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| V b | Exclusive: Form Factors from Lattice QCD Jonathan Flynn University of Southampton CKM2006, Nagoya, 1116 Dec 2006 CKM2006 14 Dec 2006 1/14 Outline B Current Calculations: FNAL-MILC and HPQCD Chiral Extrapolation Quenched

SLIDE 1

|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

SLIDE 2

Outline

B → π Current Calculations: FNAL-MILC and HPQCD Chiral Extrapolation Quenched vs Unquenched Prospects

CKM2006 14 Dec 2006 2/14

SLIDE 3

B → π: FNAL-MILC

nF = 2 + 1 asqtad staggered light

quarks, ∼ 500 cfgs

ms/8 < m < 3ms/4 with

m,vl = m,se

b-quark: tadpole-improved clover

action with Fermilab interpretation

Matching: Zb

Vμ = ρVμ(Z V Zbb V )1/2

Local sources/sinks; four source

times

Main errors: discretisation

∼ 9%

statistical ∼ 8% Results still

preliminary

Okamoto et al, npbps140 (2005) 461 Okamoto PoS (LAT2005) 013 Mackenzie et al PoS (LAT2005) 207 Van de Water LAT2006

5 10 15 20 25

2/GeV 2 0.5 1 1.5 2 2.5

Nf=2+1 (FNAL/MILC)

B−>πlν f+ f0

CKM2006 14 Dec 2006 3/14

SLIDE 4

B → π: HPQCD

nF = 2 + 1 asqtad

staggered light quarks

Use both m,vl = m,se

and m,vl = m,se with ms/8 < m,se < ms/2

NRQCD b quark with

relativistic and finite- corrections (tree-level coefficients), tadpole-improved

Heavy-light current with

ne-loop corrections:

J(0,1,2) and J(0,1,2,3,4)

k

to O(αsΛ/M, αs/(M), αsΛ)

5 10 15 20 25 q

2 (GeV 2)

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 previous f+ and f0 new f+ new f0

Main errors: Statistics and chiral

extrapolation 8%

2-loop matching 9%

prd73 (2006) 074502

CKM2006 14 Dec 2006 4/14

SLIDE 5

Chiral Extrapolations

Work with

〈π(p)|Vμ|B(mB)〉 =

2mB(μƒ + p

μ ⊥ƒ⊥)

where p⊥ = p − (p·) since in B rest frame 〈π|V0|B〉 =

2mBƒ,

〈π|Vk|B〉 =

2mBpkƒ⊥

Both FNAL-MILC and HPQCD use SχPT Extrapolation most convenient at fixed Eπ Convert to ƒ+, ƒ0 for each light mass Interpolate with some ansatz (BK, BZ, ZE, . . . ) Convert back to ƒ, ƒ⊥ at fixed Eπ Extrapolate at fixed Eπ Finally convert to physical ƒ+, ƒ0

CKM2006 14 Dec 2006 5/14

SLIDE 6

Chiral extrapolation

Simulated masses

Mackenzie et al, PoS (LAT2005) 207

CKM2006 14 Dec 2006 6/14

SLIDE 7

Chiral extrapolation

Mackenzie et al, PoS (LAT2005) 207

CKM2006 14 Dec 2006 6/14

SLIDE 8

Chiral extrapolation

Extrapolate to physical pion mass

Mackenzie et al, PoS (LAT2005) 207

CKM2006 14 Dec 2006 6/14

SLIDE 9

Chiral extrapolation

5 10 15 20 25

q

2/GeV 2

0.5 1 1.5 2 2.5

Nf=2+1 (FNAL/MILC)

B−>πlν f+ f0

Mackenzie et al, PoS (LAT2005) 207 Okamoto, PoS (LAT2005) 013

Choice of interpolation T

wisted BC

CKM2006 14 Dec 2006 6/14

SLIDE 10

Commentary

HPQCD and FNAL/MILC use same gauge

configurations

Correlations? Need confirmation by other groups using same and

different sea quark formulations

Also want checks with same and different heavy

quark implementations

CKM2006 14 Dec 2006 7/14

SLIDE 11

Quenched vs Unquenched

nƒ Heavy UKQCD clover

plb486 (2000) 111

APE clover

npb619 (2001) 565

FNAL Fermilab

prd64 (2001) 014502

JLQCD NRQCD

prd64 (2001) 114505

Shigemitsu et al 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

SLIDE 12

Quenched vs Unquenched

5 10 15 20 25 0.5 1 1.5 2 2.5 3 3.5

q2/ GeV2 f +,0(q2)

CKM2006 14 Dec 2006 9/14

SLIDE 13

Quenched vs Unquenched

5 10 15 20 25 0.5 1 1.5 2 2.5 3 3.5

q2/ GeV2 f +,0(q2)

CKM2006 14 Dec 2006 9/14

SLIDE 14

Quenched vs Unquenched with BaBar 12-bins

0.2 0.1 0.1 0.2 0.015 0.02 0.025 0.03 0.035 0.04

−z(q2, t0) Pφ f +

0.2 0.1 0.1 0.2 0.015 0.02 0.025 0.03 0.035 0.04

−z(q2, t0) Pφ f +

103|Vb| ƒ +(0) 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

SLIDE 15

Quenched vs Unquenched with BaBar 12-bins

5 10 15 20 25 0.02 0.04 0.06 0.08 0.1

q2/ GeV2 104

1 ΓTot dΓ dq2/ GeV−2

5 10 15 20 25 0.02 0.04 0.06 0.08 0.1

q2/ GeV2 104

1 ΓTot dΓ dq2/ GeV−2

Changes in |Vb|

unqenched & LCSR quenched & LCSR

ր 8%

unqenched quenched

ր 12%

unqenched HPQCD unquenched FNAL-MILC

ր 17%

FNAL-MILC numbers

as quoted by AGRS

prl95 (2005) 071802

hep-ph/0611108

CKM2006 14 Dec 2006 11/14

SLIDE 16

Prospects

FNAL/MILC MILC ensembles extended: ∼ 500 → ∼ 800 configs new correlation functions computed; smeared B sources chiral extrapolation BK → ZE for q2 interpolation to fixed Eπ combined Eπ, m fit twisted BC to ensure fixed Eπ 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

MC)

better source/sink smearing exploit ratio B → π/B → D mNRQCD to access lower q2 parametrisation: BZ → ZE

CKM2006 14 Dec 2006 12/14

SLIDE 17

Prospects

ALPHA/ROME2 HQET with nonperturbative accuracy interpolate between HQET and relativistic after taking

continuum limit

Quenched ƒBs to ∼ 3% accuracy (hep-lat/0609065), nƒ = 2

in progress; form factors to follow

CKM2006 14 Dec 2006 13/14

SLIDE 18

Variations

B → ρ Quenched results available SPQcdR hep-lat/0209116;

UKQCD jhep05, 035: good match to LCSR at moderate q2

Problem of ρ → ππ in unquenched simulations B → η Disconnected contributions B → ω ω is narrow: more attractive than ρ Ignore disconnected contributions (OZI violations small) Bs → K Needs SFF at ϒ(5S)

CKM2006 14 Dec 2006 14/14