Physics of flavor
From CKM to MNS and back
…the physics of flavor
is the flavor of physics…
Mario Campanelli NIKHEF colloqium Jan 16,2004
Introduction
 Since the theory of Cabibbo angle in 1964, we
know that eigenstates of mass and weak
interactions do not coincide.
 In the following 40 years, mixing of quarks and
leptons has been one of the main subjects in
particle physics, and this program is far from being
over.
 I will try to take you around in a trip to this field,
with a personal look to what the future could be.
weak mixing
 In the SM, fermion fields can be rotated wrt
mass eigenstates. This unitary rotation
cancels out in NC and affects CC as
 dL 
 
g

Lint  
(u L , cL , t L ) V  sL W  c.c.
2


b
Cabibbo-Kobayashi L
Maskawa mixing matrix
Also for massless particles mixing can be rotated
away. Now we know that neutrinos are massive, and
a similar matrix (Maki, Nakagawa,Sakata) can be
defined, with analogous formalism
CKM mixing matrix

Mixing is expressed in terms of 3x3
unitary matrix operating on –e/3
quark mass eigenstates
 d '  Vud Vus Vub  d 
  
 
 s'   Vcd Vcs Vcb  s 
 b'   V
 b 
V
V
ts
tb  
   td
•After unitarity requirements, the

c12c13

matrix is expressed in terms of 3
V    s12c23  c12 s 23 s13ei13
mixing angles θ12 θ23 θ13 and a

i13
s
s

c
c
s
e
12
23
12
23
13
complex phase δ13

•Exploiting the hierarchy
s12»s23»s13,
and setting λ ≡ s12, the
Wolfenstain parametrization
expands in powers of λ
s12c13
c12c23  s12 s23s13ei13
 c12 s23  s12c23s13ei13
 1  2 / 2


V 

1  2 / 2
 A3 (1    i )  A2

s13e i13 

s23c13 

c23c13 
A3 (   i ) 

2
A
  O(4 )

1

Measurements of CKM elements
(90% C.L., using constraints)
Vud comparing nuclear β
decays and μ decays
Vcd from charm
production in ν
interactions
Vus from Ke3 decays
Vub from charmless
decays b->ulν at Υ(4S)
and LEP
 0.9741  0.9756 0.219  0.226 0.0025  0.0048 


V   0.219  0.226 0.9732  0.9748 0.038  0.044 
 0.004  0.014
0.037  0.044 0.9990  0.9993 

Vcs from charm-tagged W decays in LEP, giving
|Vcs|=0.97±0.09±0.07. No b are produced, so look for heavyquark characteristics (displaced vertexes, heavy mass, leading
effects, presence of D*) in jets from W decay, possibly using
neural networks or likelihood functions.
Tighter determination comes from ratio hadronic/leptonic W
decays, leading to Σi,j|Vij|=2.039±0.025±0.001 (2 in a 3-generation
CKM matrix), and using the other values as constraint, yielding
|Vcs| = 0.996±0.013
Vcb from decays
B->D*lν
Vtb from t->b
observed events
Vtb,Vts from B
oscillations
Unitarity triangle(s)
Unitarity condition V+V=1 results in six independent costraints;
three can be represented by triangles:
 VudVus* + VcdVcs* + VtdVts*=0
λ-λ3 -λ+λ3 +A2λ5 (1-ρ-iη)=0
 VusVub* + VcsVcb* + VtsVtb*=0
Aλ4 (ρ+iη)+Aλ2 -Aλ4 -Aλ2 =0
 VudVub* + VcdVcb* + VtdVtb*=0
Aλ3 (ρ+iη)-Aλ3 +Aλ3 (1-ρ-iη)=0
The first (relative to K oscillations) and the second triangle are
“smashed” into a segment, while the third one (relative to B
physics) has sides of similar length.
However, it was shown by C.Jarsklog that the area of all triangles, half the determinant
J= |Im(VudVcbVub*Vcd*)| = |Im(VudVcsVcd*Vus*)| = …
Representations of the b triangle
We can align VcdVcb* on the x axis, and setting cos of
small angles to 1, the relation becomes
Vub* +Vtd=s12Vcb*
and rescaling by s12Vcb*, the triangle will have base
on (0,0)-(1,0) and apex on
(Re(Vub)/|s12 Vcb|,-Im(Vub)/|s12 Vcb|) =
(ρ(1- λ2 /2), η(1- λ2 /2))
 Vtb*Vtd
  arg 
*

V
 ubVud
(ρ,η)
α
*/
VudVub
VcdVcb*
β
(0,0)
VtdVtb*/
VcdVcb*
γ
(1,0)



 Vtb*Vtd
    arg  *
 VcbVcd
 Vub* Vud 

  arg
*
  VcbVcd 



B oscillations and the side of the triangle
The main constraints to the apex position (apart from
direct CP) come from |Vub| and ε from K decays.
Information on the VtdVtb*/VcdVcb* side comes from B oscillations
(virtual t production)
Vtb t
b
d,s
W
W
d,s
Vtd,ts
t
Vtd,ts
Vtb
b
Bd osc. in dileptons in Belle: ΔMd=0.503± 0.08 ±0.10 ps-1
Bs mixing
From Bd oscillations, using lattice QCD,
we can derive the relation
|Vtb*Vtd|=0.0079±0.0015; however, most of
the uncertainties cancel out in the ratio
M Bs
M Bd
M Bs Bˆ Bs f B2s | Vtb*Vts |2

M Bd Bˆ Bd f B2d | Vtb*Vtd |2
So a measurement of the Bs mixing would be the
single largest improvement in the understanding
of the CKM matrix.
The present limit from LEP, SLD is ΔMs>14.4 ps-1 at 90% C.L.
I will discuss in detail expected improvements at the Tevatron
The angle β and CP violation
 In b decays, CP violation can occur in mixing, decay or interference
between the two (decay into CP eigenstates)
±1
q
( B (t )  f )  ( B (t )  f )
i 2 dec 
 sin Mt
a f (t ) 
 Im  f e
0
0
( B (t )  f )  ( B (t )  f )
p

0
0
When tree decays are dominant, mixing and decay can result in a single weak phase,
like in the golden channel J/Ψ Ks, where
Vtb*Vtd VcbVcs* VcsVcd*
q
i 2 
 ( J / K s )  


e
p
VtbVtd* Vcb* Vcs Vcs*Vcd
CDF RunI results
Belle LP’03
sin2f1= 0.733±0.057±0.028
What about other channels?
sin 2β can also be
measured in other
charmonium channels and
channels with considerable
penguin contribution. In
that case the asymmetry
gets more complicated:
(1 |  |2 ) cos( mt )  2 Im  sin mt
a f (t ) 
1 |  |2
q Af
p Af
And rather than measuring directly sin 2β,
constraints are put to the penguin
contribution (the cosine term, zero in the
no-penguin case).

Still open (3.5% C.L.)
sin2βeff (φ KS) :
Babar: +0.45±0.43±0.07
Belle: -0.96 ±0.50
Other angles


Penguin diagrams are unavoidable in measurement
of the other angles, since no channels with
dominant tree-level are present.
Es. without penguins B->π+ π- equivalent to
B->J/ΨK, but cosine term predicted (and measured)
far from zero
The separate measurements of sine and
cosine term (together with knowledge of ρand
η) can be interpreted in the complex plane of
the ratio of tree to penguin contributions
And used to get information on α using
theoretical assumptions and the neutral
B-> π0 π0 modes
hadronic and leptonic mixing
Hadronic mixing matrix has been studied for 40
years now, elements are measured with good
precision.
Hierarchic structure, allows perturbative
expansion, expressed with a triangle whose
nonzero area predicts CP violation in the b
system, as observed.
Still much to do, but a clear picture is emerging.
 Experimental evidence of nonzero neutrino
masses (therefore a measurable mixing
matrix) only came in 1998 with atmospheric
neutrino oscillations from SuperKamiokande.
Neutrino oscillations
 If leptons mix, interaction will have non-diagonal
terms between weak eigenstates:
  H    sin 2e i ( p  p
1
|  H  
2 )x
 sin 2e
m12  m22
i
x
p1  p2
 sin 2e
m 2
i
2p
2

m
L
2
2
2
|  sin 2 sin
4 pc
In three families, the probability becomes
P(   )   
2



m
ij L
*
*
2

 4U iU iU jU j sin 1.27


E
j i


Where the MSN mixing matrix U is normally expressed with
exactly the same formalism as CKM
Some differences with hadron mixing
 Trivial:
– do not bind into mesons, no hadronic effects, direct
measurement of oscillation parameters
– stable particles in relativistic motion, oscillate like
sin2(Δm2L/E) instead of e-Γt cos(Δmt)
 Not so trivial
– can be antiparticle of itself (Majorana); in that case, two
additional phases occur, non observable in oscillations (but
in ν-less ββdecay)
– In this case, a see-saw mechanism would explain the
smallness of ν masses, being physical states mixing of a
massless left-handed state and a right-handed state at the
Plank scale; m1=MD2/MR,, m2≈MR
– No hierarchical structure of mixing matrix is emerging, two
angles are large, one is small
– Propagation in matter can largely modify oscillation pattern
The atmospheric neutrino region


νμand νe produced in
cosmic rays (appr. ratio
2:1) reach detector after
a baseline dependent on
the angle.
angular dependence of
νμ disappearance
interpreted as
oscillations; pattern not
observed for νe, so
leading oscillation must
be νμ→ντ or oscillation
into a sterile state.
However, matter propagation for neutrinos coming from
below would be different; sterile fraction <19% at 90%
C.L.
The confirmation: long-baseline beams
Oscillation observed also in the first
terrestrial long-baseline experiment
(K2K); other projects aim at precision
parameter measurement (MINOS) and
direct τ identification (CNGS)
τ events in νμ→ντ oscillation for a 3kton ICARUS in
Gran Sasso, detected using kinematic techniques
Solar neutrino region
 Historical indication of neutrino
oscillations, solar neutrinos always
seen as “a problem”.
 Final evidence from SNO, that can
see not only νe disappearance
from charge current events, but
also the other flavors via neutral
currents.
Standard solar model finally
tested after 30 years!
The confirmation: KamLAND
 All reactors in Japan are a source for the first long-baseline
reactor experiment, Kamland, that confirmed νe
disappearance (towards the maximally-mixed νμντ
combination)
Solar angle is not maximal as the atmospheric
one, but it is not small. Δm2 more than one order
of magnitude smaller than the atmospherics
The search for θ13
 The third angle, connecting νe to
the others, has not been
measured. The best limit comes
from the reactor experiment
CHOOZ. Finding this angle is the
goal of most of the future
experiments:
New reactors aim sin22θ<0.01 with:
•50 kton (10xCHOOZ) deep detector
(less BG)
•2 detectors for syst. 3%->1%
Conventional (NuMI) beam and super-beam
(JHF) can extend by similar amount
Conditions for CP violation
 Nothing is known about the phase δ. Like in the
hadronic system, it is connected to the amount
of CP violation. In vacuum, the νe→νμ oscillation
probability is made of three terms: Independent of 
P(e)=P(e)=
4c213[sin2 23s212s213+c212(sin213s213s223+ sin212s212(1-(1+s213)s223))]
-1/2c213sin212s13sin223cos[cos213- cos223-2cos212sin212]
+1/2c213sinsin212s13sin223[sin212-sin213+sin223]
CP-odd
The last term changes sign under CP, so for δ>0 the
oscillation probability does not conserve CP.
To have an observable effect, however, θ13 cannot be
so small otherwise the CP-violating term gets too
small with respect to the constant solar term
CP-even
Campanelli
How to measure CP violation
 Running an off-axis super-beam with νμ
and νμ
– low energy, few events
– systematics for cross section
– marginal sensitivity
 Coupling with a collimated β-beam from
ion decay
6He++6Li+++e- ν
e
18Ne18F
e+ νe
to have a clean νe beam and search tviolation
– feasible but challenging
– not optimal for the low-θ13 region
40 kton
400 kton
M.Mezzetto
2 years neutrino, 10 years antineutrino,
CERN-Frejus superbeam
Neutrino factories
 The most lavish way to search
for CP violation would be with
high-energy beams of νe,νμ,
νe,νμ produced in decay of
stored muons. Large (O(50
kton)) detector with muon
charge ID detect neutrinos 8 oscillation modes
after thousands of kilometers.
simultaneously
observable, strong
signature from wrongsign muons
Bueno, Campanelli, Rubbia
-ee+
e
eτ
τ
e
+eee
eτ
τ
e
Remarks on a future leptonic CP
observation
 Observing difference in oscillation probability not
sufficient to claim lepton CP discovery.
Propagation in matter is not symmetric, a
difference will be observed regardless of δ. Matter
effects can be subtracted but sensitivity degrades
above ~4000 km.
 A simultaneous measurement of θ13 and δ can
result in large correlations or degeneracy; they
can be solved by using multiple baselines or
combining neutrino factory and super-beams
A.Donini et al.
Bueno Campanelli Navas Rubbia
Some theoretical speculations
M.C.Gonzalez-Garcia
 0.9741  0.9756

V   0.219  0.226
 0.004  0.014

0.219  0.226
0.9732  0.9748
0.037  0.044
0.0025  0.0048 

0.038  0.044 
0.9990  0.9993 

 what to do with two different matrices we do not understand?
Theorists proposed several kind of models. For instance (Fritzsch), writing
 cu

V    su
 0

su
cu
0
0  e t

0  0
1  0
0  cd

s  sd
 s c  0
0
c
 sd
cd
0
0

0
1 
Some approximate relations hold:
tan u | Vub / Vcb | mu / mc
tan  d | Vtd / Vts | md / ms
According to the model, some specific
relations can hold (like φ=π/2) allowing
predictions on triangle angles
Vus  su  sd e i
Vcd   d  u e
 i
md
mu i


e
ms
mc
More speculations
Altarelli Feruglio Masina
For lepton mixing, anarchical, semianarchical and hierarchical models
predict in SU(5)xU(1) scenario a
(unification scale) mass matrix for
neutrinos of the kind
 2   


m    1 1 
  1 1


with ε=1, λ and λ2,respectively. Trasporting this
matrix to our scale yields low-energy predictions
“Anarchy” model successfully predicts large
mixing angles and small mass ratios, and a
value of θ13 close to present bounds.
Similar exercises trying to unify
both matrices require larger
symmetries like SU(10)xU(2)
Murayama
Next big thing in lepton mixing: θ13
search in JHF
Two phases (second not yet approved)
Plan to start in 2007
2008?
~1GeV  beam
sin22
Super-K: 22.5 kt
J-PARC
(Tokai)
Kamioka
Hyper-K: 1000 kt
CHOOZ excluded
at
0.75MW 50 GeV PS
4MW 50 GeV PS
Off axis 2 deg, 5 years
JHF 0.75MW + Super-Kamiokande
Future Super-JHF 4MW + Hyper-K(~1Mt) ~ JHF+SK  200
Sin2213>0.006
p

0m
sin2213

140m
280m
2 km
295 km
Next big thing in hadron mixing: ΔΓs
in CDF
Minimise error on pT
with fully reconstructed
decays Bs→Ds π
CDF ~ 65 fs (50 fs with L00)
D0 ~ 75 fs
Flavour tagging
Need everything for εD2~5%
ε = tag efficiency
D = tag correct (dilution)
At least 30 times faster
than Bd mixing
Δmd=0.502 ± 0.006 ps-1
Needs exquisite proper time
resolution
m
ct  Lxy
B
B
T
p
Yield – need >O(1000) events
So far, seen ~0.7 ev/pb-1
With improved trigger and
detector almost factor 2 gain
Add more decay modes
Bs  Ds, Ds   
Ds  , K*K, 
Triggering on heavy flavors in
hadronic environment
 CDF can have such an ambitious program
in b physics thanks to its unique trigger
system. At level 1, the XFT can measure
tracks in the chamber with eff.=96%
σ(Φ)=5mr
σ(pT)=(1.74 pT)%.
 Information is combined with silicon hits
and compared to predefined roads
stored into an associative memory
35μm  33
μm
resol  beam
 σ = 48 μm
Displaced two track trigger
Tracks: pT>2 GeV, d0>120 μm
ΣpT>5.5 GeV
Fully hadronic B decays
(B→hh’, Bs→Dsπ, D→Kπ …)
SVT impact parameter (μm)
First measurements on Bs
 Not enough luminosity to see oscillations:
measurement of relative Bs and Bd yields
Bs mixing sensitivity
SD
significan ce 
e
2
2
( ms t ) 2

2
S
SB




S=signal events
B=background events
σt proper time resolution
εD2 effettive tagging efficiency
currently:
improvements:
s=1600 ev/fb-1, S/B=2/1, εD2=4%,
σt=0.0067 ps
s=2000 ev/fb-1 with additional channels, εD2=5%
with TOF, σt=0.005 ps with L00 and event
beamline
 2σ measurement of Δms=15ps-1
from 500 pb-1 data
2.11 fb-1 (baseline) and 3.78 fb-1 (design) by 2007
ΔΓs/Γs




ΔΓs/Δms =-3π/2 mb2/mt2η(ΔΓs)/η(Δms)
SM: ΔΓs/Δms =3.7+0.8-1.5 10-3
LQCD: ΔΓs/Γs=0.12±0.06
Present 95% C.L. limit: ΔΓs/Γs<0.54
CKMindependent
QCD factors
Disentangle on a statistical
basis contributions to the
B->hh peak, then fit
lifetimes for the different
charges
Expected sensitivity:
•0.29 at 500 pb-1
•0.10 at 2 fb-1
B physics in the LHC era
 Dominated by dedicated hadron
experiment(s) LHCb (and BTeV)
 Multiple channels allow measurement
of angles α and γ
 Es. measure Φs from Bs->J/ΨΦ (5
discovery possible in 1 year) and
γ+Φs from asymmetry of Bs->DS+K-
Using the four B->hh channels precision can go to 4060 with contributions from penguins or new physics
Dalitz-plot analysis of B->π+π-π0 can
give sin(2α) and cos(2α) for δ(α) = 40
all this will lead to stronger constraints on new
physics
What can ATLAS and CMS do?
 In principle complementary to
dedicated experiments in η
coverage and larger statistics for
leptonic channels, in practice limited
by bandwidth and PID. Competitive
in rare leptonic decays like
B->μμ(X) and Bc->J/Ψ(X)
Some b-physics capability could be recovered
using a similar system to the CDF SVT, a
dedicated processor (FastTrack) for on-line
track recognition. Without interfering with the
rest of the DAQ, it “sniffs” tracker data going to
the memory buffer and stores good quality
tracks to another buffer accessible by higherlevel triggers.
Presently proposed to ATLAS as an upgrade,
for low-luminosity running as well as high-pt b
physics
Summary
 We made a quick tour in the world of flavors, trying
to stress differences and similarities between
leptons and hadrons.
 Both sectors saw in the recent past important
discoveries, and more are announced for the next
future
 Big expectations from b-factories, neutrino beams,
hadron colliders
 Although techniques are very different, the
underlying physics is the same
Three reasons to expect something new
 Both neutrino oscillations and CP-violation in b
physics are recent discoveries: much more has
to be dug
 Historically, new phenomena have been seen
first in low-energy data (neutral currents, top at
LEP; GUT from see-saw? SUSY in b decays?)
 Reductionism (driving force of physics since
Kepler and Newton): there are too many free
parameters over there. There must be some
underlying structure!