Particle Physics II

1
Particle Physics II CP violationLecture 3

• N. Tuning

2
Outline

• 1 May
• Introduction matter and anti-matter
• P, C and CP symmetries
• K-system
• CP violation
• Oscillations
• Cabibbo-GIM mechanism
• 8 May
• CP violation in the Lagrangian
• CKM matrix
• B-system
• 15 May
• B-factories
• B?J/Psi Ks
• Delta ms

3
Literature

• Slides based on courses from Wouter Verkerke and
  Marcel Merk.
• W.E. Burcham and M. Jobes, Nuclear and Particle
  Physics, chapters 11 and 14.
• Z. Ligeti, hep-ph/0302031, Introduction to Heavy
  Meson Decays and CP Asymmetries
• Y. Nir, hep-ph/0109090, CP Violation A New Era
• H. Quinn, hep-ph/0111177, B Physics and CP
  Violation

4
The
Kinetic Part
Recap from last week
For example, the term with QLiI becomes
Writing out only the weak part for the quarks
W (1/v2) (W1 i W2) W- (1/v 2) (W1 i W2)
LJmWm
5
The Higgs Potential
Recap from last week
And rewrite the Lagrangian (tedious)
(The other 3 Higgs fields are eaten by the W, Z
bosons)
6
The Yukawa Part
Recap from last week
Since we have a Higgs field we can add (ad-hoc)
interactions between f and the fermions in a
gauge invariant way.
The result is
i, j indices for the 3 generations!
With
(The CP conjugate of f To be manifestly
invariant under SU(2) )
are arbitrary complex matrices which operate in
family space (3x3) ? Flavour physics!
7
The Fermion
Masses
Recap from last week
Writing in an explicit form
The matrices M can always be diagonalised by
unitary matrices VLf and VRf such that
Then the real fermion mass eigenstates are given
by
8
The Charged
Current
The charged current interaction for quarks in the
interaction basis is
Recap from last week
The charged current interaction for quarks in the
mass basis is
The unitary matrix
With
is the Cabibbo Kobayashi Maskawa mixing matrix
Lepton sector similarly
However, for massless neutrinos VLn
arbitrary. Choose it such that VMNS 1 gt There
is no mixing in the lepton sector
9
The Standard Model Lagrangian (recap)
Recap from last week

• LKinetic Introduce the massless fermion
  fields
• Require local gauge
  invariance gt gives rise to existence of gauge
  bosons

gt CP Conserving

• LHiggs Introduce Higgs potential with ltfgt ? 0
• Spontaneous symmetry breaking

The W, W-,Z0 bosons acquire a mass
gt CP Conserving

• LYukawa Ad hoc interactions between Higgs
  field fermions

gt CP violating with a single phase

• LYukawa ? Lmass fermion weak eigenstates
  
• 
  -- mass matrix is (3x3) non-diagonal
• 
  fermion mass eigenstates
• 
  -- mass matrix is (3x3) diagonal

gt CP-violating
gt CP-conserving!

• LKinetic in mass eigenstates CKM matrix

gt CP violating with a single phase
10
Exploit apparent ranking for a convenient
parameterization

• Given current experimental precision on CKM
  element values, we usually drop l4 and l5 terms
  as well
• Effect of order 0.2...
• Deviation of ranking of 1st and 2nd generation (l
  vs l2) parameterized in A parameter
• Deviation of ranking between 1st and 3rd
  generation, parameterized through r-ih
• Complex phase parameterized in arg(r-ih)

Recap from last week
11
Deriving the triangle interpretation
Recap from last week

• Starting point the 9 unitarity constraints on
  the CKM matrix
• Pick (arbitrarily) orthogonality condition with
  (i,j)(3,1)

12
Visualizing arg(Vub) and arg(Vtd) in the (r,h)
plane
Recap from last week

• We can now put this triangle in the (r,h) plane

13
Dynamics of Neutral B (or K) mesons
Time evolution of B0 and B0 can be described by
an effective Hamiltonian
No mixing, no decay
No mixing, but with decays (i.e. H is not
Hermitian!)

• With decays included, probability of observing
• either B0 or B0 must go down as time goes by

14
Describing Mixing
Time evolution of B0 and B0 can be described by
an effective Hamiltonian
Where to put the mixing term?
Now with mixing but what is the difference
between M12 and G12?
For details, look up Wigner-Weisskopf
approximation
15
Solving the Schrödinger Equation
Solution
(a and b are initial conditions)
Eigenvectors
Dm and DG follow from the Hamiltonian
From the eigenvalue calculation
16
B Oscillation Amplitudes
For an initially produced B0 or a B0 it then
follows using
with
For B0, expect DG 0, q/p1
17
Measuring B Oscillations
For B0, expect DG 0, q/p1
Examples
Decay probability
Proper Time ?
18
Measuring B0 mixing

• What is the probability to observe a B0/B0 at
  time t, when it was produced as a B0 at t0?
• Calculate observable probility YY(t)
• A simple B0 decay experiment.
• Given a source B0 mesons produced in a flavor
  eigenstate B0gt
• You measure the decay time of each meson that
  decays into a flavor eigenstate (either B0 or B0)
  you will find that

19
Measuring B0 mixing

• You can really see this because (amazingly) B0
  mixing has same time scale as decay
• t1.54 ps
• Dm0.47 ps-1
• 50/50 point at pDm ? t
• Maximal oscillation at 2pDm ? 2t
• Actual measurementof B0/B0bar oscillation
• Also precision measurementof Dm!

20
Back to finding new measurements

• Next order of business Devise an experiment that
  measures arg(Vtd)?b and arg(Vub)?g.
• What will such a measurement look like in the
  (r,h) plane?

Fictitious measurement of b consistent with CKM
model
CKM phases
21
The B0 mixing formalism and the angle b

• Reduction to single (set of 2) amplitudes is
  major advantage in understanding B0 mixing
  physics
• A mixing diagram has (to very good approximation)
  a weak phase of 2b
• An experiment that involves interference between
  an amplitude with mixing and an amplitude without
  mixing is sensitive to the angle b!
• Small miracle of B physics unlike the K0 system
  you can easily interpret the amount of observable
  CP violation to CKM phases!

22
Find the right set of two amplitudes

• General idea to measure b Look at interference
  between B0 ? fCP and B0 ? B0 ? fCP
• Where fCP is a CP eigenstate (because both B0 and
  B0 must be able to decay into it)
• Example (not really random) B0 ? J/y KS

B0 ? f
B0 ? B0 ? f
23
Back to business Measuring b with B0 ? J/y KS

• Were going to measure arg(Vtd2)2b through the
  interference of these two processes
• We now know from the B0 mixing formalism that the
  magnitude of both amplitudes varies with time

B0 ? f
B0 ? B0 ? f
24
How can we construct an observable that measures b

• What do we know about the relative phases of the
  diagrams?

B0 ? f
B0 ? B0 ? f
f(strong)f
f(strong)f
Decays are identical
K0 mixing exactlycancels Vcs
f(weak)0
f(weak)2b
f(mixing)p/2
There is a phase difference of i between the B0
and B0bar
25
Measuring ACP(t) in B0 ? J/y KS

• What do we need to observe to measure
• We need to measure
• J/y and KS decay products
• Lifetime of B0 meson before decay
• Flavor of B0 meson at t0 (B0 or B0bar)
• First two items relatively easy
• Lifetime can be measured from flight length if B0
  has momentum in laboratory
• Last item is the major headache How do you
  measure a property of a particle before it decays?

26
Putting it all together sin(2b) from B0 ? J/y KS
B0(Dt)
B0(Dt)
ACP(Dt) sin(2ß)?sin(DmdDt)

• Effect of detector imperfections
• Dilution of ACP amplitude due imperfect tagging
• Blurring of ACP sine wave due to finite Dt
  resolution

sin2b
Imperfect flavor tagging
D?sin2b
Finite Dt resolution
Dt
Dt
27
Combined result for sin2b
hep-ex/0408127
J/? KL (CP even) mode
ACP amplitudedampened by (1-2w)w ? flav. Tag.
mistake rate
sin2ß 0.722 ? 0.040 (stat) ? 0.023 (sys)
28
Consistency with other measurements in (r,h) plane
4-fold ambiguity because we measure sin(2b), not b
Prices measurement ofsin(2b) agrees
perfectlywith other measurementsand CKM model
assumptionsThe CKM model of CP violation
experimentallyconfirmed with high precision!
2
1
without sin(2b)
h
3
4
r
Method as in Höcker et al, Eur.Phys.J.C21225-25
9,2001
29
Back to business Measuring b with B0 ? J/y KS

• Were going to measure arg(Vtd2)2b through the
  interference of these two processes
• We now know from the B0 mixing formalism that the
  magnitude of both amplitudes varies with time

B0 ? f
B0 ? B0 ? f
30
How can we construct an observable that measures b

• The easiest case calculate G(B0 ? J/y KS) at tp
  / 2Dm
• Why is it easy cos(Dmt)0 ? both amplitudes
  (with and without mixing) have same magnitude
  A1A2
• Draw this scenario as vector diagram
• NB Both red and blue vectors have unit length

sin(f)
p/22b
1-cos(f)
N(B0 ? f) ? A2 ? (1-cosf)2sin2f
1 -2cosfcos2fsin2f
2-2cos(p/22b) ? 1-sin(2b)
cos(f)
31
How can we construct an observable that measures b

• Now also look at CP-conjugate process
• Directly observable result (essentially just from
  counting) measure CKM phase b directly!

N(B0 ? f) ? A2 ? (1-cosf)2sin2f
1 -2cosfcos2fsin2f
2-2cos(p/22b) ? 1-sin(2b)


sin(f)
p/22b
1-cos(f)
CP


sin(f)
p/2-2b
N(B0 ? f) ? (1cosf)2sin2f
22cos(p/2-2b) ? 1sin(2b)
1cos(f)
32
Bs mixing

• ?ms has been measured at Fermilab 4 weeks ago!

33
Standard Model Prediction
Wolfenstein parameterization
CKM Matrix
Ratio of frequencies for B0 and Bs
(hep/lat-0510113)
Vts ?2, Vtd ?3, ?0.2240.012
34
Unitarity Triangle
CKM Matrix Unitarity Condition
35
Before the measurement Unitarity Triangle Fit

• CKM Fit result Dms 18.36.5 (1s) 11.4
  (2?) ps-1

-1.5
-2.7
from Dmd
Lower limit on Dms
from Dmd/Dms
36
Measurement .. In a Perfect World
Right Sign
Wrong Sign
what about detector effects?
37
Hadronic Bs Decays

• relatively small signal yields (few thousand
  decays)
• momentum completely contained in tracker
• superior sensitivity at higher ?ms

38
Semileptonic Bs Decays

• relatively large signal yields (several 10s of
  thousands)
• correct for missing neutrino momentum on average
• loss in proper time resolution
• superior sensitivity in lower ?ms range

39
Tagging the B Production Flavor
vertexing (same) side
e,?
opposite side

• use a combined same side and opposite side tag!
• use muon, electron tagging, jet charge on
  opposite side
• jet selection algorithms vertex, jet probability
  and highest pT
• particle ID based kaon tag on same side

40
Combined Amplitude Scan
Preliminary
25.3 ps-1
A/?A (17.25 ps-1) 3.5
How significant is this result?
41
Conclusions

• found signature consistent with Bs - Bs
  oscillations
• probability of fluctuation from random tags is
  0.5
• ?ms 17.33 0.42 (stat) 0.07 (syst) ps-1
• Vtd / Vts 0.208 0.008 (stat syst)

-0.21
-0.007
42
Outline

• 1 May
• Introduction matter and anti-matter
• P, C and CP symmetries
• K-system
• CP violation
• Oscillations
• Cabibbo-GIM mechanism
• 8 May
• CP violation in the Lagrangian
• CKM matrix
• B-system
• 15 May
• B-factories
• B?J/Psi Ks
• Delta ms

43
Remember the following

• CP violation is discovered in the K-system
• CP violation is naturally included if there are 3
  generations or more
• CP violation manifests itself as a complex phase
  in the CKM matrix
• The CKM matrix gives the strengths and phases of
  the weak couplings
• CP violation is apparent in experiments/processes
  with 2 interfering amplitudes
• The angle ß is measured through B0 ? J/y KS
• Mixing of neutral mesons happens through the
  box diagram