Transcript THE ROLE OF CP AND T IN HIGH

THE ROLE OF CP AND T
IN HIGH-ENERGY PHYSICS
L.Gatignon / CERN
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Phenomenology of CP and T
Direct CP Violation Measurements
T Violation in rare Kaon decays
Direct checks of T Violation
Outlook
27 March 2001
Symposium Marie Curie
NA48, KTEV
KTEV
CPLEAR
PHENOMENOLGY OF CP AND T
C:
Charge conjugation
Replace all particles by their anti-particles
P:
Parity
Space inversion:
T:
Time reversal
Invert the arrow of time
x  -x
t -t
CPT Theorem: within any quantum field theory, all interactions are
invariant under the succession of the three operations
C, P and T in any order.
This theorem is based on very general assumptions.
Its experimental consequences are rather well verified, such as the
identity of masses of particles and anti-particles, e.g.
m Ko – mKo  < 10-18
Actions of P and T operators
Quantity
T
P
r
r
-r
p
-p
-p

-

E
E
-E
B
-B
B
 .B
 .B
 .B
Magnetic dipole
 .E
- .E
- .E
Electric dipole
 .p
 .p
- .p
Long. polarization
.(p1 x p2)
-.(p1 x p2)
.(p1 x p2)
Like r xp
Like for
Transv. polarization
We can now verify the behaviour of these quantities under the operators
Actions of P and T operators
In High-Energy physics, direct checks of T-violation
are not so easy to do.
Here we will see 3 approaches:

Address T-related issues via CP
e.g. CP experiments NA48 and KTEV

Transverse polarization measurements
e.g. KTEV experiment

Direct measurements on time reversed
processes
e.g. CPLEAR experiment
Parity violation
1957
Parity is conserved in strong and e.m. interactions,
but violated in the weak nuclear interaction, e.g. in -decays
e

The angular distribution of e- is
I() = 1 + a .p / E
-  is a unit spin vecor alongJ
- p and E are the e- momentum
and energy

The first term, 1, is even parity
The second term, .p, is odd
parity
H
JCo60

The 60Co (J=5) nuclei are aligned
with the solenoidal field.
The J=5 nuclei decay to 60Ni (J=4) + e-
Parity is violated
C Violation
Neutrinos have  0 mass and spin ½ , therefore Jz =  ½ along
their momentump
Experimentally only Jz = - ½ (“left-handed”) neutrinos are found
and only Jz = + ½ (“right-handed”) anti-neutrinos.
Left-handed neutrino
J
n
Right-handed anti-neutrino
J
n
However, if one applies the C operator to left-handed neutrinos, one
ends up with a left-handed anti-neutrino, which does not exist
C is violated in the weak interaction
But CP transforms a left-handed n into a right-handedn
Is CP conserved ???
CP Violation
 CP violation is (via CPT) one of the feasible experimental
approaches to T-violation in high-energy physics
 Many of the T-violation studies have indeed been
performed by experiments originally designed for
CP-violation measurements (NA48, KTEV, CPLEAR,..)
 The neutral kaon system provides an excellent laboratory
for CP and T violation experiments
 CP violation is considered to be one of the necessary
elements to explain the matter dominance (over
anti-matter) in the universe.
This implies also that the matter/anti-matter ratio
increases with time, thus giving a direction to time.
THE NEUTRAL KAON SYSTEM
 Ko PRODUCTION
Ko = ds
Strong interaction
Ko =d s
 Ko DECAY
Weak interaction
KS  + o o

 68.6 %
 31.4 %
 = 0.893 10-10 s
(higher Q-value)
CP = +1 ?
KL  + - o
o o o
en
n

 12.6 %
 21.1 %
 38.8 %
 27.2 %
 = 5.17 10-8 s
(lower Q-value)
CP = -1 ?
NOTE : + - , o -o
must be CP-symmetric: CP = +1
+ - o o o o must have CP = -1
+ - , o -o must be CP-symmetric: CP = +1
Bose symmetry
C=1
No spin involved
P=1
+ - o o o o must have CP = -1
Low Q-value, hence L = 0
(L  0 strongly disfavoured)
The + -, o -o have CP = +1
(see above)
The extra o has CP = -1:
P = -1 from JP = 0- for pseudoscalar mesons
C = +1 (o  2 )
Thus: CP = (+1)2 . (-1)o . (-1)L = -1
for L=0
Ko Ko Mixing
 Ko can mix withKo via virtual
 or  states:
Ko  Ko
or
o
K     Ko
These are DS = 2 transitions

This mixing is described by a
box diagram:
Ko
K2 = { Ko -Ko } / 2
CP = -1
Ko
or

s
Ko
u, c, t
d
We can now define the following
CP eigenstates:
K1 = { Ko +Ko } / 2 CP = +1

W
W
W
s
u,c,t Ko
d
These states were naturally interpreted
as KS and KL, resp., i.e.
KS  K1
and KL  K2
1964: J.Cronin et al:
Observation of KL  2
1964: Christenson, Cronin, Fitch and Turlay observed an excess of  50 events
with 490 < m < 510 MeV/c2 in the cos distribution of the  system w.r.t. the
KL line of flight. The dashed line shows the expectation for 3 decays
CP is not a conserved quantity in the weak interaction
Explanation:
where
and
KS = ( K1 +  K2 ) /  1+2
K1  ; K2  , en, etc
KL = ( K2 +  K1 ) /  1+2
K2  , en, etc ; K1  
KS, KL are the physical eigenstates
K1, K2 are the CP eigenstates
 = 2.28 10
-3
Quark mixing is usually discussed in terms of the Cabibbo-KobayashiMaskawa framework and the unitary CKM mixing matrix:
MCKM =
(
c1
c3s1
s1s3
-c2s1 c1c2c3 – s2s3 ei
c1c2s3+c3s2 ei
c1c3s2 – c2s3 ei
-c1s2s3+c2c3 ei
s1s2
where ci = cos i and si = sin I
)
Direct and indirect CP Violation
In the CKM matrix there is a complex phase .
It can be shown in the Standard Model that this phase introduces a so-called
direct CP Violation:
K2  
i.e. a ‘direct’ transition from a CP = -1 state (K2)
to a CP = +1 state ()
This is a DS = 1 transition
W
s
It is usually described
by so-called
Penguin diagrams:
u,c,t
d
d
u,c,t
, g Zo
d
u,c,t
s
The relevant parameter is ’
d
W
, g Zo
The  final state has either I=0 or I=2
(Bose symmetry  I1)
 K1   :
CP-conserving weak decay  DI = ½ rule
i.e. DI=3/2 is suppressed by factor  = 1/20
 mainly I=0
 K2   :
CP-violating weak decay  no DI = ½ rule
i.e. DI=3/2 not suppressed
 also I=2
It can thus be shown that
’  (i /2) (Im A2 / Ao) e
with
Ai = <I=i | T | Ko> eii
i(2-o)
Define:
o = < I=0 | T | KL > / < I=0 | T | KS >
2 = < I=2 | T | KL > / < I=0 | T | KS >
 = < I=2 | T | Ks > / < I=0 | T | KS >

 ’
DI = ½ rule
Using the well-known Clebsch-Gordon coefficients
< I=0 | = 2/3 <+ -| - 1/3 <o o|
< I=2 | = 1/3 <+ -| + 2/3 <o o|
one can easily derive:
+- = <+- | KL> = ( + ’) / (1+/2)
<+- | Ks>
oo = <oo | KL> = ( - 2’) / (1+2)
<oo | Ks>
and thus
R = |oo|2 / |+-|2 = 1 – 6 Re (’/
The full calculation of ’/ is quite complicated and involves hadronic processes and
non-perturbative QCD.
In principle the most correct approach is Lattice QCD, but many other
approaches exist. For the moment the theoretical uncertainties are large , e.g. :
Re (’/) =
(4.6  3.0  0.4) 10-4
(3.4  3.4) 10-4
(10.4  8.3) 10-4
(17
+14
) 10-4
Ciuchini Jan 97
Buras Aug 96
ms = 150  20 MeV/c2
ms = 100  20 MeV/c2
Bertolini Feb 98
-10
Most of the models predict Re (’/) in the range between several 10-4 and up to about 10-3.
The superweak model (L.Wolfenstein) attributes all CP-violation to a so-called
‘superweak force’. It can explain , but predicts ’/ = 0
DIRECT CP VIOLATION MEASUREMENTS
Experiments on direct CP violation have so far measured a double ratio R:
( K L   o o ) / ( K L    - )
R
( K S   o o ) / ( K S    - )
This double ratio is related to ’/ as R = 1 – 6 ’/.
‘Only’ 1.2 10-3 precision required
on R for 2 10-4 precision on ’/,
But…..
Many systematic
effects may
st
cancel
to 1o order
between
+ o
  and   and/or
between KL and KS decays
(acceptance, rate effects,
spectrum).
The required precision is still
extreme, hence need very large
statistics
The required control over the
systematics is such that also
higher order effects must be
considered,
Backgrounds are potentially huge
and
are o different
KS KL and
+ o
    .
The experiments are therefore very delicate and difficult.
Experiments in the 1980’s:
NA31 @ CERN
E731 @ Fermilab
EXPT
+and

KL
KL + KS
KL
EXPT
+OR

KS
or
Regenerator
KS
EXPT
+and

Run KL and KS alternately
Detect - and  simultaneously
Run KL and KS simultaneously
Detect - and  alternately
(except for a small fraction of the sample)
Coherent regeneration gives identical
momentum spectra.
Very different acceptance for KL vs KS
NA31 @ CERN
E731 @ Fermilab
’/ = (23.0 ± 6.5) 10-4
’/ = (7.40± 5.9) 10-4
Stat.error 4 10-4, Systematic error 5 10-4
Stat.error 5.2 10-4, Systematic error 2.9 10-4
Dominant contributions:
Accidental activity:
Energy scale:
Neutral background:
Charged background:
Acceptance (MC):
Dominant contributions:
Accidental activity:
1.1 10-4
Energy scale:
1.6 10-4
Trigger plane:
1.2 10-4
Regenerator eff & trigger: 1.6 104
Acceptance (MC):
1.2 10-4
2.4 10-4
2.2 10-4
2.2 10-4
1.6 10-4
1.6 10-4
The combined average at the time was ’/ =
results are barely consistent with each other:
(14.8 ± 4.3) 10-4 but the two
 NA31 claimed first evidence for direct CP violation
 E731 did not see any evidence
Hence the decisions of both groups to perform more precise measurements:
NA48 @ CERN
KTEV @ Fermilab
BASIC METHOD OF NA48 AND KTEV
Both the NA48 and KTEV experiments opted for a similar technique:





Simultaneous and nearly collinear KS and KL beams
Simultaneous detection of +- and oo decays
Binning in momentum bins
Magnetic spectrometers for detecting the +- mode
Highly sophisticated e.m. calorimetry for the oo mode
Both experiments use intense beams to maximise the statistical precision.
Even though the double ratio gives inherently good control over any
systematic effects, both experiments must give great attention to
minimising systematic uncertainties on the double ratio measurement.
Nevertheless the approaches are very different, e.g.:
Separate beams
Same fiducial region
versus
versus
regeneration
extended KL region
Let us first have a somewhat closer look at NA48
NA48 - HISTORY
1990
Proposal
Nov.1991 Approved
1992-4
Beams and detector installation
Tests of calorimeter prototypes
1995
Commissioning of the magnetic spectrometer
1996
Commissioning of the Liquid Krypton calorimeter
1997
Running-in followed by first ’/ datataking (42 days)
1998
Further ’/ datataking (120 days) with improved
detector
1999
Continue ’/ datataking (129 days)
Nov. 1999 Incident on wire chambers
2000
Some systematic studies for neutral modes ?
2001
Expect to finalise ’/ datataking
16 Institutes,  150 physicists
SCHEMATIC LAYOUT OF NA48
The KS beam
RESULTS FROM NA48:
1997:
’/ = (18.5  4.5stat  5.8syst) 10-4
1998:
’/ = (12.2  2.9stat  4.0syst) 10-4
Combined:
’/ = (14.0  4.3) 10-4
(taking into account the small correlated systematics)
A final result for the data from 1997-1999 is expected soon.
More ’/ data will be taken from July till October 2001
THE KTEV MEASUREMENT OF ’/
The KTEV experiment is an improved version of E731 at Fermilab.
The main improvements are:
 Instrumented regenerator to reduce scattered kaon background
 Much better beam collimation and muon cleaning
 New CsI electromagnetic calorimeter with much improved resolution
 Higher statistics
The present result is based on less than 10% of the full statistics, i.e. less
than a quarter of the data from 1996 and 1997.
A final result on the full sample (including 1999 data) is expected soon.
The aim is to achieve a precision of 10-4 on ’/
THE KTEV REGENERATOR
It regenerates coherently the initially pure KL beam into KL +  KS
Even the KS – KL interference is clearly visible!
NA48
KTEV
weighting
KS
KL
Regenerator
Correct by MC
Simultaneous KS and KL beams
Simultaneous KS and KL beams
Simultaneous - and  detection
Simultaneous - and  detection
Acceptance differences compensated by
weighting technique
Acceptance difference simulated by MC
RESULT FROM KTEV:
’/ = (28.0  3.0stat  2.6syst  1.0MC-stat) . 10-4
WORLD AVERAGE FOR ’/:
NA48 : 14.0  4.3
.
10-4
KTEV: 28.0  3.0  2.6  1.0 . 10-4
W.Ave: 21.0  3.0 10
.
-4
i.e.: Direct CP violation is now well established at the > 5 level
More news from both experiments to come very soon !!!
T VIOLATION STUDIES IN KL  +-e+e- BY KTEV
KL  +-e+e- stems from a KL  +- followed by internal  conversion.
Two processes contribute:
 Inner Bremsstrahlung in the decay KL  +-
CP violating
 Direct emission
CP conserving
The two processes are of similar magnitude and may interfere
The interference is observable in the angle  between the  and ee planes:
dN/d = A + B sin2 + C sin ( 2
where the latter term is proportional to
sin cos = (n x ne) . p / |p|(n . ne)
This product is T-odd and CP-odd, similar to transverse polarization.
The -e+e- mass distribution for KL decays:
Before Cuts:
Ko mass
After cuts:
The angular distributions and asymmetries
Angular distribution Data vs MC
The observed asymmetry
A = 13.6  2.5stat  1.2syst %
The sincos distribution:
Good agreement between data
and Monte Carlo with the
expected asymmetry of 14%.
This is an  effect,
i.e. indirect CP violation.
The size of the effect is so big
because two amplitudes of
similar size happen to interfere.
The observed asymmetry is a T-odd, CP-odd effect. Is it also T-violation?
Difficult to say: affected by strong and electromagnetic final state interactions.
Since both conserve CP, the asymmetry is CP violation.
Final State Interactions may moderate an effect, but should not fake one.
One may therefore conclude that the observation strongly suggests T-violation
However, if the phase of +- were close to 135o (and not to 45o as observed)
and T were conserved, such an asymmetry could arise from CPT violation
in the Ko -Ko mixing.
Anyway, these measurements are extremely interesting !!!
DIRECT OBSERVATION OF T VIOLATION BY CPLEAR
The Ko -Ko mixing allows transitions from Ko into Ko and vice versa.
Time reversal invariance would imply that the probability
P() for a Ko at t=0 to be observed asKo at time 
is the same as the probability
P’() for a Ko at t=0 to be observed as a Ko at time .
Any difference between P() and P’() is a signal for T violation.
The observation of such differences requires to measure the identity Ko vsKo
at two moments, namely at production (t=0) and at the time of decay (t=).
This possibility is not available in the classical KS and KL experiments like
NA48 and KTEV, but it exists in the CP-LEAR experiment at CERN.
The aim of the experiment is to measure [P() – P’()] / [P() + P’()].
CPLEAR produces Ko and Ko through the strong interaction at time t=0:
p +p  K- + Ko
or
p +p  K -Ko,
i.e. the sign of the charged kaon tags the initial strangeness of the neutral kaon.
The semi-leptonic decays allow to tag the strangeness at decay time t = :
Ko  e+ - n
Ko  e- n
R( K o t 0  e -n t  ) - R( K o t 0  e- n t  )
Measure At ( ) 
R( K o t 0  e -n t  )  R( K o t 0  e- n t  )
LEAR: 200 MeV/cp beam
 exclusive channels, e.g.pp K+-Ko or pp  K- Ko
Thep stop in H2 gas target
and annihilate at rest
Solenoidal magnet 0.44 T
Accept 0 <  < 20 S
Tracking
Scint-Cerenkov-Scintillator
E.M.calorimeter
THE CPLEAR DETECTOR – TRANSVERSE CUT
 Select events with
4 charged tracks and
total zero charge
 One of tracks is e (neural
net, based on Cerenkov
and TOF)
 Constrained fits to select
KKo candidates
From the fits one selected
1.3 106 en events with
S resolution of 0.05
and measured decay time > 1 S
Measurements are corrected for
regeneration (Ko Ko in the
detector material) following a
one-year measurement of
regeneration amplitudes.
Asymmetry measurement offers some experimental advantages:
 Detection efficiencies cancel
 Geometrical acceptance cancels (frequent magnetic field reversals)
But nevertheless
 Different detection probabilities for charged K, , e used in
tagging the Ko vs Ko at production and at decay time:
- K+ and K- have different strong interaction cross sections. This has an effect
on primary vertex normalisation, corrected using the high statistics
available for identified Ko  - decays. The ratio of Ko to Ko events
must follow the neutral kaon time evolution, known precisely enough.
- The pion end electron from the Ko decay have also different detection
efficiencies to be detected in e.g. scintillators or triggers. Extensive studies
were made with  from minimum bias samples and e from  conversions.
 Other corrections include backgrounds from 2, 3, n
RESULT:
First evidence of Direct T Violation
Theoretical expectation : AT  4 Re ( = (6.21.4) 10-3
CONCLUSIONS AND OUTLOOK
 Indirect () and direct (’/) CP violation are now well established.
 CP and T are strongly correlated via the CPT Theorem.
 CPLEAR has now established T violation in a direct way.
 NA48 and KTEV will publish their full datasets very soon.
 Future activity will be lively and interesting:
 KLOE at Daphne: e+ e-    KS + KL will hopefully
start taking data soon (as soon as the machine problems
are solved).
 NA48 will take more data in 2001 (after drift chamber
repair) and has been approved for a high-intensity KS
experiment in 2002, measuring KS  oe+e- and for a
new experiment with simultaneous K+ and K- beams in
2003 for direct CP and T studies.
Finally, with the advent of new B-factories at SLAC and KEK
the field of CP studies has also been opened in the
B - B sector
o
o
which could be the topic of many other seminars…….
Bo -Bo sector
New accelerators (“B-factories”) and experiments have been constructed:
 Cleo (Cornell)
 Babar at SLAC (USA)
 Belle at KEK (Japan)
and others will be (about 2005):
 LHCb at CERN
 BeTev at Fermilab
(Almost) no hadronic uncertainties
CP violation in general and Direct CP violation in particular are large effects
Experimentally very difficult:
Small branching ratios
High rates required
Need to measure B decay vertex (100 m – 1 mm)
Golden channel:
Bo (Bo )  KS 
The CP violating asymmetry is parametrised by an angle :
 and  are parameters in the
CKM matrix (Wolfenstein param.):
1
A-i
V = -A
A3(1--i) -A3
1





  
Usually experiments quote values
for sin 2
World average now:
sin 2 = 0.42  0.24
Standard model:
sin 2 = 0.70  0.15