Niels Tuning (1) CP violation Lecture 5 N. Tuning.
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Transcript of Niels Tuning (1) CP violation Lecture 5 N. Tuning.
Diagonalize Yukawa matrix Yij
– Mass terms
– Quarks rotate
– Off diagonal terms in charged current couplings
Niels Tuning (3)
RecapSM Kinetic Higgs Yukawa L L L L
0( , ) ...I I
Yuk Li L Rjd Ij id dY u
L
...2 2
Kinetic Li LiI I I
Li LIi
g gu W d d W u
L
5 5*1 1 ...2 2
ij iCKM i j j j i
g gu W d d uV VW
L
, , , , ...d u
s cL L
b tR R
Mass
m d m u
d s b m s u c t m c
m b m t
L
I
ICKM
I
d d
s V s
b b
SM CKM Higgs Mass L L L L
uI
dI
W
u
d,s,b
W
Niels Tuning (4)
CKM-matrix: where are the phases?
u
d,s,b
W
• Possibility 1: simply 3 ‘rotations’, and put phase on smallest:
• Possibility 2: parameterize according to magnitude, in O(λ):
This was theory, now comes experiment
• We already saw how the moduli |Vij| are determined
• Now we will work towards the measurement of the imaginary part– Parameter: η
– Equivalent: angles α, β, γ .
• To measure this, we need the formalism of neutral meson oscillations…
Niels Tuning (5)
Meson Decays
• Formalism of meson oscillations:
• Subsequent: decay
0 ( )P t
Interference(‘direct’) Decay
Recap osc + decays
Classification of CP Violating effects
1. CP violation in decay
2. CP violation in mixing
3. CP violation in interference
Recap CP violation
Im( λf)
1. CP violation in decay
2. CP violation in mixing
3. CP violation in interference
We will investigate λf for various final states f
Recap CP violation
Niels Tuning (10)
CP eigenvalue of final state J/K0S
* * *
/ * * *s
tb td cb cs cs cdJ K
tb td cb cs cs cd
V V V V V V
V V V V V V
sin 2 ( ) sin( )CPA t mt
2ie
• CP |J/> = +1 |J/>
• CP |K0S> = +1 |K0
S>
• CP |J/K0S> = (-1)l
|J/K0S> ( S(B)=0 L(J/K0
S)=1 )
( ) ( )( ) Im( )sin
( ) ( )B fB f
CP fB fB f
t tA t mt
t t
Relative minus-sign between state and CP-conjugated state:
( S(J/)=1 )
λf contains information on final state f
Niels Tuning (11)
Recap CP in B
Investigated three final states f
• B0J/ψKs
• B0sJ/ψφ
• B0sDsK
3. CP violation in interference
λf contains information on final state f
Niels Tuning (12)
• B0sJ/ψφ
3. CP violation in interference
Recap CP in B
Remember!
Necessary ingredients for CP violation:
1) Two (interfering) amplitudes
2) Phase difference between amplitudes– one CP conserving phase (‘strong’ phase)
– one CP violating phase (‘weak’ phase)
Niels Tuning (14)
Basics
The basics you know now!
1. CP violation from complex phase in CKM matrix
2. Need 2 interfering amplitudes (B-oscillations come in handy!)
3. Higher order diagrams sensitive to New Physics
Next:
• (Direct) CP violation in decay
• CP violation in mixing (we already saw this with the kaons: ε≠0, or |q/p|≠1)
• Penguins
• The unitarity triangle
Niels Tuning (16)
Niels Tuning (18)
CKM Angle measurements from Bd,u decays
• Sources of phases in Bd,u amplitudes*
• The standard techniques for the angles:
*In Wolfenstein phase convention.
Amplitude Rel. Magnitude Weak phase
bc Dominant 0
bu Suppressed γ
td (x2, mixing) Time dependent
2β
B0 mixing + single bc decay
B0 mixing + single bu decay
Interfere bc and bu in B± decay.
β
-i
-i
γ1 1
1 1 1
1 1
e
e
bu
td
Niels Tuning (19)
Determining the angle
• From unitarity we have:
• Must interfere b u (cd) and b c(ud)
• Expect b u (cs) and b c(us) to have the same phase, with more interference (but less events)
* * *ub ud tb td cb cdV V V V V V
*ub udV V *
tb tdV V
*cb cdV V
* * * *arg argub ud cb cd ub ud cb cdV V V V V V V V 3 2
3 2
Measure γ: B0s Ds
K-/+ : both λf and λf
Niels Tuning (20)NB: In addition B s Ds
K-/+ : both λ f and λf
+Γ(Bf)=
+Γ(Bf )=
2
2
Niels Tuning (21)
Measure γ: Bs DsK-/+ --- first one f: Ds
+K-
s s
scsV
s s
s
*usV
* 2cb udV V * 4 i
ub cdV V e * 3cb usV V * 3 i
ub csV V e
• This time | Af||Af|, so |λ|1 !
• In fact, not only magnitude, but also phase difference:
Measure γ: Bs DsK-/+
Niels Tuning (22)
• Need B0s Ds
+K- to disentangle and :
• B0s Ds
-K+ has phase difference ( - ):
Niels Tuning (24)
0
0B KB KBBAABBARARBBAABBARAR
CP violation in Decay? (also known as: “direct CPV”)
HFAG:
0.133 0.030 0.009 CPA
hep-ex/0407057Phys.Rev.Lett.93:131801,2004
4.2
BBAABBARARBBAABBARAR
B fB fCP
B fB f
A
First observation of Direct CPV in B decays (2004):
ACP = -0.098 ± 0.012
Niels Tuning (25)
LHCbLHCbLHCbLHCb
CP violation in Decay? (also known as: “direct CPV”)
LHCb-CONF-2011-011LHCbLHCbLHCbLHCb
B fB fCP
B fB f
A
First observation of Direct CPV in B decays at LHC (2011):
Niels Tuning (26)
Direct CP violation: Γ( B0 f) ≠ Γ(B0f )
220 * * 4 2( ) i i iub us tb tsB K V V e V V e
2 20 * * 4 2( ) i i iub us tb tsB K V V e V V e
Only different if both δ and γ are ≠0 !
Γ( B0 f) ≠ Γ(B0f )
CP violation if Γ( B0 f) ≠ Γ(B0f )
But: need 2 amplitudes interference
220 * * 4 2( ) i i iub us tb tsB K V V e V V e * 4i i i
ub usV V e e
Amplitude 1
+
Amplitude 2
Niels Tuning (27)
Hint for new physics? B0Kπ and BKπ0
0 B K 0 B KAverage 0.049 0.040 CPA
3.6
0 B K 0 B KAverage 0.114 0.020 CPA
Redo the experiment with B instead of B0…
d or u spectator quark: what’s the difference ??B0Kπ
B+Kπ
Hint for new physics? B0Kπ and BKπ0
Niels Tuning (29)
T (tree) C (color suppressed) P (penguin)
B0→K+π-
B+→K+π0
Niels Tuning (31)
CP violation in Mixing? (also known as: “indirect CPV”: ε≠0 in K-system)
0 0P B B
0 0P B B
0 0B B0 0B B0 0B B0 0B B
gVcb* W
c
d
0 bB
d
gVcb
W
c
d
0 bB
d
X X X
X
0 0B B
t=0 t
0 0 0 0B B BP P B ?
Look for like-sign lepton pairs:Decay
Niels Tuning (32)
(limit on) CP violation in B0 mixing
Look for a like-sign asymmetry:
4
4
1
1T
q pN t N tA t
N t N t q p
As expected, no asymmetry is observed…
1q
p
CP violation in Bs0 Mixing??
Niels Tuning (33)
D0 Coll., Phys.Rev.D82:032001,2010.arXiv:1005.2757
0 0P B B
0 0P B B
0 0B B0 0B B0 0B B0 0B B
X X X
X
0 0B B
b
s
s
b
“Box” diagram: ΔB=2
φsSM ~ 0.004
φsSM
M ~ 0.04
CP violation from Semi-leptonic decays
• SM: P(B0s→B0
s) = P(B0s←B0
s)
• DØ: P(B0s→B0
s) ≠ P(B0s←B0
s)
• b→Xμ-ν, b→Xμ+ν• b→b → Xμ+ν, b→ b → Xμ-ν Compare events with like-sign μμ Two methods:
Measure asymmetry of events with 1 muon
Measure asymmetry of events with 2 muons
?
• Switching magnet polarity helps in reducing systematics
• But…: Decays in flight, e.g. K→μ K+/K- asymmetry
CP violation from Semi-leptonic decays
• SM: P(B0s→B0
s) = P(B0s←B0
s)
• DØ: P(B0s→B0
s) ≠ P(B0s←B0
s) ?
B0
s→
Ds±X
0μ
ν