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

Feb 09, 2023 399 likes •703 views

B D ( * ) 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 HFLAV16 introduction hint and puzzle HFLAV16

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SLIDE 1

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

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SLIDE 2

introduction

hint and puzzle

HFLAV’16

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SLIDE 3

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!

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SLIDE 4

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

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SLIDE 5

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)

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SLIDE 6

JLQCD’s study

w/ good chiral symmetry

domain-wall quarks good chiral symmetry

  • simple renormalization
  • no O(a) errors

simulation parameters

  • a-1 ~ 2.5, 3.6, 4.5 GeV
  • Mπ ~ 230, 300, 400, 500 MeV
  • MπL ≥ 4
  • a-1 ~ 4.5 GeV, Mπ ~ 230 MeV: on-going

Fermilab/MILC B→D*ℓν (w≥1)

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SLIDE 7

JLQCD’s study

w/ good chiral symmetry

domain-wall quarks good chiral symmetry

  • simple renormalization
  • no O(a) errors

simulation parameters

  • a-1 ~ 2.5, 3.6, 4.5 GeV
  • Mπ ~ 230, 300, 400, 500 MeV
  • MπL ≥ 4
  • a-1 ~ 4.5 GeV, Mπ ~ 230 MeV: on-going

Fermilab/MILC B→D*ℓν (w≥1)

⇒ preliminary results w/o extrapolations …

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SLIDE 8

JLQCD’s simulation

relativistic lattice QCD

w/ “relativistic” heavy quarks

  • simple renormalization
  • mQ < mb ⇒ need extrapolation

mQ / mc = 1.25, 1.252, … and mQ < 0.8 a-1

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SLIDE 9

JLQCD’s simulation

relativistic lattice QCD

w/ “relativistic” heavy quarks

  • simple renormalization
  • mQ < mb ⇒ need extrapolation

mQ / mc = 1.25, 1.252, … and mQ < 0.8 a-1 ⇔ EFT-based heavy quarks

  • NRQCD, Fermilab, RHQ, …
  • need matching to QCD
  • ften perturbative …
  • directly simulate mb
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SLIDE 10

JLQCD’s simulation

relativistic lattice QCD

w/ “relativistic” heavy quarks

  • simple renormalization
  • mQ < mb ⇒ need extrapolation

mQ / mc = 1.25, 1.252, … and mQ < 0.8 a-1 ⇔ EFT-based heavy quarks

  • NRQCD, Fermilab, RHQ, …
  • need matching to QCD
  • ften perturbative …
  • directly simulate mb

independent studies w/ (very) different systematics

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SLIDE 11

B→D(*)ℓν form factors (FFs)

( ) ( ) ( ) ( ) ( ) ( )

{ }

1 2 2

, 1

A A A

h w D p A B p w v v w v h w h

∗ ∗ µ µ ∗ µ µ

′ ′ ′ ε = ε + ′ − ε +

( ) ( ) ( ) ( ) ( ) ( )

h w h D p V B p v v v v w

µ µ µ + −

′ ′ ′ = + + −

( ) ( ) ( )

,

V

D p V B p i v v h w

∗ ∗µ ρ σ µ µνρσ

′ ′ ′ ′ ε = ε ε

In the SM

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SLIDE 12

ratio method (Hashimoto et al. ’99)

a standard way for precision calculation

( ) ( )

1

(lat) (lat) V A

V h w A D B D B h w

µ µ ∗ ∗

= → D∗ B Vµ A

µ

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SLIDE 13

ratio method (Hashimoto et al. ’99)

a standard way for precision calculation

( ) ( )

1

(lat) (lat) V A

V h w A D B D B h w

µ µ ∗ ∗

= → D∗ B Vµ A

µ

[ ]

†

| , exp , cancel

B B

B O M t − ∆ 

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SLIDE 14

ratio method (Hashimoto et al. ’99)

a standard way for precision calculation

( ) ( )

1

(lat) (lat) V A

V h w A D B D B h w

µ µ ∗ ∗

= → D∗ B Vµ A

µ

[ ]

†

| , exp , cancel

B B

B O M t − ∆  , cancel

A V

Z Z

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SLIDE 15

ratio method (Hashimoto et al. ’99)

a standard way for precision calculation

( ) ( )

1

(lat) (lat) V A

V h w A D B D B h w

µ µ ∗ ∗

= → D∗ B Vµ A

µ

[ ]

†

| , exp , cancel

B B

B O M t − ∆  , cancel

A V

Z Z

 can calculate SM FFs w/o explicit renormalization  pB = 0, |pD(*)|2 = 0, 1, 2, 3, 4 in units of (2π/L)2

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SLIDE 16

B→Dℓν form factors

 mild dependence on a, Mπ, mQ ⇒ reasonably close to physical pt.

larger mQ ⇒ larger h+ [smaller h-] ⇔ L1/2mQ [-L4/2mQ] L1, L4 ≥ 0

 typical accuracy: Δh+ ≤ 1 - 3%, Δh- ~ 40 – 60 %

h w

+ vs

h w

− vs

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SLIDE 17

B→D*ℓν form factors

1 A

h w vs

V

h w vs

 mild a, mQ, Mπ dependences / consistent w/ previous studies  typical accuracy: ΔhA1 ~ 1 - 3%, ΔhV ~ 3 %

( ) ( ) ( )

,

V

D p V B p h w

∗ µ

′ ′ ε ⇒

( ) ( ) ( ) ( )

1

,

A

D p A B p h w

∗ µ

′ ′ ′ ′ ε ⇒ ⊥ p ε

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SLIDE 18

B→D*ℓν form factors

3 A

h w vs

2 A

h w vs

 h+, hA1, hA3, hV (→ξ) ~ O(1), h-, hA2 (→0) ~ 0

 typical accuracy: ΔhA2 ≥ 40 %, ΔhA3 ~ 20 - 30 %

( ) ( ) ( ) ( ) ( )

{ }

1 2 3

, , ,

A A A

D p A B p h w h w h w

∗ µ

′ ′ ε ⇒

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SLIDE 19

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

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SLIDE 20

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

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SLIDE 21

LQCD vs HQET+QCDSR

at zero recoil

NLO HQET + QCDSR Bigi et al. ’17 Bernlochner et al. ‘17

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SLIDE 22

LQCD vs HQET+QCDSR

at zero recoil

NLO HQET + QCDSR Bigi et al. ’17 Bernlochner et al. ‘17

systematically lower / higher for A1/V1, S1/A1 ???

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SLIDE 23

LQCD vs HQET+QCDSR

at non-zero recoils

 HQET A1(w)/V1(w) + V(w)/V(1) dispersive bound ⇒ CLN A1(w)

HQET+QCDSR

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SLIDE 24

LQCD vs HQET+QCDSR

at non-zero recoils

 HQET A1(w)/V1(w) + V(w)/V(1) dispersive bound ⇒ CLN A1(w)  CLN R2 = (rhA2+hA3) / hA1 : noisy at the moment  CLN R1 = hV / hA1

⇒ Bernlochner et al. ’17: analysis of Belle unfolded / tagged data

HQET+QCDSR

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SLIDE 25

BGL vs CLN w/ Belle data

R1 = hV / hA1

Boyd-Grinstein-Lebed (BGL) ⇒ |Vcb| close to inclusive

Bernlochner-Ligeti-Papucci-Robinson ’17 see also talk by Zoltan Ligeti

CLN ⇒ lower than inclusive

Bigi-Gambino-Schacht ’17 Grinstein-Kobach ‘17

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SLIDE 26

BGL vs CLN w/ Belle data

R1 = hV / hA1

Boyd-Grinstein-Lebed (BGL) ⇒ |Vcb| close to inclusive

Bernlochner-Ligeti-Papucci-Robinson ’17 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 mQ’s

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SLIDE 27

BGL vs CLN w/ Belle data

R1 = hV / hA1

 small a, mQ, Mπ dependence  consistent w/ CLN and “BGL” fits  Belle untagged ?

Boyd-Grinstein-Lebed (BGL) ⇒ |Vcb| close to inclusive

Bernlochner-Ligeti-Papucci-Robinson ’17 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 mQ’s

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SLIDE 28

BGL vs CLN w/ Belle data

R1 = hV / hA1

 small a, mQ, Mπ dependence  consistent w/ CLN and “BGL” fits  Belle untagged ?

Boyd-Grinstein-Lebed (BGL) ⇒ |Vcb| close to inclusive

Bernlochner-Ligeti-Papucci-Robinson ’17 see also talk by Zoltan Ligeti

CLN ⇒ lower than inclusive

Bigi-Gambino-Schacht ’17 Grinstein-Kobach ‘17 talk by Paolo Gambino

new data @ a-1~4.5GeV w/ 5 mQ’s

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SLIDE 29

Summary

JLQCD’s calculation of B→D(*)ℓν form factors

 relativistic approach w/ chiral symmetric formulation

⇔ previous studies: very different systematics ⇒ Hashimoto (B→Xcℓν, poster), Colquhoun (B→πℓν, Sat)

 extrapolation to the physical point: yet to be done

mild a, Mπ, mQ dependences ⇔ reasonably controllable

 interplay w/ phenomenology / experiment

  • LQCD prediction of FFs ⇒ |Vcb|, R(D(*))
  • heavy quark scaling ⇔ data w/ different mQ’s
  • FFs beyond the SM ⇒ NP search in the Belle II era