Peter Krian

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CP violation and related issuesPart 16 CKM
matrix, summary and outlook

• Peter Krian
• University of Ljubljana and J. Stefan Institute

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Contents
Unitarity triangle revisited CP violation
revisited cosmological implications How much CP
is needed? What comes next?
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CP violation in SM
CP violation consequence of the Cabibbo-Kobayashi
-Maskawa (CKM) quark mixing matrix
Transitions between members of the same family
more probable than others -gt CKM almost a
diagonal matrix, but not completely
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CKM matrix
If VijVij ? LLCP ? CP is conserved,
otherwise not
3x3 unitary matrix 3 real parameters and 1 phase
-gt the matrix is in general complex
s12sinq12, c12cosq12 etc. CKM matrix
can accomodate the CP violation, and does it
well!
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Unitary triangles
All triangles have the same area J/2 (about
4x10-5)
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Unitarity triangle
THE unitarity triangle
Measure angles and sides f1b f2a f3g Vub
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CP violation measurements the main tool to study
the unitarity triangle
CP violation in the interference between mixing
and decay to a state accessible in both B0 and
anti-B0 decays For example a CP eigenstate fCP
like p p-
If l 1 -gt
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Angle b (f1) as sin2f1 from CP asymmetry
measurement
Asymmetry between B and anti-B decaying to the
same final CP eigenstate J/yKS
BtagB0
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Angle a (f2) from CP asymmetry measurement
Asymmetry between B and anti-B decaying to the
same final CP eigenstate p p-, complicated
analysis because of penguin diagrams
BtagB0
Spp -0.670.160.06 App 0.560.120.06 -gt
direct CP violation! Evident on this plot
Number of anti-B events lt Number of B events
aCP
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Angle a (f2) from CP asymmetry measurements
Use measured BRs and asymmetries in all three B ?
p p decays ? extract f2
Similar analysis as for B ? p p also for B ? r
r
(f2eff closer to f2)
... and for B ? r p
BaBar
Similar from B ? r r
f2 106o 8o11o
BaBar/Belle
Similar from B ? r p
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Angle g (f3) from a Dalitz plot analysis of the
interference of two decay channels
B? D0K
B-? D0K-
m2(Ksp-)
m2(Ksp-)
m2(Ksp)
m2(Ksp)
Visible asymmetry
f3 (68 1415 13 11)o
Fit with f3,d,rB free
22o lt f3 lt 113o _at_ 95 C.L.
rB 0.21 0.08 0.03 0.04
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Vub from inclusive measurements
Electron spectrum, extended momentum range
Vub (4.50 ? 0.42 ? 0.32 ? 0.21) ? 10-3
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Inclusive Vub measurements 2

• New method fully reconstruct one of the B
  mesons, check the properties of the other
  (semileptonic decay, low mass of the hadronic
  system)
• Very good signal to noise
• Low yield (full reconstruction
  efficiency is
  0.3-0.4)

Mxlt1.7 GeV/c2 / q2gt8 GeV2/c2
Total error onVub ..... 12
Vub (4.34 ? 0.22 ? 0.19 ? 0.13 ? 0.12 ?
0.33 ) ? 10-3
0.20
253 fb-1
0.22
stat
syst
b?c
b?u
theo
SF
model dep.
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Unitarity triangle with different sets of data
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Unitarity triangle with different sets of data
2004
-gt CKM matrix can accomodate the CP violation,
and does it very well! apart from some
interesting hints...
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Unitarity triangle with different sets of data
status 2002
Measurements help...
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New input from kaon physics
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Back to the motivation CP

• Initial condition of the universe NB-NB 0
• Today our vicinity (at least up to 10 Mpc)
• is made of matter and not of anti-matter

nb. baryons (matter)
Nb of photons (microwave backg)
In the early universe B B ? g ? Ng NB NB
How did we get from
(one out of 1010 baryons did not anihillate)
?
to
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Three conditions

• Three conditions (A.Saharov, 1967)
• - baryon number violation
• violation of CP and C symmetries
• - non-equillibrium state

baryon number fb
decay probability
Change in baryon number in the decay of X
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Three conditions
X decays to states with NBa ? NBb -gt baryon
number violation
In the thermal equilibrium reverse processes
would cause DB0 -gt need an out-of-equilibrium
state For example X lives long enough -gt
Universe cools down -gt no X production possible
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How to get CP baryon number violation?
NB 1/3
glu
Let f be the particle, whose decay violates the
baryon number conservation e.g. in GUT SU(5)
the Higgs boson with charge -1/3
f
NB -2/3
gudVud
? In SM the CKM matrix rotates the flavour
eigenstates into the mass eingenstates. H0
(neutral Higgs boson of SM) couples only to mass
eingenstates, coupling constants do not involve
Vij ? f couples only to u and d quarks, coupling
constants are proportional to Vij gt complex
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How to get CP baryon number violation?
u
f
glu
Tree order no r ? r
l-
Interference with the next order
trace over all fermions
Only in three-loop processes
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Not enough CP!
The contribution from the CKM matrix to the
above expression J 2x area of the uni.
triangle
Jmax1/6v3
(NB-NB)/Ng DBnX/Ng DB 10-16
ltlt (NB-NB)/Ng 10-10-10-9
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Not enough CP!

• Looking for more CP violating effects that would
  not fit into the Standard Model
• Precise determination of unitarity triangle
  parameters in various processes
• Look for effects in new systems (e.g. Bs)
• -gt need the next generation of B factories
• LHCb at the pp collider
• Super B-factory, asymmetric ee- collider at
  Y(4s). with present luminosity x20
• Look for CP in the neutrino sector