Neutral B-meson mixing in and beyond the SM with 2+1 ... · Aida X. El-Khadra (UIUC) Chris Bouchard (OSU) and Elizabeth Freeland (Art Institute of Chicago) Fermilab Lattice and MILC

Neutral B-meson mixing in and beyond the SM with 2+1 flavor lattice QCD

presented by Aida X. El-Khadra (UIUC)

Chris Bouchard (OSU) and Elizabeth Freeland (Art Institute of Chicago)

Fermilab Lattice and MILC Collaborations

Lattice 2014, New York City23-28 June 2014

Wednesday, June 25, 14

A. El-Khadra Lattice 2014, NYC, 25 June 2014

Outline

Motivation and Introduction

Lattice set-up

Correlators

Chiral-continuum extrapolation

Complete but preliminary systematic error budget

Conclusions

2Wednesday, June 25, 14



3

Laiho, Lunghi & Van de Water latticeaverages.org

Lattice 2013

Laiho, Lunghi & Van de Water (Phys.Rev.D81:034503,2010)

uncertainty onξdominates 𝛥Ms/𝛥Md band


http://arXiv.org/abs/0910.2928






4

B0

b

W

u, c, t

W

u, c, t

B0

d

d b

B0

b

B0

d

d b

Standard Model

also:

⇠ ⌘ fBs

pBBs

fBd

pBBd

�Ms�Md

= mBsmBd

⇥��VtsVtd

��2⇥ ⇠2 with

SM:

HFAG, PDG 2014 averages:

��q =

hG1 h ¯B0

q |O1|B0q i+G3 h ¯B0

q |O3|B0q iicos�q +O(1/mb)

�Mq = (known)⇥ |V ⇤tqVtb|2 ⇥ h ¯B0

q |O1|B0q i

Oi

�Md = (0.510± 0.003) ps�1

�Ms = (17.761± 0.022) ps�1 ��s/�s = 0.138± 0.012

��d/�d = 0.001± 0.010(0.6%)(0.1%) (8.7%)




5

B0

b

W

u, c, t

W

u, c, t

B0

d

d b

B0

b

B0

d

d b

Standard Model

Oi

In general :

O1 = (b��µLq�) (b⇥�µLq

⇥)

O2 = (b�Lq�) (b⇥Lq⇥)

O3 = (b�Lq⇥) (b⇥Lq�)

O4 = (b�Lq�) (b⇥Rq⇥)

O5 = (b�Lq⇥) (b⇥Rq�)

SM: BSM:

He↵ =5X

i=1

ci(µ)Oi(µ)

hOii ⌘ hB0q |Oi|B0

q i(µ) = ei m2Bq

f2Bq

B(i)Bq

(µ)

We calculate all five matrix elements.



Lattice set-up

6

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14a (fm)

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

m/se

a (G

eV)

• 14 MILC asqtad ensembles 4 lattice spacings ~ 4 sea quark masses per lattice spacing ~ 600 - 2000 configurations

× 4 time-sources per ensemble

• asqtad light valence quarks ~ 7 light valence masses per ensemble

• Fermilab b quarks

• O(a) improved four-quark operators



Lattice set-up

7

A. Bazavov et al (FNAL/MILC, Phys. Rev. D 86 (2012) 034503, arXiv:1205.7013) - “old data”

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14a (fm)

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

m/se

a (GeV

)

• 6 MILC asqtad ensembles 2 lattice spacings 4(2) sea quark masses per lattice spacing ~ 600 configurations




• O(a) improved four-quark operators



Lattice set-up

8

• 6+3 (partial) MILC asqtad ensembles 3 lattice spacings ~4 sea quark masses per lattice spacing ~ 600 - 2000 configurations




• O(a) improved 4-quark operators0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

a (fm)0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

m/se

a (GeV

)

C. Bouchard et al. (arXiv:1112.5642, Lattice 2011 proceedings)



Correlators

9

0

B0qB0

q

Oi

t1t2

with 1S smearing of source/sinkC2(t) =X

x

h�B(t,x)�†B(0, 0)i

C3,i(t1, t2) =X

x,y

h�B(t2,y)Oi(0, 0)�†B(t1,x)i



Correlators

10

0

B0qB0

q

Oi

t1t2

Fit to:

C2(t) =Nstates�1X

m=0

|Zm|2 (�1)(t+1)m⇣e�Emt + e�Em(T�t)

⌘

C3,i(t1, t2) =Nstates�1X

m,n=0

ZmZnhOimn(�1)(t1+1)m+(t2+1)ne�Emt1e�Ent2

• simultaneous fits using Bayesian constraints for excited states

• Nstates = 2 + 2

• tmin, tmax constant in physical units

• 3pt max t1,2 < T/2



Renormalization and matching

11

Operator renormalization at one-loop in perturbation theory

•

• calculated in mean-field improved lattice perturbation theory

• -NDR scheme

•

• µ = mb

↵s = ↵V (2/a)

⇣ij = ⇣ij(µ,mb, amb) = Zcont

ij � Z lat

ij

MS

hOiicont(µ) = (1 + ↵s⇣ii)hOiilat(µ) + ↵s⇣ijhOjilat(µ) +O(↵2

s)



Heavy-quark discretization errors

12

• analyze cut-off effects with (continuum) HQET

• discretization errors arise due to mismatch of coefficients of the EFT descriptions of lattice and continuum matrix elements

• discretization errors take the form

• with tree-level tadpole O(a) improvement we have errors and

⇠ ad�4fk(am0)hOki ⇠ fk(am0)(a⇤)d�4

O(a⇤)2O(↵sa⇤)




13

SU(3) heavy-meson partially-quenched rooted staggered 𝜒PT

NLO chiral logs + taste-splittings + “wrong-spin” corrections + analytic terms (up to N3LO) + B-meson hyperfine and flavor splittings + HQ discretization terms

Schematically

C. Bernard (Phys.Rev. D87 (2013) 114503, arXiv: 1303.0435)

no new LECs with simultaneous fits to the operators that mix at NLO

and [hO1i, hO2i, hO3i] [hO4i, hO5i]

hOq1i = �1

✓1 +

Wqb +Wbq

2+ Tq +Qq + T (a)

q + Q(a)q

◆+ (2�2 + 2�3)T (b)

q + (2�02 + 2�0

3)Q(b)q

NLO chiral logs + taste-splittings

wrong spin terms

LECs for hO1i, hO2i, hO3i

w.s. w.s.

+ analytic terms




14

0 0.05 0.1 0.15r1 mq

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

r 13 <O

1>

0 0.05 0.1 0.15r1 mq

-1.3-1.2-1.1

-1-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2

r 13 <O

2>

0 0.05 0.1 0.15r1 mq

0

0.1

0.2

0.3

0.4

r 13 <O

3>

0 0.05 0.1 0.15r1 mq

0.70.80.9

11.11.21.31.41.51.61.71.81.9

22.12.22.32.42.5

r 13 <O

4>

0 0.05 0.1 0.15r1 mq

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

r 13 <O

5>



Preliminary systematic error budget

15

0.4

0.5

0.6

0.7

0.8

0.9

1

r 13 <O

1>

base

NLO lt m

NLONNLO se

aN3L

OR HQ

/2no

HQ

no sp

lit f Kno

coars

eno

0.4 m

s

0.3

0.4

0.5

0.6

0.7

0.8

r 13 <O

5>

base

NLO lt m

NLONNLO se

aN3L

OR HQ

/2no

HQ

no sp

lit f Kno

coars

eno

0.4 m

s

• test stability of chiral-continuum extrapolation under changes of fit function, data included, or inputs:



source 2012 2014 2011 2014 2011 2014

comb. stat. 𝜒PT- cont.

3.7w.s. 3.2 1.5 7

1558

3-114.3-16

5-77-14

HQ disc. 0.3 0.3 4 included 4 included

inputs 0.7 included 5.1 included 5.1 included

PT 0.5 0.5 8 6.4 8 6.4

FV 0.5 0.5 1 1 1 1

total 5 1.7 1218

810

10-1511-19

8-1010-15

f2Bq

B(i)Bq

f2Bq

B(1)Bq

Bs

Bd

Bs

Bd

⇠

Preliminary systematic error budget

16Wednesday, June 25, 14


We present results for B mixing parameters on a large set of MILC asqtad ensembles

systematic error analysis is still preliminary

simultaneous chiral-continuum fits of and to account for the wrong spin terms

combine this analysis with fB , fBs to extract bag parameters (see E. Neil talk, parallel session 6G)

Conclusions

17

[hO1i, hO2i, hO3i] [hO4i, hO5i]


Documents

Neutral B-meson mixing in and beyond the SM with 2+1 ... · Aida X. El-Khadra (UIUC) Chris Bouchard (OSU) and Elizabeth Freeland (Art Institute of Chicago) Fermilab Lattice and MILC