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Cracking the Unitarity Triangle— A Quest in B Physics —
Masahiro MoriiHarvard University
Ohio State University Physics Colloquium9 May 2006
9 May 2006 M. Morii, Harvard 2
Outlinen Introduction to the Unitarity Triangle
n The Standard Model, the CKM matrix, and CP violationn CP asymmetry in the B0 meson decays
n Experiments at the B Factoriesn Results from BABAR and Belle
n Angles a, b, g from CP asymmetriesn |Vub| from semileptonic decaysn |Vtd| from B0 and Bs mixing
n Current status and outlook
g
a
b
Results presented in this talk are produced by the BABAR, Belle, and CLEO Experiments,the Heavy Flavor Averaging Group, the CKMfitter Group, and the UTfit Collaboration
The Unitarity Triangle
9 May 2006 M. Morii, Harvard 3
What are we made of?
n Ordinary matter is made of electrons and up/down quarksn Add the neutrino and we have a complete “kit”n We also know how they interact with “forces”
quarksleptons
e
e ud0Q =
1Q =
13Q =
23Q = +
strong E&M weaku Yes Yes Yesd Yes Yes Yese− No Yes Yesne No No Yes
u
u d
e
9 May 2006 M. Morii, Harvard 4
Simplified Standard Modeln Strong force is transmitted by the gluon
n Electromagnetic force by the photon
n Weak force by the W± and Z0 bosons
uu
g
dd
g
uu
g
dd
g
e−g
e−
uu
Z0
dd
Z0 Z0
e−e−
Z0
nene
du
W+
nee−
W−Note W± can “convert”
u↔ d, e↔ n
9 May 2006 M. Morii, Harvard 5
Three generationsn We’ve got a neat, clean, predictive theory of “everything”
n Why 3 sets (= generations) of particles?n How do they differ?n How do they interact with each other?
strong E&M weak
g gW±
Z 0
µ− cnµ s
t − tnt b
leptons quarkse− une d
1st generation
2nd generation
3rd generation
It turns out there are two “extra”
copies of particles
9 May 2006 M. Morii, Harvard 6
A spectrum of massesn The generations differ only by the masses
ç The structure is mysteriousn The Standard Model has no explanation
for the mass spectrumn All 12 masses are inputs to the theoryn The masses come from the interaction
with the Higgs particlen ... whose nature is unknownn We are looking for it with the Tevatron, and
with the Large Hadron Collider (LHC) in the future
310
410
510
610
710
810
910
1010
1110
Parti
cle
mas
s (eV
/c2 )
1210
e
u
c
t
d
s
b
Q = -1 0 +2/3 -1/3The origin of mass is one of the most urgent
questions in particle physics today
9 May 2006 M. Morii, Harvard 7
If there were no massesn Nothing would distinguish u from c from t
n We could make a mixture of the wavefunctions and pretend it represents a physical particle
n Suppose W± connects u¢↔ d¢, c¢↔ s¢, t¢↔ b¢
n That’s a poor choice of basis vectors
u uc ct t
=Md ds sb b
= N M and N are arbitrary3´3 unitary matrices
1 1 1
u u d d dc c s s st t b b b= = =M M M N V
Weak interactions between u, c, t, and d, s, b are “mixed” by matrix V
9 May 2006 M. Morii, Harvard 8
Turn the masses back onn Masses uniquely define the u, c, t, and d, s, b states
n We don’t know what creates massesè We don’t know how the eigenstates are chosenè M and N are arbitrary
n V is an arbitrary 3´3 unitary matrix
n The Standard Model does not predict Vn ... for the same reason it does not predict the particle masses
ud us ub
cd cs cb
td ts tb
Wu d V V V dc s V V V st b V V V b
±=V
Cabibbo-Kobayashi-Maskawa matrix or CKM for short
9 May 2006 M. Morii, Harvard 9
Structure of the CKM matrixn The CKM matrix looks like this è
n It’s not completely diagonaln Off-diagonal components are small
n Transition across generations isallowed but suppressed
n Matrix elements can be complexn Unitarity leaves 4 free parameters,
one of which is a complex phase
0.974 0.226 0.0040.226 0.973 0.0420.008 0.042 0.999
=V
There seems to be a “structure”separating the generations
This phase causes “CP violation”Kobayashi and Maskawa (1973)
9 May 2006 M. Morii, Harvard 10
What are we made of, again?n Dirac predicted existence of anti-matter in 1928
n Positron (= anti-electron) discovered in 1932
n Our Universe contains (almost) only matter
n Translation: he would like the laws of physics to be different for particles and anti-particles
e- e+
I do not believe in the hole theory, since I would like to havethe asymmetry between positive and negative electricity in thelaws of nature (it does not satisfy me to shift the empiricallyestablished asymmetry to one of the initial state)
Pauli, 1933 letter to Heisenberg
9 May 2006 M. Morii, Harvard 11
CP symmetry
n C and P symmetries are broken in weak interactionsn Lee, Yang (1956), Wu et al. (1957), Garwin, Lederman, Weinrich (1957)
n Combined CP symmetry seemed to be good n Anti-Universe can exist as long as it
is a mirror image of our Universen To create a matter-dominant Universe,
C charge conjugation particle « anti-particleP parity x ® -x, y ® -y, z ® -z
CP symmetry must be broken
e- e+
One of the three necessary conditions (Sakharov 1967)
9 May 2006 M. Morii, Harvard 12
CP violationn CP violation was discovered in KL decays
n KL decays into either 2 or 3 pions
n Couldn’t happen if CP was a good symmetry of Natureè Laws of physics apply differently to matter and antimatter
n The complex phase in the CKM matrix causes CP violationn It is the only source of CP violation in the Standard Model
Christenson et al. (1964)
(33%)LK + +
(0.3%)LK +1CP =1CP = +
Final states have different CP eigenvalues
Nothing else?
9 May 2006 M. Morii, Harvard 13
CP violation and New Physics
n The CKM mechanism fails to explain the amount of matter-antimatter imbalance in the Universen ... by several orders of magnitude
n New Physics beyond the SM is expected at 1-10 TeV scalen e.g. to keep the Higgs mass < 1 TeV/c2
n Almost all theories of New Physics introduce new sources of CPviolation (e.g. 43 of them in supersymmetry)
n Precision studies of the CKM matrix may uncover them
New sources of CP violation almost certainly exist
Are there additional (non-CKM) sources of CP violation?
9 May 2006 M. Morii, Harvard 14
The Unitarity Trianglen V†V = 1 gives us
n Experiments measure the angles a, b, g and the sides
* * *
* * *
* * *
0
0
0
ud us cd cs td ts
ud ub cd cb td tb
us ub cs cb ts tb
V V V V V VV V V V V VV V V V V V
+ + =
+ + =
+ + =
This one has the 3 terms in the same
order of magnitude
A triangle on the complex plane
1
td tb
cd cb
V VV V
ud ub
cd cb
V VV V
0
*ud ubV V
*td tbV V
*cd cbV V
9 May 2006 M. Morii, Harvard 15
The UT 1998 à 2006
95% CL
The improvements are due largely to the B Factoriesthat produce and study Bmesons
in quantity
n We did know something about how the UT looked in the last centuryn By 2005, the allowed region for the apex has shrunk to about 1/10
in area
9 May 2006 M. Morii, Harvard 16
Anatomy of the B0 systemn The B0 meson is a bound state of b and d quarks
n They turn into each other spontaneously
n This is called the B0-B0 mixing
0 ( )B bd=0 ( )B bd=
Particle charge mass lifetime
0 5.28 GeV/c2 1.5 ps0 5.28 GeV/c2 1.5 ps
Indistinguishable from the outside
0B 0B
W+
W-
b
d
d
b
9 May 2006 M. Morii, Harvard 17
Time-dependent Interferencen Starting from a pure |B0ñ state, the wave function evolves as
n Suppose B0 and B0 can decay into a same final state fCP
n Two paths can interferen Decay probability depends on:
n the decay time tn the relative complex phase
between the two paths
0B
0B
Ignoring the lifetime
0B
0BfCP
0B
t = 0 t = t
time
0pure B 0pure B 0pure B
9 May 2006 M. Morii, Harvard 18
The Golden Moden Consider
n Phase difference is
0 0B J K
b
d d
scc
0B
J
0K
d
b s
d
c c
0B 0K
J
0Bd
b
b
d
s
ds
d0K
Direct path
Mixing path
*cbV csV
*csVcbV*
tbVtdV
tdV
*tbV
*cdVcsV
csV
*cdV
* 2 *2 * 2 *2 * *arg( ) arg( ) 2 arg( ) arg( ) 2cs cb td tb cb cs cs cd cd cb td tbV V V V V V V V V V V V= =
td tbV V
cd cbV V
9 May 2006 M. Morii, Harvard 19
Time-dependent CP Asymmetryn Quantum interference between the direct and mixed paths
makes and differentn Define time-dependent CP asymmetry:
n We can measure the angle of the UT
n What do we have to do to measure ACP(t)?n Step 1: Produce and detect B0 ® fCP eventsn Step 2: Separate B0 from B0
n Step 3: Measure the decay time t
0 0 0 0
0 0 0 0
( ( ) ) ( ( ) )( ) sin(2 )sin( )( ( ) ) ( ( ) )
S SCP
S S
N B t J K N B t J KA t mtN B t J K N B t J K
= =+
Solution:Asymmetric
B Factory
0 0( )B t J K0 0( )B t J K
9 May 2006 M. Morii, Harvard 20
B Factoriesn Designed specifically for precision measurements of the CP
violating phases in the CKM matrix
SLAC PEP-II
KEKB
Produce ~108 B/year by colliding e+ and e− with ECM = 10.58 GeV
(4 )e e S BB+ +
9 May 2006 M. Morii, Harvard 21
SLAC PEP-II site
BABAR
PEP-II
I-280
Linac
9 May 2006 M. Morii, Harvard 22
Step 2:Identify the flavorof the other BDecay products often
allow us to distinguishB0 vs. B0
Asymmetric B Factoryn Collide e+ and e− with E(e+) ≠ E(e−)
n PEP-II: 9 GeV e− vs. 3.1 GeV e+ à bg = 0.56
Step 1:Reconstruct the signal Bdecaye− e+
Moving in the lab
U(4S)
Step 3:Measure Dz è Dtz c t=
e
+ +
0B
0B
9 May 2006 M. Morii, Harvard 23
Detectors: BABAR and Bellen Layers of particle detectors surround the collision point
n We reconstruct how the B mesons decayed from their decay products
BABAR Belle
9 May 2006 M. Morii, Harvard 24
J/y KS eventA B0 → J/y KS candidate (r-f view)
Muons from
Pions from
Red tracks are from the other B,which was probably B0
p −
p +
µ+
µ−
p −
p +
p +
K−
J +
SK+
9 May 2006 M. Morii, Harvard 25
CPV in the Golden Channeln BABAR measured in B0 ® J/y + KS and related decays
J/y KS
227 million eventsBBsin 2 0.722 0.040(stat.) 0.023(syst.)= ± ±
J/y KL
9 May 2006 M. Morii, Harvard 26
Three angles of the UTn CP violation measurements at the B Factories give
Angle (degree) Decay channels
aB0 ® pp, rp, rr
b B0 ® (cc)K0
g B0 ® D(*)K(*)
Precision of b is 10 times better than a and g
12.68.198.6+
1.31.221.7+
151263+
9 May 2006 M. Morii, Harvard 27
CKM precision testsn Measured angles agree with what we knew before 1999
n But is it all?n We look for small deviation from the CKM-only hypothesis by
using the precise measurement of angle b as the reference
g
a
b
Next stepsn Measure b with different methods
that have different sensitivity to New Physics
n Measure the sides
*
*tb
cb
td
cd
VV VV
*
*ubud
cd cb
VV VV
The CKM mechanism is responsible for the bulk of the CP violation in the quark sector
9 May 2006 M. Morii, Harvard 28
Angle b from penguin decaysn The Golden mode is n Consider a different decay
e.g., n b cannot decay directly to sn The main diagram has a loop
n The phase from the CKM matrix is identical to the Golden Mode
n We can measure angle b in e.g.B0 ® f + KS
b ccs
b sss
Tree
0Kb
c
sc
d
0B
/J
d
Penguin
0Kb
s
ss
d
0Bd
gW
, ,u c t , ,u c ttop is the main
contributor
9 May 2006 M. Morii, Harvard 29
New Physics in the loopn The loop is entirely virtual
n W and t are much heavier than bn It could be made of heavier particles
unknown to usn Most New Physics scenarios predict
multiple new particles in 100-1000 GeVn Lightest ones close to mtop = 174 GeVn Their effect on the loop can be as big as the SM loopn Their complex phases are generally different
W
t t
b s
%
t% t%
b s
Comparing penguins with trees is a sensitive probe for New Physics
9 May 2006 M. Morii, Harvard 30
Strange hintsn Measured CP asymmetries
show a suspicious trend
n Naive average of penguins give sin2b = 0.50 ± 0.06
n Marginal consistency from the Golden Mode(2.6s deviation)
sin 2 (penguin) sin 2 (tree)<
Need more data!
Penguin decays
Penguin modes
Golden mode
9 May 2006 M. Morii, Harvard 31
The sidesn To measure the lengths of the
two sides, we must measure|Vub| ≈ 0.004 and |Vtd| ≈ 0.008n The smallest elements – not easy!
n Main difficulty: Controlling theoretical errors due to hadronic physicsn Collaboration between
theory and experiment plays key role
g
a
b
*
*tb
cb
td
cd
VV VV
*
*ubud
cd cb
VV VV
Vtd
Vub
9 May 2006 M. Morii, Harvard 32
|Vub| – the left siden |Vub| determines the rate of the b ® u transition
n Measure the rate of b ® uℓv decay (ℓ = e or µ)
n The problem: b ® cℓv decay is much faster
n Can we overcome a 50´ larger background?
l
ubVb
u
W 22 5
2( )192
Fub b
Gb u V m=l
l
cbVb
c
W2
2( ) 1( ) 50
ub
cb
Vb ub c V
ll
9 May 2006 M. Morii, Harvard 33
n Use mu << mc à difference in kinematics
n Signal events have smaller mX à Larger Eℓ and q2
Detecting b → uℓv
2q
b c
b u
l
uX
Bu quark turns into 1 or more hardons
q2 = lepton-neutrino mass squared
mX = hadron system mass
Eℓ = lepton energy
El
b c
b u
Xm
b cb u
Not to scale!
9 May 2006 M. Morii, Harvard 34
Figuring out what we seen Cut away b ® cℓv à Lose a part of the b ® uℓv signal
n We measure
n Predicting fC requires the knowledge of the b quark’s motion inside the B meson è Theoretical uncertaintyn Theoretical error on |Vub| was ~15% in 2003
n Winter 2006:
n What happened in the last 2+1/2 years?
2( )u C ub CB X f V× =lTotal b ® uℓv rate
Fraction of the signal that pass the cut
Cut-dependentconstant predicted
by theory
expt model SF theory(3.5 2.8 4.1 4.2 )%
7.4%ub ubV V =
= HFAG Moriond 2006 average
9 May 2006 M. Morii, Harvard 35
Progress since 2003n Experiments combine Eℓ, q2, mX to maximize fC
n Recoil-B technique improves precisionsn Loosen cuts by understanding background better
n Theorists understand the b-quark motion bettern Use information from b ® sg and b ® cℓv decaysn Theory error has shrunk from ~15% to ~4% in the process
Fully reconstructedB ® hadrons
ℓv
X
BABARpreliminaryb ® cℓv
background
9 May 2006 M. Morii, Harvard 36
Status of |Vub|
n |Vub| determined to ±7.4%n c.f. sin2b is ±4.7%
Measures the length of the left side of the UT
World Average 4.45 ± 0.33c2/dof = 5.5/6
9 May 2006 M. Morii, Harvard 37
|Vtd| – the right siden Why can’t we just measure the t ® d decay rates?
n Top quarks are hard to maken
n Must use loop processes where b ® t ® dn Best known example: mixing combined with mixing
n Dmd = (0.509 ± 0.004) ps−1
n News from the Tevatron:
2 2 4( ) ( ) 10td tbt d t b V V= <
tdV
tdV
b
b
d
d
t
t
W0B 0BW
0 0-B B 0 0-s sB B2
2tdd
s ts
Vmm V
B0 oscillation frequency
Bs oscillation frequency
0.420.2117.33 0.07sm+= ±
17 21(90%CL)sm< <CDF
DØ
0.0080.0070.208td
ts
VV
+=
9 May 2006 M. Morii, Harvard 38
Radiative penguin decaysn Look for a different loop that does b ® t ® d
n Radiative-penguin decays
n
n Latest results from the B Factories:
n Translated to è
W
t t
b dtdV,u d,u d
B
W
t t
b stsV
,u d,u d
B *K
2
2*
( )( )
td
ts
VBB K V* 5( ) (4.0 0.2) 10B K = ± ×B
B(B ® rg)BABAR (0.6 ± 0.3) ´
10-6
Belle (1.3 ± 0.3) ´10-6
Average (1.0 ± 0.2) ´10-6
0.18 0.03td tsV V = ±
9 May 2006 M. Morii, Harvard 39
Impact on the UTn We can now constrain the right side of the UT
n Mixing measurements pinned down |Vtd/Vts| as precisely as sin2bn B ® rg provides a crosscheck, with sensitivity to New Physics
*
( )( )BB K
B0/Bs mixing
9 May 2006 M. Morii, Harvard 40
The UT todayAngles from CP asymmetriesSides + KL decaysCombined
9 May 2006 M. Morii, Harvard 41
The UT todayn The B Factories have dramatically
improved our knowledge of theCKM matrix n All angles and sides measured
with multiple techniquesn New era of precision CKM
measurements in search of NPn The Standard Model is alive
n Some deviations observed èrequire further attention
New Physics seems to be hidingquite skillfully
9 May 2006 M. Morii, Harvard 42
Constraining New Physics n New Physics at ~TeV scale should affect low-energy physics
n Effects may be subtle, but we have precisionn Even absence of significant effects helps to identify NP
n In addition to the UT, we explore:n rare B decays into Xsg, Xsℓ+ℓ-, tnn D0 mixing and rare D decays n lepton-number violating decays
Precision measurements at the BFactories place strong constraints on
the nature of New Physicsm
H(G
eV)
tanb
Allowed byBABAR data
b ® sg
Two Higgs doublet model
9 May 2006 M. Morii, Harvard 43
Outlookn The B Factories will pursue increasingly precise measurements
of the UT and other observables over the next few yearsn Will the SM hold up?
n Who knows?n At the same time,
we are setting a tightweb of constraints on what New Physics can or cannot be
What the B Factories achieve in the coming years will provide a foundation for future New Physics discoveries