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Sides and Angles of the Unitarity Triangle

Sides and Angles of the Unitarity Triangle. Soeren Prell Iowa State University High-energy Physics in the LHC Era 3 rd International Workshop January 4-8, 2010 Valparaiso, Chile. The CKM Matrix. W -. i. j. G F V ij. quark transition.

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Sides and Angles of the Unitarity Triangle

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  1. Sides and Angles of the Unitarity Triangle Soeren Prell Iowa State University High-energy Physics in the LHC Era 3rd International Workshop January 4-8, 2010 Valparaiso, Chile

  2. The CKM Matrix W- i j GFVij quark transition • V connects quark mass eigenstates to weak interaction eigenstates and thus describes coupling strength of quarks to charged current weak interaction • V first suggested by M. Kobayashi and T. Maskawa in 1973 to explain CP violation in Kaon mixing (Physics Nobel Prize 2008, shared with Y. Nambu); called VCKM to acknowledge N. Cabibbo Sides and Angles of the Unitarity Triangle (S.Prell)

  3. The CKM Matrix Wolfenstein’s parameterization u c t … reflects size of matrix elements (areas of squares proportional to |Vij|2) d s b • In 3-generation Standard Model CKM matrix is a unitary 3x3 matrix • Values of Vij not predicted by SM • Invariants under quark field rotations are observables (e.g. |Vij|2,VijVik*VlkVlj*) • VCKM has only 4 independent parameters • Search for physics beyond the SM by testing unitarity of CKM matrix ! Sides and Angles of the Unitarity Triangle (S.Prell)

  4. The (B) Unitarity Triangle Vud, Vcdand Vtbare well known: Vud from nuclear β decays, Vcd (= Vus) from Kaon decays, Vtb 1 from Vub and Vcb Determine Vub, Vcb, Vtd and Vts with B decays Sides and Angles of the Unitarity Triangle (S.Prell)

  5. CKM Matrix Element Magnitudes ν Vub e- Vud Vus ν b Bd u All 1st and 2nd row matrix elements are most precisely determined from leptonic and semi-leptonic decays π Vcb e- Vcd Vcs b Bd c D Vtd Vts Vtb b d b s Bd Bs t t Bs Bd t t b s d b Sides and Angles of the Unitarity Triangle (S.Prell)

  6. Vcbfrom B → D(*)lν decays Experiments fit differential B → D(*)lν decay rate for |Vcb|F(1) and |Vcb|G(1) using HQET-based form factor parameterizations • B → D(*) form factor normalizations from lattice calculations • Prelim. result from Belle with B- →D*0lν(Dungel @ EPS’09, arXiv:0910.1438, not yet included in average): B →D*lν results arXiv:0810.1657 PRD77, 032002 (2008) PRL100, 231803 (2008) PRD79, 012002 (2009) Sides and Angles of the Unitarity Triangle (S.Prell)

  7. Vcbfrom inclusive B → Xclν decays • Inclusive rate Γ(B → Xclν) can be described by expansion in powers of 1/mb(HQET, OPE) • Non-perturbative corrections up to O(1/mb3) are determined from inclusive distributions in B decays (Elep and mhad in B → Xclν and Eγin B → Xsγ decays) BaBar, arXiv:0908.0415 HFAG, Winter 2009 mhad in B → Xclν p*l > 0.8 GeV (~2.3σ larger than Vcb from excl. decays) My average (S = 2.3) Sides and Angles of the Unitarity Triangle (S.Prell)

  8. Vubfrom B → π l ν decays PRL101, 081801 (2008) • Experiments determine |Vub||f+(q2)| from measured B → π l ν rate • |f+(q2)| calculated from theory (LQCD (LCSR) at high (low) q2) PLB648, 139 (2007) arXiv:0812:1414 PRL101, 081801 (2008) arXiv:0812:1414 PRL99, 041802 (2007) PRL98, 091801 (2007) arXiv:0812:1414 FNAL/MILC + BaBar data, PRD79, 054507 (2009): 3.38 ± 0.36 Error dominated by f+(0) calculation Sides and Angles of the Unitarity Triangle (S.Prell)

  9. Vubfrom inclusive B→Xul ν decays Vub (B→πlν) • Challenges • mb5-dependence of Γ(B→Xulν) • b →c background: Γ(B→Xclν)/ Γ(B→Xulν)~50 • Select B→Xulν enhanced region in phase sp. • use shape function from B→Xsγ Eγ-spectrum and theory to extrapolate rate to full PS • New Belle multivariate analysis • Reconstruct other B in hadronic mode • Covers about 90% of B→Xulν PS Vub from incl. B→Xulν syst. higher (~1-2σ) than from B→πlν decays arXiv:0907.0379 PRL100, 171802 (2008) PRL100, 171802 (2008) PRL100, 171802 (2008) arXiv:0907.0379 I can’t average theories, will use |Vub|incl= (4.20 ±0.28)x10-3 (BLNP) My average Sides and Angles of the Unitarity Triangle (S.Prell)

  10. Vtdand Vts Experimental input: Bd0Bd0and Bs0Bs0 oscillation frequencies CDF, PRL 97, 242003 (2006) D0, PRL 97, 021802 (2006) Sides and Angles of the Unitarity Triangle (S.Prell)

  11. Vtd and Vts Improved lattice results: (HPQCD, PRD 80, 014503 (2009)) Some theoretical errors cancel in the ratio: (errors dominated by theoretical uncertainties) From neutral B0d(s) mixing From radiative B decays: BR(B → ργ) / BR(B → K*γ) Sides and Angles of the Unitarity Triangle (S.Prell)

  12. UT Apex from Vub, Vcb, Vts and Vtd UT from full fit including CKM phases Measurements of the Unitarity Triangle sides are theoretically limited ! Sides and Angles of the Unitarity Triangle (S.Prell)

  13. CKM Phases and Unitarity Triangle Angles d s b Phases in Wolfenstein convention (areas of squares proport. to |argVij|) Convention-independent definition: γ u c t βs β Sides and Angles of the Unitarity Triangle (S.Prell)

  14. Sensitivity to CKM Phases from Interference b c b d(s) J/ψ KS(Ф) c d(s) t s B(s)0 B(s)0 s c KS(Ф) J/ψ d(s) d(s) d(s) c t b V*td(s) d π- d V*td Vub u π+ u b d u b u B0 t π+ B0 V*ub π- d Time-dependent analyses to measure mixing-induced CP-asymmetries: d d b d t s b u K+ u D0 c Vub b c B+ B+ D0 s u u K+ u u 2β(s) from BB box diagrams • no weak phase in decay amplitudes 2α = 2(π – β – γ) • from BB box diagram followed by b → u decay γ • from charged B b → u decay Sides and Angles of the Unitarity Triangle (S.Prell)

  15. β from b →(cc) s decays BaBar, PRD 79,072009 (2009) statistically limited Theor. clean measurement of |S| = sin2β with B → J/ψ K0, J/ψ K*, ψ(2S)KS, ηcKS, & χc1KS by BaBar and Belle Sides and Angles of the Unitarity Triangle (S.Prell)

  16. βfrom b → s(qq) penguin loop decays BaBar, PRD 79, 052003 (2009) • In SM penguin decay amplitude is dominant and has same weak phase as b→c(cs) amplitude • expect to measure |S| = sin(2b) • SM contributions from suppressed diagrams expected to be small (Dsin(2b) = sin(2beff)- sin(2b) ~ 0.01-0.1) • Penguin decays with b → s (qq ) loop sensitive to New Physics from heavy particles • New Physics contributions could cause large D sin(2b) Sides and Angles of the Unitarity Triangle (S.Prell)

  17. β from b → s(qq) penguin loop decays Theoretically clean modes (1.3σ away from sin2β) • CP asymmetries measured by B factories in 9 different b → s (qq) modes • All measurements of sin2βeff consistent with sin2βb→c(cs) • C’s consistent with zero • Naïve average sin2βeffof all b → s (qq) modes used to be ~3σ lower than sin2β (~2004), now ~1σ • Some modes (ФK0, η’K0, K0K0K0) believed to have relatively small theoretical uncertainties • My average for clean modes Sides and Angles of the Unitarity Triangle (S.Prell)

  18. a from B0→ pp Optimal Case: Two sizeable amplitudes (P/T ~ 0.3) : b → u “tree” b → d “penguin” g PRL 98, 211801 (2007) Sππ sin2aeff = sin2(a+d ) Excluded at 95% CL Determine d from isospin analysis (Gronau & London, PRL 65, 3381 (1990)) Sides and Angles of the Unitarity Triangle (S.Prell)

  19. afrom B → pp, rr, rp 2008 2009 PRL 102, 141802 (2009) Excluded by other constraints Also prelim. BaBar result from a1π and K1π (Lombardo @ EPS’09, arXiv:0909.5646) • VV decay B → rr • separate isospin analysis for each polarization amplitude • fortunately, longitudinal polarization dominant (>90%) • Small penguin contribution in B → rr • New measurement of BR(B+→ r+r0) from BaBar stretches isospin triangles Sides and Angles of the Unitarity Triangle (S.Prell)

  20. g fromB-→ D(*)K-Decays Lopez-March @ EPS’09 3.4 σ GLW : CP eigenstates (pp, KK,etc.) Gronau & London, PLB 253, 483 (1991); Gronau & Wyler, PLB 265, 172 (1991) ADS: Flavor DCSD states (Kp) Atwood, Dunietz, & Soni, PRL 78, 3257 (1997), Atwood, Dunietz, & Soni, PRD 63, 036005 (2001) GGSZ: 3-body decays (KSpp, KSKK) Giri, Grossman, Soffer, & Zupan, PRD 68, 054018 (2003) Bondar, PRD 70, 072003 (2004) • New BaBar measurement with first evidence for ADS signal B-→ DK- • Rates of B±→ D (*) K±decays are sensitive to γ through inter- ference of b → c and b → u transitions • Need states accessible to D(*)0 and D(*)0 • Several neutral D (*) final states investigated by B factories and CDF Sides and Angles of the Unitarity Triangle (S.Prell)

  21. g fromB-→ D (*) K-Decays Poluektov @ EPS’09 2008 (prelim.) Also, from time-dependent B → D (*)K/panalyses: 2β+γ = (± 90 ± 32)o 2009 (prelim.) Model error can be reduced to ~2o using CLEO-c measurements of ψ(3770)→DD (PRD 80, 032002 (2009)) • B-→ D (*)K-decays with 3-body Dalitz analysis of D → KSππ, D → KSKKmost sensitive to γ • Belle: updated Dalitz analysis including D*0 → D0γ Sides and Angles of the Unitarity Triangle (S.Prell)

  22. UT from Angles α, β, γ (and εK) All measurements of the Unitarity Triangle angles are statistically limited ! Sides and Angles of the Unitarity Triangle (S.Prell)

  23. βs from Bs → J/ψФ decays New physics in BsBs mixing CDF/PHYS/BOTTOM/CDFR/9787, DØ Note 5928-CONF • D0 and CDF measure βs with angular dependent fit to decay time distributions of Bs → J/ψФ • Simultaneous fit for ΔΓs and βs • SM predicts βs very small (~0.02) • sensitive to new physics in Bs mixing • Prospects • D0 and CDF working on updates with 2x samples • LHCb sensitivity with 0.5 fb-1: σ(βs) = 0.02 Sides and Angles of the Unitarity Triangle (S.Prell)

  24. Global CKM Fit All constraints Other constraints CKM angles • Consistency of angles • Consistency of angles and sides from global fit • Overall good fit (CKMFitter: global p-value 45%) • ~2σ tension between sin2β and εK / Vub • correction to εK will make it worse (Buras, Guadagnoli, PRD78, 033005 (2008)) Sides and Angles of the Unitarity Triangle (S.Prell)

  25. Rare Decay: B → τν • Decay B → τν is sensitive to Vub • Decay proceeds via W annihilation in SM • also sensitive to new physics (e.g. charged Higgs) • B → τν event reconstruction at B factories • Tagging B side • Full reconstruction of B in hadronic (D(*)π/ρ, etc.) or semi-leptonic mode (D(*)lv) • Signal B side • Charged tracks • Missing energy due to ν’s • Require (no) additional energy in EM calorimeter (Eextra,EECL) Sides and Angles of the Unitarity Triangle (S.Prell)

  26. BR(B → τν) Measurements Semileptonic tag (arXiv:0912.2453) preliminary 10x signal World average • Belle • Hadronic tag • Semileptonic tag • BaBar • Hadronic tag • Semileptonic tag Sides and Angles of the Unitarity Triangle (S.Prell)

  27. Unitarity Triangle consistency ? W. Hou, PRD 48, 2342 (1992) ~2.4σ discrepancy between direct BR(B → τν) measurements and global UT analysis • Theoretical uncertainty from fB is removed in BR(B → τν) / Δmd • discrepancy remains at ~2.5σ (only remaining theoretical error is 12% from B bag factor) Effect of charged Higgs Sides and Angles of the Unitarity Triangle (S.Prell)

  28. Conclusions • Many new measurements regarding quark flavor mixing in the last few years constrain the Unitarity Triangle with increasing precision • CKM mechanism proven to be dominant mechanism for quark mixing • describes all current experimental results in quark mixing and CP violation (including measurements of CKM matrix elements (Vud, Vus, Vcd, Vcs, Vtb) not covered in this talk) • Some intrinsic discrepancies need to be resolved • Vcb and Vub (incl. vs excl. decays) • A few interesting “tensions” at the 2-3 σ level should be monitored closely in the future • β (J/ψ K0) vsεK and Vub • B → τνvsβ (J/ψ K0) • βs • Expect significant impact from upcoming experiments (LHCb, Super B factories) and improved theory/lattice calculations mostly on improving γ, βs, Vub, Vtd/ Vts Sides and Angles of the Unitarity Triangle (S.Prell)

  29. Back-up Slides Sides and Angles of the Unitarity Triangle (S.Prell)

  30. Vudfrom nuclear β Decays Towner & Hardy, PRC 79, 055502 (2009) Before nucleus- dependent corrections … GF from μ decay New Penning-trap measurements of decay energies … and after • 0+→0 + super-allowed nuclear β-decays within same isospinmultiplet (pure V decays) • Error on rad.corrections ∆RV reduced x2 (Marciano and Sirlin, PRL 96, 032002 (2006)) • Still dominant (syst.) error on Vud • Other Vud measurements compatible, but (7-10 x) less precise • n lifetime (error dominated by gA, most precise τn measurement 6σ away from earlier results), π decay (stat. limited) Sides and Angles of the Unitarity Triangle (S.Prell)

  31. Vusfrom K → πlν (Kl3) (experimental input, theory input) Preliminary measurements τ(KL) and τ(KS) (KLOE, cf. Bocchetta @ Kaon’09, Dreucci @ EPS’09) not yet in average dominated by KL lifetime } RBC-UKQCD, PRL 100, 141601 (2008) Palutan (FlaviaNet) @ Kaon ‘09 Vus from τ decays • Prelim. BaBar measurement (ICHEP’08) of BR(τ→Kν)/BR(τ →πν) gives |Vus|=0.2255(23) • Rate of incl. τ → s decays (CKM’08) gives |Vus| = 0.2165 ± 0.0026(exp) ± 0.0005(theo); 2.6σ smaller than |Vus| from Kl3 Sides and Angles of the Unitarity Triangle (S.Prell)

  32. Vus/ Vudand combined fit Ratio Vus/ Vudcan be determined independently from ratio of K → μν(KLOE, PLB 632, 76 (2006)) and π → μν decay rates From fit to Vud, Vus and Vud / Vus: Palutan (FlaviaNet) @ Kaon ‘09 HPQCD-UKQCD, PRL100, 062002 (2008) Sides and Angles of the Unitarity Triangle (S.Prell)

  33. Vcdfrom v scattering My average CLEO-c, arXiv:0906.2983 Di-muon production by neutrino on nuclei Semi-leptonic decay D →π l ν • Dominated by D →π form factor Sides and Angles of the Unitarity Triangle (S.Prell)

  34. Vcsfrom D and Ds Decays CLEO-c, arXiv:0906.2983 [PRD 79, 052001 (2009), PRD 79, 052002 (2009)] My average • Semi-leptonic D decay D → K l ν • Dominated by D → K form factor • Leptonic Ds decays Ds →(μ,τ) ν • New measurements of from CLEO-c • decay constant f(Ds) from LQCD calculation Sides and Angles of the Unitarity Triangle (S.Prell)

  35. Unitarity of udcs Matrix Constraints on New Physics • Scalar currents (charged Higgs) • 4th quark generation • |VuD| < 0.04 @ 95% CL • Exotic μ decays • BR(Exotic μ decays) < 0.0016 @ 95% CL (~7x better than bound on μ+→e+VeVμ) Cannot predict 3rd family (Vub too small to matter) (equal error contribution to 1st row unitarity check) Sides and Angles of the Unitarity Triangle (S.Prell)

  36. K. Trabelsi for CKMFitter at Beauty 2009 Sides and Angles of the Unitarity Triangle (S.Prell)

  37. Vtbfrom weak top production • From weak “single top” production cross-section in pp collisions at the Tevatron • Does not assume unitarity • 5σ observations by CDF and D0 • σ = 2.3 +0.6-0.5pb [CDF, arXiv:0903.0885] • σ = 3.9 ± 0.9 pb [D0, arXiv:0903.0850] • CDF: |Vtb| = 0.91 ± 0.11(exp) ± 0.07(theo) • D0: |Vtb| = 1.07 ± 0.12 Sides and Angles of the Unitarity Triangle (S.Prell)

  38. CKM matrix unitarity check Magnitudes of CKM matrix elements fulfill unitarity well From Vcb and Vts Sides and Angles of the Unitarity Triangle (S.Prell)

  39. Mixing-induced CP violation 2 2 Af Af B0 fCP fCP B 0 B0 B 0 Af Af Difference in decay rate for B0 and B0  CP Violation Sides and Angles of the Unitarity Triangle (S.Prell)

  40. Measurement Technique for TDCPVs B-Flavor tagging 0 z B tag Coherent BB production (p-wave) B0 B0 Reconstruction of B decays to exclusive final states Sides and Angles of the Unitarity Triangle (S.Prell)

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