neutral b-meson mixing in and beyond the sm with 2+1 ... · aida x. el-khadra (uiuc) chris bouchard...
TRANSCRIPT
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
A. El-Khadra Lattice 2014, NYC, 25 June 2014
Motivation and Introduction
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
Wednesday, June 25, 14
A. El-Khadra Lattice 2014, NYC, 25 June 2014
Motivation and Introduction
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%)
Wednesday, June 25, 14
A. El-Khadra Lattice 2014, NYC, 25 June 2014
Motivation and Introduction
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.
Wednesday, June 25, 14
A. El-Khadra Lattice 2014, NYC, 25 June 2014
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
Wednesday, June 25, 14
A. El-Khadra Lattice 2014, NYC, 25 June 2014
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
× 4 time-sources per ensemble
• asqtad light valence quarks ~ 7 light valence masses per ensemble
• Fermilab b quarks
• O(a) improved four-quark operators
Wednesday, June 25, 14
A. El-Khadra Lattice 2014, NYC, 25 June 2014
Lattice set-up
8
• 6+3 (partial) MILC asqtad ensembles 3 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 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)
Wednesday, June 25, 14
A. El-Khadra Lattice 2014, NYC, 25 June 2014
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
Wednesday, June 25, 14
A. El-Khadra Lattice 2014, NYC, 25 June 2014
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
Wednesday, June 25, 14
A. El-Khadra Lattice 2014, NYC, 25 June 2014
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)
Wednesday, June 25, 14
A. El-Khadra Lattice 2014, NYC, 25 June 2014
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⇤)
Wednesday, June 25, 14
A. El-Khadra Lattice 2014, NYC, 25 June 2014
Chiral-continuum extrapolation
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
Wednesday, June 25, 14
A. El-Khadra Lattice 2014, NYC, 25 June 2014
Chiral-continuum extrapolation
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>
Wednesday, June 25, 14
A. El-Khadra Lattice 2014, NYC, 25 June 2014
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:
Wednesday, June 25, 14
A. El-Khadra Lattice 2014, NYC, 25 June 2014
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
A. El-Khadra Lattice 2014, NYC, 25 June 2014
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]
Wednesday, June 25, 14