1. Potential for precise Unitarity Triangle angles measurements in LHC
Beach2006
7th International Conference on
Hyperons Charm and Beauty Hadrons
Lancaster 2–8th July 2006
Potential for precise Unitarity Triangle angles measurements in LHC
Marco Musy, University of Milano Bicocca

2. But: New particles may show up in loop diagrams,
Motivations
Current SM fit predicts
(including CDF result on Dms)
a = 94.6° ± 4.6°
b = 23.9° ± 1.0°
= 61.3° ± 4.5°
fs= 2.1° ± 0.2°
Desperately consistent…
But: New particles may show up in loop diagrams,
overconstrain will allow to disentangle SM components from the New Physics ones  need very high precision!

3. LHC experiments with a B in the menu
ATLAS
B physics using high-pT muon, mostly with modes involving dimuons.
100 mb
230 mb
Pythia production cross section
B physics dedicated experiment:

4. Use for calibration/systematics
pp interactions/crossing
Trigger & Tagging
n=0
LHCb
Atlas: B trigger output rate: Hz,
Tagging eeff: ~4%
CMS: 5 Hz inclusive + ~1 Hz exclusive
will both run a few years at L<21033/cm2/s
with n(pileup)<5, after that n ~ 25
LHCb: L~21032/cm2/s, n(pileup)~0.5
Tagging eeff: 4% - 5%(Bd) 7% - 9%(Bs)
Trigger output:
ATLAS/CMS
n=1
Rate
Event type
Use for physics
Use for calibration/systematics
200 Hz
Exclusive B
B (core program)
Control channels (tagging, …)
600 Hz
High mass dimuon
130 Hz of BJ/X
Tracking
300 Hz D*
65 Hz D* (mixing + CPV)
Hadron PID
900 Hz
Inclusive b (e.g. b)
550 Hz of B (data mining)
Trigger

5. b

6. 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).

7. fs

8. 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

9. 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)

10. g

11. 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  Dsπ ~ 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

12. 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°)

13. 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

14. LHCb
2 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.

15. 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

16. a

17. 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(π-πo)
ρ0π0
ρ+π-
ρ-π+
s+=m²(π+πo)
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

18. 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: )

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

20. Summary table - Angle Channel Yield* Bbb/S LHC (2/fb)
Theoretical limit 
Bd  J/Ψ KS
Bd  f KS
216k
0.8k
0.8
<2.4
σ() ≈ 0.6°
σ(b) ≈ 12°
σ() ~ 0.2°
σ(b) ~ 2° s
Bs  J/ΨΦ Bs  J/Ψη
Bs  ηcΦ
125k
12k 3k
0.3
2-3
0.7
σ(s) ≈ 1.2°
σ(s) ~ 0.2° 
Bs  DsK
Bd  ππ
Bs  KK
Bd  D0(K-π+)K*0
Bd  D0(K+π-)K*0
Bd  DCP(K+K-)K*0
B- D0(K+π-)K-
B- D0(K-π+)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°
σ() « 1°
if U-spin symmetry - 
Bd  pr, rr
14k
σ() < 10°
σ() ~ 1°
* Untagged annual yield after trigger

21. Conclusion
LHC experiments will allow to measure the Unitarity Triangle very precisely
loop processes in the flavour sector will probe high energy scale!
..why penguins have short lives