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LHCb sensitivity to 
with Bh+h- and
U-spin Symmetry
Laura Fabbri
on behalf of the LHCb collaboration
Physics at LHC
Vienna, 13 -17 July 2004
Laura Fabbri 1
Outline

Physics motivation


Bd(s)h+h- event selection


Strategy, event yields and background-to-signal
ratios
CP sensitivity


Extraction of the weak phase  from the
Bd+- and BsK+K- decays
Bayesian determination of 
Conclusions
Vienna, 13–17 July 2004
Physics at LHC
Laura Fabbri 2
CKM (new?) physics


When LHCb starts taking data
in 2007, sin2 will be already
known with very good accuracy
To isolate signals of new
physics, it is crucial to measure
the other two angles of the
Unitarity Triangle, as 
( -arg Vub)

In case of new physics, more
complementary measurements
of  will help to understand
where the new contributions
come from

Indirect CKM fits
expect 65o
 from
LHCb?
Tree Diagram
Penguin Diagram
Bh+ h- have sizeable
contribution from penguin
graphs which may evidence new
physics in loops
Vienna, 13–17 July 2004
Physics at LHC
Laura Fabbri 3
Extracting  from
Bd+- and BsK+K (B( s0) (t )  f )   (B(0s ) (t )  f )
ACPdir cos m  t  ACPmix sin m  t
ACP t  

0
0


 (B( s ) (t )  f )   (B( s ) (t )  f )
cosh
 t  ACP sinh
t
2
2
dir
0
 
ACP (Bd    )  f1 (d , ,  )
P

1  APc  APt
i

de 
 u
u
t 
mix
0
 
R
A

A

A
ACP (Bd    )  f2 (d , ,  , d )
T
P
P 
b  T
ACPdir (Bs0  K  K  )  f3 (d ,  ,  )
1
 2  Vub
Rb   1 


2  Vcb
ACPmix (Bs0  K  K  )  f4 (d ,  ,  , s )
s =-22 Bs-Bs mixing phase
d =2 Bd-Bd mixing phase
(can be probed with BsJ/)
(measured with BdJ/Ks)
4 equations and 5 unknowns: d, , d’, ’ (hadronic parameters) and 
One needs other inputs to solve for 
[R.Fleischer, Phys. Lett. B459 (1999)]
Vienna, 13–17 July 2004
Physics at LHC
Laura Fabbri 4
Using U-spin Symmetry
Bd+-  U-spin (d,s quark exchange)  BsK+K-
d  d 
U-spin symmetry  
   
6 eqs. and 5 unknowns
the system can be solved
unambiguously
dir
mix
( ACP
, ACP
) from B 0    
Unique
solution for 
dir
mix
( ACP
, ACP
) from Bs0  K  K 
dir
ACP
from B 0     and
dir
mix
( ACP
, ACP
) from Bs0  K  K 
In this example
d  55o , s  0o , d  d   0.3,
     160o ,   65o
Vienna, 13–17 July 2004
Physics at LHC
Laura Fabbri 5
Bd(s)h+hevent selection


Selection cuts are simultaneously optimized in order to
maximize S / S  B
Two major sources of backgrounds taken into account



Combinatorial background from bb inclusive events
 Due to the huge minimum bias MC statistics required for a
detailed study of combinatorial background, we make the
plausible assumption that most of the combinatorial background
will come from beauty events (presence of high pT and large IP
tracks from B)
Specific background from B decays with same two-track
topology
 e.g. BdK+-, BsK+K-, Bs+K- as backgrounds for Bd+-
After event selection, tagging and trigger algorithms are
tuned on selected events
LHCb Public Note
2003-123
Vienna, 13–17 July 2004
Physics at LHC
Laura Fabbri 6
Selection cuts
Beam axis (z)


B0(s)
IP
IPB
, K
IP
, K
L
Reconstruction and Particle ID

Each charged track identified as
a Pion or Kaon using the Particle ID
detectors (RICHs in particular)
Selection cuts on identified tracks

p

Max[pT(h+), pT(h-)]

Min[pT(h+), pT(h-)]

Max[IP/IP(h+), IP/IP(h-)]

Min[IP/IP(h+), IP/IP(h-)]

2 of common vertex
Vienna, 13–17 July 2004
Physics at LHC

Selection cuts on the
candidate B




pT
IP/IP
L/L
Invariant mass
Laura Fabbri 7
Mass spectra
signals + specific backgrounds only
Bd+-
Two-body
background
only
BdK+if not using
RICH…
17 MeV/c2
BsK+K-
Bs+K-
Mostly BdK+(same signature)
Vienna, 13–17 July 2004
Physics at LHC
Laura Fabbri 8
Proper time acceptance
and resolution
Acceptance suppression at low
proper time due to cuts on
IPs and distance of flight
1=341 fs
2=673 fs (15%)
Resolution on proper time
fitted with double Gaussian
(single Gaussian 40 fs)
Vienna, 13–17 July 2004
Physics at LHC
Laura Fabbri 9
Signal yields and
background-to-signal ratios
Event type
Bd  +Bd  K+Bs  K+KBs  +K-

Assumed
BR (x10-6)
4.8
18.5
18.5
4.8
Bbb/S
0.42
0.16
0.31
0.67
Untagged
annual yield
26000
135000
37000
5300
D2
4%
4%
6%
6%
Annual yields after L0+L1 triggers and offline
selection (assumed bb = 0.5 mb and L = 2 fb-1/yr)
Vienna, 13–17 July 2004
Physics at LHC
Laura Fabbri 10
CP sensitivity studies
Fast Monte Carlo Simulation

In order to study the sensitivity on the  angle we
generated many data samples, each corresponding to
different settings of the relevant unknown parameters:



Ms,, s, d, , etc.
The Fast Monte Carlo produces proper time and invariant
mass distributions {(t, m)k; k=1, N} of tagged B decays
(combinatorial background included).
The {(t, m)k; k=1, N} distributions are parameterized
according to the proper time acceptance, resolution and
invariant mass distributions obtained from the full
GEANT simulation, which takes into account realistic
pattern recognition, trigger and offline selection.
Vienna, 13–17 July 2004
Physics at LHC
Laura Fabbri 11
Likelihood Fit

In order to extract CP asymmetries and mistag fraction
simultaneously from data we perform a combined extended
unbinned maximum likelihood fit of Bd+ - and BdK+ (BsK+K- and Bs+K-) event samples (plus background)

BdK+ - (Bs+ K-) is a flavour specific decay and is used as
control channel




Bd+ - (BsK+ K- ) and BdK+ - (Bs+ K-) have the same two-track
topology (same tagging power)
extract the wrong tag probability from data itself
The fit is performed against 17 parameters describing the shape
of the decay rate and invariant mass distributions
In particular we obtain the joint p.d.f. for the CP
asymmetry coefficients Adir and Amix

Bivariate gaussians G(Adir, Amix) for the Bd+ - and
GKK(Adir, Amix) for the BsK+ KLHCb Public Note
2003-124
Vienna, 13–17 July 2004
Physics at LHC
Laura Fabbri 12
Bayesian approach to
determine the  p.d.f.

To propagate the experimental joint p.d.f. for Adir, Amix,
the weak mixing phases d and s to a joint p.d.f. for d, 
and  the Bayesian approach is used:
F  d , ,   
 

 A  d ,  ,   , A  d , ,  ,    
dir
mix
G
A
d
,

,

,
A


d ,,  , d

  
 GKK
dir
KK
mix
KK
s
 g 0d d   g 0s  s  d d d s
Exp. joint p.d.f.
(bivariate gaussian) for
dir
mix
(Aππ
, Aππ
)
&
dir
mix
(AKK
, AKK
)
Vienna, 13–17 July 2004
Gaussian priors for the weak mixing phases
(from LHCb BdJ/KS and BsJ/)
Physics at LHC
Laura Fabbri 13
Sensitivity on  from
Bd+- and BsK+K- (1 year)
f ( )
Correct Solution
  65o
f ( ) 
 F (d ,,  ) dd
d
Fake solution
(disappears with more statistics)
d- plane
95% confidence region
from Bd+- only
95% confidence region
from BsK+K- only
f (d )
Yellow and White contours: 68% and 95%
confidence regions using all the information
Vienna, 13–17 July 2004
Physics at LHC
Perfect U-spin
σ (γ )  5o
O(20%) U-spin breaking
would induce only a few
degrees shift on 
Laura Fabbri 14
Sensitivity scan
() vs 
d=0.3, = 160°, =65°,
s=-0.04°, s/s=0.1
() vs ms
d=0.3, = 160°, s=-0.04°,
s/s=0.1, ms=20 ps-1
Vienna, 13–17 July 2004
Physics at LHC
Laura Fabbri 15
Conclusions



The LHCb experiment will select and tag very large
samples of Bd (Bs) charmless two-body decays
By combining the measurements of the Bd+- and
BsK+K- asymmetry coefficients LHCb can measure
 with a 5° statistical uncertainty, in one year,
assuming U-spin symmetry and Standard Model
This strategy could disclose new physics effects in
penguin diagrams providing a different
measurement of  with respect to e.g.
Bs0  Ds K  and B 0  D 0K *

see LHCb talks by Eduardo Rodrigues and Sandra Amato
Vienna, 13–17 July 2004
Physics at LHC
Laura Fabbri 16
Backup slides
Vienna, 13–17 July 2004
Physics at LHC
Laura Fabbri 17
Charmless two-body decays
of B mesons: diagrams
W
W
g
W
T
Tree
γ, Z

W
PEW
electroweak Penguin
C
colour-suppressed Tree
W
P
gluonic Penguin
g
PA
Penguin Annihilation
W
γ, Z 
PCEW
W
colour-suppressed
electroweak Penguin
W
E
A
Exchange
Annihilation
Gronau, Hernandez, London and Rosner, Phys. Rev. D50 (1994) 4529
Vienna, 13–17 July 2004
Physics at LHC
Laura Fabbri 18
Bd+- and BsK+Kdecay amplitudes
Bd+-
A  Bd0  p  p    Vub*Vud ATu  Vub*Vud APu  Vcb*Vcd APc  Vtb*Vtd APt
A  Bd0       C  e i   de i  
C   3ARb  ATu  APu  APt 
de
BsK+K-
i

1  APc  APt



Rb  ATu  APu  APt 
A  Bs0  K  K    Vub*Vus ATu  Vub*Vus APu  Vcb*Vcs APc  Vtb*Vts APt
A  Bs0  K  K  
 i

1  2
i  



C
e

d
e


2
1  2 / 2



C    3ARb  ATu  APu  APt  ,
1
 2  Vub
Rb   1 


2  Vcb
Vienna, 13–17 July 2004
d e
Physics at LHC
i 
1

Rb


APc  APt
 u
u
t 
 AT  AP  AP 
Laura Fabbri 19
Distributions of selection
variables for BsK+K- and
combinatorial bb background
 bb background
——— signal
Bs Mass
Max[IP/IP(K+), IP/IP(K-)]
cut value and
accepted region
Min[IP/IP(K+), IP/IP(K-)]
2 of common vertex
Vienna, 13–17 July 2004
Bs pT
Max[pT(K+), pT(K-)]
Bs IP/IP
Min[pT(K+), pT(K-)]
Bs L/L
Physics at LHC
Laura Fabbri 20
Selection cuts
Identified tracks
Channel: Bd+ - BdK+ - BsK+ K- Bs+ KPmin (GeV/c)
2.50
2.75
2.75
2.75
Pmax (GeV/c)
100
200
125
100
(PT)each(GeV/c
)
1.2
1.2
0.8
1.4
(PT)one (GeV/c)
3.2
3.0
2.6
3.4
(IP/IP)each
6
6
5
7
(IP/IP)one
12
11
9
14
2max
4
5
5
4
1.6
1.4
1.0
1.6
2.25
2.50
2.75
2.25
(L/L)min
19
17
14
20
m (MeV/c2)
50
50
50
40
(PT)min (GeV/c)
(IP/IP)max
Vienna, 13–17 July 2004
Physics at LHC
Laura Fabbri 21
Fast MC input values
Nominal parameters:
Bd  +-, Bd  K+tagging efficiency
42%
wrong tagging fraction
35%
M
0.5 ps-1

1/1.54 ps-1
/
0
d
0.3

160o

65o
weak mixing phase
0.82
Bs  K+K-, Bs  +K-
Sensitivity scan: parameters are varied one at a time
d:
0.1
0.2
(0.3)
0.4
:
120o
140o
(160o) 180o
200o
:
55o
(65o)
75o
85o
95o
s:
0
(-0.04) -0.1
-0.2
Ms (ps-1)
15
(20)
25
30
s/ s:
0
(0.1)
0.2
Vienna, 13–17 July 2004
Physics at LHC
50%
33%
20 ps-1
1/1.46 ps-1
0.1
0.3
160o
65o
-0.04
105o
Laura Fabbri 22
Sensitivity on 
0.1
0.2
(0.3)
0.4
1.8°
2.7°
4.9°
9.0°
120°
140°
(160°)
180°
200°
3.8°
3.8°
4.9°
6.7°
5.2°
  
s
  
55°
(65°)
75°
85°
95°
105°
5.8°
4.9°
4.3°
4.7°
4.7°
4.7°
0
(-0.04)
-0.1
-0.2
4.9°
4.9°
4.9°
5.4°
s / s
0
(0.1)
0.2
d
  

  

5.2°
4.9°
4.5°
  
M s 15 ps-1 (20 ps-1) 25 ps-1 30 ps-1
  
4.0°
4.9°
5.9°
8.5°
Vienna, 13–17 July 2004
Physics at LHC
Resolution
computed as half
the 68%
confidence
interval
Laura Fabbri 23
U-spin Symmetry
How much rely on it?





U-spin symmetry in the relations d=d’ and =’ is not
broken within naïve factorization approximation (Fleischer,
Phys. Lett. B459, 1999)
Fleischer and Matias (hep-ph/0204101) allow for a SU(3)
violation of 20%: d’/d  0.8÷1.2
Matias (hep-ph/0311042) claims that a SU(3) breaking of
20% would induce only a 5o shift on ; a phase difference
=’- as large as 40o induces only a shift on  of 1o
Beneke (hep-ph/0308040) estimates through QCD
factorization a possible SU(3) violation at 30% level:
d’/d  0.85÷1.3,   ±15o
A better understanding of SU(3) breaking would be
desirable, but a O(20%) breaking does not spoil the
measurement
Vienna, 13–17 July 2004
Physics at LHC
Laura Fabbri 24
Mass spectra
signals + combinatorial beauty
background only
Bd+-
BsK+K-
Vienna, 13–17 July 2004
Physics at LHC
BsK+K-
BdK+-
Bs+K-
Laura Fabbri 25