P. Urquijo*, L. Pesantez, L. Spiller The University of Melbourne

Transcription

Global analysis
of CKM data
P. Urquijo*, L. Pesantez, L. Spiller The University of Melbourne *ARC Future Fellow, CKMFitter Group & Heavy Flavour Averaging Group AIP Congress ANU, December 2014
C41,1-131 (2005). 4 free parameters, A, ,
and
ameterisation
with
Jarlskog
like
phase
invariants
as
in
Charles
et
al.
EPJ
V
V
CP Violation & the Unitarity Triangle , A
and
i
and
4 free parameters, A, ,
taken as:
V
V
V
V
us
2
ud
cb
2
2
2
us
2
ud
us
Vus Vubnuclea
|Vud
The SM describes the mixing of quarks of is* measured from |Vud| andV
us| in superallowed
Vcb
A is
determined from |Vcb| and .
V
V
2
ud
ub
VCKM fromVangles
Vcssides measureme
Vcb
, Adifferent generations through and the i weak force.i* is, with
to be determined
and
cd
2
2
Vcd Vcb
Vud
Vus
V
V
V
Bd Unitarity Triangle (UT) td
ts
tb
Generations, 1 Phase: single source -decays and (semi)leptonic
( , )
|Vud| 3 and
|Vus| in superallowed
nuclear
K decays, re
V V
CPV in . the SM. m |Vcbof | and
R
V V
R
V V
V
V
ined from angles and sides measurements of the Bd unitarity triangle.
u
Wolfenstein parameterisation: Phase invariant, conserving CKM matrix ngle unitarity (UT) at any order in λ. *
ud ub
*
cd cb
td
t
cd
(0,0)
*
tb
*
cb
(1,0)
Angles
) 4 free parameters relating the 9 CKM elements (magnitude & phase)
*
*
V
V
V
V
td tb
cd cb
VtdVtb*
arg
,
arg
,
*
*
Rt
V
V
V
V
*
ud
ub
td
tb ⇤
2
2
V
V
V
V
|Vus
|Vcb |
cd| cb
ud ub
2
2 4
⌘
|Vud
|2
+ |Vus
|2
A
AIP 2014, Global CKM Analysis
⌘
|Vud
|2
*
+ |Vus ud ub
*
cd cb
arg
V V
V V
|2
Phillip URQUIJO
,
⇢¯ + i¯
⌘=
arg
s
2
*⇤
V
V
Vcd
V
cb
cs cb
Vts Vtb*
ecays worth combining
Important Decays in the Combination
A handle on these parameters
d ! u: Nuclear physics (superallowed dec
s ! u: Kaon physics (KLOE, KTeV, NA62)
ertainties
Th. uncertainties
⇢ ↵ B → ππ, ρρ B(b) ! D(c)`⌫
|Vcb | lvs
d,|Vs:cbCharm
physics
(CLEO-c,
| via Form factor / OPE BESIII)
α
B→D ν /form
b → factor
c l cν !(OPE)
B(b) ! D(c)`⌫ |Vcb | vs form factor
b !(OPE)
u, c and t ! d, s: B physics (Babar, Bel
(*)
(*)
B→π ν / fbM → u l tν ! b:|V
B → D K M ! `⌫(γ )
ub| via Form factor / OPE
|VUD |l vs
Top
physics (CDF/DØ, ATLAS, CMS)
Ks
✏K
(¯
⇢, ⌘¯) vs BK
|VUD⌦
| vQCD
ia Decay constant fM
β M → l ν (γ) data = weak
B → J/ψ Ks
=)
Need for had
M
,
M
|V
V
|
vs
B
s
s
d
tb td,s
B
and dec
(¯
⇢B, ⌘s¯ )→ J/ψ Φ
B ! `+ ` βs
|V
|
vs
f
εK td,s
(ρ, η ) via BK
B
Genon (LPT-Orsay)
CKM fits and lattice
K → π ν anti-‐ν ρ, η Δmd, Δms 15/09/10
6 (LPT-Orsay)
Sébastien Descotes-Genon
|Vtb Vt{d,s}| via Bag factor BB
B(s) → µ+ µ-‐
|Vt{d,s}| via Decay constant fB
Phillip URQUIJO
3
Input 2014
0.05
Data = weak ⊗ QCD → need hadronic inputs; often LQCD with our own Rfit-‐
based averaging scheme.
CP Phase
Mixing
Modulus & Sides
CKM
|Vud|
β decays
PRC 055502 (2009)
|Vus|
Kl3 (Flavianet)
f+(0)=0.9641±0.0015±0.0045
K → l ν , τ → K ν 0.00MeV
fK= (155.2±0.2±0.6) |Vus/Vud| K→lν / π→lν , τ→Kν / τ→πν 0.50
fK/fπ = 1.1942±0.0009±0.0030
|Vub|
Inclusive & Exclusive
(3.70±0.12±0.26) 10-‐3
B → τ ν (1.14 ± 0.22) 10-‐4
fBs/fBd = 1.205 ± 0.004 ± 0.007 fBs = (225.6±1.1±5.4) MeV
|Vcb|
Inclusive & Exclusive
(41.00±0.33±0.74) 10-‐3
Δ md
Bd mixing
BBs/BBd = 1.023 ± 0.013 ± 0.014
Δ ms
Bs mixing
BBs = 1.320±0.017±0.030
εK
PDG
BK = 0.7615±0.0027±0.0137
β / Φ1
J/ψ K(*) WA
0.682±0.018
α / Φ2
π π , ρ π, ρ ρ WA
Isospin
γ / Φ3
B → D(*) K(*)
fitter
Winter 14
0.55
GLW/ADS/GGSZ : large improvements Phillip URQUIJO
4
0.6
Two ecades of ofCKM
Two d
decades
CKM
[LEP, KTeV, NA48, Babar, Belle, CDF, DØ, LHCb, CMS. . . ]
[LEP, KTeV, NA48, Babar, Belle, CDF, DØ, LHCb, CMS. . . ]
1.5
1.5
excluded area has CL > 0.95
md
1.0
1.5
md
1.0
md & ms
md & ms
sin 2
0.5
0.5
K
K
K
0.0
0.0
-1.0
-0.5
-0.5
-1.0
CKM
fitter
CKM
fitter
1995
Summer 2001
K
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
-1.5
-1.0
2004
-0.5
0.0
1.5
-1.5
-1.0
2.0
L>
0.9
5
0.5
∆md
εK
η
α
Vub
Vub
-1.0
K
fitter
2006
0.5
1.0
1.5
-1.5
-1.0
-0.5
CKM
sol. w/ cos 2 < 0
(excl. at CL > 0.95)
2009
0.0
0.5
1.0
1.5
εK
-1.0
K
CKM
fitter
2.0
α
-0.5
-0.5
sol. w/ cos 2 < 0
β
γ
0.0
α
Vub
CKM
∆md & ∆ms
sin 2β
0.0
-0.5
2.0
at C
md & ms
K
K
1.5
ed
γ
1.0
0.5
0.0
1.0
lud
md
0.5
sin 2
0.0
0.0
1.5
.95
md & ms
0.5
-0.5
-0.5
2004
>0
1.0
sin 2
-1.5
-1.0
1.0
exc
.95
md
0.5
1.5
>0
1.0
K
fitter
t CL
da
lude
exc
CKM
2001
t CL
da
lude
exc
1.5
-1.0
K
1995
-1.0
Vub
Vub
Vub
-0.5
md & ms
sin 2
0.5
0.0
md
1.0
fitter
γ
sol. w/ cos 2β < 0
Winter 14
2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
ρ
2006
S. Descotes-Genon (LPT-Orsay)
2009
CKMfitter
Phillip URQUIJO
2014
5
CKM14 - 11/09/14
6
Global Fit
ed
md & ms
0 .9
5
sin 2
1
0.5
md
K
ms
2
0.0
Vub
2
1
-0.5
3
-1.0
A = 0.812+0.015
0.022
A = 0.813+0.015
0.027
= 0.2254+0.0006
0.0010
= 0.2255+0.00068
0.00035
⇢¯ = 0.145 ± 0.027
⌘¯ = 0.343 ± 0.015
⇢¯ = 0.1489+0.0158
0.0084
⌘¯ = 0.342+0.013
0.011
SL
Vub
2
K
CKM
Winter 14
2014
1
3
fitter
2012
L>
1.0
B ! ⌧⌫
2,
at C
3
|Vcb |, |Vub |SL
✏K , sin 2
lu d
|Vud |, |Vus |
md ,
exc
1.5
-1.5
-1.0
-0.5
sol. w/ cos 2
3
<0
0.0
0.5
68% CL
Phillip URQUIJO
1
6
1.0
1.5
2.0
Validity of KM picture of CP violation
0.7
0.4
md
md & ms
CKM
fitter
0.6
Winter 14
0.5
0.4
0.3
0.5
0.6
0.7
3
sin 2
1
sol. w/ cos 2
2
K
2
Vub
0.1
1
3
0.0
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
0.0
-0.4
1.0
-0.2
0.0
0.2
0.7
fitter
0.6
Winter 14
3
0.5
0.4
0.3
0.7
CP violating only
CKM
1
3
2
CP allowed only
0.4
md
sin 2
0.6
md & ms
0.8
1.0
CKM
K
fitter
Winter 14
1
sol. w/ cos 2
1
<0
0.3
K
2
2
0.2
0.2
Vub
0.1
0.1
1
3
0.0
-0.4
<0
0.2
0.1
0.4
1
2
0.5
fitter
Winter 14
0.3
0.2
0.6
CKM
K
-0.2
0.0
0.2
0.4
0.6
1
3
0.8
1.0
0.0
-0.4
Tree only
-0.2
0.0
0.2
0.4
Loop only
Validity of Kobayashi-‐Maskawa picture of CP violavon AIP 2014, Global CKM Analysis
Phillip URQUIJO
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0.6
0.8
1.0
semileptonic
|Vub| Inclusive and Exclusive
ays of getting |Vub |:
3 Approaches to determine |Vub| (HFAG Semileptonic) clusive
:
b
!
u`⌫
+
Operator
Product
Expansion
• Inclusive: b → u l ν + OPE / Heavy quark symmetry clusive
: B B!
factors
• Exclusive: → ⇡`⌫
π l ν +
+ FForm
orm factors (LCSR@low q2, LQCD@high q2) e
= 3.28 ± 0.15 ± 0.26
CKM
Winter 14
|Vub |Inc. = 4.36 ± 0.18 ± 0.44
|Exc. =
± 0.15
± 0.26
=|Vub3.70
±3.28
0.12
± 0.25
|Vub |Ave. = 3.70 ± 0.12 ± 0.26
values ⇥10 3
|Vub |Lept. = 4.29 ± 0.43 ± 0.11
FAG, with theory errors
ded linearly
stematics combined
ing Educated
Rfit
semilept. aver.
excl.
incl.
fitter
w/o |Vub|
1.0
0.8
p-value
c
= 4.36 ± 0.18 ± 0.44
[x10-3]
c
• Leptonic: B → τ ν + Decay constant (LQCD) *Separate, not in |Vub| average 0.6
0.4
0.2
0.0
0.0025
0.0030
0.0035
0.0040
|V |
ub
Phillip URQUIJO
8
0.0045
0.0050
0.0055
|Vcb| Inclusive and Exclusive
ys of getting |Vcb |:
|Vcb|, :2 b
approaches by up Product
to 3σ(if thy. Expansion
errors added in quadrature) clusive
! c`⌫ +disagree Operator
for
moments
• Inclusive: b→c l ν ⇤+ OPE / Heavy quark symmetry clusive : B ! D(
)`⌫ + Form factors
*
= 42.42 ± 0.44 ± 0.74
= 38.99 ± 0.49 ± 1.17
CKM
fitter
|Vcb |Inc. = 42.42 ± 0.44 ± 0.74
Winter 14
|Vcb |Exc. = 38.99 ± 0.49 ± 1.17
=|Vcb41.00
± 0.33
± 0.74
|Ave. = 41.00
± 0.33
± 0.74
values ⇥10
3
FAG, with theory errors
ded linearly
stematics combined
ing Educated
Rfit
semilept. aver.
excl.
incl.
w/o |Vcb|
1.0
0.8
p-value
[x10-3]
e
• Exclusive: B→D l ν + Form factors (LQCD) we add individual theory errors linearly.
0.6
0.4
0.2
0.0
0.036
0.037 0.038
0.039 0.040
0.041 0.042
|V |
cb
Phillip URQUIJO
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0.043 0.044
0.045 0.046
0.05
0.15
CK M
Leptonic: Bu→τν
0.00
0.5
0.6
$ md
0.1
fitter
FPCP 10
0.7
0.8
0.9
1.0
0.0
0.10
0.10
0.15
0.20
0.25
0.30
fBd × Sqrt[B ] (GeV)
sin 2!
Bd
Issue notin only
the value
of fBBdu→τν sinceh2.6
from
Previous tensions global fit from ave discrepancy
reduced due to Belle’s result. B(B ! ⌧ ⌫)
3⇡
m⌧2 ⌧B
=
2 ⌘ S[x ]
md
4 mW
t
B
0.20
×10
-3
Sébastien Descotes-Genon (LPT-Orsay)
1
m⌧2
mB2
!2
sin2
1
sin2 (↵ + ) |Vud |2 BBd
p-value
0.40
1.0
15/09/10
27
CKM
fitter
0.9
Winter 14
0.35
0.8
0.15
0.6
0.5
0.10
0.4
Belle 2014
0.05
0.3
0.30
f Bd (GeV)
WA
)
BR(B
0.7
All
0.25
B
0.20
LQCD
0.2
0.15
CKM
0.1
fitter
md
Winter 14
0.00
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
sin 2
0.0
0.10
0.10
0.15
0.20
0.25
f Bd × Sqrt[BB ] (GeV)
d
However, B→D(*)τν almost 5 σ away from the SM.
Phillip URQUIJO
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0.30
Figure 7: Combined constraints on 2HDM Type II parameter space (mH + , tan β) from purely leptonic
decays of K, D and B mesons. The diﬀerent sets of observables are defined in the left Figure. Darker
to lighter shades of colours correspond to (Kℓ2 /πℓ2 + τ → Kν), (D → µν), (B → τ ν) and (Ds → ℓν)
individual constraints. The complementary area of the colored region is excluded at 95% CL. For the
sake of clarity, the figure on the right displays the combined constraint alone at 95% CL. The dark
green line defines the 1σ confidence area.
Ongoing Work (Melbourne) : Flavour + LHC
Analysis of leptonic, semileptonic and radiative meson decays & direct searches to search for charged Higgs and right handed charged currents.
B→Dτν
Kµ2 / πµ2
B→τν
CKM
fitter
2HDM
All
1.0
1 - CL
0.8
0.6
0.4
0.2
0.0
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Log [ M + / tan(β) / GeV ]
10
H
3.0
Figure 8: Combined constraints on the ratio mH + / tan β derived from leptonic and semileptonic decays
All
H
Log10[ m + / GeV ]
of K, D and B mesons, in the large tan β limit.
b→sγ
2.5
19
2.0
∆ Mq + Z→ bb
M→ l ν + M→ X l ν
1.5
LEP
CKM
fitter
2HDM
1.0
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Log [ tan(β) ]
10
Phillip URQUIJO
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Figure 11: Global constraints on 2HDM parameters mH + and tan β from all analysed observables.
Each color corresponds to a diﬀerent set of observables, as quoted in the Figure. The complementary
area of the colored one is excluded at 95% CL. The horizontal black line indicates the 95% CL limit from
Leptonic: Bs→ +
–
µµ
Prediction Br(Bs→μ+ μ–)=3.65 [+0.18-‐0.30]x10-‐9, (Winter 2014) Dominated by the indirect determination of fBs through the global fit (specifically Δms).
Prediction w/o ms
Prediction w/o f Bs
Prediction
CKM
fitter
FPCP 13
LHCb+CMS
1.0
p-value
0.8
0.6
0.4
0.2
0.0
1.5
2.0
2.5
3.0
3.5
4.0
-9
Br(Bs µµ) [10 ]
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4.5
|Vcd| & |Vcs|: Leptonic Charm
• Indirect constraints (from b and s transitions) are related to |Vcd| and |Vcs| through unitarity. 1.00
B physics
Indirect
Direct
0.95
• Direct constraints combine leptonic and semileptonic D and Ds decays & neutrino-‐nucleon Direct: Leptonic
decays
scattering. semileptonic D &
|Vcs|
0.90
0.85
Nucleon & Kaon
0.80
Ds
CKM
fitter
Winter 14
0.75
0.18
0.19
•
Test o
f L
QCD p
redictions f
or l
eptonic d
ecays.
Use the global fit to predict the values of decay csts using also
0.20
0.21
0.22
0.23
0.24
|V |
0.25
0.26
cd
1.00
B physics
GF2 mM m`2
B[M ! `⌫` ] =
8⇡
Indirect
Direct
0.95
|Vcs|
0.90
0.85
Direct:
Leptonic D &
Ds
Nucleon & Kaon
0.80
CKM
fitter
Winter 14
0.75
0.18
0.19
0.20
0.21
0.22
|V |
cd
0.23
0.24
0.25
0.26
1
m`2
2
mM
!2
|Vqu qd |2 fM2 ⌧M (1 +
M`2
em )
Quantity
Process
Global fit
Input TheoryK /⇡
Expt.(1%)
fK /f
1.14+0.006
⇡
µ2
µ2
0.008
fK
K ! `⌫` , ⌧ ! K ⌫⌧
155+12
(1%)
|Vcd|: fD = 249.2±1.2±4.5 MeV (1.9%)
+11Br ~ 4.5%
fD
D ! `⌫`
206 11
(6%)
fDs
Ds ! `⌫`
261+77
%
|Vcs|: fDs/fD = 1.185±0.005±0.010 (0.9%) +10Br ~ 3(3%)
fB
B ! ⌧⌫
197 9
(5%)
Phillip URQUIJO
=)To be compared
with your favourite 13
determination of decay cs
|Vud| & |Vus|
0.230
Combined constraints from leptonic and semileptonic K decays. K l2 and ->K
All, yellow
Direct, light green
0.225
Direct constraints are in good agreement with indirect observables (β, εK). Recently improvements to τ precision. |Vus|
K l3
0.220
K l2/
l2
and ->K / ->
Lepton universality / radiative corrections in check.
decays
0.215
Indirect
CKM
fitter
Winter 14
1.0
0.9
0.970 0.975
0.980 0.985
0.645
0.990
|V |
ud
+0.015
A = 0.813 0.027
= 0.2255+0.00068
0.00035
+0.0158
Phillip URQUIJO
AIP 2014, Global⇢
CKM
Analysis
¯ = 0.1489 0.0084
µ )
0.960 0.965
BR(K
0.210
0.950 0.955
p-value
0.650
0.8
0.7
0.640
0.6
0.5
0.635
0.4
0.630
0.3
0.2
0.625
CKM
0.1
fitter
FPCP 13
0.620
1.50
1.55
1.60
BR(K
14
e ) 105
1.65
1.70
0.0
Pulls
Bs → μ μ
φs
γ
α
sin 2β
εK
Δms
Δmd
B(B→τν )
|V |
ub semilep
|V cb|semilep
B(D→μ ν )
B(Ds→μ ν )
B(Ds→τ ν )
B(D→Kν )
B(D→ πlν )
|V cs|not lattice
|V cd|not lattice
B(τK2)
B(K )
μ2
B(K )
e2
B(Ke3)
|V |
ud
0.00
0.26
0.41
1.56
1.96
0.00
1.25
1.66
1.51
0.00
0.00
0.56
0.94
1.15
0.00
0.00
0.00
0.42
1.77
0.56
1.39
0.00
0.00
CKM
fitter
Winter 14
Pulls for various inputs or parameters involved in the global fit. ( √ of difference between χ2min obtained including or not including direct information on the quantity. ) The plateau in the Rfit model for theoretical uncertainties sometimes leads to a vanishing pull. → No signs of NP within the CKM global fit paradigm analysis.
0 0.5 1 1.5 2 2.5 3 3.5
Pull (σ)
Phillip URQUIJO
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New Physics in mixing: past & future data
Neutral-B mixing
• Meson mixing,
d ⇣ |Bq (t)i ⌘ ⇣ q
i q ⌘⇣ |Bq (t)i ⌘
i
= M
Mixing
observables
|B̄q (t)i
dt |B̄q (t)i
2in SM
M and
hermitian:
mixing
due bto off-diagonal
terms
s
b
u,c,t
s
q
M12
i
q
12 /2
2
•
SM:
C
/m
SM
W
q
q
W
=)Diagonalisation:
physical |BH,L
i of masses MH,L
, widths qH,L
W
2
• NP:
C
NP/Λ
[Beneke et al 96
s
q
,|
In terms of M12
b
s
and
= arg
u,c,t
q
12 |
q
⇣
b
q
M12
q
12
⌘
Nierste and Lenz
[small in SM]
•Effective
What is tHamiltonian
he scale Λq ? approach
How different is CNP from CSM ? q
q
Mass •
difference
Mfqrom = MSHM sM
2|M
q
12 |
L =→
If deviation een u
pper b
ound o
n Λ
M dominated
by
dispersive
part
of
top
boxes
q
q
q
12
Width difference
= 2| 12 | cos( q )
q = H
µ
L
involve
one
operator
at
LO:
Q
=
q̄
(1
)b
q̄
(1
5
5 )b
• Assume NP from Trees in q negligible, test q
qµ
+
| 12 |
(B̄ (t)!` ⌫X ) (B (t)!` ⌫X )
q
Asymmetry
aoSLnly =-‐ i.e. = of
sin qboxes
qcharm
dominated
absorptive
part
for NP in loops ew P
hysics qN
+by
q (t)!` ⌫X
(
B̄
(t)!`
⌫X
)+
(B
)
|M
|
12
12
only enters M12, the real part contribution,
of the non
local
expressed as SM
expansion in 1/m2i
b
M
=
M
⇥
1
+
he
12decays 12
p/q mixing from mixing
in time-dependent
analysis
of
B
Hamiltonian. involve two operators at LO: Q and Q̃S = q̄↵⇣(1 q+ ⌘5 )b q̄ (1 +
| 12 |
q⇤ Q, taming
right set for 12
,
depending
mainly
on
”phase” Mq ' arg(M12 ) + O |M q |1/mb -correctio
12
• 3 x 3 CKM matrix is unitary.
pow
, B,
B̃S ; µ, mb
Phillip
URQUIJO
AIP 2014, Global CKM Analysis = f [f
bastien Descotes-Genon (LPT-Orsay)
CKM
s fits and latticeBs
15/09/10
31
,B
.
.
.]
1/m
16 b
NP in B{d,s} & K mixing: Input
• Observables not affected by NP first used to constrain CKM: |Vud|,|Vus|, |Vcb|, |Vub|, Φ3 and Φ2=π−Φ3−Φ1eff((c anti-‐c)K) • NP impact estimated from Meson mixing Δms, Δmd, |εK|, Lifetime difference ΔΓs, & semileptonic asymmetry ASL, Time dep. CP asymmetries βs, Φ1, and Φ2 (decay-‐mixing interference)
2003
2013
1.5
LHCb Upg.+ Belle II
1.5
1.5
CKM
fitter
1.0
0.5
Vub
0.0
-0.5
-0.5
-1.0
-1.0
-0.5
0.0
0.5
1.0
1.5
fitter
2.0
Stage II
2013
( )
1.0
0.0
-1.5
-1.0
CKM
fitter
2003
0.5
CKM
( )
1.0
0.5
Vub
Vub
0.0
-1.5
-1.0
( )
-0.5
& ( ) & Vub
-0.5
& ( ) & Vub
( )
-1.0
0.0
0.5
1.0
1.5
2.0
-1.5
-1.0
-0.5
• Qualitative change after 2003: first Φ3 and Φ2 constraints
Phillip URQUIJO
17
0.0
0.5
1.0
1.5
2.0
NP in Bd mixing: Fit results
2003
2013
CKM
3.0
CKM
2003
2013
2.0
0.5
1.5
0.5
0.5
2.0
2.5
3.0
0.5
1.5
0.4
0.3
0.2
0.5
0.1
0.1
0.1
1.5
0.6
0.3
0.2
0.2
1.0
2.0
1.0
1.0
0.3
0.5
0.7
0.4
0.4
0.0
0.0
0.8
2.5
d
d
d
0.5
1.0
0.0
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.0
0.0
0.0
0.1
0.2
0.3
0.4
hd
hd
hd
• at 95% NP≲(many × SM) ⟹ NP≲(0.3 × SM) ⟹ NP≲(0.05 × SM)
2
2
0.9
0.6
0.6
1.5
CKM
fitter
0.7
0.7
2.0
Stage II
0.8
2.5
0.8
2.5
3.0
0.9
fitter
0.9
fitter
1.0
1.0
1.0
p-value
p-value
p-value
3.0
LHCb Upg.+ Belle II
2
|Cij | (4⇡)
|Cij |
h ' 1.5 t 2
' t 2
2
| ij | GF ⇤
| ij |
✓
4.5 TeV
⇤
= arg(Cij
◆2
t⇤
ij )
By Stage II, Λ ~ 20 TeV (tree) Λ ~ 2 TeV (loop)
• Stage II: similar sensitivity to gluino masses explored at LHC 14TeV
Phillip URQUIJO
18
0.5
0.0
Summary
CKM global analysis finds that most constraints are in very good agreement. … but some inputs are not so well resolved yet e.g. |Vqb| The KM mechanism is obviously at work at O(10%) but there is still room for New Physics, particularly in the mixing of mesons. Multi TeV scale can be probed in loops. 2 Major Reference Publications out very soon … 1. Heavy Flavour Averaging Group, Publication in PLB, (Preprint available in Dec 2014) 2. CKMFitter Analysis of 10 years of CKM measurements to be submitted to PRD (Jan 2015). Many more for the future… Sensitivity studies and impact on global New Physics analyses the “Belle II Theory Interface Platform” report (2016). Eagerly awaiting LHC run-‐2 (ATLAS) and Belle II.
Phillip URQUIJO
19
Backup
The CKMfitter group
More results on http://ckmfitter.in2p3.fr
Jérôme Charles
Olivier Deschamps
Sébastien Descotes-Genon
Ryosuke Itoh
Heiko Lacker
Evan Machefer
Andreas Menzel
Stéphane Monteil
Valentin Niess
José Ocariz
Jean Orloff
Alejandro Perez
Wenbin Qian
Vincent Tisserand
Karim Trabelsi
PU
Luiz Vale Silva
Phillip URQUIJO
Theory
CPT Marseille (FR)
LHCb
LPC Clermont-Ferrand (FR)
Theory
LPT Orsay (FR)
Belle/Belle II
KEK Tsukuba (JP)
ATLAS/BABAR Humboldt-Universität Berlin (DE)
LHCb
ATLAS
Humboldt-Universität Berlin (DE)
LHCb
LHCb
ATLAS/BABAR LPNHE Paris (FR)
Theory
BABAR
IPHC Strasbourg (FR)
LHCb
LAPP Annecy-Le-Vieux (FR)
LHCb/BABAR
LAPP Annecy-Le-Vieux (FR)
Belle/Belle II
KEK Tsukuba (JP)
Belle/Belle II
The University of Melbourne (AU)
Theory
LPT Orsay (FR)
21
corresponding likelihood L = exp( 2 /2)
CKMfitter M
ethodology
all values within range of syst treated on the same footing
Statistical framework
Methodology
Global parameters q
= (A, f,it ⇢¯,t⌘¯o . C
. .)KM to be
determined q = (A,λ,ρ ̄,η ̄...) Oexp experimental values of the observables
OthF(q)
theoretical
description
in
model
■ Global
fit to CKMto parameters
• Use requentist approach bauild (p-‐value) functions c2
+ o
Use
Frequentist
Hypothesis testing
to and 2
In the case f Gaussian (Experimental) uncertainties In •case
of experimental
(Gaussian)
uncertainties,
likelihoods
build statistical significance
(p-value)
8
✓
◆2
Y functions from which estimates
X Oth (q)
O
and exp
2
L(q) =
LO (q)
(q) = 2 ln L(q) =
O
confidence intervals are 6 obtained;
testO
O
statistic = Maximum Likelihood Ratio = 2.
4
2 (q̂) =
2 (q)
• Estimator ˆ m
aximum l
ikelihood: Estimator +
q̂qmaximum
likelood:
min
q
Dedicated RFit scheme for the treatment
2(q) for
a given qsystematics.
for qTheoretical
= q0 ) obtained from
•Confidence
χ2(qˆ) = ofmlevel
intheoretical
0 (p-value
q χ
2
2 (q ) = 2 (q )
2 (q) (distributed like 2 law of dim(q))
min
q
0
0
systematics
considered
as additional
• Confidence level for are
a given q0 obtained from ∆χ2(q0) parameters-5 .
5
= χ2(q0) −nuisance
minq χ2(q) What to do in the case of systematic uncertainties,
which stand out of this picture ?
Illustrative Rfit example
black: Gaussian+flat pdf for syst, red: RFit
= weak for QCD
need for hadronic
• Dedicated ■Rdata
Fit scheme the treatment of Sébastien
(LPT-Orsay)
fits and8 lattice
inputs;
oftenDescotes-Genon
LQCD
with
our
own averaging CKM
Sébastien Descotes-Genon
CKM fits and
lattice
theoretical s(LPT-Orsay)
ystematics. Theoretical systematics are 15/09/10
scheme (OOA), following an algorithmic
x
considered as additional nuisance parameters.
scheme
with an ‘Educated
RFit’
approach.
N [0,1]
Observation
Gaussian
Systematic
stat. error bounded in [- ; ]
Parameter
Phillip URQUIJO
x
22
Inputs to the Standard CKM fit
Parameter
|Vud | (nuclei)
|Vus | (K`3 )
|Vcd | (⌫N )
|Vcs | (W ! cs̄)
|Vub |
|Vcb |
B(B ! ⌧
B(Ds ! µ
B(Ds ! ⌧
B(D ! µ
B(K ! e
B(K ! µ
B(⌧ ! K
B(K ! µ
B(⌧ ! K
⌫⌧ )
⌫µ)
⌫⌧ )
⌫µ)
⌫e)
⌫µ)
⌫⌧ )
⌫ µ )/B(⇡ ! µ ⌫ µ )
⌫ ⌧ )/B(⌧ ! ⇡ ⌫ ⌧ )
D!⇡
|Vcd |f+
(0)
D!K
|Vcs |f+
(0)
|"K |
md
ms
sin(2 )[cc̄]
( s )J/
+
+
00
S⇡⇡
, C⇡⇡
, C⇡⇡
,B⇡⇡ all charges
+
+
00
00
S⇢⇢,L , C⇢⇢,L , S⇢⇢ , C⇢⇢
,B⇢⇢,L all charges
0
0
B ! (⇢⇡) ! 3⇡
B
B
B
! D(⇤) K (⇤)
! D(⇤) K (⇤)
! D(⇤) K (⇤)
Errors
GS
TH
Value ± Error(s)
Reference
0.97425 ± 0 ± 0.00022
0.2247 ± 0.0006 ± 0.0011
0.230 ± 0.011
0.94+0.32
0.26 ± 0.13
(3.70 ± 0.12 ± 0.26) ⇥ 10 3
(41.00 ± 0.33 ± 0.74) ⇥ 10 3
[1]
[4, 3]
[4]
[4]
[5, 6]
[5]
?
?
?
?
?
?
?
?
?
?
(1.14 ± 0.22) ⇥ 10 4
(5.54 ± 0.24) ⇥ 10 3
(5.44 ± 0.22) ⇥ 10 2
(3.74 ± 0.17) ⇥ 10 4
(1.581 ± 0.008) ⇥ 10 5
0.6355 ± 0.0011
(0.700 ± 0.010) ⇥ 10 3
1.344 ± 0.0041
(6.53 ± 0.11) ⇥ 10 2
[7, 5]
[5]
[5]
[8, 9]
[4]
[2]
[4]
[2]
[10]
?
?
?
?
?
?
?
?
?
?
-
0.148 ± 0.004
0.712 ± 0.007
[11]
[11, 12]
?
?
-
(2.228 ± 0.011) ⇥ 10 3
(0.507 ± 0.004) ps 1
(17.762 ± 0.023) ps 1
0.682 ± 0.018
0.013+0.083
0.090
[4]
[5]
[13, 5]
[5]
[5]
?
?
?
?
?
-
Inputs to isospin analysis
Inputs to isospin analysis
Time-dependent Dalitz analysis
[14]
[15]
[16]
?
?
?
-
Inputs to GLW analysis
Inputs to ADS analysis
GGSZ Dalitz analysis
[17]
[18]
[19]
?
?
?
-
Phillip URQUIJO
23
Lattice Averages
Educated Rfit used to combine the results, with different treatment of statistical and systematic errors • Product of (Gaussian + Rfit) likelihoods for central values • Product of Gaussian (stat) likelihoods for stat. uncertainty • Syst. uncertainty for the combination: the oen with the most precise method Conservative combinations: • the best of all estimates is the limit. (combining 2 methods with similar systematics does not reduce the intrinsic uncertainty encoded as a systematic) • best estimate should not be penalised by less precise methods.
Phillip URQUIJO
24
CKMFitter Lattice Averages: E.g. B mixing
3.3
Beauty mesons
fBs
Reference
Article
ETMC13
HPQCD11
FNAL-MILC11
HPQCD12
HPQCD13
[54]
[55]
[51]
[56]
[57]
Nf
Mean
Stat
Syst
2
2+1
2+1
2+1
2+1+1
228
225.0
242.0
228.0
224.0
5
2.9
5.1
1.4
2.5
9
5.4
21.2
17.5
7.2
225.6
1.1
5.4
Our average
fBs /fB
Reference
Article
Nf
Mean
Stat
Syst
ETMC13
FNAL-MILC11
HPQCD12
HPQCD13
[54]
[51]
[56]
[57]
2
2+1
2+1
2+1
1.206
1.229
1.188
1.205
0.010
0.013
0.012
0.004
0.026
0.046
0.025
0.007
1.205
0.003
0.007
Our average
4
Semileptonic form factors
4.1
K ! ⇡`⌫
Phillip URQUIJO
25
The Bs UT
0.10
L
at C
ed
lud
exc
K
⇢¯s =
.95
>0
0.05
⌘¯s =
md & ms
Bs
md
+0.00046
0.00797 0.00085
+0.00060
0.01832 0.00068
Vub
0.00
s
s
=
sin 2
arg
✓
Vcs Vcb⇤
⇤
Vts Vtb
-0.05
CKM
fitter
s
K
Winter 14
-0.10
-0.10
-0.05
0.00
0.05
Bs
Input
−0.013+0.083-‐0.090
Indirect
0.01817 −0.00068−0.00060
0.10
Phillip URQUIJO
26
◆
NP in B{d,s} & K mixing: Input
Uncertainties expected on future measurements over the coming decade. Expecting (& need) Δ2-‐3% on |Vub|.
|Vud |
|Vus | (K`3 )
|✏K |
md [ps 1 ]
ms [ps 1 ]
|Vcb | ⇥ 103 (b ! c`¯
⌫)
3
|Vub | ⇥ 10 (b ! u`¯
⌫)
sin 2
↵ (mod ⇡)
(mod ⇡)
( s )J/
B(B ! ⌧ ⌫) ⇥ 104
B(B ! µ⌫) ⇥ 107
AdSL ⇥ 104
AsSL ⇥ 104
m̄c
m̄t
↵s (mZ )
BK
fBs [GeV]
BBs
fBs /fBd
BBs /BBd
B̃Bs /B̃Bd
B̃Bs
⌘B
✏
1
⌘cc
⌘ct
⌘tt
2003
0.9738 ± 0.0004
0.2228 ± 0.0039 ± 0.0018
(2.282 ± 0.017) ⇥ 10 3
0.502 ± 0.006
> 14.5 [95% CL]
41.6 ± 0.58 ± 0.8
3.90 ± 0.08 ± 0.68
0.726 ± 0.037
—
—
—
—
—
10 ± 140
—
1.2 ± 0 ± 0.2
167.0 ± 5.0
0.1172 ± 0 ± 0.0020
0.86 ± 0.06 ± 0.14
0.217 ± 0.012 ± 0.011
1.37 ± 0.14
1.21 ± 0.05 ± 0.01
1.00 ± 0.02
—
—
0.55 ± 0 ± 0.01
1
0±0±1
0.47 ± 0 ± 0.04
0.5765 ± 0 ± 0.0065
2013
0.97425 ± 0 ± 0.00022
0.2258 ± 0.0008 ± 0.0012
(2.228 ± 0.011) ⇥ 10 3
0.507 ± 0.004
17.768 ± 0.024
41.15 ± 0.33 ± 0.59
3.75 ± 0.14 ± 0.26
0.679 ± 0.020
(85.4+4.0
3.8 )
(68.0+8.0
8.5 )
+0.0450
0.0065 0.0415
1.15 ± 0.23
—
23 ± 26
22 ± 52
1.286 ± 0.013 ± 0.040
165.8 ± 0.54 ± 0.72
0.1184 ± 0 ± 0.0007
0.7615 ± 0.0026 ± 0.0137
0.2256 ± 0.0012 ± 0.0054
1.326 ± 0.016 ± 0.040
1.198 ± 0.008 ± 0.025
1.036 ± 0.013 ± 0.023
1.01 ± 0 ± 0.03
0.91 ± 0.03 ± 0.12
0.5510 ± 0 ± 0.0022
0.940 ± 0.013 ± 0.023
1.87 ± 0 ± 0.76
0.497 ± 0 ± 0.047
0.5765 ± 0 ± 0.0065
Stage I
id
0.22494 ± 0.0006
id
id
id
42.3 ± 0.4
3.56 ± 0.10
0.679 ± 0.016
(91.5 ± 2)
(67.1 ± 4)
0.0178 ± 0.012
0.83 ± 0.10
3.7 ± 0.9
7 ± 15
0.3 ± 6.0
1.286 ± 0.020
id
id
0.774 ± 0.007
0.232 ± 0.002
1.214 ± 0.060
1.205 ± 0.010
1.055 ± 0.010
1.03 ± 0.02
0.87 ± 0.06
id
id
id
id
id
id
Stage II
id
id
id
id
id
42.3 ± 0.3
3.56 ± 0.08
0.679 ± 0.008
(91.5 ± 1)
(67.1 ± 1)
0.0178 ± 0.004
0.83 ± 0.05
3.7 ± 0.2
7 ± 10
0.3 ± 2.0
1.286 ± 0.010
id
id
0.774 ± 0.004
0.232 ± 0.001
1.214 ± 0.010
1.205 ± 0.005
1.055 ± 0.005
id
id
id
id
id
id
id
id
• “Stage I”~2019: Belle II 5 ab-1, LHCb 8 fb-1
• “Stage II” ~2024:
Belle II 50 ab-1,
LHCb 50 fb-1
“id”=identical
Table 1: Central
valuesGlobal
and uncertainties
used in our analysis.
When
two uncertainties are27
shown,
Phillip
URQUIJO
AIP 2014,
CKM Analysis
Φ3/γ Determination
Theory is “pristine” in these approaches, << 1% on Φ3 Accessed via interference between B–→D0K– and B–→anti-‐D0K–
3
A∝λ
Favoured
3
A∝λ
2
2 iφ 3
ρ +η e
Suppressed
⇤
|Asuppressed |
Vub Vcs
€ r
€ ⇥ [colour supp.] = 0.1
⇡
B =
⇤
|Afavoured |
Vcb Vus
0.2
Relative weak phase is Φ3, Relative strong phase is δR
3 D0 mode categories: • DCP, CP eigenstates [GLW] • Dsup, Doubly cabibbo suppressed [ADS] • 3-‐Body [GGSZ] AIP 2014, Global CKM Analysis
3 B modes: D*K, DK, DK*
Phillip URQUIJO
28
δB and rB → Φ3
CKM
rB(DK) using B
fitter
(*) (*)
CKM
D K decays
Winter 14
0.6
0.6
p-value
p-value
0.8
0.4
DK
0.0
0.0
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0
20
40
60
80
100
120
140
D*K 0.120+0.018-‐0.020
-‐50+13-‐15°
DK* 0.137+0.045-‐0.047
107+35-‐42°
180
LHCb GLW+ADS
LHCb GGSZ
LHCb Combined
CKM
fitter
Winter 14
1.0
0.8
0.8
0.6
0.6
p-value
1.0
0.4
0.2
0.0
160
Belle GLW+ADS
Belle GGSZ
Belle Combined
Winter 14
121.1+8.2-‐9.3°
strong phase δR
RB Ratio
fitter
0.0972+0.0063-‐0.0064
(DK)
B
rB(DK)
CKM
δB
0.4
0.2
0.2
RB
Full Frequentist treatment on MC basis
1.0
0.8
p-value
(*) (*)
D K decays
Winter 14
Full Frequentist treatment on MC basis
1.0
(DK) using B
B
fitter
0.4
0.2
0
20
40
60
80
100
120
140
160
180
0.0
0
20
40
Phillip URQUIJO
60
80
29
100
120
140
160
180
Φ3/γ Results
Impact of LHCb is striking, with massive improvements since 2010.
GLW+ADS
GGSZ
Combined
CKM
fitter
fitter
Winter 14
1.0
1.0
0.8
0.8
0.6
0.6
p-value
p-value
Winter 14
0.4
0.2
0.0
Belle
LHCb
BaBar
CKM
Combined
0.4
0.2
0
20
40
60
80
2010
[comb]
[fit] =
100
120
140
160
180
0.0
0
20
2012
= (71+21
25 )
(67.2+3.9
3.9 )
[comb]
[fit] =
40
60
80
100
120
140
160
2014
= (66+12
12 )
(67.1+4.3
4.3 )
Phillip URQUIJO
[comb] = (66+89 )
[fit] = (66.4+1.2
3.3 )
30
180
NP in Bs mixing: Fit results
2003
2013
LHCb Upg.+ Belle II
p-value
p-value
1.0
3.0
CKM
2003
0.8
2.0
0.5
1.5
0.4
1.0
0.3
0.2
0.5
0.5
1.0
1.5
2.0
2.5
3.0
0.0
0.7
2.0
0.6
0.5
1.5
0.4
0.4
1.0
0.3
0.2
0.5
1.0
0.3
0.2
0.5
0.1
0.1
0.1
0.0
0.0
0.8
2.5
0.6
s
s
0.5
0.9
fitter
0.7
0.6
1.5
CKM
Stage II
0.8
2.5
0.7
2.0
0.9
fitter
2013
2.5
1.0
3.0
CKM
0.9
fitter
p-value
1.0
s
3.0
0.0
0.0
hs
0.1
0.2
0.3
0.4
0.5
0.0
0.0
0.0
0.1
0.2
0.3
0.4
hs
hs
• At 95% NP≲(many × SM) ⟹ NP≲(0.3 × SM) ⟹ NP≲(0.05 × SM)
• Sensitivity now similar to that of Bd mixing, with precision to exceed Bd
in the future → due to Δms.
Further model dependent studies are presented in the paper.
Phillip URQUIJO
31
0.5
0.0
Semileptonic Decays
Indirect
Input
|Vus|
0.224488+0.001909-‐0.000066 (0.4%)
0.2247±0.0006±0.0011 (0.5%)
|Vcb|
(41.4+2.4-‐1.4)10-‐3 (4.6%)
(41.00±0.33±0.74)10-‐3 (2.0%)
|Vub|
(3.43+0.25-‐0.08)10-‐3 (5.0%)
(3.70±0.12±0.26)10-‐3 (7.7%)
|Vcb| direct input driven
Powerful predictions to be compared to semileptonic charm.
Expt. |Vcq|×f(0)
LQCD fD→π/K(0)
|Vcd| 0.22537+0.00068-‐0.0003 (0.3%)
0.148±0.004(2.7%)
0.666±0.020±0.048 (7.8%)
|Vcs| 0.973395+0.000095−0.000176 (0.01%)
0.712±0.007(1.0%)
0.747±0.011±0.034 (4.8%)
Phillip URQUIJO
Indirect
32

P. Urquijo*, L. Pesantez, L. Spiller The University of Melbourne

Transcription

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