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

Sides and Angles of the Unitarity Triangle (S.Prell) The CKM Matrix 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 i W - j GFVij quark transition HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

The CKM Matrix 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 ! Wolfenstein’s parameterization d s b u c t point out symmetry perfect, except for Vub and Vtd … reflects size of matrix elements (areas of squares proportional to |Vij|2) HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

The (B) Unitarity Triangle Vud, Vcd and Vtb are 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 HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

CKM Matrix Element Magnitudes 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 ν b Bd c D Vtd Vts Vtb b d b s Bd t Bd Bs t Bs t t d b s b HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

Vcb from B → D(*)lν decays B →D*lν results arXiv:0810.1657 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): PRD77, 032002 (2008) PRL100, 231803 (2008) PRD79, 012002 (2009) Update plot HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

Vcb from 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 Eγ in B → Xsγ decays) Comment on error estimate BaBar, arXiv:0908.0415 mhad in B → Xclν HFAG, Winter 2009 p*l > 0.8 GeV (~2.3σ larger than Vcb from excl. decays) My average (S = 2.3) HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

Vub from B → π l ν decays PRL101, 081801 (2008) PLB648, 139 (2007) arXiv:0812:1414 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) 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 HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

Vub from inclusive B→Xu l ν decays Vub (B→πlν) I can’t average theories, will use |Vub|incl = (4.20 ±0.28)x10-3 (BLNP) arXiv:0907.0379 PRL100, 171802 (2008) 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 Check slide arXiv:0907.0379 Vub from incl. B→Xulν syst. higher (~1-2σ) than from B→πlν decays My average HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

Vtd and Vts Experimental input: Bd0Bd 0 and Bs0Bs 0 oscillation frequencies CDF, PRL 97, 242003 (2006) D0, PRL 97, 021802 (2006) HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

Vtd and Vts From neutral B0d(s) mixing Improved lattice results: From radiative B decays: BR(B → ργ) / BR(B → K*γ) Improved lattice results: (HPQCD, PRD 80, 014503 (2009)) Some theoretical errors cancel in the ratio: (errors dominated by theoretical uncertainties) HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

UT Apex from Vub, Vcb, Vts and Vtd UT from full fit including CKM phases Explain CL regions Measurements of the Unitarity Triangle sides are theoretically limited ! HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

CKM Phases and Unitarity Triangle Angles d s b u c t γ β βs Phases in Wolfenstein convention (areas of squares proport. to |argVij|) Convention-independent definition: HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

Sensitivity to CKM Phases from Interference KS(Ф) c b d(s) s B(s)0 J/ψ t V*td(s) 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 c b d(s) s B(s)0 J/ψ KS(Ф) t d b B0 V*td u π - π+ V*ub d b u B0 π - π+ Vub Time-dependent analyses to measure mixing-induced CP-asymmetries: s b u c B+ D0 K+ u b c s B+ K+ D0 Vub HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

β from b →(cc) s decays Theor. clean measurement of |S| = sin2β with B → J/ψ K0, J/ψ K*, ψ(2S)KS, ηcKS, & χc1KS by BaBar and Belle BaBar, PRD 79,072009 (2009) statistically limited HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

β from 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) HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

β from b → s(qq) penguin loop decays 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 sin2βeff of 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 Theoretically clean modes (1.3σ away from sin2β) HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

a from B0 → pp g Sππ  sin2aeff = sin2(a + d ) 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)) HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

Sides and Angles of the Unitarity Triangle (S.Prell) a from B → pp, rr, rp • 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 2008 2009 PRL 102, 141802 (2009) Excluded by other constraints Also prelim. BaBar result from a1π and K1π (Lombardo @ EPS’09, arXiv:0909.5646) HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

g from B- → D(*)K- Decays 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 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- HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

g from B- → D (*) K- Decays • B- → D (*)K- decays with 3-body Dalitz analysis of D → KSπ π, D → KSKK most sensitive to γ Belle: updated Dalitz analysis including D*0 → D0γ Poluektov @ EPS’09 Add comment on model error in BaBar analysis 2008 (prelim.) 2009 (prelim.) Also, from time-dependent B → D (*)K/p analyses: 2β+γ = (± 90 ± 32)o Model error can be reduced to ~2o using CLEO-c measurements of ψ(3770)→DD (PRD 80, 032002 (2009)) HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

UT from Angles α, β, γ (and εK) Define epsilonK All measurements of the Unitarity Triangle angles are statistically limited ! HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

βs from Bs → J/ψ Ф decays • D0 and CDF measure βs with angular dependent fit to decay time distributions of Bs → J/ψ Ф 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 New physics in BsBs mixing CDF/PHYS/BOTTOM/CDFR/9787, DØ Note 5928-CONF HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

Sides and Angles of the Unitarity Triangle (S.Prell) Global CKM Fit Other constraints All 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)) Replace CKM fitter plot HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

Sides and Angles of the Unitarity Triangle (S.Prell) Rare Decay: B → τ ν Decay B → τ ν is sensitive to Vub Decay proceeds via W annihilation in SM also sensitive to new physics (e.g. charged Higgs) B → τ ν 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) HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

BR(B → τ ν) Measurements Semileptonic tag (arXiv:0912.2453) preliminary 10x signal Revise world average (cite reference, check HFAG) Belle Hadronic tag Semileptonic tag BaBar World average HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

Unitarity Triangle consistency ? ~2.4σ discrepancy between direct BR(B → τ ν) measurements and global UT analysis Theoretical uncertainty from fB is removed in BR(B → τ ν) / Δmd discrepancy remains at ~2.5σ (only remaining theoretical error is 12% from B bag factor) Effect of charged Higgs W. Hou, PRD 48, 2342 (1992) HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

Sides and Angles of the Unitarity Triangle (S.Prell) 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) vs εK and Vub B → τν vs β (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 Importance for direct searches at LHC, flavor structure of new physics HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

Sides and Angles of the Unitarity Triangle (S.Prell) Back-up Slides HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

Vud from nuclear β Decays • 0+→0 + super-allowed nuclear β-decays within same isospin multiplet (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) Towner & Hardy, PRC 79, 055502 (2009) Before nucleus- dependent corrections … GF from μ decay New Penning-trap measurements of decay energies … and after HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

} Vus from 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) 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 Palutan (FlaviaNet) @ Kaon ‘09 HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

Vus / Vud and combined fit Palutan (FlaviaNet) @ Kaon ‘09 Ratio Vus / Vud can be determined independently from ratio of K → μν (KLOE, PLB 632, 76 (2006)) and π → μν decay rates HPQCD-UKQCD, PRL100, 062002 (2008) From fit to Vud, Vus and Vud / Vus: HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

Sides and Angles of the Unitarity Triangle (S.Prell) Vcd from v scattering Di-muon production by neutrino on nuclei Semi-leptonic decay D →π l ν Dominated by D →π form factor My average CLEO-c, arXiv:0906.2983 HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

Sides and Angles of the Unitarity Triangle (S.Prell) Vcs from D and Ds Decays 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 CLEO-c, arXiv:0906.2983 [PRD 79, 052001 (2009), PRD 79, 052002 (2009)] My average HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

Unitarity of udcs Matrix Cannot predict 3rd family (Vub too small to matter) (equal error contribution to 1st row unitarity check) 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) HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

Sides and Angles of the Unitarity Triangle (S.Prell) K. Trabelsi for CKMFitter at Beauty 2009 HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

Vtb from 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 +0.6-0.5 pb [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 0.91+/-0.08 HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

CKM matrix unitarity check Magnitudes of CKM matrix elements fulfill unitarity well From Vcb and Vts HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

Mixing-induced CP violation 2 2 Af Af B0 fCP B 0 fCP B 0 Af B0 Af Difference in decay rate for B0 and B0  CP Violation HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)

Measurement Technique for TDCPVs B-Flavor tagging z B tag Coherent BB production (p-wave) B0 B0 Reconstruction of B decays to exclusive final states HEP 2010 Sides and Angles of the Unitarity Triangle (S.Prell)