introduction hint and puzzle HFLAV16 introduction hint and puzzle - PowerPoint PPT Presentation

B → D ( * ) ℓν from lattice QCD with domain-wall quarks Takashi Kaneko (KEK, SOKENDAI) for the JLQCD collaboration KEK-FF 2019, Feb 14-16, 2019

introduction hint and puzzle HFLAV’16

introduction hint and puzzle HFLAV’16 realistic lattice studies only with staggered-type light quarks B → Dℓν : Fermilab/MILC’15, HPQCD’15, HPQCD’17 (w ≥ 1) B → D*ℓν : Fermilab/MILC’14, HPQCD’17 (w=1) … and previous talk!

introduction hint and puzzle HFLAV’16 realistic lattice studies only with staggered-type light quarks B → Dℓν : Fermilab/MILC’15, HPQCD’15, HPQCD’17 (w ≥ 1) B → D*ℓν : Fermilab/MILC’14, HPQCD’17 (w=1) … and previous talk! independent calculations are welcome

JLQCD’s study w/ good chiral symmetry domain-wall quarks good chiral symmetry • simple renormalization • no O( a ) errors Fermilab/MILC B →D*ℓν ( w ≥1 )

JLQCD’s study w/ good chiral symmetry domain-wall quarks good chiral symmetry • simple renormalization • no O( a ) errors Fermilab/MILC simulation parameters B →D*ℓν ( w ≥1 ) • a -1 ~ 2.5, 3.6, 4.5 GeV • M π ~ 230, 300, 400, 500 MeV • M π L ≥ 4 • a -1 ~ 4.5 GeV, M π ~ 230 MeV: on - going

JLQCD’s study w/ good chiral symmetry domain-wall quarks good chiral symmetry • simple renormalization • no O( a ) errors Fermilab/MILC simulation parameters B →D*ℓν ( w ≥1 ) • a -1 ~ 2.5, 3.6, 4.5 GeV • M π ~ 230, 300, 400, 500 MeV • M π L ≥ 4 • a -1 ~ 4.5 GeV, M π ~ 230 MeV: on - going ⇒ preliminary results w/o extrapolations …

JLQCD’s simulation relativistic lattice QCD w/ “relativistic” heavy quarks • simple renormalization • m Q < m b ⇒ need extrapolation m Q / m c = 1.25, 1.25 2 , … and m Q < 0.8 a -1

JLQCD’s simulation relativistic lattice QCD w/ “relativistic” heavy quarks • simple renormalization • m Q < m b ⇒ need extrapolation m Q / m c = 1.25, 1.25 2 , … and m Q < 0.8 a -1 ⇔ EFT-based heavy quarks • NRQCD, Fermilab, RHQ, … • need matching to QCD often perturbative … • directly simulate m b

JLQCD’s simulation relativistic lattice QCD w/ “relativistic” heavy quarks • simple renormalization • m Q < m b ⇒ need extrapolation m Q / m c = 1.25, 1.25 2 , … and m Q < 0.8 a -1 ⇔ EFT-based heavy quarks • NRQCD, Fermilab, RHQ, … • need matching to QCD often perturbative … • directly simulate m b independent studies w/ (very) different systematics

B → D ( * ) ℓν form factors (FFs) In the SM ( ) ( ) ( ) ( ) ( ) ( ) ′ ′ ′ = + + − D p V B p v v h w v v h w µ + − µ µ ( ) ( ) ( ) ′ ′ ′ ′ ∗ ∗µ ρ σ ε = ε ε , D p V B p i v v h w µ µνρσ V ( ) ( ) ( ) ( ) ′ ′ ′ ∗ ∗ ε = ε + , 1 D p A B p w h w µ µ A 1 { } ( ) ( ) ′ ∗ − ε + v v h w v h w µ µ A A 2 2

ratio method (Hashimoto et al. ’99) a standard way for precision calculation D ∗ B ∗ ( ) V µ (lat) D V B h w µ = → V ( ) ∗ (lat) h w D A B A µ A 1 µ

ratio method (Hashimoto et al. ’99) a standard way for precision calculation D ∗ B ∗ ( ) V µ (lat) D V B h w µ = → V ( ) ∗ (lat) h w D A B A µ A 1 µ [ ] − ∆ † cancel  | , exp , B O M t B B

ratio method (Hashimoto et al. ’99) a standard way for precision calculation D ∗ B ∗ ( ) V µ (lat) D V B h w µ = → V ( ) ∗ (lat) h w D A B A µ A 1 µ [ ] − ∆ † cancel cancel  | , exp , , B O M t Z Z B B A V

ratio method (Hashimoto et al. ’99) a standard way for precision calculation D ∗ B ∗ ( ) V µ (lat) D V B h w µ = → V ( ) ∗ (lat) h w D A B A µ A 1 µ [ ] − ∆ † cancel cancel  | , exp , , B O M t Z Z B B A V  can calculate SM FFs w/o explicit renormalization  p B = 0 , | p D (*) | 2 = 0, 1, 2, 3, 4 in units of (2π/ L ) 2

B →Dℓν form factors + vs − vs h w h w  mild dependence on a , M π , m Q ⇒ reasonably close to physical pt. larger m Q ⇒ larger h + [smaller h - ] ⇔ L 1 /2 m Q [ - L 4 /2 m Q ] L 1 , L 4 ≥ 0  typical accuracy: Δ h + ≤ 1 - 3%, Δ h - ~ 40 – 60 %

B →D*ℓν form factors vs vs h w h w 1 A V  mild a , m Q , M π dependences / consistent w/ previous studies  typical accuracy: Δ h A 1 ~ 1 - 3%, Δ h V ~ 3 % ( ) ( ) ( ) ( ) ( ) ( ) ( ) ′ ′ ′ ′ ′ ′ ∗ ∗ ε ⇒ ε ⇒ ⊥ ε , , D p V B p h w D p A B p h w p µ µ V A 1

B →D*ℓν form factors vs vs h w h w 2 3 A A  h + , h A 1 , h A 3 , h V ( →ξ ) ~ O (1) , h - , h A 2 ( → 0) ~ 0  typical accuracy: Δ h A 2 ≥ 40 %, Δ h A 3 ~ 20 - 30 % { } ( ) ( ) ( ) ( ) ( ) ′ ′ ∗ ε ⇒ , , , D p A B p h w h w h w µ A A A 1 2 3

LQCD vs HQET+QCDSR Caprini-Lellouch-Neubert (CLN) parametrization of FFs  FFs w/ definite spin - parity quantum numbers  use NLO HQET relations (QCDSR input) ~ small NNLO in ratios

LQCD vs HQET+QCDSR Caprini-Lellouch-Neubert (CLN) parametrization of FFs  FFs w/ definite spin - parity quantum numbers  use NLO HQET relations (QCDSR input) ~ small NNLO in ratios Bigi-Gambino-Schacht ‘17  comparison b/w HQET+QCDSR and LQCD available at that time

LQCD vs HQET+QCDSR at zero recoil NLO HQET + QCDSR Bigi et al. ’17 Bernlochner et al. ‘17

LQCD vs HQET+QCDSR at zero recoil NLO HQET + QCDSR Bigi et al. ’17 Bernlochner et al. ‘17 systematically lower / higher for A 1 / V 1 , S 1 / A 1 ???

LQCD vs HQET+QCDSR at non-zero recoils HQET+QCDSR  HQET A 1 ( w )/ V 1 ( w ) + V ( w )/ V (1) dispersive bound ⇒ CLN A 1 ( w )

LQCD vs HQET+QCDSR at non-zero recoils HQET+QCDSR  HQET A 1 ( w )/ V 1 ( w ) + V ( w )/ V (1) dispersive bound ⇒ CLN A 1 ( w )  CLN R 2 = ( rh A 2 + h A 3 ) / h A 1 : noisy at the moment  CLN R 1 = h V / h A 1 ⇒ Bernlochner et al. ’17: analysis of Belle unfolded / tagged data

BGL vs CLN w/ Belle data R 1 = h V / h A 1 Boyd-Grinstein-Lebed (BGL) Bernlochner-Ligeti-Papucci-Robinson ’17 ⇒ |V cb | close to inclusive see also talk by Zoltan Ligeti CLN ⇒ lower than inclusive Bigi-Gambino-Schacht ’17 Grinstein-Kobach ‘17

BGL vs CLN w/ Belle data R 1 = h V / h A 1 Boyd-Grinstein-Lebed (BGL) Bernlochner-Ligeti-Papucci-Robinson ’17 ⇒ |V cb | close to inclusive see also talk by Zoltan Ligeti CLN ⇒ lower than inclusive Bigi-Gambino-Schacht ’17 Grinstein-Kobach ‘17 new data @ a -1 ~4.5GeV w/ 5 m Q ’s

BGL vs CLN w/ Belle data R 1 = h V / h A 1 Boyd-Grinstein-Lebed (BGL) Bernlochner-Ligeti-Papucci-Robinson ’17 ⇒ |V cb | close to inclusive see also talk by Zoltan Ligeti CLN ⇒ lower than inclusive Bigi-Gambino-Schacht ’17 Grinstein-Kobach ‘17  small a , m Q , M π dependence new data @ a -1 ~4.5GeV w/ 5 m Q ’s  consistent w/ CLN and “BGL” fits  Belle untagged ?

BGL vs CLN w/ Belle data R 1 = h V / h A 1 Boyd-Grinstein-Lebed (BGL) Bernlochner-Ligeti-Papucci-Robinson ’17 ⇒ |V cb | close to inclusive see also talk by Zoltan Ligeti CLN ⇒ lower than inclusive talk by Paolo Gambino Bigi-Gambino-Schacht ’17 Grinstein-Kobach ‘17  small a , m Q , M π dependence new data @ a -1 ~4.5GeV w/ 5 m Q ’s  consistent w/ CLN and “BGL” fits  Belle untagged ?

Summary JLQCD’s calculation of B → D ( * ) ℓν form factors  relativistic approach w/ chiral symmetric formulation ⇔ previous studies: very different systematics ⇒ Hashimoto ( B → X c ℓν , poster), Colquhoun ( B →πℓν , Sat)  extrapolation to the physical point: yet to be done mild a , M π , m Q dependences ⇔ reasonably controllable  interplay w/ phenomenology / experiment LQCD prediction of FFs ⇒ |V cb | , R ( D ( * ) ) • heavy quark scaling ⇔ data w/ different m Q ’s • FFs beyond the SM ⇒ NP search in the Belle II era •