo angle • tree level B decays • oscillations • angles • overall constraints detailed insight from talks by K. Abe and Y. Pan (0,1) (0,0) B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  2. |Vus| BNL E865 PDG2002 f+(0) Vus PDGKe3 Braverage: (4.82 ± 0.06)% from K+(0) →p0(-) l+ne average w/ E865 |Vus|fromE865 designed for K+→ p+m+e- search 1 week dedicated Ke3 run 1998 Br(K+ →p0 e+ne ) = (5.17 ± 0.02 ± 0.09 ± 0.04)% Unitarity…?: |Vus|= 0.2272 ± 0.0028 |Vud|2 + |Vus|2 + |Vub|2 = 1 |Vud|direct=0.9740 ± 0.0005(SFT) |Vus|direct=0.2201 ± 0.0024 (Ke3,w/o E865) ± 0.0020 theoretical uncertainty (f+(0)); (E865,hep-ex/0305042) |Vus|unitarity = √(1 - |Vud|2direct) =0.2265 ± 0.0022 ~2 s discrepancy solved by E865? B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  3. Vub Vcb |Vcb|,|Vub| From tree-level B decays Apex of unitarity triangle must lie within the band (independent of new physics); constrains the side Rb Rb B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  4. |Vcb|,|Vub| • exclusive • mainlyB→ D*ln (higher stat., • lower th. uncertainty); • also B→ Dln as check • inclusive • total s.l. width + moments • of differential distributions • From tree-level • (s.l.) B decays • Vcb • Vub W l n B Xc,u • exclusive • B → p,r,w,h ln; • HQS not helpful, high th. • uncertainty • inclusive • total s.l. b → ulnwidth; • limited phase space, larger • th. uncertainty than b → cln B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  5. q ln B(vB) D*(vD*) |Vcb|from exclusive decays Measurement of w distribution known kinematic factor form factor (Belle,PLB526, 247(02)) In the heavy quark limit: F(w)=x(w) x(1)=1 Extrapolation of dG/dw to w=1→F(1)|Vcb| Belle Z0 r2 and F(1)|Vcb| free parameters (I.Caprini et al., Nucl.Phys.B530,153(98)) U(4s) w B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  6. |Vcb|from B → D*ln meas. error dominated by systematics: Z0: modeling of D** bckg U(4s):e(pslow) HFAG, winter’03 0.7M BB 11M BB 3M BB F(1) = 0.91 ± 0.04 |Vcb|=(41.9 ± 1.1 ± 1.8)x10-3 exp. F(1) B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  7. |Vcb|from inclusive decays Measurement of semileptonic width Gsl ~1% accuracy on |Vcb| Br(b → cln)/tb = Kth |Vcb|2 ~5% uncertainty on |Vcb| Operator Product Expansion: two parameters to O(1/mb2): l1(kin. energy of b); l2 (hyperfine int. energy); + mb= mB -L use to constrain/check theory corrections described by same parameters also for different moments of differential distributions X = El, Mh, Eg B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  8. |Vcb|from inclusive decays L[GeV] several moments measured: l1[GeV2] <Eg>; <(Eg-<Eg>)2>; (Delphi,hep-ex/ 0210046(02), M.Calvi,Delphi, CKM Workshop, Durham’03) Delphi Cleo 1st,2nd,3rd lepton energy and hadronic mass moments; Eg[GeV] Eg from b → sg; (Cleo,PRL87, 251807(01); Cleo,PRL87, 251808,(01); Cleo,PRD67, 072001(03)) Cleo also moments of - hadronic mass spectrum - lepton energy from B → Xln; BaBar:moments of hadronic mass; p* dependence stronger than expected, analysis ongoing; B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  9. exp.: Gsl,L, l1,r1,r2 |Vcb|from inclusive decays HFAG Winter’03 average using world average Gsl = (0.434±0.008)10-10 MeV LEP: Br(B → Xln)=(10.65±0.23)% (advantage: full lepton spectrum) (some measurements not yet included) and combining different measured moments, also 3rd (sensitive to O(1/mb3), multiparameter fits): 2.2M BB 22M BB (C.W.Bauer et al.,PRD67,054012(03); M.Battaglia et al.,PLB556,41(03)) 82M BB |Vcb|= (41.4 ± 0.7 ± 0.6)x10-3 exp. th. th.: as, O(1/mb4) B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  10. |Vub|from exclusive decays B → wln M(p+p-p0); higher p*l Measurements of Br(B → Xuln); several measurements exist: BaBar, Belle, Cleo covering B → p±,p0,r±,r0,w,h ln lower p*l b → cln signal • similar as b → cln, • but inlimited interval • of q2 (Cleo, pln, rln) • p*l,El (Belle, wln), • (BaBar, rln) (C.Schwanda,Belle,CKM Workshop,Durham’03) • extrapolate to full range • (q2, El) using • different models; • fit to obtain yield • (use isospin relations to • connect p(r)±ln and p(r)0ln ) source of theoretical uncertainty B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  11. |Vub|from exclusive decays q2[GeV2] q2[GeV2] (L.Gibbons,Cleo, CKM Workshop,Durham’03) average • Cleo:B → pln, • B → rln • 2D M(Xuln), DE fit • separately in • three q2 bins • lower syst. • from e(q2); • low probability • ISGW2; evaluation of th. uncertainty; difficult to combine; |Vub|= (3.42 ± 0.22 ± 0.55)x10-3 exp. th. B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  12. |Vub|from inclusive decays (plots from M.Luke,CKM Workshop, Durham’03) q2 l n El p MX p B Semileptonic width b → uln sensitive to Vub in analog way as b → cln sensitive to Vcb; looser selection criteria q2 tighter selection criteria larger th.error • Variables separating • b → uln from b → cln: • lepton energy El; • hadronic inv. mass Mx; • leptonic inv. mass q2; MX2 Number of measurements using different individual variable or combination of those. B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  13. g p K S/B~0.3 D p B1 fully reconstructed (Mbc) B2 U(4s) l p Mbc[GeV] n S/B~2.5 Xu |Vub|from inclusive decays CMS: Mbc=√(Ebeam2-pB2) DE=EB-Ebeam • Hadronic invariant mass • at U(4s) need to • separate decay • products of two B’s; • large sample of B’s • → can use fully • reconstructed events; BaBar: B → D(*)+np e~0.4% selecting p*l>1 GeV on recoiling side; (D.del Re, BaBar, Moriond’03) B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  14. |Vub|from inclusive decays Belle:simulated annealing technique; minimize calculate MX on recoiling side; exchange particle signal ↔ tagging side fit with b→uln, b→cln, bckg.; extract Br(B→Xuln)/Br(B→Xln) b→cln subtracted (D.del Re, BaBar, Moriond’03) (A.Sugiyama,Belle,Moriond’03) B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  15. |Vub|from inclusive decays Inclusive Vub summary (HFAG winter’03): no average for B factories; all measurements suffer from th. uncertainty; lepton endpoint results: error from sh.f.,th.,sg completely correlated exp. syst. uncorrelated 9.5M BB 22M BB 86M BB |Vub|= (4.28 ± 0.17 ± 0.62)x10-3 82M BB exp. th. B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  16. Vtd Vtd 1 1 Vts Vcb l l |Vtd|,|Vts| From Bd,s oscillations Apex of unitarity triangle must lie within the band; constrains the side Rt Rt B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  17. Bd oscillations HFAG,winter’03 1.2% relative error on Dmd to extract |Vtd| FBd√BBd = 220±35MeV (LQCD) B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  18. Bs oscillations instead of Dms free parameter, fit A at fixed value of Dms → A(Dms); no oscillations: A=0; oscillations at given Dms: A=1 Dms excluded @95% C.L. where A(Dms)+1.645sA < 1 Amplitude method: (Aleph,CERN-EP-2002-16) Aleph: combination of 3 methods; -exclusive (Bs → Ds(*)p(a1,r)), -semi-inclusive (rec. Ds and lepton), -inclusive (semileptonic); sp/p ~12% sL~370mm increasing p and L resolution increasing stat. inclusively rec. D vtx.; pB using pmiss and pD; sA~exp(Dm2ss2t/2)! B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  19. Bs oscillations HFAG, winter’03: average of amplitude measurements; data ± 1.645s data ± 1s next test of SM in CKM fits; Tevatron domain until LHC; 95% C.L. 14.4ps-1 B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  20. b → ccs b → ccd b → sss Angle sin2f1(b) …is one of the angles of UT…  measured in B → J/Y Ks B → D+D- B → f Ks B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  21. average: -0.38±0.41; b → sss, penguin only w/ different phase, one suppressed by O(l2); th. clean, with increased stat. might reveal new phenomena sin2f1(b) HFAG, winter’03 1±0.07 precision measurement, limited by stat. (by factor of 2; ~50% more stat. already waiting) 88M BB 82M BB 84M BB 82M BB 89M BB 82M BB B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  22. b → uud Angle sin2f2(a) …is another angle of UT… …but more difficult to access than f1! measured in B → p+p- significant B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  23. sin2f2(a)fromB → pp sin2f2 “summary”: (H.Sagawa,FPCP’03) 2s lines Belle B → pp: (|P/T|=0.3, sin2f1) f2 d 78o ≤ f2 ≤ 152o @95%C.L. (independent of d) B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  24. Standard fit: use measured observables and th. parameters to constrain the region in (r,h) plane CKM fit (CKM Fitter group, http://ckmfitter/in2p3.fr) Inputs(some): Experimental |Vud|, |Vus|, |Vub|, |Vcb| eK, Dmd, Dms, sin2f1, mt,… Theoretical hB, fBd√BBd, x, BK,… Rfit approach: theoretical uncertainties ↔ constant likelihood Minimize and compute CL. nice plots B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  25. r h r h UT constraints (CKM Fitter group, http://ckmfitter/in2p3.fr) 90% C.L. contour all “knowledge” but sin2f1 (overlaid) including sin2f1 B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  26. how about sin2f2? constraint determines arcs through (r,h)=(0,0) and (1,0) with center and radius depending on f2; UT constraints f2=78o 95% C.L. consistent with other measurem. f2=118o f2=152o PDG values 2002 + Belle sin2f1 (H.Sagawa,FPCP’03) B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  27. Summary Vud:5x10-4 accuracy, theoretically limited, PIBETA Vus: unitarity OK, disagreement in Ke3 (E865), KLOE, NA48; Vcb:excl. limited by F(1), moments will improve th.ambig.; Vub:q2 dependence starting (Belle,Cleo); inclusive Mx, q2 will be improved (Ba/lle); th. ambiguities resolved -through tests of models (exclusive); -through moments measurements (b → sg); excl./incl. disagreement? Vtd,Vts:Dmd already very precise, also improvement on tB; Dms important constraint on UT, domain of D0, CDF; sin2f1: real precision measurement, NP could be seen by Ba/lle (e.g. fKs); sin2f2: just started, although complicated, will give important constraint on UT; B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  28. r h r h …to conclude Dms & Dmd Dms & Dmd |eK| |eK| |Vub/Vcb| |Vub/Vcb| |eK| |eK| ½ of current error on Vub, sin2f1 (400fb-1) same with current sin2f1 value from fKs and ½ error B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  29. backup slide Vud,Vus summary (Hardy,Towner, Eur.Phys.J.A15(2002)) PERKEO II Grenoble (E865,hep-ex/ 0305042) (H.Abele et al., PRL 88(2002)) (ALEPH,hep-ex/ 0211057) PIBETA PSI KLOE, NA48 (D.Pocanic, CKM Workshop, Durham,2003) experimental error + theor. uncertainty experimental error -nucl.b decays (1±5x10-4) limited by th. uncertainty; - important check expected from p b decays with ~1/2 error; - new measurement by E865 vs. average of older, systematics under better control? - new measurements coming; B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  30. Vcb from B → D*ln (Aleph,PLB395,373(97)) backup slide • w • reconstruction • q2=(pl+pn)2 • pmiss (+ MC • corrections) • s(w)~0.10; …or q2=(pB-pD*)2 s(w)~0.03; also D** bckg. suppression (Z0) (U(4s)) (Belle,PLB526, 247(02)) Belle U(4s) • F(w) • parametrization; single • (slope) parameter r2 r2 and F(1)|Vcb| free parameters (I.Caprini et al., Nucl.Phys.B530,153(1998)) w B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  31. Vcbfrom D*ln by DELPHI backup slide Br(B0→ D*+l-n) = (4.70 ± 0.13 ± 0.34)% Syst. error dominated by D** w distribution modeling (± 5.1% on Vcb) Two narrow states, D1 & D2* (1+,2+) well established Br(B → D2*ln)/Br(B → D1ln) < 0.6 @95% CL - agreement with HQET when O(1/mc) corrections taken into account; - use such model for form factors and vary relevant parameters in the range consistent with experimental results; - syst. error is the max. difference from central value when F(1)Vcb measurement repeated for each parameter variation; (LEP,CDF,SLD,CERN-EP/2001-050) B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  32. Moments from BaBar backup slide <MX2-MD2> [GeV2] l1,L free due to the fact <MX2-MD2> ≥ fD**(MD**2-MD2)+ +fD*(MD*2-MD2)+ +fD(MD2-MD2) ?? excited state production saturated by D** ?? (M.Luke,CKM Workshop,Durham’03) p*[GeV] predicted dependence with l1,L as measured at p*=1.5 GeV theoretical error similar to experimental (N.Uraltsev,CKM Workshop,Durham’03) new results expected B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  33. g p K D p B1 fully reconstructed (Mbc) B2 U(4s) l p n X backup slide Vcb inclusive from Belle fully reconstructed B: B → D(*)p±, D(*)r±, D(*)a1±; D0 → Kp, K3p, Kpp0, Ks2p; D± → K2p CMS: Mbc=√(Ebeam2-pB2) DE=EB-Ebeam (Belle,DPF’03) B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  34. backup slide Vcb inclusive from Belle Lepton spectrum on semileptonic side: (p*>0.6 GeV, extrap. to full interval) individual Br (B0,B±,e,m) measured Br(B → Xln)= (11.19±0.20±0.31)% stat. syst. (PID e, extrap.) (Belle,DPF’03) B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  35. Vub exclusive from BaBar backup slide (L.H.Wilden,K.R.Schubert,BaBar,CKM Workshop,Durham’03) • B → p±,p0,r±,r0,w en; 50fb-1; • two El regions: 2-2.3 GeV (b →cln bckg.), 2.3-2.7 GeV (continuum • bckg.); • |cosqBY|<1.1, Y=r+l, rejects wrong comb.; • continuum suppression (NN); • isospin relations: G(B0 → r-e+n)=2G(B+ →r0e+n), G(B0 → p-e+n)=2G(B+ →p0e+n) • quark model relation: G(B+ →r0e+n)= G(B+ →we+n) • fit DE=Ehad+El +pmiss-Ebeam and Mhad=m(pp(p)) (only DE for p modes) • 9 parameters: Br(B → r/wln), Br(B → pln), • b →uln feeddown (norm. in two El regions) • inclusive (parton level calc. with param. from B → Xsg) + expected reson. • b →cln (norm. in each channel) • extrapolate to entire El using 5 different form factors (LQCD, sum • rules, quark models, HQET (relates B and D semil. modes)) Br(B → r-e+n)=(3.29±0.42±0.47±0.55)10-4 stat. syst. th. largest single contrib. -feed-down modeling; -detector simul. (n recon.) full spread of central values for diff. form f. B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  36. Vub from inclusive decays backup slide q2 l n El p MX p B kin. limit b → cln (plot M.Luke,CKM Workshop, Durham’03) Semileptonic width b → uln sensitive to Vub in analog way as b → cln sensitive to Vcb; ~80% of b → uln cuts larger th. uncertainty parton level • Variables separating • b → uln from b → cln: • lepton energy El; • hadronic inv. mass Mx; • leptonic inv. mass q2; • Number of measurements using • different individual variable • or combination of those. MX2[GeV2] including Fermi motion (“shape function” - model) B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  37. |Vub| = (4.11 ± 0.34 ± 0.44 ± 0.23 ± 0.24)x10-3 |Vub| = (4.43 ± 0.29 ± 0.50 ± 0.25 ± 0.35)x10-3 |Vub| = (4.26 ± 0.28 ± 0.48 ± 0.24 ± 0.34)x10-3 exp. fu th. sg Cleo (rescaled) BaBar Belle is shape function really same stat.+syst. above formula shape function backup slide Vub from lepton energy from Br to Vub: (N.Uraltsev et al., CKM Workshop, CERN’02) • to extrapolate partial Br in limited momentum range to full range → needb → uln model: parton level convoluted with shape function Fermi motion); (F.De Fazio,M.Neubert, JHEP06,017(99))

  38. (A.Sugiyama, Belle, Moriond’03) Belle hadronic mass and q2 backup slide minimization by exchanging particles (50 times); different initial (random) W (10 times); finally require W small enough; reconstruct MX and q2; signal region: q2>7 GeV2, MX<1.5 GeV; • lepton selection • n reconstruction • pseudo reconstruction of B • reconstruction of MX and q2 from MC: multidimensional p.d.f. for correct and wrong comb. composed of pB*, EB*, M2miss,… check of annealing quality B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  39. backup slide Vcb,Vub summary th.error. F(1), in future LQCD? Vcb= (42.6 ± 1.2 ± 1.9)x10-3 D*ln exp. th. Vcb= (41.4 ± 0.7 ± 0.6)x10-3 inclusive exp. th. exp. error will be reduced soon (moments), 1/mb4 Vub= (3.42 ± 0.22 ± 0.55)x10-3 exclusive exp. th. need official averaging procedure, test models exp. th. Vub= (4.28 ± 0.17 ± 0.62)x10-3 lepton endpoint more precise b → sg different methods – th. consistency B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  40. backup slide B oscillations summary Summary: Ba/lle:300fb-1s ~0.04% tB limiting factor; (simultaneous fit); Dmd= 0.502 (1 ± 0.012) ps-1 next test of SM in CKM fits; Tevatron domain until LHC; e.g. D0 5s sign. w/ 2fb-1 @Dms ~ 17ps-1; CDF needs O(103) Bs → Ds(*)np for same; Dms< 14.4 ps-1 @95% C.L. FBd√BBd ~ ±15% in CKM fits FBs√BBs ~ ±15% x ~ ± 6% (V.Jain,D0,FPCP’03) ~450 B → D0mX/pb-1 → ~40 Bs → DsmX/pb-1 B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  41. backup slide Vtd,Vts From Bd,s oscillations Rt can be constrained using Dmd largest uncertainty measured or usingDmd/Dms measurement source of th. uncertainty B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  42. (3.4s) CP in B → pp (2.2s) direct CP in B → pp direct CP sin2f2(a) backup slide Interpretation: tree + tree level strong phase diff. P-T weak phase (changes sign) B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  43. sin2f2(a) backup slide f2eff depends on d, f3, f2 and |P/T| p =f1 +f2 +f3 →f2eff depends on d, f1, f2 and |P/T| penguin amplitudes B → K+p- and B → p+p- are equal →limits on |P/T| (~0.3); considering all interval of dvalues one can obtain interval of f2 values; isospin relations can be used to constrain d (or better to say f2 -f2eff); B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  44. backup slide UT constraints Comparison of Vub values theoretical uncertainty: constant C.L. exclusive/inclusive consistentcy Vubexcl – Vublepton= 0.86 ± 0.28 ± ??? exp. uncorr.th. (H.Lacker,FPCP’03) B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

  45. backup slide Rfit (A.Hoecker et al.,Eur.Phys.J.C21,225(01)) Th. quantities – “reasonable range”, not statistically distributed, frequentist approach; th. predictions, depending on model parameters ymod knowledge on th. para. allowed range of th.param. uniform Ltheo ≠ uniform p.d.f. minimization: CL built from MC simulations; generation of pseudo exp. with optimal ymod using Lexp; B. Golob, University of Ljubljana Physics in Collision 2003, Zeuthen

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