1. NP in CP-violation at LHC(b)
Andrey Golutvin
ITEP/CERN
NP in CP-violation
at LHC(b)

2. Current SM fit predicts
(including CDF result on Dms)
a = 94.6° ± 4.6°
b = 23.9° ± 1.0°
= 61.3° ± 4.5°
Theoretical limitations for the sides:
Extraction of |Vub|
Lattice calculation of
Present experimental precision on angles:
= +5°/-16°
b = ± 1.0°
= ± 30°
Mean values of angles and sides are in desperate agreement with predictions
UT may stay closed for quite some time !!!

3. To define the apex of UT
one needs to know at least 2 independent quantities out of 2 sides:
and 3 angles: ,  and 
Straightforward strategy to search for NP contribution:
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 NP signal

4. Unfortunately such approach has very limited sensitivity
to the NP contribution
 is more constrained by Rt.
However NP effects may
cancel out: Rt is proportional to
the ratio of “identical” loop graphs:
boxes or penguins
Due to geometry of UT
the dependence of  on
 is rather moderate:

5. Measure the same observable in the processes
Alternative approach
Measure the same observable in the processes
mediated by different topologies: trees, penguins or boxes
Examples:
- Penguin vs Box
|Vts| can be extracted either from the measurement of (ms) or
BR(BK*). The same applies for |Vtd|
, where
describes short-range effects
Hope that some uncertainties of lattice calculations
are cancelled out in the ratio

6. Extraction of  from penguins (through : B,  and )
Tree vs Penguin
Extraction of  from penguins (through : B,  and )
and various tree topologies
Current experimental precision on  determined in trees and loops
leaves the room of ~ 40° for the difference
Finally, the measurement of the s is a very sensitive test of SM !!!
In the rest of the talk LHCb sensitivities to the measurement
of , s and  are presented
Slides from LHCb talks at the BEACH (M. Musy) and
LHC Physics (J. Rademacker, L.Fernandez and O. Deschamps) conferences

7. Basic Principle & Tagging.
Decay products (RICH)
Decay time ~ flight distance (VELO)
Flavour at creation - opposite-side or same- side (Bs only) Tagging.
Same-side tagging
N events with tagging efficiency ε and mis-tag fraction ω are statistically equivalent to perfectly tagged events.

8. b

9. b from B0  J/y Ks LHCb Atlas LHCb
The ‘gold plated’ channel at B-factories
already well measured by Babar/Belle
Still an important measurement:
background subtracted
=0 in SM
=sin 2b
LHCb
In one year, 2/fb, with 216k events, s(sin2b)~0.02, s(b)~0.6°
Atlas
will achieve similar sensitivity with 30/fb
Comparing with other channels may indicate NP in penguin diagrams
Scaling of 1 year sensitivity from J/yKs to fKs:
s(sin2beff)~0.4, Yield:0.8k, B/S<2.4 (preliminary).

10. fs

11. fs from Bs J/ (η,η’…) Bs J/ is the Bs counterpart of B0J/ KS
In SM fS = -2arg(Vts) = -2l2h ~ -0.04
Sensitive to New Physics effects in the Bs-Bs system if NP in mixing  fS = fS(SM) + fS(NP)
2 CP-even, 1 CP-odd amplitudes, angular analysis needed to separate, then fit to fS, DGS, CP-odd fraction
Channels used
Yield
(103/2 fb-1)
B/S
<>
(fs)
mass
(MeV/c2)
BsJ/(-+)(K+K-)
131
0.12 36 14
Bsc(h-h+h-h+)(K+K-) 3
0.6 30 12
BsJ/(-+) ()
8.5
2.0 37 34
BsJ/(-+) (+-0())
3.0 20
BsJ/ (-+) ’(+- ())
2.2 32 19
BsDs(K+K--) Ds(K+K-+)
4.0
0.3 56 6

12. LHCb Atlas With SM inputs: Dms=17.5/ps, fS=-0.04, DGs/Gs = 0.15
and 2/fb stat:
LHCb
Atlas
will reach s(s) ~ 0.08 (10/fb, Dms=20/ps, 90k J/ evts)
CMS
will reach s(s) ~ 0.07 (10/fb, on J/ evts, no tagging)

14. g

15. LHCb
g from Bs  D±s K+
2 same order tree level amplitudes (3) : large asymmetries, NP components unlikely!
From the measurement 4 rates and 2 time-dependent asymmetries one gets g+fs (with fs from BsJ/yf)
DsK asymmetries (5 years, ms=20 ps–1)
Ds–K+
Ds+K–
Yield: 5.4k signal events in 2/fb,
residual contamination from
Bs  Ds ~ 10%
S/B > 1 at 90% CL
Precision: s(g) ~ 13°
(Dms = 17.3/ps , -20°<Dstrong<20°)
Discrete ambiguities in g can be resolved if DGs large enough, or using B0→Dp and U-spin symmetry

16. g from B0  D0 K*
[Phys. Lett. B270, 75 (1991)]
A1 = A(B0  D0K*0): bc transition, phase 0
A2 = A(B0  D0K*0): bu transition, phase +
A3 = 2 A(B0  DCPK*0) = A1+A2, because DCP=(D0+D0)/2
Measuring 6 decay rates (self-tagged and time-integrated)
allows extraction of g
Modes (+CP conj.)
Yield (2/fb)
S/Bbb (90%CL)
B0  D0 (K+p-) K*0 (K+p-)
3.4 k
> 2.0
B0  D0 (K-p+) K*0 (K+p-)
0.5 k
> 0.3
B0  D0CP (K+K-) K*0 (K+p-)
0.6 k
LHCb
Precision: s(g) ~ 8° (in 1year, 2/fb, for 55°<g<105°, -20°<D<20°)

17. Double Cabibbo-suppressed
g from B±  D K±
[Atwood, Dunietz, Soni method]
New
value
Measure relative rates of B-→ D(Kp) K- and B+→ D(Kp) K+
Two interfering tree B-diagrams, one colour-suppressed (rB ~0.077)
Two interfering tree D-diagrams, one Double Cabibbo-suppressed (rDKp ~0.06)
 large interference because of similar amplitudes!
colour-suppressed
colour-allowed
Weak phase diff.: 
Magnitude ratio: rB
Strong phase diff.: dB
}K-
}p+
Cabibbo-favoured
D0{ c u d s
Double Cabibbo-suppressed
Magnitude ratio: rDKp
Strong phase diff.: dDKp
measure:
favoured ~60k evts
suppressed ~0.5k evts

18. LHCb
3 observables, 5 parameters (g, dB, rB , dDKp, rDKp) , rDKp ~0.06 known
add more D-decays to constrain further:
D → Kppp (Cabibbo favoured + DCS)
4 new rates with 2 new parameters, dDK3p ; rDK3p ~0.06
D → KK (CP eigenstate)
2 new rates, no new unknown: rDKK = 1 ; dDKK = 0
this may come
from CLEO-C
 7 relative rates and 5 unknowns: g, rB, dB, dDK, dDK3
Precision: s(g) ~ 4°- 13° in 1 year, 2/fb
depending on dDK (-25°< dDK <25°)
and on dDK3 (-180°< dDK3 <180°)
Extraction of g via Dalitz study (D Kspp) is under investigation.

22. g from B  pp, Bs KK LHCb p/K Bd/s  solve for g Precision: s(g) ~ 5°
Large penguin contributions, sensitive to NP!
Evaluation of and parameters
from time-dependent measured asymmetry
depend on g, mixing phases,
and ratio of penguin/tree = d eiq
Assume U-spin symmetry dpp = dKK qpp = qKK
(and fs,d from BsJ/yf, BJ/yKs )
g () d
Bs  KK (95% CL)
B   (95% CL)
 solve for g
LHCb
Precision: s(g) ~ 5°
(but model dependent)
Expected Yield (1year, 2/fb)
26k B ,
37k BsKK,
135k BK

23. a

24. 90% of experiments have σ < 10°
LHCb
a from B0  r p
[Snyder,Quinn,1993]
Thanks to the interferences between the transitions B  rp  π-πoπ+
we can simultaneously extract  with amplitudes and strong phases
from the time dependence of the tagged Dalitz plot
Simulate the experimental effects:
resolution, acceptance, wrong tag, ...
Assume B/S=1 (mix of flat and resonant r)
Maximize the likelihood wrt αfit and the
background ratios rfit (12D fit)
s-=m²(-o)
ρ00
ρ+-
ρ-+
s+=m²(+o)
70 expts averaged (L=2fb-1)
85% converge to the correct solution*
αgen
90% of experiments have σ < 10°
*prob. of mirror solutions decreases with stats, down to ~0.2% for 10/fb

25. a from B0  r r LHCb Yields in 2/fb:
Measuring the time dependent asymetry of B ➛ ρ+ρ- provide eff =  + Δ
Aoo Δα
A+-/√2
A+o = A-o
with
LHCb is not competitive with current B-factory performance in r+r-. The main contribution of LHCb to the rr analysis could be the measurement of the B ➛ r0r0 mode
Yields in 2/fb:
B ➛ ρ+ρ- : 2k (B/S<5, 90%CL)
B± ➛ ρ±ρ0 : 9k (B/S ~ 1)
B ➛ ρ0ρ0 : ~0.5k, assuming a BR=
(Babar: )

26. a from B0  rp, rr combined LHCb 1 year data World Ave 2006
LHCb 2 fb-1

27. Summary table Angle Channel Yield* Bbb/S LHC (2/fb)  Bd  J/Ψ KS
Bd  f KS
216k
0.8k
0.8
<2.4
σ() ≈ 0.6°
σ(b) ≈ 12° s
Bs  J/ΨΦ Bs  J/Ψη
Bs  ηcΦ
125k
12k 3k
0.3
2-3
0.7
σ(s) ≈ 1.2° 
Bs  DsK
Bd  
Bs  KK
Bd  D0(K-+)K*0
Bd  D0(K+-)K*0
Bd  DCP(K+K-)K*0
B- D0(K+-)K-
B- D0(K-+)K-
5.4k
26k
37k
0.5k
2.4k
0.6k
60k 2k
<1.0
<0.7
<0.3
<2.0
0.5
σ() ≈ 13°
σ() ≈ 5°
σ() ≈ 8°
σ() ≈ 4°-13° 
Bd  pr, rr
14k
σ() < 10°
* Untagged annual yield after trigger

28. Summary Measurement of s with ~1° precision in 1 year
Measurement of  in trees and loops and check for consistency:
- Many channels for the tree topologies  expect to reach a few degrees
sensitivity in 1 year
The measurement of  in loops should be possible in B with <10°
precision. For the study of  final states, the measurement of BR(B00)
together with the measurements of asymmetries at B factories will further
improve precision
If difference is observed we need a model to relate
# of degrees in  to masses and couplings of NP !!!