Semi-leptonic form factors for B s K and B s D s Oliver Witzel - - PowerPoint PPT Presentation

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Semi-leptonic form factors for B s K and B s D s Oliver Witzel (RBC-UKQCD collaborations) Lattice 2018, East Lansing, MI, July 27, 2018 RBC- and UKQCD collaborations BNL/RBRC Columbia U U Edinburgh U Southampton

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SLIDE 1

Semi-leptonic form factors for Bs → Kℓν and Bs → Dsℓν

Oliver Witzel (RBC-UKQCD collaborations) Lattice 2018, East Lansing, MI, July 27, 2018

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SLIDE 2

RBC- and UKQCD collaborations

BNL/RBRC Yasumichi Aoki (KEK) Mattia Bruno Taku Izubuchi Yong-Chull Jang Chulwoo Jung Christoph Lehner Meifeng Lin Aaron Meyer Hiroshi Ohki Shigemi Ohta (KEK) Amarjit Soni Columbia U Ziyuan Bai Norman Christ Duo Guo Christopher Kelly Bob Mawhinney Masaaki Tomii Jiqun Tu Bigeng Wang Tianle Wang Evan Wickenden Yidi Zhao U Edinburgh Peter Boyle Guido Cossu Luigi Del Debbio Tadeusz Janowski Richard Kenway Julia Kettle Fionn O’haigan Brian Pendleton Antonin Portelli Tobias Tsang Azusa Yamaguchi U Southampton Jonathan Flynn Vera G¨ ulpers James Harrison Andreas J¨ uttner James Richings Chris Sachrajda Stony Brook University Jun-Sik Yoo Sergey Syritsyn (RBRC) U Connecticut Tom Blum Dan Hoying (BNL) Luchang Jin (RBRC) Cheng Tu U Colorado Boulder Oliver Witzel KEK Julien Frison U Liverpool Nicolas Garron MIT David Murphy Peking U Xu Feng York U (Toronto) Renwick Hudspith

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SLIDE 3

RBC- and UKQCD collaborations

BNL/RBRC Yasumichi Aoki (KEK) Mattia Bruno Taku Izubuchi Yong-Chull Jang Chulwoo Jung Christoph Lehner Meifeng Lin Aaron Meyer Hiroshi Ohki Shigemi Ohta (KEK) Amarjit Soni Columbia U Ziyuan Bai Norman Christ Duo Guo Christopher Kelly Bob Mawhinney Masaaki Tomii Jiqun Tu Bigeng Wang Tianle Wang Evan Wickenden Yidi Zhao U Edinburgh Peter Boyle Guido Cossu Luigi Del Debbio Tadeusz Janowski Richard Kenway Julia Kettle Fionn O’haigan Brian Pendleton Antonin Portelli Tobias Tsang Azusa Yamaguchi U Southampton Jonathan Flynn Vera G¨ ulpers James Harrison Andreas J¨ uttner James Richings Chris Sachrajda Stony Brook University Jun-Sik Yoo Sergey Syritsyn (RBRC) U Connecticut Tom Blum Dan Hoying (BNL) Luchang Jin (RBRC) Cheng Tu U Colorado Boulder Oliver Witzel KEK Julien Frison U Liverpool Nicolas Garron MIT David Murphy Peking U Xu Feng York U (Toronto) Renwick Hudspith

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SLIDE 4

introduction

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SLIDE 5

introduction Bs → Kℓν Bs → Ds ℓν conclusion

Why Bs meson decays?

γ γ α α

d

m ∆

K

ε

K

ε

s

m ∆ &

d

m ∆

SL ub

V

ν τ ub

V

b

Λ ub

V

β sin 2

(excl. at CL > 0.95) < 0 β

  • sol. w/ cos 2

excluded at CL > 0.95

α β γ

ρ

  • 1.0
  • 0.5

0.0 0.5 1.0 1.5 2.0

η

  • 1.5
  • 1.0
  • 0.5

0.0 0.5 1.0 1.5

excluded area has CL > 0.95 ICHEP 16

CKM

f i t t e r

[http://ckmfitter.in2p3.fr] ◮ Alternative, tree-level determination of |Vcb|

and |Vub| from Bs → Dsℓν and Bs → Kℓν

→ Commonly used B → πℓν and B → D(∗)ℓν → Long standing 2 − 3σ discrepancy between

exclusive (B → πℓν) and inclusive (B → Xuℓν)

→ B → τν has larger error → Alternative, exclusive (Λb → pℓν) determination [Detmold, Lehner, Meinel, PRD92 (2015) 034503]

3 / 18

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SLIDE 6

introduction Bs → Kℓν Bs → Ds ℓν conclusion

Why Bs meson decays?

R(D)

0.2 0.3 0.4 0.5 0.6

R(D*)

0.2 0.25 0.3 0.35 0.4 0.45 0.5

BaBar, PRL109,101802(2012) Belle, PRD92,072014(2015) LHCb, PRL115,111803(2015) Belle, PRD94,072007(2016) Belle, PRL118,211801(2017) LHCb, FPCP2017 Average SM Predictions

= 1.0 contours

2

χ ∆

R(D)=0.300(8) HPQCD (2015) R(D)=0.299(11) FNAL/MILC (2015) R(D*)=0.252(3) S. Fajfer et al. (2012)

) = 71.6%

2

χ P( σ 4 σ 2

HFLAV

FPCP 2017

[HFLAV] ◮ Alternative tests of lepton flavor violations → Determine e.g. RD(∗)

s

from Bs decays to compare with RD(∗) from B decays Rτ/µ

D(∗) ≡ BF(B → D(∗)τντ)

BF(B → D(∗)µνµ)

◮ Nonperturbative lattice calculation favor Bs over B decays (higher precision) ◮ Only the spectator quark differs: RD(∗)

s

may be a good proxy for RD(∗)

3 / 18

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SLIDE 7

introduction Bs → Kℓν Bs → Ds ℓν conclusion

Why Bs meson decays?

R(D)

0.2 0.3 0.4 0.5 0.6

R(D*)

0.2 0.25 0.3 0.35 0.4 0.45 0.5

BaBar, PRL109,101802(2012) Belle, PRD92,072014(2015) LHCb, PRL115,111803(2015) Belle, PRD94,072007(2016) Belle, PRL118,211801(2017) LHCb, FPCP2017 Average SM Predictions

= 1.0 contours

2

χ ∆

R(D)=0.300(8) HPQCD (2015) R(D)=0.299(11) FNAL/MILC (2015) R(D*)=0.252(3) S. Fajfer et al. (2012)

) = 71.6%

2

χ P( σ 4 σ 2

HFLAV

FPCP 2017

[HFLAV] ◮ Alternative tests of lepton flavor violations → Determine e.g. RD(∗)

s

from Bs decays to compare with RD(∗) from B decays Rτ/µ

D(∗) ≡ BF(B → D(∗)τντ)

BF(B → D(∗)µνµ)

◮ Nonperturbative lattice calculation favor Bs over B decays (higher precision) ◮ Only the spectator quark differs: RD(∗)

s

may be a good proxy for RD(∗)

0.2 0.3 0.4 0.5 0.6

R(D)

0.2 0.25 0.3 0.35 0.4 0.45 0.5

R(D*)

BaBar, PRL109,101802(2012) Belle, PRD92,072014(2015) LHCb, PRL115,111803(2015) Belle, PRD94,072007(2016) Belle, PRL118,211801(2017) LHCb, PRL120,171802(2018) Average Average of SM predictions

= 1.0 contours

2

χ ∆

0.003 ± R(D) = 0.299 0.005 ± R(D*) = 0.258

) = 74%

2

χ P( σ 4 σ 2

HFLAV

Summer 2018

◮ HFLAV updated SM prediction, RD(∗):

averaging [Bigi, Gambino PRD94(2016)094008]

[Bernlochner, Ligeti, Papucci, Robinson PRD95(2017)11500] [Bigi, Gambino, Schacht JHEP11(2017)061][Jaiswal, Nandi, Patra JHEP12(2017)060]

3 / 18

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SLIDE 8

introduction Bs → Kℓν Bs → Ds ℓν conclusion

|Vub| from exclusive semileptonic Bs → Kℓν decay

Bs K W ℓ ν

  • q2 = M2

Bs + M2 K − 2MBsEK

s u b

◮ Conventionally parametrized by (neglecting term ∝ m2 ℓf 2 0 )

dΓ(Bs→Kℓν) dq2

=

G 2

F

192π3M3

Bs

  • M2

Bs + M2 K − q22− 4M2 BsM2 K

3/2 ×|f+(q2)|

2×|Vub|2

experiment known nonperturbative input CKM

4 / 18

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SLIDE 9

introduction Bs → Kℓν Bs → Ds ℓν conclusion

Nonperturbative input

◮ Parametrizes interactions due to the (nonperturbative) strong force ◮ Use operator product expansion (OPE) to identify short distance contributions ◮ Calculate the flavor changing currents as point-like operators using lattice QCD

⇒ Nonperturbative calculation: lattice QCD

→ Additional challenge mb = 4.18GeV ∼ 1000 × md mc = 1.28GeV ∼ 270 × md

5 / 18

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SLIDE 10

introduction Bs → Kℓν Bs → Ds ℓν conclusion

Set-up

◮ RBC-UKQCD’s 2+1 flavor domain-wall fermion and Iwasaki gauge action ensembles → Three lattice spacings a ∼ 0.11 fm, 0.08 fm, 0.07 fm; one ensemble with physical pions [PRD 78 (2008) 114509][PRD 83 (2011) 074508][PRD 93 (2016) 074505][JHEP 1712 (2017) 008] ◮ Unitary and partially quenched domain-wall up/down quarks [Kaplan PLB 288 (1992) 342], [Shamir NPB 406 (1993) 90] ◮ Domain-wall strange quarks at/near the physical value ◮ Charm: M¨

  • bius domain-wall fermions optimized for heavy quarks [Boyle et al. JHEP 1604 (2016) 037]

→ Simulate 3 or 2 charm-like masses then extrapolate/interpolate ◮ Effective relativistic heavy quark (RHQ) action for bottom quarks [Christ et al. PRD 76 (2007) 074505], [Lin and Christ PRD 76 (2007) 074506] → Builds upon Fermilab approach [El-Khadra et al. PRD 55 (1997) 3933] → Allows to tune the three parameters (m0a, cP, ζ) nonperturbatively [PRD 86 (2012) 116003] → Smooth continuum limit; heavy quark treated to all orders in (mba)n

6 / 18

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SLIDE 11

Bs → Kℓν

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SLIDE 12

introduction Bs → Kℓν Bs → Ds ℓν conclusion

Bs → Kℓν form factors

tVµ tsink b q l t0

t u s

◮ Parametrize the hadronic matrix element for the flavor changing vector current V µ

in terms of the form factors f+(q2) and f0(q2)

K|V µ|Bs = f+(q2)

  • pµ

Bs + pµ K − M2

Bs −M2 K

q2

qµ + f0(q2)

M2

Bs −M2 K

q2

qµ

◮ Calculate 3-point function by → Inserting a quark source for a “light” propagator at t0 → Allow it to propagate to tsink, turn it into a sequential source for a b quark → Use another “light” quark propagating from t0 and contract both at t

8 / 18

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SLIDE 13

introduction Bs → Kℓν Bs → Ds ℓν conclusion

Determining Bs → Kℓν form factors f+ and f0 on the lattice

◮ Updating calculation [PRD 91 (2015) 074510] with new values for a−1 and RHQ parameters ◮ New analysis directly fitting form factors and accounting for excited state contributions ◮ On the lattice we prefer using the Bs-meson rest frame and compute

f(EK) = K|V 0|Bs/

  • 2MBs

and f⊥(EK)pi

K = K|V i|Bs/

  • 2MBs

◮ Both are related by

f0(q2) = √

2MBs M2

Bs −M2 K

  • (MBs − EK)f(EK) + (E 2

K − M2 K)f⊥(EK)

  • f+(q2) =

1

√

2MBs

  • f(EK) + (MBs − EK)f⊥(EK)
  • 9 / 18
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SLIDE 14

introduction Bs → Kℓν Bs → Ds ℓν conclusion

Chiral-continuum extrapolation using SU(2) hard-kaon χPT

0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 f BsK q MBs

PRELIMINARY

C1 C2 M1 M2 M3 F1 fit p = 26% fit p||= 88%

0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045

E 2

K /M 2 Bs

0.3 0.4 0.5 0.6 0.7 0.8 f

BsK ||

/

q

MBs

PRELIMINARY

f⊥(MK, EK, a2) =

1 EK +∆c(1) ⊥

×

  • 1 +

δf⊥ (4πf )2 + c(2) ⊥ M2

K

Λ2 + c(3) ⊥ EK Λ + c(4) ⊥ E2

K

Λ2 + c(5) ⊥ a2 Λ2a4

32

  • f(MK, EK, a2) =

1 EK +∆c(1)

  • ×
  • 1 +

δf (4πf )2 + c(2)

  • M2

K

Λ2 + c(3)

  • EK

Λ + c(4)

  • E2

K

Λ2 + c(5)

  • a2

Λ2a4

32

  • with δf non-analytic logs of the kaon mass

and hard-kaon limit is taken by MK/EK → 0

◮ Error budget not yet released for presentation

10 / 18

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SLIDE 15

introduction Bs → Kℓν Bs → Ds ℓν conclusion

Kinematical extrapolation (z-expansion)

◮ Map q2 to z with minimized magnitude in the semileptonic region: |z| ≤ 0.146

z(q2, t0) = √

1−q2/t+−√ 1−t0/t+

√

1−q2/t++√ 1−t0/t+

with t± = (MB ± Mπ)2 t0 ≡ topt = (MB + Mπ)(√MB − √Mπ)2

[Boyd, Grinstein, Lebed, PRL 74 (1995) 4603] [Bourrely, Caprini, Lellouch, PRD 79 (2009) 013008]

0.1 0.0 0.1 z 0.0 0.1 0.2 0.3 0.4 0.5 0.6 (1−q2 /M 2

+/0)f +/0

P R E L I M I N A R Y

z-fit, K =2 z-fit, K =3

0.2 0.1 0.0 0.1 z 0.0 0.1 0.2 0.3 0.4 0.5 0.6 (1−q2 /M 2

+/0)f +/0

P R E L I M I N A R Y

z-fit, K =3, q2=0-constraint

◮ Express f+ as convergent power series ◮ f0 is analytic, except for B∗ pole ◮ BCL with poles M+ = B∗ = 5.33 GeV

and M0 = 5.63 GeV

◮ Exploit kinematic constraint f+ = f0 at q2 = 0 → Include HQ power counting to constrain

size of f+ coefficients

  • vs. z

11 / 18

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SLIDE 16

introduction Bs → Kℓν Bs → Ds ℓν conclusion

Kinematical extrapolation (z-expansion)

◮ Map q2 to z with minimized magnitude in the semileptonic region: |z| ≤ 0.146

z(q2, t0) = √

1−q2/t+−√ 1−t0/t+

√

1−q2/t++√ 1−t0/t+

with t± = (MB ± Mπ)2 t0 ≡ topt = (MB + Mπ)(√MB − √Mπ)2

[Boyd, Grinstein, Lebed, PRL 74 (1995) 4603] [Bourrely, Caprini, Lellouch, PRD 79 (2009) 013008]

5 10 15 20 25 q2 [GeV2 ] 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 f

Bs→K +/0

P R E L I M I N A R Y

z-fit, K =2 z-fit, K =3

5 10 15 20 25 q2 [GeV2 ] 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 f

Bs→K +/0

P R E L I M I N A R Y

z-fit, K =3, q2=0-constraint

◮ Allows to compare shape of form factors → Obtained by other lattice calculations → Predicted by QCD sum rules and alike ◮ Combination with experiment leads to the

  • verall normalization: |Vub|
  • vs. q2

11 / 18

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SLIDE 17

Bs → Dsℓν

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SLIDE 18

introduction Bs → Kℓν Bs → Ds ℓν conclusion

|Vcb| from exclusive semileptonic Bs → Dsℓν decay

Bs Ds W ℓ ν

  • q2 = M2

Bs + M2 Ds − 2MBsEDs

s c b

◮ Conventionally parametrized by (neglecting term ∝ m2 ℓf 2 0 )

dΓ(Bs→Dsℓν) dq2

=

G 2

F

192π3M3

Bs

  • M2

Bs + M2 Ds − q22− 4M2 BsM2 Ds

3/2 ×|f+(q2)|

2×|Vcb|2

experiment known nonperturbative input CKM

13 / 18

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SLIDE 19

introduction Bs → Kℓν Bs → Ds ℓν conclusion

Charm extra-/interpolation for Bs → Dsℓν

| p |2 / ( 2 π / L )2 1 2 3 4 amDs 0.85 0.90 0.95 1.00 1.05 1.10 1.15 f

B

s

→D

s

( q

2

) 0.70 0.75 0.80 |p|2 /(2π/L)2 1 2 3 4 a m

D

s

0.85 0.90 0.95 1.00 1.05 1.10 1.15 f

Bs → Ds +

( q

2

) 1.1 1.2 1.3 | p |2 / ( 2 π / L )2 1 2 3 4 amDs 0.85 0.90 0.95 1.00 1.05 1.10 1.15 f

B

s

→D

s

( q

2

) 0.70 0.75 0.80 |p|2 /(2π/L)2 1 2 3 4 a m

D

s

0.85 0.90 0.95 1.00 1.05 1.10 1.15 f

Bs → Ds +

( q

2

) 1.1 1.2 1.3

preliminary preliminary

◮ Simulate charm quarks using MDWF → Similar action as for u, d, s quarks → “Fully” relativistic setup simplifies renormalization → Established by calculating fD(s) [Boyle et al. JHEP 1712 (2017) 008] ◮ Coarse ensembles → Extrapolate three charm-like masses ◮ Medium and fine ensembles → Interpolate between two charm-like masses ◮ Analysis of data at third, finer lattice spacing

will help to better estimate uncertainty

14 / 18

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SLIDE 20

introduction Bs → Kℓν Bs → Ds ℓν conclusion

Chiral-continuum extrapolation

8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0

q2 [GeV2 ]

0.7 0.8 0.9 1.0 1.1 1.2 1.3

f Bs→Ds (q2) f Bs→Ds

+

(q2)

PRELIMINARY

C1 C2 M1 M2 M3 F1 Pade (0,1) (single pole) for global fit, p||= 40%, p = 18% Pade (0,2), (1,2), (2,2), (1,3) pole model independent from cl. and m 2

π

◮ No light valence quarks, no need for χPT ◮ Account for dependence on → charm quark mass → lattice spacing → light sea-quark mass

f (q, a) = α0 + α1MDs + α2a2 + α3M2

π

1 + α4q2/M2

Bs

15 / 18

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SLIDE 21

introduction Bs → Kℓν Bs → Ds ℓν conclusion

z-expansion

0.02 0.00 0.02 z 0.60 0.65 0.70 0.75 0.80 0.85 0.90 (1−q2 /M 2

+/0)f +/0

P R E L I M I N A R Y

z-fit, K =2 z-fit, K =3

0.02 0.00 0.02 z 0.60 0.65 0.70 0.75 0.80 0.85 0.90 (1−q2 /M 2

+/0)f +/0

P R E L I M I N A R Y

z-fit, K =3, q2=0-constraint

2 4 6 8 10 12 q2 [GeV2 ] 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 f

Bs→Ds +/0

P R E L I M I N A R Y

z-fit, K =2 z-fit, K =3

2 4 6 8 10 12 q2 [GeV2 ] 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 f

Bs→Ds +/0

P R E L I M I N A R Y

z-fit, K =3, q2=0-constraint

◮ BCL with poles M+ = B∗ c = 6.33 GeV and M0 = 6.42 GeV

16 / 18

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SLIDE 22

conclusion

slide-23
SLIDE 23

introduction Bs → Kℓν Bs → Ds ℓν conclusion

Conclusion

◮ In the final stages to complete Bs → Kℓν and Bs → Dsℓν form factor calculation → As usual, carefully estimating all systematic uncertainties is tedious → Can even require additional simulations ◮ Our lattice calculation also includes → B → πℓν, B → πℓ+ℓ− → B → K ∗ℓ+ℓ− → B → D(∗)ℓν → Bs → K ∗ℓ+ℓ− → Bs → D∗ s ℓν → Bs → φℓ+ℓ− → . . .

17 / 18

slide-24
SLIDE 24

introduction Bs → Kℓν Bs → Ds ℓν conclusion

Resources and Acknowledgments

USQCD: Ds, Bc, and pi0 cluster (Fermilab), qcd12s cluster (Jlab) RBC qcdcl (RIKEN) and cuth (Columbia U) UK: ARCHER, Cirrus (EPCC) and DiRAC (UKQCD)

18 / 18

slide-25
SLIDE 25

appendix

slide-26
SLIDE 26

2+1 Flavor Domain-Wall Iwasaki ensembles

L a−1(GeV) aml ams Mπ(MeV) # configs. #sources C1 24 1.784 0.005 0.040 338 1636 1

[PRD 78 (2008) 114509]

C2 24 1.784 0.010 0.040 434 1419 1

[PRD 78 (2008) 114509]

M1 32 2.383 0.004 0.030 301 628 2

[PRD 83 (2011) 074508]

M2 32 2.383 0.006 0.030 362 889 2

[PRD 83 (2011) 074508]

M3 32 2.383 0.008 0.030 411 544 2

[PRD 83 (2011) 074508]

C0 48 1.730 0.00078 0.0362 139 40 81/1 ⋆

[PRD 93 (2016) 074505]

M0 64 2.359 0.000678 0.02661 139 — —

[PRD 93 (2016) 074505]

F1 48 2.774 0.002144 0.02144 234 70 + 28 24

[JHEP 1712 (2017) 008]

⋆ All mode averaging: 81 “sloppy” and 1 “exact” solve [Blum et al. PRD 88 (2012) 094503]

◮ Lattice spacing determined from combined analysis [Blum et al. PRD 93 (2016) 074505] ◮ a: ∼ 0.11 fm, ∼ 0.08 fm, ∼ 0.07 fm