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					    Beauty Physics at LHCb

    b
p                            p
    b
                  Andrey Golutvin
                Vladimir Shevchenko

                    ITEP & CERN

     11th INTERNATIONAL MOSCOW SCHOOL OF PHYSICS
         Session «Particle Physics» February 8-16, 2008
                 Outline

     ABC of LHC

1    Flavor physics – informal introduction
     The CKM matrix and Unitarity Triangle
     LHCb detector
     Search for New Physics in CP violation
2    Physics of loops
     Rare decays at LHCb
     Conclusions
                   Jet d’ Eau     Mont Blanc,
LHCb experiment:    140 m          4808 m
700 physicists
50 institutes
15 countries

                                                CERN
                                LHCb

                                            ATLAS


  CMS
                                                    ALICE
                     ABC of LHC

• Tonnel length - 27 kilometers

• Depth below ground - between 50 and 175 meters

•   p-p beams, 2808 bunches, 1.15×1011 particles/bunch

• v = 0.99999998 c

• Energy        s  14 TeV        Etotal  200 Etotal
                                    LHC          Tevatron



• Nominal luminosity <L> ~ 1034 cм-2 сек -1
  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.
                       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 beams
                                                                and p fixed-target
                                                                beams all running
                                                                in parallel with LHC
                       The LHC
From an article in the CERN Courier   Original idea




                                      Reality
• Dipole magnets used to deflect the particles
  Radius  [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 is
  used for active dipole field →  ~ 2800 m
  So to reach p = 7 TeV requires B = 8.3 T
• Beams focused using quadrupole magnets
  By alternating Focusing and Defocusing                    The LHC has 1232 dipoles
  quadrupoles, can focus in both x and y views                      392 quadrupoles

                                          y
                                N-pole        S-pole

                                                 Beam
                                                        x
                                S-pole        N-pole
View of LHC tonnel
   Flavor physics:
informal introduction
        The Standard Model Zoo
SU(3)SU(2)U(1) [ g; W, Z; ]

 u    c    t 
  
 d     
        s     
               b
            

 e         
  
      
             
                
  e        


                       Mass hierarchies (from hep-ph/0603118). The
                      heaviest fermion of a given type has unit mass.

  Masses come out of interactions in the Standard Model
  and these interactions conserve (or do not conserve…)
                    particular symmetries.
      Invariance properties with respect to transformations
             have been always important in physics
                           3
 1. translations in    R            1. momentum
                       3
 2. rotations in   R                2. angular momentum

 3. time translations               3. energy



       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)
      U(1) × SU(2) × SU(3)
        photon             Z, W         gluon
                                                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
  Besides continuous symmetries of prime importance in
  high energy physics are discrete transformations


  • С – charge conjugation
  • P – space inversion
  • Т – time reflection


Experimental fact: strong and electromagnetic interactions
in the SM are C, P, T, CP, CT, PT and CPT invariant.
Maximal symmetry is not so interesting…




  Beauty         slightly broken symmetry
The breaking should not be too strong, however…
СРТ theorem:
Antiparticles and their interactions are indistinguishable from
particles moving along the same world-lines but in opposite
directions in 3+1 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.
            Weak interactions violate P-parity




T.D.Lee, C.N.Yang, 1956                C.S.Wu, 1957
L.D.Landau, 1959:    J.Cronin, V.Fitch, 1964: CP-violation
hypothesis of        discovery in neutral K-mesons
combined CP-parity   decays.
conservation
In the world of elementary particles:
          (CPLEAR 1999)

                             neutral kaon
                         decay time distribution
                                   
                           anti-neutral kaon
                         decay time distribution




                            CP violation
Later CP-violation has been beautifully measured by experiments
               BaBar and BELLE at the B factories


   These are machines (in the US and Japan) running on the (4S)
   resonance: e+e-  (4S)  B0B0 or B+B-
 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) = - sin2b sin Dm t
   in the Standard Model
 BABAR+BELLE measure
  sin2b = 0.674 ± 0.026
 This can be compared with
  the indirect measurement
  from other constraints on the
  Unitarity Triangle
                             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:

                                     dL 
                                      +
  Lint 
         g2
            u L , cL , t L  VCKM  sL W + h.c.
                               ˆ

          2                         b 
                                     L
          d '  Vud       Vus Vub  d 
                                  
          s '    Vcd    Vcs Vcb  s 
          b'   V                  b 
            td           Vts Vtb  
   It is easy to show that arbitrary complex unitary N×N
   matrix can be parameterized by N(N-1)/2 generalized
   Euler angles and (N-1)(N-2)/2 complex phases.

  For N<3 the matrix can always be rotated to an equivalent
  one which is real. But not for N=3.

In other words, there exist 3×3 unitary matrices which cannot
 be made real whatever phases quark fields are chosen to have.
                          Baryogenesis

 Big Bang (~ 14 billion years ago) → matter and antimatter equally
  produced; followed by annihilation → nbaryon/ng ~ 10-10
  Why didn‟t 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 quarks
  For CP violation to occur there must be at least 3 generations of quarks
  So 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 baryogenesis
  Other sources of CP violation expected → good field to search for new
  physics                                                               24
CKM matrix can be parameterized by four parameters in many
different ways. The so called «Wolfenstein parametrization» is
based on expansion in powers of


  Vus + O( )  0.2272  0.0010
                7
  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

                             VijVik 
                                   *

                       arg
                            V V
                                     
                                   * 
                             lj lk 

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»      J  Im ViV jb Vib V j* ~ 3 10 -5
                                             *
  Off-diagonal unitarity conditions can be represented as
  triangles on complex plane.



Vud Vus Vub                    Vud Vub + Vcd Vcb + Vtd Vtb  0
             
                                        *          *          *



 Vcd Vcs Vcb                   Vud Vtd
                                        *
                                            + Vus Vts + Vub Vtb
                                                     *          *
                                                                      0
V            
 td Vts Vtb                         The Unitarity triangle:

All 6 unitarity triangles have
equal area but only two of                  *                    *
                                                             VtdVtb
                                       V V
                                        ud ub
them are not degenerate.
                                                                 b
B-mesons decays are                                      *
very sensitive to СР !
                                                    VcdVcb
                          The Unitarity triangle
  ,   1 - 2 2 ,                                         b: Bd mixing phase
     Im                        B0   ,  ,  ,.....
                                           *
                                       VtdVtb                       : Bs mixing phase
                                           *                       : weak decay phase
                                       VcdVcb
VudVub*                                            B 0  J /yK S , .....
                                                               0

      *
Vcd Vcb                                 b
          0                                         1 Re                       *
                                          Im                                   VudVtd
Bd  DK , DK *                                                                      *
Bs  Ds K              - 2         *
                                                                
                                                                               Vcd Vcb
                                                                                         Bs  J /y, .....
                                                                                          0
                                     VubVtb
Bd  D*               + 2b             *
                                                                                                  
                                     Vcd Vcb
                                                       -                         b+
 Precise determination
 of parameters through                             0                    *           *            Re
 B-decays study.                                                       VusVts / VcdVcb
   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°



                                                                               29
     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: , b 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
                   Topologies in B decays
                                  Trees
                             b                        q1

                                                           q2
                            Bq              W−
                                                           d, s

                                 Penguins
    W–
                                  W−                                   W−
b                  q                                  d (s) b              u,c,t   d (s)
         u, c, t        b               u, c, t
                                                             l+                        q
                                          Z, γ                                 g
                                                             l−                        q
                                  Boxes
                                  V*ib              Viq
                        b                 u,c,t                   q
                   Bq            W+                   W−              Bq
                       q                  u, c, t                 b
                                  Viq               V*ib
     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: , b 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
   The sensitivity of standard approach is limited due to:

   - Geometry of UT (UT is almost rectangular)
Comparison of precisely measured b with  is not meaningful due to error
propagation: 3° window in b corresponds to (245)° window in 
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 DMd/DMs.
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
                     Complementary Strategy

                           *
Compare observables VtsVtb and UT angles: , b and 
measured in different topologies:


In trees:



                           Theoretical uncertainty in Vub extraction

                            *
Set of observables for VtsVtb (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*, )
           Search for NP comparing observables
            measured in tree and loop topologies
  b(tree+box) in B J/y Ks            (peng+tree) in B,,
  (tree) in many channels             b(peng+box) in B Ks
  (tree+box) in Bs J/y              (peng+box) in Bs 




New heavy particles, which may contribute to d- and s- penguins,
could lead to some phase shifts in all three angles:

(NP) = (peng+tree) - (tree)
b(NP) = b(BKs) - b(BJ/yKs)    ≠     0
(NP) = (Bs) - (BsJ/y)
     Search for NP comparing observables
     measured in tree and loop topologies


Contribution of NP to processes mediated by loops
             (present status)

 to boxes:

 b 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)
    (b(NP)) ~8°                          (s-penguin)
    ((NP)) not measured                (s-penguin)

  PS    b(NP) =  (NP)
        (NP) measured in B and B decays may differ depending
        on penguin contribution to  and  final states



                                                                              37
   LHCb is aiming at search for
          New Physics
in CP-violation and Rare Decays
        Large Hadron Collider - LHCb
• Bunch crossing frequency: ~ 40 MHz
• Number of reactions in unit of time:
               N bunches                   Inelastic pp reactions
    N  L              N react
                  T                bunch

  since pp inelastic ~ 80 mbarn
  for nominal LHC luminosity
     N ~ 8108 N react        20
                       bunch
• For LHCb L ~ 2 × 1032 cm-2s-1
   (local defocusing of the beam)
    → multi-body interactions are
   subdominant
                                                       -                                       b
                                                      bb angular
                                                      distribution                             b
                                                                    b
                                                                        b




                                                       PT of B-hadron
                                                                            100μb

                                                                                       230μb

                                                                              Pythia

• vertices and momenta reconstruction
• effective particle identification (π, К, μ, е, γ)                             η of B-hadron
• triggers
           View of the LHCb cavern

                Calorimeters
                                                  Magnet
Muon detector                  RICH-2    OT

                                                           RICH-1


                                                                  VELO




                               It’s full!
       Installation of major structures is essentially complete
              LHCb in its cavern
                                    Offset interaction point (to make
              Shielding wall
                                    best use of existing cavern)
              (against radiation)




Electronics
+ CPU farm


                                           Detectors can be moved
                                           away from beam-line
                                           for access
                    LHCb detector
                                                        ~ 300 mrad




p               p                                           10 mrad




       
Forward spectrometer (running in pp collider mode)
Inner acceptance 10 mrad from conical beryllium beam pipe
                LHCb detector




     
Vertex locator around the interaction region
Silicon strip detector with ~ 30 m impact-parameter resolution
•
                      Vertex detector
    Vertex detector has silicon microstrips with r geometry
    approaches 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
               LHCb detector




    
Tracking system and dipole magnet to measure angles and
momenta Dp/p ~ 0.4 %, mass resolution ~ 14 MeV (for Bs  DsK)
            LHCb detector




 

Two RICH detectors for charged hadron identification
            LHCb detector

                                 e


                                     h




 
Calorimeter system to identify electrons, hadrons and
neutrals. Important for the first level of the trigger
                  LHCb detector

                                                




      
Muon system to identify muons, also used in first level of trigger
   S :     LHC prospects

Bs J/y is the Bs counterpart of B0J/y 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, DGS, 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, Dms=20/ps, 90k J/y evts)
UT angle  : LHCb               (BaBAr & BELLE & Tevatron ~12° precision for  at best)

 Interference between tree-level decays
 Favored: Vcb Vus*                                                        Vcs* Vub: suppressed
                                  s                                   u
                                      K(*)-      Common       K(*)-   s
      b                           u                                                     u
 B-                                             final state                                 B-
      u                           c                                   c                 b
                                  u   D(*)0                   D(*)0   u
                                                   f
           
          A B - D 0 K -        r ei e -i                     Parameters: γ,
          AB                  B
                                        B
                -
                    D0 K -                                      (rB, δB) 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- / π+π– , Ksπ0
   (ADS): Use doubly Cabibbo-suppressed decays, e.g. D0  K+π -
   (Dalitz): Use Dalitz plot analysis of 3-body D0 decays, e.g. Ks π+ π-

 Mixing induced CPV measurement in Bs  Ds K decays
  Specific for LHCb
UT angle  : LHCb summary table




  Combined precision after 2 fb-1 ()  5 (from tree only)
  LHCb (10fb-1 ) and SFF (50-75 ab-1) & SLHCb (>100 fb -1) sensitivities

                           Channel               Yield          Precision
        LHCb              From tree channels                   () < 3

                          Bd +-0                 70k       () < 4
                           B  +0, +-,00   45k,10k,5k

                      b    Bd  J/y()KS            1200k      (sin2b) < 0.01
                           Bd  KS                    4k       (sin2b) ~ 0.1

                      s   Bs  J/y()                 750k   (s) ~ 0.01
                           Bs                          20k   (s) ~ 0.05


SFF & SLHCb                                                                    SLHCb (stat. only)
                                                                                 ~ 0.003
  > 2014                                                                        < 1 (BsDsK)
                                                                                  -
                                                                                  -
                                                                                  -



                                                                               S(K0S) 0.02-0.03
                                                                               S()   0.01
               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?
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

 i  f               f Si         SS +  1      S 1 + iT
           f

       1  n n                      2 Im T  T  T     +

               n


                                                   Im T  Re T
                   i 2 Im T i   i T n
  Sum over                                2
 everything!                                      by means of dispersion
                               n                    relations (causality)

                           
                                          2
 At order e2                                  Each green arrow is nontrivial.
                                                 Deep relations between
                              n                     trees and loops.
  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:
                                         2      1 
           +                   V (r )  1 +  log       
                                       r  3     cme r 
 b) the energy stored by the static magnetic field is different
 from its classical value: H 2 / 2
                                       H 2   2H 2 
      classic +                         1 -       
                                        2  45 me4 
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.
  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:


                s           u, c, t          d
             K0     W+                  W−       K0
                d           u, c, t          s
                      Viq             V*ib

Notice that it is the same diagram which describes oscillations
of B-mesons if we replace s-quark by b-quark!
 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 Dm12 (which is nothing
but the oscillation frequency)
                 Dm12
            G2 ~ 2     ~ GF  M W ~ 10 -6 GeV - 2
                          2     2

                f K mK
while experimental result is G2 ~ 10 -13 GeV -2 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):
                     2
                   GF
             G2 ~       (mc - mu ) 2 sin 2  cos 2 
                  16 2
 Comparison of calculated G2 with experimentally measured
  Dm12 leads to correct prediction for mc ~ 1 GeV
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!
           Computation of Loop processes

Main theoretical tool here is the formalism of effective
low-energy ( μ << MW ) Hamiltonians


 f H   DF 1
       eff     i 
                   GF *
                          
                      V fjVij        C ( ) 
                                           k          f Ok (  ) i
                    2                 k

  Notice that full Hamiltonian is μ-independent! (at each order in αs)

In Wilson’s operator product expansion the quantities                    –
coefficient functions – take into account physics at large
scales p > μ, while local operators        care about
low energy (p < 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.
                    How does it work in practice?

  Simple example – Fermi interaction
                                                                 gW
                                 μ-                                                          νμ
 In the SM muon decay is
                                                                 W-
 described by the diagram                                                     gW         e-
                                                                                         νe
  The corresponding amplitude
                              2                            There are two different scales:
                             g
 e   (1 -  5 ) e         W
                                      (1 -  5 )     M W  6.5  10 3 GeV 2 and
                                                             2

                         q 2 - MW
                                2
                                                           q 2 ~ m  1.110-2 GeV 2
                                                                  2

                        2
                       gW    8G
Thus one can replace 2       F                                                                   νμ
                     q - MW
                          2
                               2
   G                                                                               GF
A  F  8  [e   (1 -  5 ) e     (1 -  5 )  ]         μ   -
                                                                                                  e-
    2
                                                                         -5             -2        νe
 (factor 8/√2 is of historical origin)             GF  1.166 10 GeV
  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) :
                                    
                   2
                 GF
                       M W VtbVtd S0 ( xt )[b   (1 -  5 )q  b   (1 -  5 )q]
                                  2
   D
 H effB  2             2   *

                16  2

                       coefficient
                        function
M.Vysotsky, „80                                               local
T.Inami, C.Lim,„81                                          operator
  Rare decays of main interest at LHCb
radiative «penguin» decays B → K* γ, Bs → φ γ, B → Kφγ,
 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
 b  s exclusive

                                             Bs 
LHCb control channel: Bd  K*     BELLE observed 16±8 events
~75k signal events per 2fb-1     2 weeks run at (5S); no TDCPV




                                       LHCb annual yield ~11k
                                       with B/S < 0.6
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.
 Consider angular momentum book-keeping
 at the quark level. In s-quark rest frame (pb = pγ) we have:

                           s 
      b                    or
                           s 
      b
But coupling between bL and bR in this frame (and hence the ratio
γL / γR ) is proportional to small parameter mb    ms
                                                 ~
                                            pb       mb
                     Bs → φ γ
Due to the mixing between Bs and anti-Bs two states
with the masses m1 , m2 and widths Γ1 , Γ2 are formed.
The time-dependent decay width with CP-eigenstate and
a photon at the final state is given by



where ΔΓq = | Γ1 - Γ2 | and Δmq = | 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.
    b  s exclusive (will be presented by Lesya Schutska)
                     Mixing induced CP asymmetries

 BKs0  (B-factories)




S = - (2+O(s))sin(2b)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 :
                                                        (AD) = 0.09
   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
                  B  [  KK ]K
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).

                                           s
             s
             s
                               P
                          Y (J )             b          B
K
                                            q
 If only s-wave contributes, Clebsch-Gordan coefficients
 are trivial (=1) and there is no sensitivity to λ.




 Introducing helicity factor as
 dΓ/dΦ can be rewritten as



If J = 1 contributions dominate:
  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
                   B → K* μμ



                                                   ?
A very important property is   ..and position of its zero,
forward-backward asymmetry..   which is robust in SM:
                                 AFB(s), fast MC, 2 fb–1




                      eff
                  2C7
           s0  - eff
                 C9 (s0 )           s = (m)2 [GeV2]
 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




       AFB(s), fast MC, 2 fb–1

                                        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
          s = (m)2 [GeV2]
  Bs                                  Will be presented by Diego
                                               Martinez Santos


  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) < 5.810-8

LHCb




                                                                      79
                           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 < 2010
 b vs Rb and  vs Rt (Input from theory !)
 b(NP) and (NP): if non-zero  NP in penguins
           in Rare decays
 BR(Bs  ) down to SM prediction < 2010
 Photon helicity in exclusive bs decays
 FBA & transversity amplitudes in exclusive bsll decays     < 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

                    high pT                    B’s

Need much improved precision because any measurement
           in b-system constrains NP models

				
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