Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 1
B-mixingWhat did we learn from LHCb in 2011?
b
d
t,c,u
t,c,u
W-
b
db
dt,c,u t,c,uW
-b
d
Alexander LenzCERN, Theory Division
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 2
Content
■ Introduction
■ CKM+: The CKM paradigm is great■ CKM0: The CKM paradigm might be better■ CKM−: The CKM paradigm is violated by New Physics!
■ Status of B-mixing after Moriond 2012
■ Wish-list for Experiments
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 3
Introduction I
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 4
Introduction II - Baryon Asymmetry
symmetric initial conditions(Inflation: initial asymmetry is wiped out)
⇒ Nmatter = Nantimatter
But we exist and stars and...
Search for annihilation lines, nucleosynthesis, CMB,...
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 5
Introduction II - Baryon Asymmetry
Search for annihilation lines, nucleosynthesis, CMB,...
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 6
Introduction II - Baryon Asymmetry
Search for annihilation lines, nucleosynthesis, CMB,...
ηB =nB − nB̄
nγ≈ 6 · 10−10
How can this be created from symmetric initial conditions?
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 7
Introduction II - Baryon Asymmetry
Search for annihilation lines, nucleosynthesis, CMB,...
ηB =nB − nB̄
nγ≈ 6 · 10−10
How can this be created from symmetric initial conditions?
1967 Sakharov: The fundamental laws of nature must have several properties,in particular
CP-violation: 1964 K-Mesons (NP 1980) 2000 B-Mesons
Can our fundamental theory cope with these requirements?
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 8
Success of the SM I
Elegant description of nature at per mille precision
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 9
Success of the SM II
Elegant description of nature at per mille precision
• Electroweak precision tests
measσ) / meas - Ofit
(O
-3 -2 -1 0 1 2 3
tmbm
cm
WΓWM
)2
Z(M
(5)
hadα∆
b0R
c0R
bA
cA
0,bFBA
0,cFBA
)FB
(Qlepteff
Θ2sin
(SLD)lA
(LEP)lA
0,lFBA
lep0R
0had
σZΓZM
0.3
-0.0
-0.0
0.2
-1.3
-0.1
-0.8
0.1
0.6
-0.1
2.5
0.9
-0.7
-2.0
0.2
-0.9
-1.0
-1.7
0.1
0.1G fitter SM
AU
G 11
[GeV]tm140 150 160 170 180 190 200
[GeV
]W
M
80.15
80.2
80.25
80.3
80.35
80.4
80.45
80.5
80.55
=114 GeV
HM
=300 GeV
HM =1000 GeV
HM
WAtop band for mσ1
WAW
band for Mσ1
68%, 95%, 99% CL fit
top, mWcontours excl. M
68%, 95%, 99% CL fit contours , incl. Higgs searches
t, mWexcl. M
=114 GeV
HM
=300 GeV
HM =1000 GeV
HM
G fitter SM
AU
G 11
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 10
Success of the SM IIIElegant description of nature at per mille precision
• CKM-mechanism NP 2008How can CP-violation be incorporated in the SM?
1972 only u,d and s-quarks were known, Kobayashi and Maskawa postulatedsix quarks!
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 11
CKM+: Status of CKM in early 2012
Good overall consistency
VCKM =
0.97426± 0.00030 0.22545± 0.00095 0.00356± 0.00020
0.22529± 0.00077 0.97341± 0.00021 0.04508+0.00075−0.00528
0.00861+0.00021−0.00037 0.04068± 0.00138 0.999135+0.000057
−0.000018
Fit from A.L, Nierste, CKMfitter 1008.1593see also UTfit 1010.5089, Lunghi/Soni 1010.6069, Laiho/Lunghi/Van de Water
1102.3917, PDG, HFAG ...
NP 2008
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 12
CKM+: The status of CKM in early 2012
γ
γ
αα
dm∆Kε
Kε
sm∆ & dm∆
ubV
βsin 2
(excl. at CL > 0.95) < 0βsol. w/ cos 2
excluded at CL > 0.95
α
βγ
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
1.5excluded area has CL > 0.95
Summer 11
CKMf i t t e r
Picture from A.L, Nierste, CKMfitter 1008.1593, see also UTfit, Lunghi/Soni, Laiho et al...
A = 0.815+0.011
−0.029
λ = 0.22543(77)
ρ̄ = 0.1444+0.029
−0.018
η̄ = 0.342(16)
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 13
CKM+: b → sγ- Another success of CKM
Br(b→ sγ)Exp = (3.55± 0.26) · 10−4
Br(b→ sγ)Theo = (3.15± 0.23) · 10−4
Exp: HFAG, BaBar, BELLE, CLEOTheory in NNLO Misiak et al. 2007,...List of References in Misiak, PoS(FPCP 2010)025
8 8
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 14
CKM0: The first row: Vud
■ Nuclear β-decay■ Neutron β-decay■ Pion β-decay
|Vud| = 0.97425± 0.00022
PDG 2010, Hardy, Towner 2009
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 15
CKM0: The first row: Vus
■ Kl3-decays■ Hadronic τ decays■ Semi leptonic Hyperon decays
|Vus| = 0.2254± 0.0013
Antonelli et al. 1005.2323; Boyle et al. 1004.0886
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 16
CKM0: The first row: Vub
Exclusive |Vub| = 0.00351± 0.00047
Inclusive |Vub| = 0.00432± 0.00027
B → τν |Vub| = 0.00504± 0.00064
Fit |Vub| = 0.00356± 0.00020
HFAG; HPQCD 2007; MILC Fermilab 2008;Ball/Zwicky 2005; Lange/Neubert/Paz 2005;Andersen/Gardi 2006,2008; Gambino/Giordano/Ossola/Uraltsev 2007; Aglietti/Di
Lodovico/Ferrera/Ricciardi 2009; Aglietti/Ferrera/Ricciardi 2007; Bauer/Ligeti/Luke2001,...
■ Vub is actually of order λ4 and not λ3: 0.00356 = (0.2254)3.79
■ Hadronic uncertainties (lattice, LCSR) underestimated?■ Soni and Lunghi: do not to use Vub in the global fit■ Crivellin0907.2461; Buras/Gemmler/Isidori 1007.1993: RH currents ⇒ incl. 6= excl.
■ New Physics in B → τν vs. Bd-mixing
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 17
CKM0: The first row: Vub′
Test the accuracy of the CKM elements of the first row:
δ(Vud) = 0.00022
δ(Vus) = 0.00130
δ(Vub) = 0.00020√1− V 2
ud − V 2us = 0.00564+0.02669
−0.00564
Investigate a hypothetical 4th generation of fermionsAssume VCKM4 is unitary
⇒ Vub′ can still be much larger than Vub: Vub′ < 0.04 ≈ λ2
Bobrowski, A.L., Rohrwild, Riedl, 0902.4883; Buras et al. 2010; Eberhardt, A.L.,Rohrwild 1005.3505; Das, London, Sinha, Soffer 1008.4925; Alok, Dighe, London1011.2634; Soni and Nandi 1011.6091;...
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 18
CKM0: The second row: Vcd
■ Semi leptonic Charm decays D → πlν
■ Charm Production in Neutrino Interactions
|Vcd| = 0.230± 0.011
PDG 2010
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 19
CKM0: The second row: Vcs
■ Neutrino Scattering■ On-shell W decays■ Semi leptonic Charm decays
|Vcs| = 1.023± 0.036
PDG 2010
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 20
CKM0: The second row: Vcb
■ B → Xclν
■ B → D(∗) transitions
Inclusive |Vcb| = (41.85± 0.43± 0.59) · 10−3
Exclusive |Vcb| = (38.85± 0.77± 0.84) · 10−3
HFAG 2010; Gambino/Uraltsev (2004); Benson/Bigi/Uraltsev (2005);Benson/Bigi/Mannel/Uraltsev (2003);...■ Inclusive is again larger■ Try to make some combinations
|Vcb| =
{(40.6± 1.3) · 10−3 PDG 2010(40.89± 0.38± 0.59) · 10−3 1008.1593
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 21
CKM0: The second row: Vcb′
Test the accuracy of the CKM elements of the second row:
δ(Vcd) = 0.011
δ(Vcs) = 0.036
δ(Vcb) = 0.013
Investigate a hypothetical 4th generation of fermionsAssume VCKM4 is unitary
⇒ Vcb′ can still be much larger than Vcb: Vcb′ < 0.15 ≈ λ
Bobrowski, A.L., Rohrwild, Riedl, 0902.4883; Buras et al. 2010; Eberhardt, A.L.,Rohrwild 1005.3505; Das, London, Sinha, Soffer 1008.4925; Alok, Dighe, London1011.2634; Soni and Nandi 1011.6091;
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 22
CKM0: The third row: Vtd
Im Vtd vs. Re Vtd
Eberhardt,
A.L.,Rohrwild
1005.3505
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 23
CKM0: The third row: Vts
Vts vs. Re Vts
Eberhardt,
A.L.,Rohrwild
1005.3505
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 24
CKM0: The third row: Vtb
Im Vtb vs. Re Vtb
Eberhardt,A.L., Rohrwild
1005.3505
Single Top production Wagner 1101.4235; CDF 0903.0885,1004.1181; D0 0903.0850
Vtb = 0.88± 0.07
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 25
CKM0: The CKM values should be known better!
■ Overall picture looks very good: CKM+
■ But looking in more detail: CKM0
◆ more precise value of Vus desireable◆ Vub problem◆ more precise values of Vcx needed◆ (almost) no direct information on Vtx
There is still a lot of room for deviations ⇒ Look for it — LHCb, SuperB-factories
■ It becomes worse (or more interesting?): CKM−
There are several hints for deviations from the CKM picture!
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 26
CKM−: Flavor Physics in the news
■ 17.5.2010 New York TimesA new Clue to explain existence
■ 19.5.2010 BBC NewsNew Clue to anti-matter mystery
■ 20.5.2010 Scientific AmericanFermilab finds new mechanism for matter’s dominance over antimatter
■ 20.5.2010 The TimesAtom-smasher takes man closer to heart of matter
■ 25.5.2010 SpiegelNeue Asymmetrie zwischen Materie und Antimaterie entdeckt
■ 28.5.2010 ScienceHints of greater matter-antimatter asymmetry challenge theorists
■ 28.5.2010 Die ZeitRätselhafte Asymmetrie
■ 29.5.2010 Chicago TribuneFermilab test throws off more matter than antimatter - and this matters
■ ...
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 27
The dimuon asymmetry■ 1005.2757 Dzero (submitted sunday, 16.5.2010) 178 citations
Evidence for an anomalous like-sign dimuon charge asymmetry
V.M. Abazov,36 B. Abbott,74 M. Abolins,63 B. S. Acharya,29 M. Adams,49 T. Adams,47 E. Aguilo,6 G.D. Alexeev,36
Selected for a Viewpoint in PhysicsPHYSICAL REVIEW D 82, 032001 (2010)
We measure the charge asymmetry A of like-sign dimuon events in 6:1 fb 1 of p $p collisions recorded
with the D0 detector at a center-of-mass energyffiffiffi
sp ¼ 1:96 TeV at the Fermilab Tevatron collider. From
A, we extract the like-sign dimuon charge asymmetry in semileptonic b-hadron decays: Absl ¼ 0:00957# 0:00251 ðstatÞ # 0:00146 ðsystÞ. This result differs by 3.2 standard deviations from the
standard model prediction AbslðSMÞ ¼ ð 2:3þ0:5 0:6Þ ' 10 4 and provides first evidence of anomalous
CP violation in the mixing of neutral B mesons.
DOI: 10.1103/PhysRevD.82.032001 PACS numbers: 13.25.Hw, 11.30.Er, 14.40.Nd
[1] A. Lenz and U. Nierste, J. High Energy Phys. 06 (2007)
072.
[2] C. Amsler et al., Phys. Lett. B 667, 1 (2008), and 2009
partial update for the 2010 edition.
[3] A. D. Sakharov, Pis’ma Zh. Eksp. Teor. Fiz. 5, 32 (1967)
[15] V.M. Abazov et al. (D0 Collaboration), Nucl. Instrum.
Methods Phys. Res., Sect. A 565, 463 (2006).
[16] S. N. Ahmed et al., arXiv:1005.0801 [Nucl. Instrum.
Methods Phys. Res. Sect. A (to be published)]; R.
Angstadt et al., arXiv:0911.2522.
17.5.’10 NYT: “A new clue to explain existence” (26.5 · 106 google entries)
■ 1106.6308: 9 fb−1, Absl = (−0.787± 0.172(stat)± 0.093(syst))% ⇒ 3.9σ
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 28
TeVatron gave us many presents, and then ...
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 29
Mixing I
Time evolution of a decaying particle: B(t) = exp [−imBt− ΓB/2t]can be written as
id
dt
(|B(t)〉
|B̄(t)〉
)=
(M̂ −
i
2Γ̂
)(|B(t)〉
|B̄(t)〉
)
BUT: In the neutral B-system transitions like Bd,s → B̄d,s are possible due toweak interaction: Box diagrams
b
d
t,c,u
t,c,u
W-
b
db
dt,c,u t,c,uW
-b
d
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 30
Mixing II
Mixing is a macroscopic quantum effect!
It was observed in
■ K0-system: 1950s (see text books, regeneration...)■ Bd-system: 1986■ Bs-system: 2006■ D0-system: 2007
Strongly suppressed in the SM (due to virtual top-quarks)New physics effects might be of comparable size
?Is QCD under control?
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 31
Mixing III
Time evolution of a decaying particle: B(t) = exp [−imBt− ΓB/2t]can be written as
id
dt
(|B(t)〉
|B̄(t)〉
)=
(M̂ −
i
2Γ̂
)(|B(t)〉
|B̄(t)〉
)
BUT: In the neutral B-system transitions like Bd,s → B̄d,s are possible due toweak interaction: Box diagrams
b
d
t,c,u
t,c,u
W-
b
db
dt,c,u t,c,uW
-b
d
⇒ off-diagonal elements in M̂, Γ̂: M12, Γ12 (complex)Diagonalization of M̂, Γ̂ gives the physical eigenstates BH and BL with themasses MH , ML and the decay rates ΓH , ΓL
CP-odd: BH := p B + q B̄ , CP-even: BL := p B − q B̄ with |p|2 + |q|2 = 1
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 32
Mixing IV
|M12|, |Γ12| and φ = arg(−M12/Γ12) can be related to three observables:
■ Mass difference: ∆M :=MH −ML = 2|M12|(1− 1
8|Γ12|
2
|M12|2sin2 φ+ ...
)
|M12| : heavy internal particles: t, SUSY, ...
■ Decay rate difference: ∆Γ := ΓL − ΓH = 2|Γ12| cosφ(1 + 1
8|Γ12|
2
|M12|2sin2 φ+ ...
)
|Γ12| : light internal particles: u, c, ... (almost) no NP!!!
■ Flavor specific/semileptonic CP asymmetries:
B̄q → f and Bq → f̄ forbiddenNo direct CP violation: |〈f |Bq〉| = |〈f̄ |B̄q〉|e.g. Bs → D−
s π+ or Bq → Xlν (semileptonic)
asl ≡ afs =Γ(Bq(t) → f)− Γ(Bq(t) → f)
Γ(Bq(t) → f) + Γ(Bq(t) → f)= −2
(∣∣∣∣q
p
∣∣∣∣− 1
)= Im
Γ12
M12=
∆Γ
∆Mtanφ
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 33
The Mass Difference ∆M
Calculating the box diagram with an internal top-quark yields
M12,q =G2F
12π2(V ∗tqVtb)
2M2WSo(xt)BBq
f2BqMBq
η̂B (Inami, Lim ’81)
■ Hadronic matrix element: 83BBq
f2BqMBq
= 〈B̄q|(b̄q)V−A(b̄q)V−A|Bq〉
■ Perturbative QCD corrections η̂B (Buras, Jamin, Weisz, ’90)
Theory 1102.4274 vs. Experiment : HFAG 11
∆Md = 0.543± 0.091 ps−1 ∆Md = 0.507± 0.004 ps−1
ALEPH, CDF, D0, DELPHI, L3,
OPAL, BABAR, BELLE, ARGUS, CLEO
∆Ms = 17.30± 2.6 ps−1 ∆Ms = 17.70± 0.12 ps−1
CDF, D0, LHCb
Important bounds on the unitarity triangle and new physics
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 34
Determination of Γ12
Sensitive to real intermediate states ⇒ much more complicated than M12
1. OPE I: Integrate out W: like M12 ∝ f2BB
2. OPE II: Heavy quark expansion ⇒ Γ(j)i ∝ f2B
∑CkBK
Γ12 =
(Λ
mb
)3(Γ(0)3 +
αs4π
Γ(1)3 + ...
)+
(Λ
mb
)4(Γ(0)4 + ...
)+
(Λ
mb
)5(Γ(0)5 + ...
)+ ...
1996: Beneke, Buchalla, Dunietz1998: Beneke, Buchalla, Greub, A.L., Nierste
2003: Ciuchini, Franco, Lubicz, Mescia, Tarantino; Beneke, Buchalla, A.L., Nierste2006: A.L., Nierste
2007: Badin, Gabbiani, Petrov
∆Γs = ∆Γ0s
(1 + δLattice + δQCD + δHQE
)
= 0.142 ps−1 (1− 0.14− 0.06− 0.19)
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 35
HQE under attack!
OPE II might be questionable - relies on quark hadron duality
■ Mid 90’s: Missing Charm puzzle nExp.c < nSMc , semi leptonic branching ratio
■ Mid 90’s: Λb lifetime is too short■ before 2003: τBs
/τBd≈ 0.94 6= 1
■ 2010/2011: Di-muon asymmetry too large
Theory arguments for HQE
⇒ calculate corrections in all possible “directions”, to test convergence⇒ Γ12 seems to be ok!
⇒ test reliability of OPE II via lifetimes (no NP effects expected) “directions”, totest convergence⇒ τ(B+)/τ(Bd) Experiment and theory agree within hadronic uncertainties
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 36
HQE under attack!
OPE II might be questionable - relies on quark hadron duality
■ 2012: n2011PDGc = 1.20± 0.06 vs. nSMc = 1.20± 0.04
Eberhardt, Krinner, A.L., Rauh in prep.
■ Mid 90’s: Λb lifetime is too short■ before 2003: τBs
/τBd≈ 0.94 6= 1
■ 2010/2011: Di-muon asymmetry too large
Theory arguments for HQE
⇒ calculate corrections in all possible “directions”, to test convergence⇒ Γ12 seems to be ok!
⇒ test reliability of OPE II via lifetimes (no NP effects expected) “directions”, totest convergence⇒ τ(B+)/τ(Bd) Experiment and theory agree within hadronic uncertainties
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 37
HQE under attack!
OPE II might be questionable - relies on quark hadron duality
■ 2012: n2011PDGc = 1.20± 0.06 vs. nSMc = 1.20± 0.04
Eberhardt, Krinner, A.L., Rauh in prep.
■ HFAG ’03 τΛb= 1.212± 0.052 ps−1 −→ HFAG ’11 τΛb
= 1.425± 0.032 ps−1
Shift by 4σ ⇒Eagerly waiting for new LHCb results!!!■ before 2003: τBs
/τBd≈ 0.94 6= 1
■ 2010/2011: Di-muon asymmetry too large
Theory arguments for HQE
⇒ calculate corrections in all possible “directions”, to test convergence⇒ Γ12 seems to be ok!
⇒ test reliability of OPE II via lifetimes (no NP effects expected) “directions”, totest convergence⇒ τ(B+)/τ(Bd) Experiment and theory agree within hadronic uncertainties
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 38
HQE under attack!
OPE II might be questionable - relies on quark hadron duality
■ 2012: n2011PDGc = 1.20± 0.06 vs. nSMc = 1.20± 0.04
Eberhardt, Krinner, A.L., Rauh in prep.
■ HFAG ’03 τΛb= 1.212± 0.052 ps−1 −→ HFAG ’11 τΛb
= 1.425± 0.032 ps−1
Shift by 4σ ⇒Eagerly waiting for new LHCb results!!!■ Moriond 2012 LHCb: τBs
/τBd= 1.001± 0.014 LHCb-CONF-2012-002
■ 2010/2011: Di-muon asymmetry too large
Theory arguments for HQE
⇒ calculate corrections in all possible “directions”, to test convergence⇒ Γ12 seems to be ok!
⇒ test reliability of OPE II via lifetimes (no NP effects expected) “directions”, totest convergence⇒ τ(B+)/τ(Bd) Experiment and theory agree within hadronic uncertainties
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 39
The Bs lifetime
Moriond 2012 LHCb vs SM A.L., Nierste 2011
τBs
τBd
Exp= 1.001± 0.014
τBs
τBd
SM= 0.996...1.000
■ 0.940± 0.014 would have been a desaster for SM = may be NP :-)■ Update of effective lifetimes
Fleischer et al used 1011.1096, 1109.1112, 1109.5115: τBs= 1.477 ps
Exp. SM-old SM-new
τEff(K+K−) 1.468± 0.046 1.390± 0.032 1.43± 0.03
τEff(ψf0) 1.70± 0.12 1.582± 0.036 1.63± 0.03
τFS 1.417± 0.042 −−− 1.54± 0.03
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 40
HQE under attack!
OPE II might be questionable - relies on quark hadron duality
■ 2012: n2011PDGc = 1.20± 0.06 vs. nSMc = 1.20± 0.04
Eberhardt, Krinner, A.L., Rauh in prep.
■ HFAG ’03 τΛb= 1.212± 0.052 ps−1 −→ HFAG ’11 τΛb
= 1.425± 0.032 ps−1
Shift by 4σ ⇒Eagerly waiting for new LHCb results!!!■ Moriond 2012 LHCb: τBs
/τBd= 1.001± 0.014 LHCb-CONF-2012-002
■ 2010/2011: Di-muon asymmetry too large — Test Γ12 with ∆Γs!
Theory arguments for HQE
⇒ calculate corrections in all possible “directions”, to test convergence⇒ Γ12 seems to be ok!
⇒ test reliability of OPE II via lifetimes (no NP effects expected) “directions”, totest convergence⇒ τ(B+)/τ(Bd) Experiment and theory agree within hadronic uncertainties
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 41
∆Γs in NLO-QCD I
A brief history of theory predictions
′81... Hagelin; Buras et al.;... ∆Γ ∝ O(0.15 ps−1
)
′93 Aleksan et al.; ... ∆Γ ∝ O(0.10 ps−1
)
′96 Beneke, Buchalla, Dunietz ∆Γs =(0.11+0.07
−0.06
)ps−1
′00 Beneke, A.L. ∆Γs = (0.06± 0.03) ps−1
′03 Ciuchini, et al ∆Γs = (0.050± 0.016)ps−1
′06 A.L., Nierste ∆Γs = (0.096± 0.036)ps−1
′11 A.L., Nierste ∆Γs = (0.087± 0.021)ps−1
Crucial dependence on non-perturbative parameters!2011 fBs
= 231± 15 MeV used.Newer Results:■ 1110.4510 - HPQCD:fBs
= 225± 4 MeV ⇒ ∆Γs = (0.083± 0.017) ps−1
■ 1112.3051 - Fermilab:fBs= 242± 9.5 MeV ⇒ ∆Γs = (0.095± 0.021) ps−1
■ 1201.3956 - chiral QM:fBs= 262±? MeV ⇒ ∆Γs = (0.112±?) ps−1
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 42
∆Γs in NLO-QCD II
Improvement in theoretical accuracy
∆ΓSMs 2011 2006
Central Value 0.087 ps−1 0.096 ps−1
δ(BR̃2
) 17.2% 15.7%
δ(fBs) 13.2% 33.4%
δ(µ) 7.8% 13.7%
δ(B̃S,Bs) 4.8% 3.1%
δ(BR0) 3.4% 3.0%
δ(Vcb) 3.4% 4.9%
δ(BBs) 2.7% 6.6%
... .... ...∑δ 24.5% 40.5%
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 43
Finally ∆Γs is measured! (naive: 6.1σ)
∆ΓSMs = (0.087± 0.021) ps−1
LHCb from Bs → J/ψφ Dunietz, Fleischer, Nierste
LP 2011 ∆Γs = (0.123± 0.031) ps−1 ⇒∆ΓExp
s
∆ΓSMs
= 1.41± 0.50
Moriond 2012 ∆Γs = (0.116± 0.019) ps−1 ⇒∆ΓExp
s
∆ΓSMs
= 1.33± 0.39
■ D0 8fb−1 1109.3166: ∆Γs = (0.163± 0.065) ps−1
■ CDF 9.6fb−1 Public Note 10778: ∆Γs = (0.068± 0.027) ps−1
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 44
Finally ∆Γs is measured! (naive: 6.1σ)
Get rid off the dependence on fBs(No NP in ∆M )
∆Γs∆Ms
= 10−4 ·
[46.2 + 10.6
B̃′S
B−
(13.2
BR̃2
B− 2.5
BR0
B+ 1.2
BRB
)]
= 0.0050± 0.0010
HQE vs. Experiment
(∆Γs∆Ms
)Exp
/
(∆Γs∆Ms
)SM
= 1.30± 0.34
HQE works also for Γ12!How precise does it work? 30%? 10%?
Still more accurate data needed! TeVatron, LHCb, Super-B(elle)
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 45
∆ΓCPs /Γs = 2Br(Bs → D
(∗)+s +D
(∗)−s )?
■ 1993 Aleksan; Le Yaouanc, Olivre, Pene, Raynal:The above equation holds in the limit: mc → ∞;mb − 2mc → 0;Nc → ∞Corresponds to negligible 3-body final state contributions to Γs12
∆ΓsΓs
∝ O(0.15)
■ 1107.4325 Chua, Hou, Shen Reanalysis of the exclusive approach◆ 2-body final states contribute 0.100± 0.030 to ∆Γ/Γ
Aleksan et al were lucky...◆ 3-body final states contribute about 0.06...0.08
This is comparable to 2-body final states! ⇒ bad approximation ⇒ test exp.
We strongly discourage from the inclusion of Br(Bs→ D(∗)+ +D(∗)−) in averages with∆Γs determined from clean methods.
A.L., Nierste; hep-ph/0612167
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 46
Semi leptonic CP-asymmetries afs and ∆Γd
SM predictions: A.L., U. Nierste, 1102.4274; A.L. 1108.1218
asfs = (1.9± 0.3) · 10−5 φs = 0.22◦ ± 0.06◦
adfs = − (4.1± 0.6) · 10−4 φd = −4.3◦ ± 1.4◦
Absl = 0.406assl + 0.594adsl = (−2.3± 0.4) · 10−4
Experimental bounds
asfs = (−1150± 610) · 10−5 (HFAG 11)
φs = −51.6◦ ± 12◦ (A.L., Nierste, CKMfitter, 1008.1593)
= −0.1◦ ± 5.0◦ LHCb Moriond 2012
adfs = − (49± 38) · 10−4 (HFAG 11)
∆ΓdΓd
= (−17± 21) · 10−3 (Belle EPS 2011 )
Absl = −(7.87± 1.72± 0.93) · 10−3(D0,1106.6308)
Absl(Exp.)/Absl(Theory) = 34 3.9− σ-effect
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 47
New Physics in B-Mixing I
Γ12,s = ΓSM12,s , M12,s =MSM
12,s ·∆s ; ∆s = |∆s|eiφ∆
s
∆s = r2se2iθs = CBs
e2iφBs = 1 + hse2iσs
∆Ms = 2|MSM12,s| · |∆s|
∆Γs = 2|Γ12,s| · cos(φSMs + φ∆s
)
∆Γs∆Ms
=|Γ12,s|
|MSM12,s|
·cos(φSMs + φ∆s
)
|∆s|
asfs =|Γ12,s|
|MSM12,s|
·sin(φSMs + φ∆s
)
|∆s|
sin(φSMs ) ≈ 1/240
For |∆s| = 0.9 and φ∆s = −π/4 onegets the following bounds in thecomplex ∆-plane :
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 48
New Physics in B-Mixing II
Combine all data till end of 2011 and neglect penguinsfit of ∆d and ∆s 1203.0238 (update of 1008.1593) soon v2!
expα
)s
(BSL
) & ad
(BSL & aSLA
sm∆ & dm∆SM point
)d
β+2d ∆φsin(
)>0d
β+2d ∆φcos(
d∆Re -2 -1 0 1 2 3
d∆Im
-2
-1
0
1
2
excluded area has CL > 0.68
End of 2011
CKMf i t t e r mixing dB -
d New Physics in B
)s
(BSL
) & ad
(BSL & aSLA
FSsτ & sΓ ∆
sm∆ & dm∆s
β-2s ∆φ
SM point
s∆Re -2 -1 0 1 2 3
s∆Im
-2
-1
0
1
2
excluded area has CL > 0.68
End of 2011
CKMf i t t e r mixing sB -
s New Physics in B
■ Fits not so good anymore (LHCb vs. Dzero)■ B → τν vs. sin 2β solved with φ∆d — No tension for ǫK
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 49
The dimuon asymmetry
The central value of the di µasymmetry is larger than theoretically possible!
AMax.sl ≈ (0.594± 0.022)(5.4± 1.0) · 10−3 sin(φ
SMd + φ∆d )
|∆d|
+(0.406± 0.022)(5.0± 1.1) · 10−3 sin(φSMs + φ∆s )
|∆s|
≈ (−3.1;−4.8[1σ];−9.0[3σ]) · 10−3
AD0sl = (−7.8± 2.0) · 10−3 A.L. 1108.1218
Possible solutions:
■ HQE violated by O(200%− 3300%) now excluded!■ Huge new physics in Γ12? - No! Bobeth, Haisch 1109.1826■ Contradiction to Bs → J/ψφ from LHCb? - Be aware of Penguins!■ Stat. fluctuation (1.5 σ) of the D0 result? (Actual value is below -4.8 per mille?)
Independent measurements of semi leptonic asymmetries needed!
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 50
?New physics in Γ12?
■ Large (O(200− 3400%) NP effects in Γ12? Why not seen somewhere else?
A new operator bs→ X with Mx < MB contributes not only to assl but also tomany more observables, e.g.:◆
b b
q q
Γ3 ⇒
{τ(Bs)/τ(Bd)
∆Γs
◆
b b
Γ0 ⇒
τ(Bx)
Bsl
Br(b→ s no charm)
◆ M12, operator mixing with e.g. b→ sγ, ...
◆ A promising candidate for X seems to be τ+ + τ− -> Bobeth, Haisch ’11.Current best bound Br(Bs → ττ < 5%) - LHCb should do better :-)
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 51
?New physics in Γ12?
■ Missing charm puzzle , e.g.Bigi et al ’94; Bagan et al. ’94; Falk, Wise, Dunietz ’95, Neubert ’97... A.L.
,hep-ph/0011258Look at inclusive b-decay into 0, 1, 2 c-quarksDefine r(x charm) := Γ(b→x charm)
Γsl: m5
bV2cb cancels; Γsl seems safe
The average number of charm quarks per b-decay reads
nc = 0 + [r(1c) + 2r(2c)]BExp.sl
= 1 + [r(2c)− r(0c)]BExp.sl
= 2− [r(1c) + 2r(0c)]BExp.sl
Buchalla, Dunietz, Yamamoto ’95◆ nExp.
c < nTheoryc = missing charm puzzle
May be enhanced b→ s g... Kagan ...◆ latest Data from BaBar and CLEO agree within large uncertainties
Recent and future experiments can do better!◆ Any unknown, even invisible decay mode has an effect on r(0, 1, 2 charm)
!!! ⇒ Need new experimental values for r(0c, 1c, 2c) = Γ0c,1c,2c/Γsl and Bsl!!!
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 52
?New physics in Γ12?
Step I: Forget about all the bounds and fit ∆Γ, asl and ∆M :
SM
)dδIm(-10 -5 0 5 10
) sδIm
(
-10
-5
0
5
10
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0p-value
End of 2011
CKMf i t t e r New Physics Scenario IV
A.L, Nierste, CKMfitter 1203.0238Step II: Take your favourite model which gives new contributions to Γ12
■ Determine contributions to δd, δs■ Determine contributions to τBs
, nc, ....■ Exclude the model :-)
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 53
How large are Penguins?
Angular analysis of Bs → J/ψφ at CDF, D0 and LHCb:
SSMψφ = 0.0036± 0.002 → sin
(2βs−φ
∆s − δPeng,SMs − δPeng,NP
s
)= 0.002± 0.087
LHCb Moriond 2012Is this a contraction to the dimuon asymmetry?
Depends on the possible size of penguin contributions
■ SM penguin are expected to be very smallbut see also Faller, Fleischer; Mannel 2008
■ NP penguins might be larger
But: even small penguin contributions have a sizeable effect! A.L. 1106.3200
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 54
Wish-list for Experiments
a) Congratulations to LHCb for the first measurement of ∆Γs!◆ Still more precision needed: LHCb, TeVatron, Super-B Bs → J/ψη(
′)
◆ Do not use Br(Bs → D(∗)+s D
(∗)−s ) = ∆ΓCP
2Γ - check size of 3-body FS!
b) τBs= (1.001± 0.014)τBd
: strong constraint on NP and duality violation◆ Combine with other determinations of τBs
: LHCb, ATLAS?, CMS?◆ Bs: Effective lifetimes, flavor specific lifetimes (2.x sigma deviation)◆ τΛb
, ...
c) Di muon asymmetry Absl◆ HQE fails? No! At most 30− 40% — more precise test via τ(Bs),∆Γs, ...◆ NP acts in Γ12? No! At most 40%! — More precise tests viaτ(Bs),∆Γs,∆Γd, nc, Bsl, r(0, 1, 2 charm), Bs → ττ, B → Kττ, ...
◆ ???◆ Experimental cross-check via adsl and assl!
d) φLHCbs ≪ φAb
sls How large is the penguin pollution?
◆ Even small penguins can be important!◆ Values for many penguin modes e.g. Bs → J/ψKs, K
0K̄0, φφ, η(′)η(
′)...
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 55
What to do list - Theory
Test of HQE with lifetimes
• τB+/τBdand τBs/τBd
fits well ⇒ currently no hints for deviations from HQE
• Precise non-perturbative matrix elements for 4-quark oper ators urgently needed
• Beautiful Mesons and Baryons on the Lattice ECT* Trento, 2-6 April 2012• Perturbative improvements of lifetime predictions
Theoretical predictions for mixing observables
• Precise decay constants and Bag parameter for ∆M
• Additional Bag parameters at dimension 6 and 7 for Γ12
• αs/mb corrections for Γ12
• α2s corrections for Γ12
Theoretical predictions for charm mixing observables
• Push HQE to its limits
• Try to imrove the exclusive approach
Update of theoretical predictions for inclusive rates - con trol penguins!!!
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 56
Moriond 2012: Conclusion from B-Mixing
It is actually not bad, what the Grinch left for us
Expansion in 1/mb works so well,What does this tell about charm? 1/mc ≈ 3 · 1/mb
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 57
CKM−: How large are Penguins? II
Many observables in the Bs mixing system:
Elimination of ΓTheo12 via ( No hint for incorrectness of ΓTheo
12 except: Absl is 1.5σabove bound)
assl = −∆Γ
∆M
Sψφ√1− Sψφ2
·δ
not possible at that simple level, because δ 6= 1
δ =tan
(φSMs + φ∆s
)
tan(−2βSM
s + φ∆s + δpeng,SMs + δpeng,NPs
)
A.L. 1106.3200
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 58
CKM−: How large are Penguins? III
0.5 1.0 1.5 2.0 2.5 3.0Φ
- 1.0
- 0.5
0.5
1.0
1.5
2.0∆
■ Above relation can be used to determine δpeng,SMs + δpeng,NPs
■ To extract φ∆s one needs Γs,SM12
δpeng,SMs + δpeng,NPs = 10◦
δpeng,SMs + δpeng,NPs = 5◦
δpeng,SMs + δpeng,NPs = 2◦
δpeng,SMs + δpeng,NPs = 0◦
φSMs = 0.22◦ ± 0.06◦
−2βs = (2.1± 0.1)◦
A.L. 1106.3200
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 59
Lifetimes: τB+/τBd in NLO-QCD I
τ1τ2
= 1 +
(Λ
mb
)3 (Γ(0)3 +
αs4π
Γ(1)3 + ...
)+
(Λ
mb
)4 (Γ(0)4 + ...
)+ ...
2002: Beneke, Buchalla, Greub, A.L., Nierste; Franco, Lubicz, Mescia, Tarantino
2004: Greub, A.L., Nierste; 2008 A.L.
E1
d
b
d
b
E2
d
b
d
b
E3
d
b
d
b
E4
d
b
d
b
d
b
d
b
u
c D1
d
b
d
b
u
c D2
d
b
d
b
u
c D3
d
b
d
b
u
c D4
d
b
d
b
u
c
D5
d
b
d
b
u
c D6
d
b
d
b
u
c D7
d
b
d
b
u
c D8
d
b
d
b
u
c D9
d
b
d
b
u
c D10
d
b
d
b
u
c D11
[τ(B+)
τ(B0d)
]
LO,NLO,HFAG10
= 1.047± 0.049 ↔ 1.063± 0.027 ↔ 1.071± 0.009
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 60
Lifetimes: τB+/τBd in NLO-QCD II
τ1τ2
= 1 +
(Λ
mb
)3 (Γ(0)3 +
αs4π
Γ(1)3 + ...
)+
(Λ
mb
)4 (Γ(0)4 + ...
)+ ...
2002: Beneke, Buchalla, Greub, A.L., Nierste; Franco, Lubicz, Mescia, Tarantino
2004: Greub, A.L., Nierste; 2008 A.L.
E1
d
b
d
b
E2
d
b
d
b
E3
d
b
d
b
E4
d
b
d
b
d
b
d
b
u
c D1
d
b
d
b
u
c D2
d
b
d
b
u
c D3
d
b
d
b
u
c D4
d
b
d
b
u
c
D5
d
b
d
b
u
c D6
d
b
d
b
u
c D7
d
b
d
b
u
c D8
d
b
d
b
u
c D9
d
b
d
b
u
c D10
d
b
d
b
u
c D11
[τ(B+)
τ(B0d)
]
LO,NLO,HFAG11
= 1.047± 0.049 ↔ 1.044± 0.024 ↔ 1.079± 0.007
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 61
Lifetimes: τB+/τBd in NLO-QCD III
τB+
τBd
− 1 = 0.0324
(fB
200MeV
)2
[(1.0± 0.2)B1 + (0.1± 0.1)B2
− (17.8± 0.9)ǫ1 + (3.9± 0.2)ǫ2 − 0.26]
with non-perturbative input from Becirevic hep-ph/0110124
B1 = 1.10± 0.20
B2 = 0.79± 0.10
ǫ1 = −0.02± 0.02
ǫ2 = 0.03± 0.01
Update urgently needed!
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 62
Lifetimes: Lifetimes of heavy hadrons
■ τ(B+)/τ(Bd): HQE seems to fit, but we need urgently more precise hadronicmatrix elements
■
τ(Bs)
τ(Bd)= 0.996...1.000 ↔ 0.969± 0.017 HFAG 2011
A.L. 1102.4274 ↔ 1.004± 0.018 LHCb-Conf2011-049
More data as well as non-perturbative matrix elements needed
■ τ(Λb), τ(Ξb) and τ(Bc): more data and further theory work (perturbative andnon-perturbative) neccessary
■ τ(D), D-mixing: work in progressBigi, Uraltsev 2001; Bobrowski, A.L., Riedl, Rohrwild 1002.4794; 1011.5608;Bobrowski, A.L. Nierste, Prill, to appearIt is not unplausible that HQE might give reasonable estimates
Seminar, NIKHEF, Amsterdam A. Lenz, March 22nd 2012 - p. 63
Theory statements about CPV in D before LHCb