Beauty Physics at LHCb

1
Beauty Physics at LHCb
Andrey Golutvin Vladimir Shevchenko ITEP CERN
11th INTERNATIONAL MOSCOW SCHOOL OF
PHYSICS Session Particle Physics February 8-16,
2008
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Outline

• ABC of LHC
• Flavor physics informal introduction
• The CKM matrix and Unitarity Triangle
• LHCb detector
• Search for New Physics in CP violation
• Physics of loops
• Rare decays at LHCb
• Conclusions

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2
3
Mont Blanc, 4808 m
Jet d Eau 140 m
LHCb experiment 700 physicists 50 institutes 15
countries
CERN
LHCb
ATLAS
CMS
ALICE
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ABC of LHC

• Tonnel length - 27 kilometers
• Depth below ground - between 50 and 175 meters
• p-p beams, 2808 bunches, 1.1510
  particles/bunch
• v 0.99999998 c
• Energy
• Nominal luminosity ltLgt 1034 c?-2 ??? -1

11
5
Energy of a proton in the beam 7 TeV 10-6 J
It is about kinetic energy of a flying mosquito
Question why not to use mosquitos in particle
physics?
Answer because NAvogadro 6.022?1023 (mol)-1
Energy of a mosquito is distributed among
1022 nucleons.
On the other hand, total energy stored in each
beam is 2808 bunches ? 1011 protons/bunch ? 7
TeV/proton 360 MJ It is explosive energy of
100 kg TNT or kinetic energy of Admiral
Kuznetsov cruiser traveling at 8 knots.
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Particle acceleration

• Charged particles influenced by applied electric
  and magnetic fields according to the Lorentz
  force F q (E v ? B) dp/dt
• E field ? energy gain, B field ? curvature
• CERN has a wide variety of accelerators, some
  dating back to 1950s
• LHC machine re-uses the tunnel excavated for
  previous accelerator (LEP)Others (PS/SPS) used
  to accelerate protons before injection into the
  LHC

Neutrino beam,low energy beamsand p
fixed-target beams all running in parallel with
LHC
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The LHC
Original idea
From an article in the CERN Courier
8

• Dipole magnets used to deflect the
  particlesRadius r m 3.33 p GeV / B T
• For the LHC, the machine has to fit in the
  existing 27 km tunnel, about 2/3 of which isused
  for active dipole field ? r 2800 mSo to reach
  p 7 TeV requires B 8.3 T
• Beams focused using quadrupole magnetsBy
  alternating Focusing and Defocusing quadrupoles,
  can focus in both x and y views

The LHC has 1232 dipoles 392 quadrupoles
9
View of LHC tonnel
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Flavor physics informal introduction
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The Standard Model Zoo
SU(3)?SU(2)?U(1) g W, Z ?
Masses come out of interactions in the
Standard Model and these interactions conserve
(or do not conserve) particular symmetries.
Mass hierarchies (from hep-ph/0603118).
The heaviest fermion of a given type has unit
mass.
12
Invariance properties with respect to
transformations have been always important in
physics

• momentum
• angular momentum
• energy

• translations in
• rotations in
• time translations

invariance
conservation
Gauge symmetry invariance with respect to
transformations in internal space
In the SM this space has structure of U(1)
SU(2) SU(3)
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U(1) SU(2) SU(3)
gluon
photon
Z, W
And gravity is everywhere
leptons
quarks
Quarks are unique probes of the whole internal
space, hence flavor physics has to deal with
weak, electromagnetic and strong interactions
altogether
14

• Besides continuous symmetries of prime importance
  in high energy physics are discrete
  transformations
• ? charge conjugation
• P space inversion
• ? time reflection

Experimental fact strong and electromagnetic
interactions in the SM are C, P, T, CP, CT, PT
and CPT invariant.
15
Maximal symmetry is not so interesting
Beauty slightly broken symmetry
16
The breaking should not be too strong, however
17
Our world
Wonderland
Our world ? Wonderland mirror-symmetry is broken
18
Wonderland
Our world
DNA
Mirror symmetry is 100 broken
19
??? theorem Antiparticles and their interactions
are indistinguishable from particles moving along
the same world-lines but in opposite directions
in 31 dimensional space-time.
In particular, the mass of any particle is
strictly equal to the mass of its antiparticle
(experimentally checked in 1 part to 1018 in
K-meson studies).
The SM strictly conserves CPT. There are no
however any theoretical reason why C, P and T
should conserve separately.
Often in physics if something can happen it
does.
20
Weak interactions violate P-parity
T.D.Lee, C.N.Yang, 1956
C.S.Wu, 1957
21
L.D.Landau, 1959 hypothesis of combined
CP-parity conservation
J.Cronin, V.Fitch, 1964 CP-violation discovery
in neutral K-mesons decays.
22
In the world of elementary particles (CPLEAR
1999)
neutral kaon decay time distribution anti-neutral
kaon decay time distribution
23
Later CP-violation has been beautifully measured
by experimentsBaBar and BELLE at the B factories

• These are machines (in the US and Japan) running
  on the ?(4S) resonance ee- ? ?(4S) ? B0B0 or
  BB-
• The CP asymmetry A(t) G(B0 ? J/y KS) - G(B0 ?
  J/y KS) G(B0 ? J/y KS) G(B0 ? J/y
  KS)
• A(t) - sin 2b sin Dm t in the Standard Model
• BABAR BELLE measuresin 2b 0.674 0.026
• This can be compared withthe indirect
  measurementfrom other constraints on
  theUnitarity Triangle

24
M. Kobayashi, T.Maskawa, 1974 theoretical
mechanism for CP-violation in the SM
Idea nontrivial superposition of non-interacting
particles forms flavor eigenstate that interacts
weakly In other words it is impossible to
diagonalize simultaneously the mass term and
charged currents interaction term
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It is easy to show that arbitrary complex unitary
NN matrix can be parameterized by N(N-1)/2
generalized Euler angles and (N-1)(N-2)/2 complex
phases.
For Nlt3 the matrix can always be rotated to an
equivalent one which is real. But not for N3.
In other words, there exist 33 unitary matrices
which cannot be made real whatever phases quark
fields are chosen to have.
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Baryogenesis

• Big Bang ( 14 billion years ago) ? matter and
  antimatter equally produced followed by
  annihilation ? nbaryon/ng 10-10Why didnt all
  the matter annihilate (luckily for us)?
• No evidence found for an antimatter world
  elsewhere in the Universe
• One of the requirements to produce an asymmetric
  final state (our world) from a symmetric
  matter/antimatter initial state (the Big Bang)is
  that CP symmetry must violated Sakharov, 1967
• CP is violated in the Standard Model, through the
  weak mixing of quarksFor CP violation to occur
  there must be at least 3 generations of quarksSo
  problem of baryogenesis may be connected to why
  three generations exist, even though all normal
  matter is made up from the first (u, d, e, ?e)
• However, the CP violation in the SM is not
  sufficient for baryogenesisOther sources of CP
  violation expected ? good field to search for new
  physics

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CKM matrix can be parameterized by four
parameters in many different ways. The so called
Wolfenstein parametrization is based on
expansion in powers of
28
It is convenient to discuss the properties of CKM
matrix in parametrization-invariant terms. Such
invariant are absolute values of the matrix
elements and angles between them
If any of these angles is different from zero, it
means that there is a complex phase in CKM
matrix which cannot be rotated away. This
violates CP.
Jarlskog invariant
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Off-diagonal unitarity conditions can be
represented as triangles on complex plane.
The Unitarity triangle
All 6 unitarity triangles have equal area but
only two of them are not degenerate. B-mesons
decays are very sensitive to ?? !
?
?
?
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The Unitarity triangle
? Bd mixing phase ? Bs mixing phase ? weak
decay phase
Im
?
?
?
0
1
Re
Im
?
?
??
???
Precise determination of parameters
through B-decays study.
0
Re
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UT as a standard approach to test the consistency
of SM
Mean values of angles and sides of UT are
consistent with SM predictions

• Accuracy of sides is limited by theory
• Extraction of Vub
• Lattice calculation of

• Accuracy of angles is limited
• by experiment
• 13
• b 1
• 25

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Standard method to search for New Physics
Define the apex of UT using at least 2
independent quantities out of 2 sides and 3
angles ?, ? and ? Extract quantities Rb and ?
from the tree-mediated processes, that are
expected to be unaffected by NP, and compare
computed values for with direct measurements in
the processes involving loop graphs. Interpret
the difference as a signal of NP
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Topologies in B decays
Trees
Penguins
Boxes
Vib
Viq
q
u,c,t
b
W-
W
u, c, t
q
b
Viq
Vib
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Standard method to search for New Physics
Define the apex of UT using at least 2
independent quantities out of 2 sides and 3
angles ?, ? and ? Extract quantities Rb and ?
from the tree-mediated processes, that are
expected to be unaffected by NP, and compare
computed values for with direct measurements in
the processes involving loop graphs. Interpret
the difference as a signal of NP
35
The sensitivity of standard approach is limited
due to - Geometry of UT (UT is almost
rectangular)
Comparison of precisely measured ? with ? is not
meaningful due to error propagation 3 window in
? corresponds to (24?5) window in ?
36
Precision comparison of the angle ? and side Rt
is very meaningful !!! However in many NP
scenarios, in particular with MFV,
short-distance contributions are cancelled out in
the ratio of ?Md/?Ms. So the length of the Rt
side may happen to be not sensitive to NP
Precision measurement of ? will effectively
constrain Rt and thus calibrate the lattice
calculation of the parameter
37
Complementary Strategy

• Compare observables and UT angles ?,
  ? and ?
• measured in different topologies
• In trees

Theoretical uncertainty in Vub extraction
Set of observables for (at the moment
not theoretically clean)
Theoretical input improved precision of lattice
calculations for fB , BB and B??,?,K
formfactors Experimental input precision
measurement of BR(B?K?, ??)
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Search for NP comparing observables measured in
tree and loop topologies
?(pengtree) in B???,??,?? ?(pengbox) in B??
Ks ?(pengbox) in Bs?? ?

• ?(treebox) in B? J/? Ks
• ?(tree) in many channels
• ?(treebox) in Bs? J/? ?

New heavy particles, which may contribute to d-
and s- penguins, could lead to some phase shifts
in all three angles ??(NP) ?(pengtree) -
?(tree) ??(NP) ?(B??Ks) - ?(B?J/?Ks) ?
0 ??(NP) ?(Bs???) - ?(Bs?J/??)
39
Search for NP comparing observables measured in
tree and loop topologies

• Contribution of NP to processes mediated by loops
• (present status)
• to boxes
• ? vs Vub / Vcb is limited by theory (10
  precision in Vub) (d-box)
• ? not measured with any accuracy
  (s-box)
• to penguins
• ?(??(NP)) 30
  (d-penguin)
• ?(??(NP)) 8
  (s-penguin)
• ?(??(NP)) not measured
  (s-penguin)
• PS ??(NP) ?? (NP)
• ??(NP) measured in B??? and B???
  decays may differ depending
• on penguin contribution to ?? and
  ?? final states

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LHCb is aiming at search for New Physics in
CP-violation and Rare Decays
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Large Hadron Collider - LHCb

• Bunch crossing frequency 40 MHz
• Number of reactions in unit of time
• since ?pp inelastic 80 mbarn
• for nominal LHC luminosity
• N 8?108
• For LHCb L 2 1032 cm-2s-1
• (local defocusing of the beam)
• ? multi-body interactions are
• subdominant

Inelastic pp reactions
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b
b

• vertices and momenta reconstruction
• effective particle identification (p, ?, µ, ?,
  ?)
• triggers

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Current view of LHCb experimental area
Current view of LHCb experimental area
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View of the LHCb cavern
Calorimeters
Magnet
Muon detector
RICH-2
OT
RICH-1
VELO
Its full! Installation of major structures is
essentially complete
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LHCb in its cavern
Offset interaction point (to make best use of
existing cavern)
Shielding wall(against radiation)
Electronics CPU farm
Detectors can be moved away from beam-line for
access
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LHCb detector
300 mrad
p
p
10 mrad
?
Forward spectrometer (running in pp collider
mode)Inner acceptance 10 mrad from conical
beryllium beam pipe
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LHCb detector
?
Vertex locator around the interaction
region Silicon strip detector with 30 mm
impact-parameter resolution
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Vertex detector

• Vertex detector has silicon microstrips with rf
  geometryapproaches to 8 mm from beam (inside
  complex secondary vacuum system)
• Gives excellent proper time resolution of 40 fs
  (important for Bs decays)

Beam
Vertex detector information is used in the trigger
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LHCb detector
?
Tracking system and dipole magnet to measure
angles and momenta Dp/p 0.4 , mass resolution
14 MeV (for Bs ? DsK)
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LHCb detector
?
Two RICH detectors for charged hadron
identification
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LHCb detector
e
h
?
Calorimeter system to identify electrons, hadrons
and neutrals. Important for the first level of
the trigger
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LHCb detector
m
?
Muon system to identify muons, also used in first
level of trigger
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?S LHC prospects
Bs ?J/?? is the Bs counterpart of B0?J/? KS

• In SM ?S - 2arg(Vts) - 2?2? - 0.04
• Sensitive to New Physics effects in the Bs-Bs
  system if NP in mixing ? ?S ?S(SM)
  ?S(NP)
• 2 CP-even, 1 CP-odd amplitudes, angular analysis
  needed to separate, then fit to ?S, ??S, CP-odd
  fraction
• LHCb yield in 2 fb-1 131k, B/S 0.12

LHCb
0.021
0.021
ATLAS
will reach s(?s) 0.08 (10/fb, ?ms20/ps, 90k
J/?? evts)
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UT angle g LHCb (BaBAr BELLE Tevatron
12 precision for ? at best)

• Interference between tree-level decays

Vcs Vub suppressed
Favored Vcb Vus
u
s
Common final state
K()-
K()-
s
u
u
b
B-
B-
b
c
c
u
D()0
D()0
u
u
f
Parameters ?, (rB, dB) per mode

• Three methods for exploiting interference (choice
  of D0 decay modes)
• (GLW) Use CP eigenstates of D()0 decay, e.g.
  D0 ? K K- / pp , Ksp0
• (ADS) Use doubly Cabibbo-suppressed decays,
  e.g. D0 ? Kp -
• (Dalitz) Use Dalitz plot analysis of 3-body D0
  decays, e.g. Ks p p-

• Mixing induced CPV measurement in Bs ? Ds K
  decays
• Specific for LHCb

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UT angle g LHCb summary table
Combined precision after 2 fb-1 ?(?) ? 5? (from
tree only)
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LHCb (10fb-1 ) and SFF (50-75 ab-1) SLHCb (gt100
fb -1) sensitivities
LHCb
SFF SLHCb
SLHCb (stat. only) 0.003 lt 1?
(Bs?DsK) - - -
gt 2014
S(?K0S) 0.02-0.03 S(??) 0.01
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Physics of loops
Loops can be also explored in rare decays. But
before discussing LHCb prospects let us take
more general attitude and ask ourselves why is
it important to study loop processes in general?
58
Main reason is the following loop physics is
intimately related to overall integrity and the
deepest features of quantum theory (Heisenberg
uncertainty principle, unitarity, causality etc).
Example optic theorem all that
Sum over everything!
by means of dispersion relations (causality)
2
Each green arrow is nontrivial. Deep relations
between trees and loops.
At order e2
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Loop processes contain loop momentum integrals
and hence can indirectly probe physics at large
mass scale
Example quantum electrodynamics at small
distances or in strong fields is sensitive to
the electron mass in loops

a) the potential between static sources deviates
from Coloumb law at small distances

b) the energy stored by the static magnetic field
is different from its classical value

60
Analogously rare B-decays mediated by loop
processes are sensitive to heavy particles masses
and couplings logarithmically for radiative
penguins and power-like for box diagrams. However
the concrete form of functional dependence is
much more complicated than in considered simple
examples.
61
Loop processes contain sums over all relevant
degrees of freedom (Lorentz structure of the
interaction, symmetries related to New particles
etc).
Example neutral kaon oscillations
Neutral K-mesons made of d and anti-s quarks
oscillate in vacuum with the frequency 1010
sec-1 because of the following loop process,
mediated by box diagram
d
u, c, t
s
W-
W
u, c, t
d
s
Viq
Vib
Notice that it is the same diagram which
describes oscillations of B-mesons if we replace
s-quark by b-quark!
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Suppose we know nothing about the existence of
heavy c- and t-quarks.
Then naïve estimate of the box diagram with one
internal u-quark gives for the level splitting
(which is nothing but the oscillation
frequency)
while experimental result is
It seems we have a problem
Solution GIM - S.Glashow, J.Iliopoulos,
L.Maiani, 1970 Box diagram with internal c-quark
cancels the one with u-quark (up to the quarks
mass difference)
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Comparison of calculated with
experimentally measured leads to
correct prediction for
This is how it actually happened GIM mechanism
was suggested in 1970, while direct experimental
discovery of c-quark took place only in 1974!
Historical remark 1. Perhaps even more
spectacular is that the famous Kobayashi-Maskawa
paper where the quarks of third generation (b-
and t-quarks) and current paradigm of
CP-violation were introduced was also published
a few months before c-quark discovery (and about
four years before b-quark discovery).
Historical remark 2. Original idea about
possible fourth quark (c-quark) Was suggested by
M.Gell-Mann in his original 1964 paper devoted
to the quark model with three light quarks (u-,
d-, and s- quarks) on aesthetic grounds of
symmetry between quarks and leptons.
Historical remark 3. The analogous mixing matrix
in lepton sector was proposed by Z.Maki,
M.Nakagawa and S.Sakata in 1962, i.e. well
before CKM!
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Computation of Loop processes
Main theoretical tool here is the formalism of
effective low-energy ( µ ltlt MW ) Hamiltonians
Notice that full Hamiltonian is µ-independent!
(at each order in as)
In Wilsons operator product expansion the
quantities coefficient functions
take into account physics at large scales p gt µ,
while local operators care about low
energy (p lt µ) physics.
New Physics can manifest itself both via
corrections to SM coefficient functions (the so
called minimal flavor violation scenario) and
via new operators.
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How does it work in practice?
Simple example Fermi interaction
In the SM muon decay is described by the diagram
The corresponding amplitude
There are two different scales
and
Thus one can replace
(factor 8/v2 is of historical origin)
66
Not so simple example neutral B-mesons
mixing. This process is described by box
diagrams
The corresponding effective Hamiltonian has the
form (leading order in QCD coupling)
coefficient function
M.Vysotsky, 80 T.Inami, C.Lim,81
local operator
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Rare decays of main interest at LHCb
radiative penguin decays B ? K ?, Bs ? f ?, B
? Kf?, related mode B ? K µµ and box decays,
notably Bs ? µµ
Name penguin was coined by John Ellis in 1977
as a result of the darts bet between him and
Melissa Franklin
Different views
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b ? s? exclusive
Bs? ?? BELLE observed 168 events 2 weeks run at
?(5S) no TDCPV
LHCb control channel Bd ? K? 75k signal
events per 2fb-1
LHCb annual yield 11k with B/S lt 0.6
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b ? s? exclusive
b ? ? (L) (ms/mb) ? ?(R)
Measurement of the photon helicity is very
sensitive test of SM Methods - mixing induced
CP asymmetries in Bs ? ?? , B?Ks ?0? - ?b ? ??
asymmetries in the final states angular
distributions are sensitive
to the photon and ?b polarizations. - Photon
helicity can be measured directly using
parity-odd triple correlation (P(?), P(h1) ?
P(h2)) between photon and 2 out of 3 final state
hadrons. Good examples are B? ?K? and B? K???
decays
71
The effective Hamiltonian for these processes has
the form
In the SM
Thus the photons are dominantly right-handed in
the decays of B-mesons and left-handed in the
decays of anti-B mesons
Real life is a little bit more complicated, npQCD
corrections also contribute to wrong helicity
amplitude But not much.
72
Consider angular momentum book-keeping at the
quark level. In s-quark rest frame (pb p?) we
have
or
But coupling between bL and bR in this frame (and
hence the ratio ?L / ?R ) is proportional to
small parameter
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Bs ? f ?
Due to the mixing between Bs and anti-Bs two
states with the masses m1 , m2 and widths G1 ,
G2 are formed.
The time-dependent decay width with CP-eigenstate
and a photon at the final state is given by
where ?Gq G1 - G2 and ?mq m1 - m2
for q s or d
where
if neither nor is small (in SM
CKM angle ) we have a chance to
find from the time-dependent rate.
This is exactly the case of Bs mesons.
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b ? s? exclusive (will be presented by Lesya
Schutska)

• Mixing induced CP
  asymmetries
• B?Ks?0 ? (B-factories)

S - (2O(?s))sin(2?)ms/mb (possible
contribution from b?s?g) - 0.022 0.015

P.Ball and R.Zwicky hep-ph/0609037 Present
accuracy S -
0.21 0.40 (BaBar 232M BB)
S - 0.10 0.31 (BELLE 535M BB)

• Bs ? ?? (LHCb)

LHCb sensitivity with 10fb-1 ?(A?) 0.09
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b ? s? exclusive
Measuring the photon polarization in B ? h1h2h3
? decays
The measurement of the photon helicity requires
the knowledge of the spin direction of the
s-quark emitted from the penguin loop. Use the
correlation between s-spin and angular momentum
of the hadronic system (needs partial-wave
analysis !!!)
Promising channels for LHCb
Expected yield

per 2
fb-1 BR(B ? K?-??) 2.5 ? 10-5 rich
pattern of resonances 60k BR(B ?
K??) 3 ? 10-6 highly distinctive
final state 7k Sensitivity to
photon helicity measurement is being studied
76
The b-quark from initial B meson decays into a
photon and s-quark. The latter forms the hadron
system Y (together with the spectator), which is
characterized by total angular momentum J and its
projection. Strong dynamics causes consequent
decay of Y into a pseudoscalar meson (where the
spectator quark goes) and a vector or tensor
(where the s-quark goes).
77
If only s-wave contributes, Clebsch-Gordan
coefficients are trivial (1) and there is no
sensitivity to ?.
Introducing helicity factor as dG/dF can be
rewritten as
If J 1 contributions dominate
78
B ? K?? (will be presented by
William Reece)
In SM this b?s penguin decay contains
right-handed calculable contribution but this
could be added to by NP resulting in modified
angular distributions
SM
79
B ? K µµ
?
A very important property is forward-backward
asymmetry..
..and position of its zero, which is robust in
SM
80
B ? K?? LHCb prospects

• Forward-backward asymmetry AFB (s) in ??-
• rest frame is a sensitive NP probe
• Predicted zero of AFB (s) depends on Wilson
• coefficients C7eff / C9eff

• 7.2 k events / 2fb-1 with B/S 0.4
• After 10 fb-1zero of AFB located to 0.28
• GeV2 providing 7 stat. error
• on C7eff / C9eff
• Full angular analysis gives better
• discrimination between models. Looks
• promising

81
Will be presented by Diego Martinez Santos
Bs ? ??
Very smal BR in SM (3.4 0.5) x 10-9
This decay could be strongly enhanced in some
SUSY models. Example CMSSM
Current limit from CDF BR(Bs???) lt 5.8?10-8
LHCb
82
OUTLOOK
Clean experimental signature of NP is unlikely at
currently operating experiments

• From now to 2014
• A lot of opportunities (LHCb will start data
  taking this summer)
• Important measurements to search for NP and test
  SM in CP violation
• ? if non-zero ? NP in boxes lt 2010
• ? vs Rb and ? vs Rt (Input from theory !)
• ??(NP) and ??(NP) if non-zero ? NP in
  penguins
• in Rare decays
• BR(Bs ? ??) down to SM prediction lt 2010
• Photon helicity in exclusive b?s? decays
• FBA transversity amplitudes in exclusive
  b?sll decays lt 2010

After 2014 ATLAS and
CMS might or might not discovered New Particles.
At the same time LHCb might or might not see NP
phenomena beyond SM. In either case it is
important to go on with B physics at SFF
Upgraded LHCb Need much improved precision
because any measurement in
b-system constrains NP models
high pT
Bs