| V b | Exclusive: Form Factors from Lattice QCD Jonathan Flynn - PowerPoint PPT Presentation

| V b | Exclusive: Form Factors from Lattice QCD Jonathan Flynn University of Southampton CKM2006, Nagoya, 11–16 Dec 2006 CKM2006 14 Dec 2006 1/14

Outline B → π Current Calculations: FNAL-MILC and HPQCD Chiral Extrapolation Quenched vs Unquenched Prospects CKM2006 14 Dec 2006 2/14

� Main errors: � n F = 2 + 1 asqtad staggered light � discretisation � m s / 8 < m  < 3 m s / 4 with � statistical ∼ 8% � Results still � b -quark: tadpole-improved clover B → π : FNAL-MILC � Matching: Z b � Local sources/sinks; four source quarks, ∼ 500 cfgs ∼ 9% m , vl = m , se preliminary action with Fermilab interpretation � V μ = ρ V μ ( Z  V Z bb V ) 1 / 2 2.5 N f =2+1 (FNAL/MILC) 2 f + times 1.5 f 0 Okamoto et al, npbps140 (2005) 461 1 B− > π l ν Okamoto PoS (LAT2005) 013 0.5 Mackenzie et al PoS (LAT2005) 207 0 0 5 10 15 20 25 2 /GeV 2 Van de Water LAT2006 q CKM2006 14 Dec 2006 3/14

� n F = 2 + 1 asqtad � Use both m , vl = m , se B → π : HPQCD � NRQCD b quark with 3 2.8 2.6 previous f + and f 0 2.4 new f + 2.2 staggered light quarks � Main errors: new f 0 2 1.8 � Statistics and chiral � Heavy-light current with 1.6 1.4 and m , vl � = m , se with 1.2 1 � 2-loop matching 9% m s / 8 < m , se < m s / 2 0.8 0.6 0.4 0.2 0 relativistic and finite-  0 5 10 15 20 25 2 (GeV 2 ) q corrections (tree-level coefficients), tadpole-improved extrapolation 8% one-loop corrections: J ( 0 , 1 , 2 ) and J ( 0 , 1 , 2 , 3 , 4 ) to 0 k O ( α s Λ /M, α s / ( M ) , α s  Λ ) prd73 (2006) 074502 CKM2006 14 Dec 2006 4/14

� Work with Chiral Extrapolations � Both FNAL-MILC and HPQCD use S χ PT � Extrapolation most convenient at fixed E π � Convert to ƒ + , ƒ 0 for each light mass μ � 〈 π ( p ) | V μ | B ( m B  ) 〉 = 2 m B (  μ ƒ � + p ⊥ ƒ ⊥ ) � Interpolate with some ansatz (BK, BZ, ZE, . . . ) � Convert back to ƒ � , ƒ ⊥ at fixed E π where p ⊥ = p − ( p ·  )  since in B rest frame � Extrapolate at fixed E π � Finally convert to physical ƒ + , ƒ 0 � � 〈 π | V 0 | B 〉 = 〈 π | V k | B 〉 = 2 m B p k ƒ ⊥ 2 m B ƒ � , CKM2006 14 Dec 2006 5/14

Chiral extrapolation Simulated masses Mackenzie et al, PoS (LAT2005) 207 CKM2006 14 Dec 2006 6/14

Chiral extrapolation Mackenzie et al, PoS (LAT2005) 207 CKM2006 14 Dec 2006 6/14

Chiral extrapolation Extrapolate to physical pion mass Mackenzie et al, PoS (LAT2005) 207 CKM2006 14 Dec 2006 6/14

Chiral extrapolation � 2.5 N f =2+1 (FNAL/MILC) 2 f + 1.5 f 0 � Choice of interpolation 1 � T B− > π l ν 0.5 0 0 5 10 15 20 25 2 /GeV 2 q Mackenzie et al, PoS (LAT2005) 207 Okamoto, PoS (LAT2005) 013 wisted BC CKM2006 14 Dec 2006 6/14

� HPQCD and FNAL/MILC use same gauge � Correlations? Commentary � Need confirmation by other groups using same and � Also want checks with same and different heavy configurations different sea quark formulations quark implementations CKM2006 14 Dec 2006 7/14

Quenched vs Unquenched n ƒ Heavy UKQCD 0 clover plb486 (2000) 111 APE 0 clover npb619 (2001) 565 FNAL 0 Fermilab prd64 (2001) 014502 JLQCD 0 NRQCD prd64 (2001) 114505 Shigemitsu et al 0 NRQCD aniso prd66 (2002) 074506 FNAL prelim 2 + 1 Fermilab PoS (LAT2005) 013, 207 HPQCD 2 + 1 NRQCD prd73 (2006) 074502 CKM2006 14 Dec 2006 8/14

Quenched vs Unquenched 3.5 3 2.5 f + , 0 ( q 2 ) 2 1.5 1 0.5 0 5 10 15 20 25 q 2 / GeV 2 CKM2006 14 Dec 2006 9/14

Quenched vs Unquenched 3.5 3 2.5 f + , 0 ( q 2 ) 2 1.5 1 0.5 0 5 10 15 20 25 q 2 / GeV 2 CKM2006 14 Dec 2006 9/14

Quenched vs Unquenched with BaBar 12-bins 0.04 0.04 0.035 0.035 0.03 0.03 P φ f + P φ f + 0.025 0.025 0.02 0.02 0.015 0.015 � 0.2 � 0.1 0 0.1 0.2 � 0.2 � 0.1 0 0.1 0.2 − z ( q 2 , t 0 ) − z ( q 2 , t 0 ) ƒ + ( 0 ) 10 3 | V b | Unquenched HPQCD & FNAL-MILC & LCSR 4 . 01 ( 34 ) 0 . 236 ( 22 ) HPQCD & FNAL-MILC 4 . 16 ( 40 ) 0 . 216 ( 29 ) HPQCD 4 . 42 ( 52 ) 0 . 207 ( 31 ) FNAL-MILC 3 . 79 ( 49 ) 0 . 239 ( 39 ) Quenched LQCD & LCSR 3 . 71 ( 27 ) 0 . 262 ( 21 ) LQCD 3 . 70 ( 28 ) 0 . 265 ( 30 ) CKM2006 14 Dec 2006 10/14

Quenched vs Unquenched with BaBar 12-bins � Changes in | V b | 0.1 0.1 � FNAL-MILC numbers dq 2 / GeV − 2 dq 2 / GeV − 2 0.08 0.08 0.06 0.06 d Γ d Γ Γ Tot 0.04 0.04 Γ Tot 1 1 10 4 10 4 � See also Ball 0.02 0.02 0 5 10 15 20 25 0 5 10 15 20 25 q 2 / GeV 2 q 2 / GeV 2 unqenched & LCSR as quoted by AGRS ր 8% quenched & LCSR prl95 (2005) 071802 unqenched ր 12% quenched hep-ph/0611108 unqenched HPQCD ր 17% unquenched FNAL-MILC CKM2006 14 Dec 2006 11/14

� FNAL/MILC � MILC ensembles extended: ∼ 500 → ∼ 800 configs � new correlation functions computed; smeared B sources � chiral extrapolation � BK → ZE for q 2 interpolation to fixed E π � combined E π , m fit � twisted BC to ensure fixed E π Prospects � discretisation error � use finer lattice-spacing � improve action/operators (Kronfeld-Oktay hep-lat/0610069) � HPQCD � go beyond 1-loop current matching (2-loop pt, high- β � better source/sink smearing � exploit ratio B → π/B → D � mNRQCD to access lower q 2 � parametrisation: BZ → ZE MC) CKM2006 14 Dec 2006 12/14

� ALPHA/ROME2 � HQET with nonperturbative accuracy Prospects � interpolate between HQET and relativistic after taking � Quenched ƒ B s to ∼ 3% accuracy ( hep-lat/0609065 ), n ƒ = 2 continuum limit in progress; form factors to follow CKM2006 14 Dec 2006 13/14

� B → ρ � Quenched results available SPQcdR hep-lat/0209116; � Problem of ρ → ππ in unquenched simulations � B → η Variations � Disconnected contributions � B → ω � ω is narrow: more attractive than ρ � Ignore disconnected contributions (OZI violations small) � B s → K � Needs SFF at ϒ ( 5 S ) UKQCD jhep05, 035 : good match to LCSR at moderate q 2 CKM2006 14 Dec 2006 14/14