Unitarity Triangle Sides at e + e - colliders Phillip Urquijo - PowerPoint PPT Presentation

Unitarity Triangle Sides at e + e - colliders Phillip Urquijo University of Bonn On behalf of the Belle Collaboration

Sides of the UT • New physics 0.7 R t excluded area has CL > 0.95 m & m CKM � � s m d � searches in flavour f i t t e r d 0.6 Winter 12 require precise, 0.5 R u V td V tb* over-constraining 0.4 � V cd V cb* measurements of 0.3 sides and angles. � 2 V ud V ub* 0.2 V V cd V cb* ub 0.1 � � • Must measure CKM 1 3 0.0 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 � matrix elements, UT CKM fundamental Measurement δ V/V Ref. Parameter parameters of the SM V ub ** (4.4±0.5)10 -3 10% cannot be predicted. V cb (4.1±0.1)10 -2 3% PDG PDG • Limiting test is V td ( Δ md)** (8.4±0.6)10 -3 7% V td /V ts (mix) 3% |V ub | Vs sin2 Φ 1 V cd 0.228±0.006 3% 1209.0085 V tb :single-t ~1.03±0.04 4% 1302.1773 2 Phillip URQUIJO UT sides at e + e - , FPCP 2013

Sides of the UT • New physics 0.7 0.7 R t excluded area has CL > 0.95 excluded area has CL > 0.95 m & m CKM CKM � � s m d � � � searches in flavour f i t t e r f i t t e r d 0.6 0.6 K 3 Winter 12 Winter 12 require precise, sin 2 0.5 � 0.5 R u 1 sol. w/ cos 2 < 0 � 1 V td V tb* over-constraining (excl. at CL > 0.95) 0.4 0.4 � � � V cd V cb* measurements of 2 � 0.3 0.3 K sides and angles. � � 2 2 V ud V ub* 0.2 0.2 V V cd V cb* ub 0.1 0.1 � � � � • Must measure CKM � 1 1 3 3 2 0.0 0.0 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 � � matrix elements, UT CKM fundamental Measurement δ V/V Ref. Parameter parameters of the SM V ub ** (4.4±0.5)10 -3 10% cannot be predicted. V cb (4.1±0.1)10 -2 3% PDG PDG • Limiting test is V td ( Δ md)** (8.4±0.6)10 -3 7% V td /V ts (mix) 3% |V ub | Vs sin2 Φ 1 V cd 0.228±0.006 3% 1209.0085 V tb :single-t ~1.03±0.04 4% 1302.1773 2 Phillip URQUIJO UT sides at e + e - , FPCP 2013

Access to R u & R t through B decays B → X c,u l ν Δ m d e,µ _ _ |V tb | |V td | b d _ |V ub | or |V cb | ν W t b _ _ c,u d,u t d b _ _ d,u |V td | |V tb | B → τν B → X s,d γ γ b τ t H + ,W + d,s b |V ub | |V tb | _ u ν W + |V td | or |V ts | + some |V cd | (leptonic&semileptonic) at the end Phillip URQUIJO UT sides at e + e - , FPCP 2013 3

, u ∗ V V ( ρ ρ ρ ρ , η η η η ) η td tb ∗ V V ∗ V V cd cb R u α Φ 2 ud ub ∗ V V Φ 3 γ cd cb Φ 1 β ( 0 , 0 ) ( 1 , 0 ) ρ |V ub | Crisis inclusive |V ub | GGOU =4.39±0.15 +0.12-0.14 )10 -3 ➛ I will discuss strategies to resolve this anomaly. exclusive |V ub |=(3.23 ± 0.30) 10 -3 Phillip URQUIJO UT sides at e + e - , FPCP 2013

Semileptonic Decays tree level, short distance: Decay properties depend b → c e ν directly on | V cb | & | V ub | and m b in the perturbative regime ( α sn ). e W ν b c 5 Phillip URQUIJO UT sides at e + e - , FPCP 2013

Semileptonic Decays tree level, short distance: Decay properties depend B → D e ν directly on | V cb | & | V ub | and m b in the perturbative regime ( α sn ). e W ν quarks are bound by soft B [ ] D b c gluons: non-perturbative long distance interactions of b quark with the light quark in + long distance: the B . 5 Phillip URQUIJO UT sides at e + e - , FPCP 2013

Semileptonic Decays tree level, short distance: Decay properties depend B → D e ν directly on | V cb | & | V ub | and m b in the perturbative regime ( α sn ). e W ν quarks are bound by soft B [ ] D b c gluons: non-perturbative long distance interactions of b quark with the light quark in + long distance: the B . Departure from the heavy quark symmetry can be expressed as ( Λ QCD / m Q ) n corrections 5 Phillip URQUIJO UT sides at e + e - , FPCP 2013

|V cb | & Heavy Quark Parameters inclusive Phillip URQUIJO UT sides at e + e - , FPCP 2013

Inclusive |V cb | O perator P roduction E xpansion predicts the total rate as: b s b 2 2 5 2 3 3 G m 0 µ µ ρ ρ 2 V F b ( 1 A ) A [ c ( r ) c ( r , , ) c ( r , D , LS ) ...] π G Γ = + × + + + + SL cb EW pert 0 2 3 3 2 2 3 3 192 m m m m m π b b b b b Free quark decay Non-perturbative QCD Pert. suppressed by 1/m b2 b � m b , m c: renormalisation scheme enormalisation scheme dependent μ π 2 (- λ 1 ) - kinetic energy of b-quark, Λ QCD2 /m b2 μ G2 ( λ 2 ) - chromomagnetic coupling Non perturbative parameters Λ QCD3 /m b3 ρ D , ρ LS ( ρ 1 , τ 1-3 ) (Spin-orbit, Darwin terms) derived from data. large phase space needed for quark-hadron duality 7 Phillip URQUIJO UT sides at e + e - , FPCP 2013

|V cb | from Inclusive B → X c l + ν & B → X s γ � • HQE params & |V cb | from n n 2 2 3 3 M | M d f ( E , m , m , , , , ) = τ ∫ Γ = µ µ ρ ρ x E B x 0 b c G D LS  E π > 0 spectral “moments” E 0 quark masses Non-perturbative Cut-off parameters alculations in “kinetic” and “1S” mass schemes Moments can be • Need high resolution access to B rest frame, calculated for cut-off in E l unfolded: Hadronic invariant mass ` recoil Lepton momentum π − X u π + Photon energy B . . . e + ¯ ν ` • Use hadronic tag B tag → D (*) Y Υ (4 S ) (Y= n π , m π 0 , p K s , q K...), e − to infer signal B : flavour, charge, p 4 tag B µ + π − J/ ψ K + µ − 8 Phillip URQUIJO UT sides at e + e - , FPCP 2013

|V cb | Determination • Inclusive SL decay recoiling against B tag &' $!# • Unfold to true (Belle) or & • linear calibration in X c multiplicity (Babar) !"# ? ! !%# ? &'' • radiative corrections • Extra constraint on m b from radiative moments. Hadron mass Lepton momentum Photon Energy X,true 16 1500 Entries per 0.1 GeV/c 0 . 05 ≤ E miss − c | � p miss | < 0 . 2GeV 600 600 ] 14 0 2 6 ≤ N Xc ≤ 7 B data 2000 2000 ) B B Continuum Belle D, D* 2 > [(GeV/c B X e 12 → ν 2 2 control control c entries / 80 MeV/c entries / 80 MeV/c Truth 140 fb -1 500 500 B X e → ν 10 Events/0.1 GeV u 1600 1600 1000 Secondaries 8 X,reco 400 400 Combinatorial 6 1200 1200 Babar 2 <m Continuum 4 300 300 2 500 800 800 5 10 15 2 2 2 ] <m > [(GeV/c ) ] 200 200 X,true D** 16 400 400 ] 100 100 0 0 0 0 0 1 1 2 2 3 3 4 4 0 0 0.4 0.6 0.8 0.4 0.6 0.8 1 1 1.2 1.4 1.6 1.8 1.2 1.4 1.6 1.8 2 2 2.2 2.4 2.2 2.4 2 2 1.5 2 2.5 3 3.5 m m [GeV/c [GeV/c ] ] *B p (GeV/c) X X E * (GeV) γ e 350 350 Belle., PRD.75.032005 (2007) BABAR, PRD 81, 032003 (2010) Babar, PRD 86 112008 (2012) Belle, PRD.75.032001 (2007) 9 Phillip URQUIJO UT sides at e + e - , FPCP 2013

|V cb | Inclusive • Global fit to Semileptonic (and Radiative) spectra: 4.7 PRD 81, 032003 (2010) 4.6 Babar ] 3 2 66 measured moments → |V cb |, m b , m c and non-pert. ) 4.5 2 > [(GeV/c 4.4 params. 4.3 • Kinetic : O( α s /m b2 ) JHEP 1109 ( 2011 ) 055 4.2 X 2 <m 4.1 • 1S : PRD 70, 094017 (2004); PRD 78, 032016 ( 2008 ) 4 • Additional constraints needed for m b : X s γ or m c . 3.9 2 0 0.5 1 1.5 2 * [GeV/c] p [GeV/c] l,min [arXiv:1207.1158] ] 6 ) -3 -3 10 10 × × 43.5 | Kinetic | | cb cb cb 43 1S scheme |V |V |V Kinetic HFAG scheme 0.043 scheme EOF11 43 42.5 Xlv 0.042 Xlv 42.5 42 Xlv+m c 42 Xlv 0.041 41.5 X constraint � s X s γ constraint m constraint 41.5 c 41 0.04 4.5 4.6 4.7 4.5 4.6 4.7 4.55 4.6 m (GeV) 1S 2 m [GeV/c ] 1S 2 m [GeV/c ] b b b 10 Phillip URQUIJO UT sides at e + e - , FPCP 2013

|V cb | Global Fit Results • Theory errors dominate the fit, results depend on off diagonal covariance. • Consistency between X c l ν and X s γ Scheme Constraint |V cb |10 -3 X 2 /ndf • χ 2 low: further X s γ 41.94 ± 0.43(fit) ± 0.59(th) 27/59 kinetic kinetic understanding of m c 41.88 ± 0.44(fit) ± 0.59(th) 24/59 errors needed X s γ 41.96 ± 0.45 23/59 1S 1S - 42.37 ± 0.65 14/48 arXiv:1303.0958 • New 1S fit to B → X s γ (only) 17 2.0 l= 0.5 GeV NNLL + O H a s 2 L for m b . Model- 1 d G C 72 dE g NLL + O H a s L 16 » C 7incl V tb V ts * » ¥ 10 3 1.5 independent description of shape function 15 1.0 • To be extended/applied to Standard Model 14 0.5 V ub . Preliminary H exp. + theo. uncertainties L 0.0 13 1.6 1.8 2.0 2.2 2.4 2.6 4.65 4.7 4.75 4.8 4.85 m b 1 S @ GeV ê c 2 D E g H GeV L 11 Phillip URQUIJO UT sides at e + e - , FPCP 2013

Quark Masses: m c & m b HFAG PDG 2012 Kinetic scheme b → s γ , b → cl ν HPQCD HISQ 1004.4285 u, d, s sea m c , b → cl ν b → cl ν ETMC 1010.3659 n f =2 u, d sea 1S scheme SIMBA b → s γ ( λ =0.5) Chetyrkin et al 0907.2110 b → s γ , b → cl ν Dehnadi et al 1102.2264 b → cl ν contnm 1.22 1.24 1.26 1.28 1.3 1.32 1.34 4.5 4.6 4.7 4.8 m c (m c , n f =4) (GeV) m [GeV] b These m b used for V ub (Kinetic scheme fit result also translated into SF scheme.) 12 Phillip URQUIJO UT sides at e + e - , FPCP 2013

|V cb | exclusive Phillip URQUIJO UT sides at e + e - , FPCP 2013