Andrey Golutvin
ITEP & CERN
Promising measurements for the test
of SM and search for New Physics
- In CP - violation
- In rare decays
LHCb upgrade workshop,
Edinburgh, 2007
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In CP-violation
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Mean values of angles and sides of UT are
entirely consistent with SM predictions
Inputs:
Vub
Vcb
Δmd
Δms
B → τν
εK
sin2β
α
γ
Accuracy of sides is limited by theory:
- Extraction of |Vub|
- Lattice calculation of
Accuracy of angles
is limited by experiment:
α= ± 13°
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β = ± 1.5°
γ = ± 25°
Standard strategy to search for New Physics
Define the apex of UT
using at least 2 independent quantities out of 2 sides:
and 3 angles: α, β and γ
Extract quantities Rb and γ 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 signal of NP
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At present the sensitivity of standard approach is limited due to:
- Theoretical uncertainties in sides
- Experimental uncertainties in α and γ angles
- Geometry of UT (UT is almost rectangular)
Comparison of precisely measured β with γ is not meaningful due to error
propagation: 3° window in β corresponds to (24±5)° window in γ
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Precision comparison of the angle γ and side Rt is very meaningful !!!
However in many NP scenarios, in particular with MFV, short-distance
contributions are cancelled out in the ratio of ΔMd/ΔMs.
So the length of the Rt side may happen to be not sensitive to NP
Precision measurement of γ will
effectively constrain Rt and thus
calibrate the lattice calculation
of the parameter
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Complementary Strategy
trees
Compare experimental observables
measured in different topologies:
q1
b
q2
W−
Bq
d, s
d-/s- penguins
W–
b
W−
W−
q b
u, c, t
d (s) b
u, c, t
mγ
b
L +m
l+
Z, γ
qγ
R
u,c,t
d (s)
q
g
q
l−
d-/s- boxes
V*ib
q
u, c, t
b
Bq
Viq
W−
W+
u, c, t
q
Viq
b
V*ib
Bq
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|VtsVtb*| and UT angles: α, β and χ
trees vs box loops vs penguin loops
In trees:
β(tree) is measured in BÆ J/ψKs
α(tree) = π - β(tree) - γ(tree)
χ(tree) is measured in BÆ J/ψφ
Theoretical uncertainty in Vub extraction
Precision measurements of angles in tree topologies should be possible.
Eventually LHCb will measure β, γ, and χ with σ(β) ~ 0.5°, σ(γ) ~ few° and
σ(χ) ~ 1° precision respectively
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Proposed set of observables
For |VtsVtb*| (at the moment not theoretically clean):
Theoretical input: improved precision of lattice calculations
for BØfB and BÆπ,ρ,K* formfactors
Experimental input: precision measurement of BR(BÆK*γ, ργ)
For the angles:
(theoretically clean)
Measure α(peng) in BÆρρ,ρπ,ππ
β(peng) in BÆφKs
χ(peng) in BsÆφφ
New heavy particles, which may contribute to d- and s- penguins,
would lead to some phase shifts in all three angles:
δα(NP) = α(peng) - α(tree)
δβ(NP) = β(BÆφKs) - β(BÆJ/ψKs)
δχ(NP) = χ(BÆφφ) - χ(BÆJ/ψφ)
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Contribution of NP to processes mediated by loops
Present status:
To boxes:
- β vs Rb is limited by theory (~10% precision in Rb) (d-box)
- χ not measured yet
(s-box)
To penguins:
- σ(δα(NP)) ~ 30°
- σ(δ2β(NP)) ~8° (2.6σ hint)
- σ(δχ(NP)) not measured yet
(d-penguin)
(s-penguin)
(s-penguin)
ps δβ(NP) = δχ (NP)
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In Rare Decays
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- Radiative penguins
- Electroweak penguins
- Very rare decays Bs,d Æ μμ, eμ
Experimental challenge: keep backgrounds under control
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Exclusive radiative
penguins
LHCb control channel: Bd Æ K*γ
~75k signal events per 2fb-1
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Radiative Penguin Decays
γR
m qγ R
+
γL
W–
mb
W+
q
b
+m b
m qγ L
q
b
u, c, t
u, c, t
Measurement of the photon polarization is very sensitive test of SM
Methods:
- mixing induced CP asymmetries in Bs Æ φγ , BÆKs π0γ
- Λb Æ Λγ : asymmetries in the final states angular distributions are
sensitive to the photon and Λb polarizations.
- Photon helicity can be measured directly using converted photons in BÆK*γ decay
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or parity-odd triple correlation (P(γ),[ P(h1) × P(h2)]) between photon and 2 out of 14
final state hadrons. Good examples are BÆ φKγ and BÆ Kππγ decays
Mixing induced CP asymmetries
- B Æ BÆKsπ0 γ (B-factories)
S = - (2+O(αs))sin(2β)ms/mb + (possible contribution from bÆsγg) = - 0.022 ± 0.015
P.Ball and R.Zwicky hep-ph/0609037
Present accuracy:
S = - 0.21 ± 0.40 (BaBar : 232M BB)
S = - 0.10 ± 0.31 (BELLE: 535M BB)
- Bs Æ φ γ
( LHCb annual yield ~11 k , B/S ~0.6 )
Polarized Λb decays:
Λb Æ Λ(1115)γ
Λ(1115) Æ pπ violates pariry
Assuming Λb polarization > 20% LHCb can measure γ(R) component
down to 20% (in 1 years of data taking). Limitation - low annual yield
(~675 events) Æ requires efficient performance of tracking system.
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Measuring the photon polarization in
B Æ h1h2h3 γ decays
The measurement of the photon helicity requires the knowledge of the spin direction
of the s-quark emitted from the penguin loop. Use the correlation between s-spin
and angular momentum of the hadronic system (needs partial-wave analysis !!!)
The average value of the triple product [ P(γ) × [P(h1) × P(h2)]] has opposite signs
for left – and right-handed photons
M.Gronau,Y.Grossman,D.Pirjol,A.Ryd PRL 88, 5, 2002
D.Atwood,T.Gershon,M.Hazumi,A.Soni hep-ph/0701021 v 1
Promising channels for LHCb:
Expected per 2 fb-1
BR(B+ Æ K+π-π+γ) ~ 2.5 × 10-5 rich pattern of resonances
highly distinctive final state
BR(B+ Æ K+φγ) ~ 3 × 10-6
Sensitivity to photon polarization measurement to be studied
~40k
~10k
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Exclusive bÆsμμ decaus
Bd Æ K*0μ+μB+ Æ K+μ+μBs Æ φ μ+μ-
Λb Æ Λ μ+μ-
Described by a combination of
γ - and Z – penguins and box
diagrams Æ Sensitive to New
Physics: SUSY, graviton
exchanges, extra dimensions …
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Kreuger, Matias hep-ph/0502060
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B s,d Æ μ+μBs Æ μ+μ- measurement seems to be possible (see talk by O. Schneider)
Bd decay has a SM BR an order of magnitude lower ; not reachable with
present LHCb configuration. Can probe NP models with different contribution
to s- and d-loops
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LHCb Prospects
LHCb Sensitivity
Limit at 90% C.L.
(signal+bkg is observed)
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BR (x10-9)
BR (x10-9)
(only bkg is observed)
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5σ
Expected CDF+D0 Limit
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SM prediction
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10
3σ
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Uncertainty in
bkg prediction
SM prediction
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0.4
0.5
Integrated Luminosity (fb-1)
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Integrated Luminosity (fb-1)
Background is assumed to be dominated by combinations of bÆμ-X bÆμ+X
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events.
Important measurements to test SM and Search for NP
In CP-violation:
-β vs Rb and γ vs Rt (Input from theory !)
-χ : if non-zero Æ NP in boxes
-δα(NP), δβ(NP) and δχ(NP): if non-zero Æ NP in penguins
In rare decays:
-Photon polarization in exclusive radiative penguins
- Measurement of FBA, zero point, transversity amplitudes in BÆsll
exclusive decays (K*μμ, φμμ, …)
- Measurement of BR(B s,d Æ μμ) down to SM predictions
- Search for lepton flavor violation
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