1. LHCb Rare Decays Status
WG6 – CKM 2006
Nagoya, Japan
Jeremy Dickens
on behalf of the LHCb Collaboration

2. Outline LHCb detector Bs  mm Bd  K*mm Measurement of RK
Signal yield and B/S
Forward-backward asymmetry sensitivity
Tranversity angles sensitivity
Measurement of RK
Radiative decays
Bd  K*g
Bs  fg
Lb Lg
14/12/06
Jeremy Dickens

3. LHCb Detector Forward peaked, correlated bb-pair production
250 mrad
10 mrad
Vertex Locator
Dipole magnet
Tracking system
Calorimeters
Muon system
RICH detectors
(B), rad
Forward peaked, correlated bb-pair production
sbb  500mb with L  2 x 1032 cm-2 s-1
For 1 nominal year (107 sec)  1012 bb-pairs
LHCb is a forward spectrometer
14/12/06
Jeremy Dickens

4. Bs  mm Branching ratio ~ 3.5 x 10-9 in Standard Model
Sensitive to New Physics and can be strongly enhanced by SUSY (by up to factor ~100)
Current limit from Tevatron CDF + D0 with 1 fb-1 is ~ 7 x 10-8 at 90% CL
Expected limit with 8 fb-1 is ~ 2 x 10-8 at 90% CL
14/12/06
Jeremy Dickens

5. Bs  mm: Mis-ID background
Extremely low branching ratio  issue is background rejection
Combinatorial – with muons mainly from b decays
Studied with bb and b  mX, b  mX samples
Mis-identified Hadrons – eg Bs  pp, Kp and KK
For example Br(Bs  Kp)  5 x 10-6, so need mis-id rate O(1%) per track
For a 1% mis-id rate, LHCb expects of order 1 event per fb-1 in 2s mass window
14/12/06
Jeremy Dickens

6. Bs  mm: N-counting experiment
Perform N-counting experiment in 3 variables:
Combined geometry variable (impact parameters, distance of closest approach, lifetime, vertex isolation)
Particle-ID (likelihood for p or K to be mis-id as m)
Invariant mass
signal
Arbitrary normalization
bb inclusive
b μX, b  μX (component)
geometry variable
signal
Arbitrary normalization
bb inclusive
b μX, b  μX (component)
Invariant mass (MeV)
For geometry variable > 0.4 background is dominated by b  mX, b  mX
14/12/06
Jeremy Dickens

7. Bs  mm: N-counting experiment
For example, with a cut on geometry (> 0.4) and invariant mass (± 30 MeV) expect:
~19 signal events per fb-1 (SM)
[54, 295] background events per fb-1 (90% CL)
Better sensitivity from N-counting method
Each variable is divided into several bins
b  m-X, b  m+X used to compute expected background in each 3D bin
Limited MC statistics  many bins have little or zero background
Background is shifted upward in each bin so that total background has 90% probability to be below this value
Compute confidence levels for observation and exclusion
No cut actually applied in the analysis
14/12/06
Jeremy Dickens

8. Bs  mm 5 3 Limit at 90% CL (only bkg is observed)
Integrated Luminosity (fb-1)
BR (x10-9)
Expected CDF+D0 Limit
Uncertainty in
bkg prediction
SM prediction
LHCb Sensitivity (signal+bkg is observed)
Integrated Luminosity (fb-1)
BR (x10-9) 5 3
SM prediction
Background assumed to be dominated by combinations of b  m- X and b  m+ X
14/12/06
Jeremy Dickens

9. Bd  K*mm
Branching ratio and forward-backward asymmetry (FBA) sensitive to New Physics
Branching ratio (Babar/Belle) = x 10-6
FBA defined as asymmetry between m+ (m-) in forward and backward directions in m+m- pair rest frame, with respect to the B (B) direction
Position of the zero crossing is sensitive to new physics
+ 0.38
– 0.32 m+ m- K* B0 q
From hep-ph/
Standard Model d Bd b s K* m g m
14/12/06
Jeremy Dickens

10. Bd  K*mm: Backgrounds Background dominated by b  mX, b  mX
Sample
LHCb Simulation BR()
No. evts per 2fb-1
Bd  smm (no K*)
4 x 10-6
44 ± 10
Bu  smm
14 ± 4
b  mX, b  mX
1.2%
1770 ± 320
b  m c( m)
2.7%
1310 ± 280
TOTAL
3100 ± 430
Signal
1.22 x 10-6
7700 ± 180 ± 2200
B/S = 0.4 ± 0.1
Statistical
From BR()
Background dominated by b  mX, b  mX
In the majority of these events, all the particles used to build the “B” came from b-decays
Large fraction from b  m c ( m )
Also expect some background from non-resonant Bd  Kpmm events
Rate from this source not certain (not included in table above)
14/12/06
Jeremy Dickens

11. Bd  K*mm: FBA sensitivity
Toy model based on LHCb simulation:
Large sample of generator level events
Smaller sample of fully simulated events (include detector effects)
Take resolutions, acceptances and background from the fully simulated events, in bins of Mmm (03 GeV) and qFBA (0p)
Mmm (qFBA) resolution ~ 10 MeV (4 mrad)  ~3% (~1%) of bin width
Sample from (fluctuated) generator level distributions, applying the acceptance functions, to simulate a large number of 2 (10) fb-1 experiments.
Calculate and fit FBA for each data set to find the zero-crossing point
Quoted sensitivity is then the standard deviation of the fitted zero points from a large number of experiments
14/12/06
Jeremy Dickens

12. Bd  K*mm: FBA sensitivity
Neglected non-resonant background for now
Consider two types of background
Asymmetric in qFBA (expect 240 ± 75 events per 2 fb-1)
Fraction of the b  m c ( m) sample
For example: B+  m+ n D0 ( K+ m- n) and B-  m- n D0 ( K- m+ n)
For both cases, we make the angle with the muon direct from the b, which tends to have higher momentum than the muon from the charm, so is more likely to be forward in the mm rest frame
Symmetric in qFBA (expect 1700 ± 250 events per 2 fb-1)
All events in the b  mX, b  mX sample (muons from different b-decays)
Some events in the b  m c ( m) sample, where the K and p come from different b-decays to the two muons – the charge of the K is uncorrelated with the charge of the muon direct from the b
14/12/06
Jeremy Dickens

13. Bd  K*mm: FBA sensitivity
Generator zero-crossing point: s0 = 4.10 GeV2
From 1000 experiments of 2 fb-1:
No background s0 = 4.17 ± 0.38 GeV2
With background s0 = 4.11 ± 0.52 GeV2
With 10 fb-1 (with background) s0 = 4.17 ± 0.28 GeV2
Fitted zero-point (GeV2)
With 10 fb-1
Example 2 fb-1 experiment
Mmm2 (GeV2)
14/12/06
Jeremy Dickens

14. Bd  K*mm: Non-resonant events
Simulation of these events is currently Jetset fragmentation
Spectra and rate are very uncertain!
LHCb simulation uses BR(Bd  Kpmm) = 1 x 10-6 in full mass range
Gives non-resonant background of 4550 ± 200 events per 2 fb-1
Probably an overestimate – will eventually measure this
Identical from a selection point of view, but without the K* mass constraint
For FBA, can be treated as signal, under certain conditions…
(hep-ph/ )
Region I: soft pion, energetic kaon
Shifts zero of FBA and larger theory errors
Region II: energetic Kp pair
Can be treated as B  Xmm and X  Kp
Region III: soft kaon, energetic pion
Amplitude suppressed so very few events…
Defined by kinematics
Drawn for Mmm = 2 GeV
14/12/06
Jeremy Dickens

15. Bd  K*mm: Non-resonant events
Simulation of these events is currently Jetset fragmentation
Spectra and rate are very uncertain!
LHCb simulation uses BR(Bd  Kpmm) = 1 x 10-6 in full mass range
Gives non-resonant background of 4550 ± 200 events per 2 fb-1
Probably an overestimate – will eventually measure this
Identical from a selection point of view, but without the K* mass constraint
For FBA, can be treated as signal, under certain conditions…
(hep-ph/ )
Region I: soft pion, energetic kaon
Shifts zero of FBA and larger theory errors
Region II: energetic Kp pair
Can be treated as B  Xmm and X  Kp
Region III: soft kaon, energetic pion
Amplitude suppressed so very few events…
Defined by kinematics
Drawn for Mmm = 2 GeV
14/12/06
Jeremy Dickens

16. Bd  K*mm: Non-resonant events
Simulation of these events is currently Jetset fragmentation
Spectra and rate are very uncertain!
LHCb simulation uses BR(Bd  Kpmm) = 1 x 10-6 in full mass range
Gives non-resonant background of 4550 ± 200 events per 2 fb-1
Probably an overestimate – will eventually measure this
Identical from a selection point of view, but without the K* mass constraint
For FBA, can be treated as signal, under certain conditions…
(hep-ph/ )
Region I: soft pion, energetic kaon
Shifts zero of FBA and larger theory errors
Region II: energetic Kp pair
Can be treated as B  Xmm and X  Kp
Region III: soft kaon, energetic pion
Amplitude suppressed so very few events…
Defined by kinematics
Drawn for Mmm = 2 GeV
14/12/06
Jeremy Dickens

17. Bd  K*mm: Non-resonant events
Simulation of these events is currently Jetset fragmentation
Spectra and rate are very uncertain!
LHCb simulation uses BR(Bd  Kpmm) = 1 x 10-6 in full mass range
Gives non-resonant background of 4550 ± 200 events per 2 fb-1
Probably an overestimate – will eventually measure this
Identical from a selection point of view, but without the K* mass constraint
For FBA, can be treated as signal, under certain conditions…
(hep-ph/ )
Region I: soft pion, energetic kaon
Shifts zero of FBA and larger theory errors
Region II: energetic Kp pair
Can be treated as B  Xmm and X  Kp
Region III: soft kaon, energetic pion
Amplitude suppressed so very few events…
Defined by kinematics
Drawn for Mmm = 2 GeV
14/12/06
Jeremy Dickens

18. Bd  K*mm: Transversity angles
Recent theoretical work has highlighted other asymmetries to study (Phys Rev D71: , 2500)
Describe the decay in terms of 4 parameters
s = mm mass squared
ql = FBA angle (between m and B in mm rest-frame)
qK* = equivalent K* angle (between K and B in K* rest-frame)
f = angle between K* and mm decay planes
FL extracted from ql, qK* and f distributions
AT(2) extracted from qK* and f distributions
14/12/06
Jeremy Dickens

19. Bd  K*mm: Transversity angles
Toy MC created to describe ql, qK* and f distributions
SM predictions used as input values
Inputs are averaged (weighted by cross-section in each bin)
Background distributions added (without non-resonant component)
Analysis performed in 4 bins of s (0 < s < 9 GeV2)
Mmm2 range
Resolutions
AT(2) FL
0.05  0.49
0.180
0.037
0.49  1.96
0.400
0.033
1.96  6.25
0.470
0.018
6.25  9.0
0.31
0.020 FL
AT(2)
A possible 2fb-1 measurement
14/12/06
Jeremy Dickens

20. RK b  lls suppressed by 1/aEM with respect to b  sg
Sensitive to SUSY, extra-dimensions…
In SM RK = 1 ± 0.001
Neutral Higgs corrections could be O(10%)
Measure RK  1  New Physics
CDF 95% CL limit on Bs  mm
LHCb 10 fb-1 yields
Bd  eeK ~ 10k
Bd  mmK ~ 19k
Gives RK = 1 (fixed) ± 0.043
14/12/06
Jeremy Dickens

21. Radiative Decays b  sg proceeds only via loop diagram
Sensitive to New Physics, eg charged Higgs, gluino, neutralino loops
Decay
2 fb-1 yield
B/S
Bd  K*g
35000
< 0.7
Bs  fg
9000
< 2.4
Bd  wg 40
< 3.5 g t W b s
Decay
2 fb-1 yield
B/S
Lb  L g
750
< 42
Lb  L(1520) g
4200
< 10
Lb  L (1670) g
2500
< 18
Lb  L (1690) g
2200
Lb decays need special reconstruction since L flies  L vertex doesn’t define the Lb vertex
Sensitivity under study
14/12/06
Jeremy Dickens

22. Conclusions Bs  mm Bd  K*mm
Potential to exclude BR between 10-8 and SM with 0.5 fb-1
Potential for 3s (6s) observation with ~ 2 fb-1 (10 fb-1)
Bd  K*mm
Yield per 2 fb-1 of 7700 ± 180(stat) ± 2200(branching ratio)
B/S = 0.4 ± 0.1 (without non-resonant events)
FBA zero-crossing point s0 = 4.2 ± 0.5 GeV2 for 2 fb-1 (± 0.3 for 10 fb-1)
Potential to measure K* polarisation with higher precision than SM errors
10 fb-1 measurement RK = 1 (fixed) ± 0.043
Good potential for study of radiative B-decays
LHCb has good sensitivity for new physics discovery
14/12/06
Jeremy Dickens

23. SPARE
14/12/06
Jeremy Dickens

24. Bd  K*mm: FBA From hep-ph/0106067 From Phys Rev D55 4273 14/12/06
Jeremy Dickens

25. Bd  K*mm Non-resonant background (Bd  Kpmm)
Current branching ratio in LHCb simulation is 1 x 10-6
Not yet observed – may be too large? (hep-ex/ )
Recent theoretical work suggests that in some kinematic regions (requires energetic Kp pair), these events should have the same FBA as the signal (resonant) events
May be able to treat the events as signal (hep-ph/ )
14/12/06
Jeremy Dickens

26. Bd  K*mm: FBA sensitivity
Toy model based on LHCb simulation:
Large sample of generator level events (5.5M)
Smaller sample (550k) of fully simulated events (include detector effects)
Take generator level distributions, binned in Mmm (03 GeV) and qFBA (0p)
Mmm (qFBA) resolution ~ 10 MeV (4 mrad)  ~3% (~1%) of bin width
Apply fluctuated acceptance function in each Mmm x qFBA bin
Measured using the 550k fully simulated events
Now have “Expected distributions”
In each bin of Mmm sample X events (Poisson fluctuated) from “Expected distributions”
Add background (see later) – now have “Experimental Distributions”
Remove (un-fluctuated) acceptance
Assume same acceptance for signal and background
Calculate and fit FBA to find the zero-crossing point
Quoted sensitivity is then the standard deviation of the fitted zero points from a large number of experiments
14/12/06
Jeremy Dickens

27. Bd  K*mm: Transversity Anglesf
14/12/06
Jeremy Dickens

28. Bd  K*mm: Transversity Angles
qK*
14/12/06
Jeremy Dickens