lhcb sensitivity to with b h + h - and u-spin symmetry
DESCRIPTION
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. Outline. Physics motivation Extraction of the weak phase from the B d + - and B s K + K - decays - PowerPoint PPT PresentationTRANSCRIPT
Laura Fabbri 1
LHCb sensitivity to with Bh+h- and U-spin Symmetry
Physics at LHCPhysics at LHCVienna, 13 -17 July 2004 Vienna, 13 -17 July 2004
Laura Fabbrion behalf of the LHCb collaboration
Vienna, 13–17 July 2004 Physics at LHC Laura Fabbri 2
Outline
Physics motivation Extraction of the weak phase from the
Bd+- and BsK+K- decays
Bd(s)h+h- event selection Strategy, event yields and background-to-
signal ratios CP sensitivity
Bayesian determination of Conclusions
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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 Bh+ h- have sizeable
contribution from penguin graphs which may evidence new physics in loops
from LHCb?
Indirect CKM fits
expect 65o
Tree Diagram
Penguin Diagram
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()(,,)()(,,,)()(,,)()(,,,)dirCPdmixCPdddirsCPmixssCPABfdABfdABKKfdABKKfdϑϑφϑϑφ+−+−+−+−→=→=′′→=′′→=01020304
Extracting from Bd+- and BsK+K-
4 equations and 5 unknowns: d, ϑ, d’, ϑ’ (hadronic parameters) and
One needs other inputs to solve for
()()()()()(())(())cossin(())(())coshsinhdirmixssCPCPCPssCPBtfBtfAmtAmtAtBtfBtftAtΔΓΓ→−Γ→Δ⋅+Δ⋅==ΔΓΔΓΓ→+Γ→⋅−⋅000022
s =-22 Bs-Bs mixing phase(can be probed with BsJ/)
d =2 Bd-Bd mixing phase(measured with BdJ/Ks)
[R.Fleischer, Phys. Lett. B459 (1999)]
ctiPPuutTPPbAAdeRAAAϑ⎛⎞−=⎜⎟+−⎝⎠1
ubbcbVRV⎛⎞≡−⎜⎟⎝⎠2112
PT
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⎩⎨⎧
′=
′=⇒
ϑϑdd
U-spin symmetry6 eqs. and 5 unknowns
the system can be solved unambiguously
Unique solution for
oo
os
od dd
65,160
,3.0,0,55
==′=
=′===
ϑϑ
φφ
−+→ 0from),( BAA mixCP
dirCP
−+→ KKBAA smixCP
dirCP
0from),(
−+
−+
→
→
KKBAA
BA
smixCP
dirCP
dirCP
0
0
from),(
andfrom ππ
Using U-spin Symmetry
Bd+- U-spin (d,s quark exchange) BsK+K-
In this example
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Bd(s)h+h- event selection
Selection cuts are simultaneously optimized in order to maximize
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. BdK+-, BsK+K-, Bs+K- as backgrounds for Bd+-
After event selection, tagging and trigger algorithms are tuned on selected events
/SSB+
LHCb Public Note 2003-123
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Selection cuts
B0(s)
, K
, KIP
IPIPB L
Beam axis (z)
Selection cuts on the candidate B pT
IP/IP
L/L
Invariant mass
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
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Mass spectrasignals + specific backgrounds
only
Bd+- BdK+-
BsK+K- Bs+K-
Two-body background only
Mostly BdK+-
(same signature)
if not using RICH…
17 MeV/c2
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Proper time acceptance and resolution
Resolution on proper time fitted with double
Gaussian(single Gaussian 40 fs)
1=341 fs2=673 fs (15%)
Acceptance suppression at low proper time due to cuts on IPs and distance
of flight
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Signal yields and
background-to-signal ratios
Event type AssumedBR (x10-6)
Bbb/S Untaggedannual yield
D2
Bd +- 4.8 0.42 26000 4%
Bd K+- 18.5 0.16 135000 4%
Bs K+K- 18.5 0.31 37000 6%
Bs +K- 4.8 0.67 5300 6%
Annual yields after L0+L1 triggers and offline selection (assumed bb = 0.5 mb and L = 2 fb-1/yr)
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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, ϑ, 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.
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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 BdK+ - (BsK+K- and Bs+K-) event samples (plus background) BdK+ - (Bs+ K-) is a flavour specific decay and is used as
control channel Bd+ - (BsK+ K- ) and BdK+ - (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+ - andGKK(Adir, Amix) for the BsK+ K-
LHCb Public Note 2003-124
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Bayesian approach to determine the p.d.f.
()()()()()()()()(),,,,, ,, , ,,,,,, dirmixddirmixsKKKdssddKsKKGAdAdGAFddAgdgddππππππϑγϑγφϑγϑγϑγφφφφφ=×××××∫∫00
Exp. joint p.d.f. (bivariate gaussian)
for (, ) & (, )dirmix∂∂∂∂dirmixKKKKAAAAGaussian priors for the weak mixing
phases(from LHCb BdJ/KS and BsJ/)
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:
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)(df
Sensitivity on from Bd+- and BsK+K- (1
year) d d()(,,)fFddϑϑ=∫∫
95% confidence region from BsK+K-
only
95% confidence region from Bd+- only
()oóã≈5Perfect U-spin
O(20%) U-spin breaking would induce only a few
degrees shift on YellowYellow and WhiteWhite contours: 68% and 95% confidence regions using all the
information
Fake solution(disappears with more
statistics)
)(fCorrect
Solution 65o
d- plane
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Sensitivity scan
() vs ms
() vs d=0.3, = 160°, =65°, s=-0.04°,
s/s=0.1
d=0.3, = 160°, s=-0.04°, s/s=0.1, ms=20 ps-1
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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 BsK+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. and see LHCb talks by Eduardo Rodrigues and Sandra Amato
ssBDK±→ 0m * BDK→ 00
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Backup slides
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Charmless two-body decays of B mesons:
diagrams
W
g
oZã,
W
W
W
WoZã, W W
W g
TTree
C colour-suppressed
Tree
Pgluonic Penguin
PAPenguin Annihilation
PEW
electroweak Penguin
PCEW
colour-suppressed electroweak Penguin
E Exchange
A Annihilation
Gronau, Hernandez, London and Rosner, Phys. Rev. D50 (1994) 4529
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Bd+- and BsK+K-
decay amplitudes ()****uuctTPPPdubudubudcbcdtbtdABVVAVVAVVAVVApp+−→=+++0
()()iidABCedeγϑππ+−→=−0 ()uutTPPbCARAAAλ≡+−3
ctiPPuutTPPbAAdeRAAAϑ⎛⎞−≡⎜⎟+−⎝⎠1
()****uuctsusTuscstsPPPububcbtbABKKVVAVVAVVAVVA+−′′′′→=+++0
()/ iisABKKCedeγϑλλλλ′+−⎛⎞−′′→=+⎜⎟−⎝⎠2022112
(), uutTPPbctiPPuutTPPbCARAAAAAdeRAAAϑλ′′′′′≡+−′′⎛⎞−′≡⎜⎟′′′+−⎝⎠31
Bd+-
BsK+K-
ubbcbVRV⎛⎞≡−⎜⎟⎝⎠2112
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Distributions of selection variables for BsK+K- and
combinatorial bb background
bb background
——— signal
cut value andaccepted
region
2 of common vertex
Max[pT(K+), pT(K-)]
Min[pT(K+), pT(K-)]
Max[IP/IP(K+), IP/IP(K-)]
Min[IP/IP(K+), IP/IP(K-)]
Bs Mass
Bs pT
Bs IP/IP
Bs L/L
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Selection cuts
Channel: Bd+ - BdK+ - BsK+ K-
Bs+ K-
Pmin (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
(PT)min (GeV/c) 1.6 1.4 1.0 1.6
(IP/IP)max 2.25 2.50 2.75 2.25
(L/L)min 19 17 14 20
m (MeV/c2) 50 50 50 40
can
did
ate
B
Iden
tifi
ed
tr
acks
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Fast MC input values
Nominal parameters: Bd +-, Bd K+- Bs K+K-, Bs +K-
tagging efficiency 42% 50% wrong tagging fraction 35% 33% M 0.5 ps-1 20 ps-1
1/1.54 ps-1 1/1.46 ps-1
/ 0 0.1 d 0.3 0.3 ϑ 160o 160o
65o 65o
weak mixing phase 0.82 -0.04
Sensitivity scan: parameters are varied one at a time d: 0.1 0.2 (0.3) 0.4 ϑ: 120o 140o (160o) 180o 200o
: 55o (65o) 75o 85o 95o 105o
s: 0 (-0.04) -0.1 -0.2
Ms (ps-1) 15 (20) 25 30
s/ s: 0 (0.1) 0.2
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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°
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°
0 (0.1) 0.2
5.2° 4.9° 4.5°
15 ps-1 (20 ps-1) 25 ps-
1
30 ps-
1
4.0° 4.9° 5.9° 8.5°
d( )
( )
( )
( )
( )
( )
ϑ
sφ
ss /
sM
Resolution computed as half the 68% confidence
interval
Sensitivity on
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U-spin Symmetry
How much rely on it? U-spin symmetry in the relations d=d’ and ϑ=ϑ’ 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 ϑ=ϑ’-ϑ 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, ϑ ±15o
A better understanding of SU(3) breaking would be desirable, but a O(20%) breaking does not spoil the measurement
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BsK+K-
Mass spectrasignals + combinatorial beauty
background only
Bs+K-BsK+
K-
BdK+-
Bd+-