the physics of flavor

1
From CKM to MNS and back
Physics of flavor

• the physics of flavor
• is the flavor of physics

Mario Campanelli NIKHEF colloqium Jan 16,2004
2
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.

3
weak mixing

• In the SM, fermion fields can be rotated wrt mass
  eigenstates. This unitary rotation cancels out in
  NC and affects CC as

Cabibbo-Kobayashi-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
4
CKM mixing matrix

• Mixing is expressed in terms of 3x3 unitary
  matrix operating on e/3 quark mass eigenstates

• After unitarity requirements, the matrix is
  expressed in terms of 3 mixing angles ?12 ?23 ?13
  and a complex phase d13

• Exploiting the hierarchy s12s23s13,
• and setting ? s12, the Wolfenstain
  parametrization expands in powers of ?

5
Measurements of CKM elements (90 C.L., using
constraints)

• Vud comparing nuclear ß decays and µ decays

Vus from Ke3 decays
Vub from charmless decays b-gtul? at ?(4S) and LEP
Vcd from charm production in ? interactions
Vcb from decays B-gtDl?
Vcs from charm-tagged W decays in LEP, giving
Vcs0.970.090.07. No b are produced, so look
for heavy-quark 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 Si,jVij2.0390.0250.001
(2 in a 3-generation CKM matrix), and using the
other values as constraint, yielding Vcs
0.9960.013
Vtb from t-gtb observed events
Vtb,Vts from B oscillations
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Unitarity triangle(s)

• Unitarity condition VV1 results in six
  independent costraints three can be represented
  by triangles
• VudVus VcdVcs VtdVts0 ?-?3 -??3 A2?5
  (1-?-i?)0
• VusVub VcsVcb VtsVtb0 A?4 (?i?)A?2 -A?4
  -A?2 0
• VudVub VcdVcb VtdVtb0 A?3 (?i?)-A?3 A?3
  (1-?-i?)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(VudVcbVubVcd) Im(VudVcsVcdVus)
is the same, and proportional to direct CP
violation.
7
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 Vtds12Vcb
• 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) (?(1-
  ?2 /2), ?(1- ?2 /2))

(?,?)
VtdVtb/ VcdVcb
a
VudVub/ VcdVcb
ß
?
(0,0)
(1,0)
8
B oscillations and the side of the triangle
The main constraints to the apex position (apart
from direct CP) come from Vub and e from K
decays.
Information on the VtdVtb/VcdVcb side comes
from B oscillations (virtual t production)
Vtd,ts
Vtb
t
d,s
b
W
W
t
d,s
b
Vtd,ts
Vtb
Bd osc. in dileptons in Belle ?Md0.503 0.08
0.10 ps-1
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Bs mixing
From Bd oscillations, using lattice QCD, we can
derive the relation VtbVtd0.00790.0015
however, most of the uncertainties cancel out in
the ratio
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 ?Msgt14.4 ps-1
at 90 C.L.
I will discuss in detail expected improvements at
the Tevatron
10
The angle ß and CP violation

• In b decays, CP violation can occur in mixing,
  decay or interference between the two (decay into
  CP eigenstates)

1
When tree decays are dominant, mixing and decay
can result in a single weak phase, like in the
golden channel J/? Ks, where
CDF RunI results
Belle LP03
sin2f1 0.7330.0570.028
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What about other channels?
sin 2ß can also be measured in other charmonium
channels and channels with considerable penguin
contribution. In that case the asymmetry gets
more complicated
And rather than measuring directly sin 2ß,
constraints are put to the penguin contribution
(the cosine term, zero in the no-penguin case).
Still open (3.5 C.L.) sin2ßeff (f KS) Babar
0.450.430.07 Belle -0.96 0.50
12
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-gtp p- equivalent to
  B-gtJ/?K, but cosine term predicted (and
  measured) far from zero

The separate measurements of sine and cosine term
(together with knowledge of ?and ?) can be
interpreted in the complex plane of the ratio of
tree to penguin contributions
And used to get information on a using
theoretical assumptions and the neutral B-gt p0
p0 modes
13
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.

14
Neutrino oscillations

• If leptons mix, interaction will have
  non-diagonal terms between weak eigenstates

In three families, the probability becomes
Where the MSN mixing matrix U is normally
expressed with exactly the same formalism as CKM
15
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(?m2L/E) instead of e-Gt
  cos(?mt)
• Not so trivial
• can be antiparticle of itself (Majorana) in that
  case, two additional phases occur, non observable
  in oscillations (but in ?-less ßßdecay)
• In this case, a see-saw mechanism would explain
  the smallness of ? masses, being physical states
  mixing of a massless left-handed state and a
  right-handed state at the Plank scale
  m1MD2/MR,, m2MR
• No hierarchical structure of mixing matrix is
  emerging, two angles are large, one is small
• Propagation in matter can largely modify
  oscillation pattern

16
The atmospheric neutrino region

• ?µand ?e produced in cosmic rays (appr. ratio
  21) reach detector after a baseline dependent on
  the angle.
• angular dependence of ?µ disappearance
  interpreted as oscillations pattern not observed
  for ?e, so leading oscillation must be ?µ??t or
  oscillation into a sterile state.

However, matter propagation for neutrinos coming
from below would be different sterile fraction
lt19 at 90 C.L.
17
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 t identification (CNGS)
t events in ?µ??t oscillation for a 3kton ICARUS
in Gran Sasso, detected using kinematic techniques
18
Solar neutrino region

• Historical indication of neutrino oscillations,
  solar neutrinos always seen as a problem.
• Final evidence from SNO, that can see not only ?e
  disappearance from charge current events, but
  also the other flavors via neutral currents.

Standard solar model finally tested after 30
years!
19
The confirmation KamLAND

• All reactors in Japan are a source for the first
  long-baseline reactor experiment, Kamland, that
  confirmed ?e disappearance (towards the
  maximally-mixed ?µ?t combination)

Solar angle is not maximal as the atmospheric
one, but it is not small. ?m2 more than one order
of magnitude smaller than the atmospherics
20
The search for ?13

• The third angle, connecting ?e 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 sin22?lt0.01 with
• 50 kton (10xCHOOZ) deep detector (less BG)
• 2 detectors for syst. 3-gt1

Conventional (NuMI) beam and super-beam (JHF) can
extend by similar amount
21
Conditions for CP violation

• Nothing is known about the phase d. Like in the
  hadronic system, it is connected to the amount of
  CP violation. In vacuum, the ?e??µ oscillation
  probability is made of three terms

Independent of ?
P(?e???)P(????e) 4c213sin2 ?23s212s213c212(sin
2?13s213s223 sin2?12s212(1-(1s213)s223))
-1/2c213sin2?12s13sin2?23cos?cos2?13-
cos2?23-2cos2?12sin2?12 1/2c213sin?sin2?12s13sin
2?23sin2?12-sin2?13sin2?23
CP-even
Campanelli
CP-odd
The last term changes sign under CP, so for dgt0
the oscillation probability does not conserve CP.
To have an observable effect, however, ?13 cannot
be so small otherwise the CP-violating term gets
too small with respect to the constant solar term
22
How to measure CP violation

• Running an off-axis super-beam with ?µ and ?µ
• low energy, few events
• systematics for cross section
• marginal sensitivity
• Coupling with a collimated ß-beam from ion decay
• 6He?6Lie- ?e
• 18Ne?18F e ?e
• to have a clean ?e beam and search t-violation
• feasible but challenging
• not optimal for the low-?13 region

40 kton
400 kton
M.Mezzetto
2 years neutrino, 10 years antineutrino,
CERN-Frejus superbeam
23
Neutrino factories

• The most lavish way to search for CP violation
  would be with high-energy beams of ?e,?µ, ?e,?µ
  produced in decay of stored muons. Large (O(50
  kton)) detector with muon charge ID detect
  neutrinos after thousands of kilometers.

?-????ee ?e??? ?e??t ????t
????e ?????ee- ?e??? ?e??t ????t ????e
8 oscillation modes simultaneously observable,
strong signature from wrong-sign muons
Bueno, Campanelli, Rubbia
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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 d.
  Matter effects can be subtracted but sensitivity
  degrades above 4000 km.
• A simultaneous measurement of ?13 and d can
  result in large correlations or degeneracy they
  can be solved by using multiple baselines or
  combining neutrino factory and super-beams

Bueno Campanelli Navas Rubbia
A.Donini et al.
25
Some theoretical speculations
M.C.Gonzalez-Garcia

• what to do with two different matrices we do not
  understand?

Theorists proposed several kind of models. For
instance (Fritzsch), writing
Some approximate relations hold
According to the model, some specific relations
can hold (like fp/2) allowing predictions on
triangle angles
26
More speculations
Altarelli Feruglio Masina

• For lepton mixing, anarchical, semi-anarchical
  and hierarchical models predict in SU(5)xU(1)
  scenario a (unification scale) mass matrix for
  neutrinos of the kind

with e1, ? and ?2,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 ?13 close to present bounds.
Similar exercises trying to unify both matrices
require larger symmetries like SU(10)xU(2)
Murayama
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Next big thing in lepton mixing ?13 search in JHF
Two phases (second not yet approved)
2008?
Plan to start in 2007
1GeV n beam
Super-K 22.5 kt
J-PARC (Tokai)
Kamioka
Hyper-K 1000 kt
0.75MW 50 GeV PS
at
4MW 50 GeV PS
Off axis 2 deg, 5 years
CHOOZ excluded
JHF 0.75MW Super-Kamiokande
Future Super-JHF 4MW Hyper-K(1Mt) JHFSK
? 200
Sin22q13gt0.006
sin22q13
p
p
n
140m
0m
280m
2 km
295 km
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Next big thing in hadron mixing ?Gs in CDF
Minimise error on pT with fully
reconstructed decays Bs?Ds p CDF 65 fs (50 fs
with L00) D0 75 fs Flavour tagging Need
everything for eD25 e tag efficiency D tag
correct (dilution) Yield need gtO(1000)
events So far, seen 0.7 ev/pb-1 With improved
trigger and detector almost factor 2 gain Add
more decay modes

• At least 30 times faster
• than Bd mixing
• ?md0.502 0.006 ps-1
• Needs exquisite proper time resolution

Bs ? Ds?, Ds ? ? ? Ds ? ??, KK, ???
29
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 s(F)5mr
• s(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 ? s 48 µm
Displaced two track trigger Tracks pTgt2 GeV,
d0gt120 µm SpTgt5.5 GeV Fully hadronic B decays
(B?hh, Bs?Dsp, D?Kp )
SVT impact parameter (µm)
30
First measurements on Bs

• Not enough luminosity to see oscillations
  measurement of relative Bs and Bd yields

31
Bs mixing sensitivity

• Ssignal events
• Bbackground events
• st proper time resolution
• eD2 effettive tagging efficiency

currently s1600 ev/fb-1, S/B2/1, eD24,
st0.0067 ps ? 2s measurement of ?ms15ps-1 from
500 pb-1 data
improvements s2000 ev/fb-1 with additional
channels, eD25 with TOF, st0.005 ps with L00
and event beamline 2.11 fb-1 (baseline) and 3.78
fb-1 (design) by 2007
32
?Gs/Gs

• ?Gs/?ms -3p/2 mb2/mt2?(?Gs)/?(?ms)
• SM ?Gs/?ms 3.70.8-1.5 10-3
• LQCD ?Gs/Gs0.120.06
• Present 95 C.L. limit ?Gs/Gslt0.54

CKM-independent QCD factors
Disentangle on a statistical basis contributions
to the B-gthh peak, then fit lifetimes for the
different charges

• Expected sensitivity
• 0.29 at 500 pb-1
• 0.10 at 2 fb-1

33
B physics in the LHC era

• Dominated by dedicated hadron experiment(s) LHCb
  (and BTeV)
• Multiple channels allow measurement of angles a
  and ?
• Es. measure Fs from Bs-gtJ/?F (5s discovery
  possible in 1 year) and ?Fs from asymmetry of
  Bs-gtDSK-

Using the four B-gthh channels precision can go to
40-60 with contributions from penguins or new
physics
Dalitz-plot analysis of B-gtpp-p0 can give
sin(2a) and cos(2a) for d(a) 40
all this will lead to stronger constraints on new
physics
34
What can ATLAS and CMS do?

• In principle complementary to dedicated
  experiments in ? coverage and larger statistics
  for leptonic channels, in practice limited by
  bandwidth and PID. Competitive in rare leptonic
  decays like B-gtµµ(X) and Bc-gtJ/?(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 higher-level
triggers. Presently proposed to ATLAS as an
upgrade, for low-luminosity running as well as
high-pt b physics
35
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

36
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!