Hadronic B decays from SCET

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					Hadronic B decays from
         SCET
        Christian Bauer
             LBNL
     FPCP 2006, Vancouver
         Outline of the Talk



Introduction
Hadronic B deays in SCET
Phenomenology of Hadronic B decays
Conclusions
Introduction
        Flavor Physics in the SM
    Decays mediated by electroweak gauge bosons
    Propagate over distance scale 1/MEW 0.005 fm

    Much less than distance of colliding particles 0.1 fm


               d                          u              d
                                                             u
               u                          u
b                  u       b                d   b                u
                       +
                                Flavor                Local
     Charged                   Changing             4-fermion
     Current                    Neutral              operator
                               Current
Flavor Physics beyond the SM
    Loop diagrams can get many additional contributions
    Propagate over distance scale 1/MEW 0.005 fm

    Much less than distance of colliding particles 0.1 fm


               d                          u              d
                                                             u
               u                          u
b                  u       b                d   b                u
                       +
                                Flavor                Local
     Charged                   Changing             4-fermion
     Current                    Neutral              operator
                               Current
         The Curse of QCD
The weak interaction we are after is masked by QCD
effects, which are completely non-perturbative
         The Curse of QCD
The weak interaction we are after is masked by QCD
effects, which are completely non-perturbative
         The Curse of QCD
The weak interaction we are after is masked by QCD
effects, which are completely non-perturbative

                               Weak interaction
                              effect we are after
         The Curse of QCD
The weak interaction we are after is masked by QCD
effects, which are completely non-perturbative

                               Weak interaction
                              effect we are after

                               Non-perturbative
                               effects from QCD
         The Curse of QCD
The weak interaction we are after is masked by QCD
effects, which are completely non-perturbative

                                Weak interaction
                               effect we are after

                                Non-perturbative
                                effects from QCD

   Crucial to understand long distance physics to
  extract weak flavor physics from these decays
     Effective Field Theories

Separate short distance from long distance effects

Short distance physics is calculable perturbatively

Long distance physics simplifies in limit ΛQCD/Q→0

Long distance physics is independent of the details of
effects at short distances

Measure the long distance effects in one process and
use results in other processes
Hadronic B deays in
       SCET
CWB, Pirjol, Rothstein, Stewart
       Kinematics


    E mB/2          E mB/2
π              B             π

Typical size of hadrons 1/ΛQCD


             E ΛQCD
              General Idea
SCET is effective theory describing interactions of
collinear with soft particles
Separate distance scales d 1/E and d 1/ΛQCD and study
interactions of long distance modes

Factorization theorems emerge naturally in SCET
  Separate d 1/E & d 1/Λ. Study non-perturbative effects
  in limit ΛQCD/E→0

  At leading order, coupling between soft and collinear
  simple and in many cases absent
Factorization is not assumed in SCET. The theory will
tell you when amplitudes factorize and when not
                       SCET in pictures
                          E mB/2             E mB/2
                     π                  B                 π
              1fm
                                                                E mb/2         u
               b              u E mb/2              (b)
      0.1fm
                                                                               d
                              b quark decays into three light quarks, two in the
Heavy b quark almost              same direction, one in opposing direction
 at rest in B meson




1fm           !                0.4fm                  0.2fm                !       1fm


        energetic quark requires spectator       two quarks are very close until
          of the B meson to form pion.             far from B meson. Thus no
            Factorization more subtle             coupling between B and pion
                Kinematics

       π
               Interpolatingfi
                Interpolating
           E mB/2
                         π
                  B Kinematics
                               fi
                               E mB/2


                                Kinematics
B meson described by DOF with k µ ∼ ΛQCD
  Interpolating field                 k µ ∼5 QCD
                                           Λ
                       B            ¯s h
                                    q¯s γ h
                                     q
                         k µ ∼ (Λ2 /Eπ , Eπ , ΛQCD )
                                 QCD
Pions described by DOF with k µ ∼ (Λ2 /Eπ , Eπ , ΛQCD )
                                    QCD
  Interpolating field
                           π        ¯n γ 5 ξn
                                    ξ 5
                                    ¯
                                    xiγ ξ
Relevant Energy Scales
    Relevant Energy scales
           √
mb ∼ 5 GeV, EΛ ∼ 1.3 GeV, Λ ∼ 0.5 GeV
    Integrating out fluctuations ~ mb:
   Generates local four quark operators
                p2 ∼ EΛ
      Caveat: Charm Penguins
Four quark operators two charm quarks
      d,s       c         qµ
                                 q        Charm quark pair
  b           !s (mv)
              ....
                                     q   can propagate over
                c
                        !s ( )             long distances
 Matching at μ mb not all onto local operators

How large are these long distance contributions?
            Acc=[Leading Order] [v∗αs(2mc)]
               Relevant Energy Scale
       Relevant Energy scales
                            √
The relevant scales are mb , EΛ ∼ 1.3 GeV, Λ
               Relevant Energy Scale
       Relevant Energy scales
                            √
The relevant scales are mb , EΛ ∼ 1.3 GeV, Λ




               π


   B                       π
                  Relevant Energy Scale
       Relevant Energy scales
                            √
The relevant scales are mb , EΛ ∼ 1.3 GeV, Λ


Relevant Energy Scales
           √      π
       mb , EΛ ∼ 1.3 GeV, Λ



   B         p2 ∼ EΛ          π
                  Relevant Energy Scale
       Relevant Energy scales
                            √
The relevant scales are mb , EΛ ∼ 1.3 GeV, Λ

    Integrating out fluctuations ~ √EΛ:
Relevant Energy Scales functions
     Generates so-called jet
           √      π
       mb , EΛ ∼ 1.3 GeV, Λ



   B         p2 ∼ EΛ          π
                 Relevant Energy Scale
       Relevant Energy scales
                            √
The relevant scales are mb , EΛ ∼ 1.3 GeV, Λ

    Integrating out fluctuations ~ √EΛ:
Relevant Energy Scales functions
     Generates so-called jet
           √      π        Obtainfactorization formula
       mb , EΛ ∼ 1.3 GeV, Λ
                         similar in structure to QCDF
                                     (BBNS)
   B         p2 ∼ EΛ            π
                  Relevant Energy Scale
         Relevant Energy scales
                            √
The relevant scales are mb , EΛ ∼ 1.3 GeV, Λ

    Integrating out fluctuations ~ √EΛ:
Relevant Energy Scales functions
     Generates so-called jet
            √      π        Obtainfactorization formula
        mb , EΛ ∼ 1.3 GeV, Λ
                          similar in structure to QCDF
                                      (BBNS)
   B          p2 ∼ EΛ            π


       Interaction starts at subleading order
  Universality of jet functions
 Only a single jet function arises for these decays
 The same jet function as in semileptonic decays
 This jet function gets convoluted with B and light
 meson wave function

                        Define
                 ζJBL   = J ϕB ϕL

Resums the jet function to all orders in αs(√ΛE)

   Only rely on perturbation theory in αs(mb)
Relevant Energy Scales
  The factorization formula
           √      M1
       mb , EΛ ∼ 1.3 GeV, Λ



   B         p2 ∼ EΛ          M2
 Relevant Energy Scales
   The factorization formula
             √      M1
         mb , EΛ ∼ 1.3 GeV, Λ


The factorization formula
    B     p ∼ EΛ   2
                                           M2
              Z
                               Bπ
   A = N fπ du dz T1J (u, z)ζJ (z)φπ (u)
                Z                ff
       + ζ Bπ fπ du T1ζ (u)φπ (u) + λ(f ) Aππ
                                     c      c
                                           c¯
 Relevant Energy Scales
   The factorization formula
             √      M1
         mb , EΛ ∼ 1.3 GeV, Λ


The factorization formula
    B     p ∼ EΛ   2
                                           M2
              Z
                               Bπ
   A = N fπ du dz T1J (u, z)ζJ (z)φπ (u)
                Z                ff
       + ζ Bπ fπ du T1ζ (u)φπ (u) + λ(f ) Aππ
                                     c      c
                                           c¯
 Relevant Energy Scales
   The factorization formula
             √      M1
         mb , EΛ ∼ 1.3 GeV, Λ


The factorization formula
    B     p ∼ EΛ   2
                                           M2
              Z
                               Bπ
   A = N fπ du dz T1J (u, z)ζJ (z)φπ (u)
                Z                ff
       + ζ Bπ fπ du T1ζ (u)φπ (u) + λ(f ) Aππ
                                     c      c
                                           c¯
 Relevant Energy Scales
   The factorization formula
             √      M1
         mb , EΛ ∼ 1.3 GeV, Λ


The factorization formula
    B     p ∼ EΛ   2
                                           M2
              Z
                               Bπ
   A = N fπ du dz T1J (u, z)ζJ (z)φπ (u)
                Z                ff
       + ζ Bπ fπ du T1ζ (u)φπ (u) + λ(f ) Aππ
                                     c      c
                                           c¯
 Relevant Energy Scales
   The factorization formula
             √      M1
         mb , EΛ ∼ 1.3 GeV, Λ


The factorization formula
    B     p ∼ EΛ   2
                                           M2
              Z
                               Bπ
   A = N fπ du dz T1J (u, z)ζJ (z)φπ (u)
                Z                ff
       + ζ Bπ fπ du T1ζ (u)φπ (u) + λ(f ) Aππ x2
                                     c      c
                                           c¯
Phenomenology
                     Outline

Parameter counting
Implications of small phases
  Determining γ from B→ππ
  Sum rules in B→Kπ
Full SCET analysis
  Determination of hadronic parameters
  Predictions for remaining observables
     Parameter counting
     Number of hadronic parameters

      no                    SCET SCET
             SU(2)   SU(3)
     expns                 +SU(2) +SU(3)
ππ     11     7/5             4
                     15/13
Kπ     15     11             +5(6)   4

KK     11     11     +4/+0   +3(4)
   The factorization formulaI
  Implications of small phases
             Measuring γ from B→ππ
Amplitudes (using isospin and no EW penguins)
          ¯
        A(B 0 → π + π − ) = e−iγ |λu | T − |λc | P
             ¯
         A(B 0 → π 0 π 0 ) = e−iγ |λu | C + |λc |P
      √
       2A(B − → π 0 π − ) = e−iγ |λu | (T + C)
     The factorization formulaI
    Implications of small phases
               Measuring γ from B→ππ
  Amplitudes (using isospin and no EW penguins)
              ¯
            A(B 0 → π + π − ) = e−iγ |λu | T − |λc | P
                 ¯
             A(B 0 → π 0 π 0 ) = e−iγ |λu | C + |λc |P
he factorization πformula 2|λu| (T + C)
       √
         2A(B − → 0 π − ) = e−iγ
  5 hadronic parameters + γ
                 |λc |
       pc   ≡ −        Re (P/T )
                |λu |
                 |λc |
       ps   ≡ −        Im (P/T )
                |λu |
       tc   ≡ |T |/|T + C|
      T C ≡ |T + C|
            ≡ Im (C/T )
     The factorization formulaI
    Implications of small phases
               Measuring γ from B→ππ
  Amplitudes (using isospin and no EW penguins)
              ¯
            A(B 0 → π + π − ) = e−iγ |λu | T − |λc | P
                 ¯
             A(B 0 → π 0 π 0 ) = e−iγ |λu | C + |λc |P
                      Hadronic C)
he factorization πformula 2|λu| (T +Parameters
       √     −    0 −
         2A(B → π ) = e−iγ
  5 hadronic parameters + γ
                                    Gronau, London (‘90)
       pc   ≡ −
                 |λc |
                       Re (P/T )   |BR(π + π − ) = (5.0 ± 0.4)
                |λu |
                                    BR(π 0 π − ) = (5.5 ± 0.6)
                 |λc |
       ps   ≡ −
                |λu |
                       Im (P/T )    BR(π 0 π 0 ) = (1.45 ± 0.29)
       tc   ≡ |T |/|T + C|              Cπ+ π− = −0.37 ± 0.10
      T C ≡ |T + C|                     Sπ+ π− = −0.50 ± 0.12
            ≡ Im (C/T )                 Cπ0 π0 = −0.28 ± 0.40|
     The factorization formulaI
    Implications of small phases
               Measuring γ from B→ππ
  Amplitudes (using isospin and no EW penguins)
              ¯
            A(B 0 → π + π − ) = e−iγ |λu | T − |λc | P
                 ¯
             A(B 0 → π 0 π 0 ) = e−iγ |λu | C + |λc |P
                      Hadronic C)
he factorization πformula 2|λu| (T +Parameters
       √     −    0 −
         2A(B → π ) = e−iγ
  5 hadronic parameters + γ
                                    Gronau, London (‘90)
       pc   ≡ −
                 |λc |
                       Re (P/T )   |BR(π + π − ) = (5.0 ± 0.4)
                |λu |
                                    BR(π 0 π − ) = (5.5 ± 0.6)
                 |λc |
       ps   ≡ −
                |λu |
                       Im (P/T )    BR(π 0 π 0 ) = (1.45 ± 0.29)
       tc   ≡ |T |/|T + C|              Cπ+ π− = −0.37 ± 0.10
      T C ≡ |T + C|                     Sπ+ π− = −0.50 ± 0.12
            ≡ Im (C/T )                 Cπ0 π0 = −0.28 ± 0.40|
     The factorization formulaI
    Implications of small phases
               Measuring γ from B→ππ
  Amplitudes (using isospin and no EW penguins)
              ¯
            A(B 0 → π + π − ) = e−iγ |λu | T − |λc | P
                 ¯
             A(B 0 → π 0 π 0 ) = e−iγ |λu | C + |λc |P
                      Hadronic C)
he factorization πformula 2|λu| (T +Parameters
       √     −    0 −
         2A(B → π ) = e−iγ
  5 hadronic parameters + γ
                                    Gronau, London (‘90)
                 |λc |             |BR(π + π − ) = (5.0 ± 0.4)




                ?
       pc   ≡ −        Re (P/T )
                |λu |
                                    BR(π 0 π − ) = (5.5 ± 0.6)
                 |λc |
       ps   ≡ −
                |λu |
                       Im (P/T )    BR(π 0 π 0 ) = (1.45 ± 0.29)
       tc   ≡ |T |/|T + C|              Cπ+ π− = −0.37 ± 0.10
      T C ≡ |T + C|                     Sπ+ π− = −0.50 ± 0.12
            ≡ Im (C/T )                 Cπ0 π0 = −0.28 ± 0.40|
Getting rid of one parameter
The SCET analysis contains four hadronic parameters
Allows us to eliminate one of the 5 in isospin
In the limit Λ/E→0 one parameter vanishes


                 Im(C/T)=O(αs,Λ/mb)


This allows to use the 5 well measured observables to
              determine the CKM angle γ
                                                        Extracting γ                                                                         5
                      Hadronic parameters
                        as function of γ
                            (t)                                                                          (t)
           CK M               ! = 0 and w/o C00
                                          2                                                            ! = 0 and w/o C00
1.2         fitter
           LP 2005
                               (c)
                      isospin ! =ε and w/o C00
                                   0                                             1.2                      (t)  o    o    o
                                                                                                       |! | < 5 , 10 , 20 and w/o C00
                                    3   1.5                                                              (t)
                      bound with C
                                     00      ε1 C00
                                              w/o                                                      ! = 0 and with C00
 1                                                 1                              1
                                                                                                                              20o




                                                                        1-CL
                                                                                           isospin analysis
                                                 0.5                                       without C00
0.8                                                                 γ            0.8




                                                                        1 – CL
          20          30    40        50                70     80
                                                -0.5                                                                          10o
0.6                                                                              0.6
                            ε2                    -1                                          CKM fit
                                       ε4
                                      CKM fit                                                   no " in fit
0.4                                             -1.5
                                          no " in fit                            0.4

                                                                                                                              5o
0.2
          0.6
                SCET allowed region                          isospin             0.2
                                                  0.2        bound
 0        0.4                                                                     0
      0    20         40   60    80        100 120 140 160 180                         0   20       40         60    80    100 120 140 160 180
          0.2                                                                                                       α (deg)
                                 "    (deg)             80                                                          "     (deg)
                 70                  75                                          Grossman, Ligeti, Hoecker, Pirjol (‘05)
      -0.2
 3: Left plot: confidence level for α imposing τ = 0 in the t- (solid line) and c-conventions (dashed line) without using
      fit.         0.4       Flat triangle                                       Slightly old data.
n the -0.4 The t-convention curve uses β as an input. Also shown are the results of the traditional isospin analysis [3, 18]

                                                                           Including EW penguins, get
(light shaded region) and without (dark shaded region) using C00 . The dot with 1σ error bar shows the predicton from
lobal CKM fit (not including the direct measurement of α) [18]. Right plot: confidence level for α imposing τ = 0 in the
      -0.6

                                                                                      α=75֯֯
vention with (dotted line) and without (solid line) using the C00 result in the fit. Also shown are the constraints in the
      -0.8
vention imposing |τ | < 5◦ , |τ | < 10◦ , and |τ | < 20◦ (dashed lines). The shaded region is the same as in the left plot.
 Implications ofDefinition of Sumrule
Definition ofSum rules small phases II
             Sumrules B→Kπ Lipkin, Gronau, Rosner,
                      for
                                                   Buras et al, Beneke et al
Define Observables
         2Br(B − → π 0 K − )             |∆1 = (1 + R1 )ACP (π 0 K − )
   |R1 =               ¯
               − → π−K 0)
                             −1
          Br(B                               = 0.040 ± 0.040
       = 0.004 ± 0.086
                                         ∆2 = (1 + R2 )ACP (π − K + )|
             ¯
         Br(B 0 → π − K + )τB −
    R2 =                                     = −0.097 ± 0.016
         Br(B          ¯ B −1
               − → π − K 0 )τ 0
                                                                ¯
                                         ∆3 = (1 + R3 )ACP (π 0 K 0 )
       = −0.157 ± 0.055
               ¯        ¯                    = −0.021 ± 0.133
         2Br(B 0 → π 0 K 0 )τB −
    R3 =      ¯ 0 → π − K 0 )τB 0 − 1|                 ¯
          Br(B          ¯                ∆4 = ACP (π − K 0 )
       = 0.026 ± 0.105                       = −0.02 ± 0.04

   Combinations vanish to LO in = |λu/λc|, PEW/P
                                ε
      R1-R2+R3=O(ε2)                  Δ1-Δ2+Δ3-Δ4=O(ε2)
                 Factorization – Christian Bauer – p.5 Factorization – Ch
    Predictions for the Ri and Δi
Experimental Results:
   R1+R2-R3=0.19±0.15   Δ1-Δ2+Δ3-Δ4= 0.14±0.15
    Predictions for the Ri and Δi
Experimental Results:
   R1+R2-R3=0.19±0.15         Δ1-Δ2+Δ3-Δ4= 0.14±0.15
SCET Prediction:
  (modest assumptions about hadronic parameters)

              R1+R2-R3=O(ε2)=0.028±0.021

           Δ1-Δ2+Δ3-Δ4 ε2sin(φi-φj) = 0±0.013
    Predictions for the Ri and Δi
Experimental Results:
   R1+R2-R3=0.19±0.15         Δ1-Δ2+Δ3-Δ4= 0.14±0.15
SCET Prediction:
  (modest assumptions about hadronic parameters)

              R1+R2-R3=O(ε2)=0.028±0.021

           Δ1-Δ2+Δ3-Δ4 ε2sin(φi-φj) = 0±0.013

              Pretty firm predictions
    Need better data to check these predictions
     The B→PP predictions
              Branching ratios
                                       -6
             The Branching ratios (x10 )
 0   0                                           $
K0 "                                    #=83
K_ !0
K_ ! 0
    +
K !_
 0
K0 !
     0
K "
!0 !0
 + 0
! !_                               Theory
!+ !                               Data
         0   5      10     15     20        25
      The B→PP predictions
                 CP asymmetries

                     The CP asymmetries
S(! 0 ! 0 )
A(!0 ! 0 )
   _
A(K ! 0 )                                   "=83
                                                   #
   0 _
A(K ! )
A(K0 !0 )
S(K0 ! 0 )
    _ +
A(K ! _ )
C(!+ !_ )                                 Theory
S(!+ ! )                                  Data
              -0.5 -0.25   0   0.25 0.5 0.75 1.0
                                                                                                                          17


                            Adding Isosinglets
TABLE VII: Predicted CP averaged branching ratios (×10−6 , first row) and direct CP asymmetries (second row for each mode)
for ∆S = 0 and ∆S = 1 B decays (separated by horizontal line) to isosinglet pseudoscalar mesons. The Theory I and Theory II
                                                                                       Williamson, Zupan (’06)
columns give predictions corresponding to Solution I, II sets of SCET parameters. The errors on the predictions are estimates
of SU(3) breaking, 1/mb corrections and errors due to SCET parameters, respectively. No prediction on CP asymmetries is
given, if [−1, 1] range is allowed at 1σ.

Mode                  Exp.                           Theory I                                Theory II
B− → π− η             4.3 ± 0.5 (S = 1.3)            4.9 ± 1.7 ± 1.0 ± 0.5                   5.0 ± 1.7 ± 1.2 ± 0.4
                      −0.11 ± 0.08                   0.05 ± 0.19 ± 0.21 ± 0.05               0.37 ± 0.19 ± 0.21 ± 0.05
B− → π− η             2.53 ± 0.79 (S = 1.5)          2.4 ± 1.2 ± 0.2 ± 0.4                   2.8 ± 1.2 ± 0.3 ± 0.3
                      0.14 ± 0.15                    0.21 ± 0.12 ± 0.10 ± 0.14               0.02 ± 0.10 ± 0.04 ± 0.15
¯
B0 → π0 η             < 2.5                          0.88 ± 0.54 ± 0.06 ± 0.42               0.68 ± 0.46 ± 0.03 ± 0.41
                      −                              0.03 ± 0.10 ± 0.12 ± 0.05               −0.07 ± 0.16 ± 0.04 ± 0.90
¯
B0 → π0 η             < 3.7                          2.3 ± 0.8 ± 0.3 ± 2.7                   1.3 ± 0.5 ± 0.1 ± 0.3
                      −                              −0.24 ± 0.10 ± 0.19 ± 0.24              −
¯
B 0 → ηη              < 2.0                          0.69 ± 0.38 ± 0.13 ± 0.58               1.0 ± 0.4 ± 0.3 ± 1.4
                      −                              −0.09 ± 0.24 ± 0.21 ± 0.04              0.48 ± 0.22 ± 0.20 ± 0.13
¯
B 0 → ηη              < 4.6                          1.0 ± 0.5 ± 0.1 ± 1.5                   2.2 ± 0.7 ± 0.6 ± 5.4
                      −                              −                                       0.70 ± 0.13 ± 0.20 ± 0.04
¯
B0 → η η              < 10                           0.57 ± 0.23 ± 0.03 ± 0.69               1.2 ± 0.4 ± 0.3 ± 3.7
                      −                              −                                       0.60 ± 0.11 ± 0.22 ± 0.29
¯    ¯
B0 → K0η              63.2 ± 4.9 (S = 1.5)           63.2 ± 24.7 ± 4.2 ± 8.1                 62.2 ± 23.7 ± 5.5 ± 7.2
                      0.07 ± 0.10 (S = 1.5)          0.011 ± 0.006 ± 0.012 ± 0.002           −0.027 ± 0.007 ± 0.008 ± 0.005
¯    ¯
B0 → K0η              < 1.9                          2.4 ± 4.4 ± 0.2 ± 0.3                   2.3 ± 4.4 ± 0.2 ± 0.5
                      −                              0.21 ± 0.20 ± 0.04 ± 0.03               −0.18 ± 0.22 ± 0.06 ± 0.04
B− → K−η              69.4 ± 2.7                     69.5 ± 27.0 ± 4.3 ± 7.7                 69.3 ± 26.0 ± 7.1 ± 6.3
                      0.031 ± 0.021                  −0.010 ± 0.006 ± 0.007 ± 0.005          0.007 ± 0.005 ± 0.002 ± 0.009
B− → K−η              2.5 ± 0.3                      2.7 ± 4.8 ± 0.4 ± 0.3                   2.3 ± 4.5 ± 0.4 ± 0.3
                      −0.33 ± 0.17 (S = 1.4)         0.33 ± 0.30 ± 0.07 ± 0.03               −0.33 ± 0.39 ± 0.10 ± 0.04
                                                                                                                          17


                            Adding Isosinglets
TABLE VII: Predicted CP averaged branching ratios (×10−6 , first row) and direct CP asymmetries (second row for each mode)
for ∆S = 0 and ∆S = 1 B decays (separated by horizontal line) to isosinglet pseudoscalar mesons. The Theory I and Theory II
                                                                                       Williamson, Zupan (’06)
columns give predictions corresponding to Solution I, II sets of SCET parameters. The errors on the predictions are estimates
of SU(3) breaking, 1/mb corrections and errors due to SCET parameters, respectively. No prediction on CP asymmetries is
given, if [−1, 1] range is allowed at 1σ.

Mode                  Exp.                           Theory I                                Theory II
B− → π− η             4.3 ± 0.5 (S = 1.3)            4.9 ± 1.7 ± 1.0 ± 0.5                   5.0 ± 1.7 ± 1.2 ± 0.4
                      −0.11 ± 0.08                   0.05 ± 0.19 ± 0.21 ± 0.05               0.37 ± 0.19 ± 0.21 ± 0.05
B− → π− η             2.53 ± 0.79 (S = 1.5)          2.4 ± 1.2 ± 0.2 ± 0.4                   2.8 ± 1.2 ± 0.3 ± 0.3
                      0.14 ± 0.15                    0.21 ± 0.12 ± 0.10 ± 0.14               0.02 ± 0.10 ± 0.04 ± 0.15
¯
B0 → π0 η             < 2.5                          0.88 ± 0.54 ± 0.06 ± 0.42               0.68 ± 0.46 ± 0.03 ± 0.41
                      −                              0.03 ± 0.10 ± 0.12 ± 0.05               −0.07 ± 0.16 ± 0.04 ± 0.90
¯
B0 → π0 η             < 3.7                          2.3 ± 0.8 ± 0.3 ± 2.7                   1.3 ± 0.5 ± 0.1 ± 0.3
                      −                              −0.24 ± 0.10 ± 0.19 ± 0.24              −
¯
B 0 → ηη              < 2.0                          0.69 ± 0.38 ± 0.13 ± 0.58               1.0 ± 0.4 ± 0.3 ± 1.4
                      −                              −0.09 ± 0.24 ± 0.21 ± 0.04              0.48 ± 0.22 ± 0.20 ± 0.13
¯
B 0 → ηη              < 4.6                          1.0 ± 0.5 ± 0.1 ± 1.5                   2.2 ± 0.7 ± 0.6 ± 5.4
                      −                              −                                       0.70 ± 0.13 ± 0.20 ± 0.04
¯
B0 → η η              < 10                           0.57 ± 0.23 ± 0.03 ± 0.69               1.2 ± 0.4 ± 0.3 ± 3.7
                      −                              −                                       0.60 ± 0.11 ± 0.22 ± 0.29
¯    ¯
B0 → K0η              63.2 ± 4.9 (S = 1.5)           63.2 ± 24.7 ± 4.2 ± 8.1                 62.2 ± 23.7 ± 5.5 ± 7.2
                      0.07 ± 0.10 (S = 1.5)          0.011 ± 0.006 ± 0.012 ± 0.002           −0.027 ± 0.007 ± 0.008 ± 0.005
¯    ¯
B0 → K0η              < 1.9                          2.4 ± 4.4 ± 0.2 ± 0.3                   2.3 ± 4.4 ± 0.2 ± 0.5
                      −                              0.21 ± 0.20 ± 0.04 ± 0.03               −0.18 ± 0.22 ± 0.06 ± 0.04
B− → K−η              69.4 ± 2.7                     69.5 ± 27.0 ± 4.3 ± 7.7                 69.3 ± 26.0 ± 7.1 ± 6.3
                      0.031 ± 0.021                  −0.010 ± 0.006 ± 0.007 ± 0.005          0.007 ± 0.005 ± 0.002 ± 0.009
B− → K−η              2.5 ± 0.3                      2.7 ± 4.8 ± 0.4 ± 0.3                   2.3 ± 4.5 ± 0.4 ± 0.3
                      −0.33 ± 0.17 (S = 1.4)         0.33 ± 0.30 ± 0.07 ± 0.03               −0.33 ± 0.39 ± 0.10 ± 0.04
                  Summary

Very important to understand hadronic physics to find
physics beyond the standard model
Effective field theories great tool to separate long
distance from short distance effects
SCET is effective theory constructed to describe
processes with energetic particles
Factorization formula can be derived for B→PP
Predictive power without expansion in αs(√ΛE)
Detailed analysis of hadronic B decays available

				
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posted:1/24/2011
language:English
pages:50