Interference
Interference and
and
quantum
quantum coherence
coherence
in
in beauty
beauty and
and charm
charm
Anton
Anton Poluektov
Poluektov
The
The University
University of
of Warwick,
Warwick, UK
UK
Budker
Budker Istitute
Istitute of
of Nuclear
Nuclear Physics,
Physics, Russia
Russia
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A bit of my CV
Graduated from Novosibirsk State University (Russia)
PhD at Budker Institute of Nuclear Physics (2007):
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“Measurement of CKM phase γ at Belle experiment”.
University of Warwick (UK) and LHCb since 2009.
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Data preselection (“stripping”) developer and coordinator (2011–2012)
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“Beauty decays to open charm” WG convener (Jan 2013 – Mar 2015)
Research interests:
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Studies of CP violation in B hadron decays
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Analysis techniques involving amplitude analyses, Dalitz plot analyses
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Spectroscopy of beauty and charmed hadrons
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Plan
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Main physics objectives: CP violation and the angle γ
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Technique: amplitude analyses
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Experimental results on γ
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Mostly Belle and LHCb analyses I was involved in.
But other results are there (especially BaBar!)
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Other use cases: indirect CPV and mixing
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Extensions for future: multibody B decays, baryonic decays
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Tools for amplitude analyses
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Future prospects
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Baryogenesis and baryon asymmetry
Baryogenesis:
Baryon number violation
● C and CP violation
● Should occur outside of
thermal equilibrium
(A.D. Sakharov, 1967)
●
Don't need New Physics for baryon number violation: sphaleron mechanism in SM
Although some SM extensions include anomalous B violation
C and CP are violated in the SM, but CP violation is too weak.
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How do we search for New Physics
Can directly search for new heavy particles in high-energy collisions (Atlas, CMS)
Indirect searches in heavy flavours: heavy particles are produced virtually and cause
subtle effects in precision measurements wrt. Standard Model predictions. (LHCb)
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Rare decays, e.g. B(s) → μ+μ-, B0 → K*μ+μ-
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CP violation measurements
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CP violation in the SM
CP violation occurs in the SM charged currents
Cabibbo-Kobayashi-Maskawa (CKM) matrix
Unitarity condition => “geometrical” representation as a triangle (Unitarity Triangle)
Experimentally
measurable
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B-factories
Electron-positron colliders (B factories)
Production of bb pairs at threshold in
e+e− collisions
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Clean environment
Efficient reconstruction of
neutral modes
Efficient flavour tagging
Belle (KEKB, KEK)
Low production cross-section
(especially Bs)
Small boost (artificially by asymmetric
energies), low time resolution
BaBar (PEP-II, SLAC)
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LHCb
One-arm spectrometer optimised for studies
of B and D decays. Forward geometry: 2<η<5
✔
Good vertexing
- Measure Bd and Bs oscillations, reject prompt background
Particle identification - Flavour tagging, misID background
✔
Calorimetry
- Reconstruction of neutral particles (γ, π0)
✔
Efficient trigger, including hadronic modes
✔
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Direct CP violation
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Asymmetry in decay amplitudes
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The only possibility for charged B mesons
Interference between two different diagrams is needed for CP violation
Two possible types of transitions:
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Tree
QCD penguin
b→c transitions
Final states with
open charm
Probe CKM angle γ
Not affected by NP
Charmless final states
Potentially contain
information on γ.
Can be affected by NP
(loops!)
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Measurement of γ
“Reference wave”
A~1
CP violation occurs if D is reconstructed
in a final state accessible to both D0 and D0
Magnitude is determined by the ratio of two
amplitudes: rB=0.1 for DK, ~0.01 for Dπ
[f]DK-
B-
“Object wave”
A~rBeiδe±iγ
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Are we actually measuring γ?
Yes! Irreducible theory corrections are
only in 2nd order EW transitions.
Brod, Zupan, JHEP 1401 (2014) 051
|δγ|<10-7 !
O(1014) years running upgraded LHCb
to reach the theory limit :)
Unique system: both factorisation and interference:
Yu. Grossman (CKM2012)
A = ABAD+ eiγ ABAD
Take several B amplitudes AB (M unknown parameters)
several D amplitudes AD (N unknown parameters)
MxN observables, but only M+N unknowns => can extract all from experiment!
At ~1° precision, need to consider
effects of D0 mixing.
B → Dπ, is sensitive to it already now
(rB~0.01)
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D0K+
D0K+
B+
(f)DK+
D0K+
LPNHE seminar
D0K+
Time
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γ from counting measurements
LHCb, PLB 713 (2012) 351
“GLW mode”:
D→KK, ππ
“ADS mode”: fav. B→DK, sup. D→πK
and sup. B→DK, fav. D→Kπ
4.5σ
4.0σ
LHCb, 1 fb-1 sample (2011)
5.8σ observation of CP violation in the combination of B→D(hh)K modes
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Dalitz plot analyses: kinematics
Two-body decay is completely determined
by energy-momentum conservation.
No internal degrees of freedom.
Three-body decay has two degrees of
freedom.
e.g. m2(ab), m2(bc)
Approach introduced by Richard Dalitz (1925-2006)
for studies of kaon decays
R. Dalitz, “On the analysis of tau-meson data and the
nature of the tau-meson.”, Phil. Mag. 44 (1953) 1068
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Dalitz plot analyses: dynamics
Flat nonresonant amplitude
Scalar resonance in ab channel
Scalar resonance in bc channel
Scalar resonance in ac channel
Vector resonance in ab channel
Tensor (J=2) resonance in ab channel
Interfering scalars in ab and bc, δ=0°
Interfering scalars in ab and bc, δ=90°
Interfering scalars in ab and bc, δ=180°
Interfering scalar and vector in ab
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D → Ksπ+π− Dalitz plot
The best kind of decay to study the D0-D0 admixture we have e.g. in B → DK
m2(KSπ−) (GeV2/c4)
But not only that!
f0(980)
ρ (770)
0
K*+(892)
K*─(892)
Large branching ratio: 2.8%
● No neutral particles in the final state
● Large interference between D 0 and D0
● Large phase variations
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m2(KSπ+) (GeV2/c4)
Can be obtained from large flavour-tagged sample D*+ → D0π
(>100k events at B-factories and LHCb)
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Dalitz plot analysis for γ
Giri, Grossman, Soffer, Zupan, Phys.Rev. D68 (2003) 054018
Bondar (2002), unpublished
Multibody final state of D0 results in the interference pattern
that is directly sensitive to the phase difference between D 0 and D0
m2(KSπ−) (GeV2/c4)
B
D0K+
+
D0K+
(KSπ+π−)K+
rBeiδe±iγ=x±+iy±
m2(KSπ+) (GeV2/c4)
First prelim. result using this technique reported by Belle in 2003: arXiv:hep-ex/0308043
followed by 3 papers with increasing dataset.
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y=rBsin(δB±γ)
GGSZ analysis at Belle
2γ
x=rBcos(δB±γ)
Belle, 600 fb-1 sample
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Belle, Phys.Rev. D81 (2010) 112002
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Introducing model independence
The problem with such approach is that it depends on the model of D0 → KSππ
amplitude. What we need is not only |A|2, but also phase difference ΔδD
Use quantum coherence in e+e− →γ* →DD !
D0
e+
ΔδD
e−
D0
The two D mesons are in a state with negative C parity, and are described by the
common antisymmetric wave function:
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If we reconstruct one D in CP-eigenstate (e.g. D0 → K+K-) the other has to have
the opposite CP-parity, even if it decays to D0 → Ksππ
If both D decay to Ksππ, their Dalitz distributions will be correlated
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Binned model-independent analysis
So, the two D mesons include all the information we need, how to extract it?
Binned Dalitz distribution. Work with number of bins Ki and averaged
m2(KSπ−) (GeV2/c4)
ci=<cos ΔδD>, si=<sin ΔδD>
Correlated DD:
Ki
K-i
CP-tagged D:
D from B → DK:
m2(KSπ+) (GeV2/c4)
Simple algebraic system of equations solvable wrt. x, y (and thus γ)
However, is the bin size is large, interference pattern is smeared.
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Binned model-independent analysis
A. Bondar, A.P., Eur.Phys.J.C55:51-56,2008
First approximation: choose the binning based on (model-based) phase difference Δδ D
Even better: maximise a certain functor Q(binning) related to expected sensitivity
Start with ΔδD, divide the plot into small pixels, change bin assignment
for each pixel, so that Q increases.
As a result, expect only ~10% loss in stat. precision due to binning.
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CLEO results with quantum-correlated D0D0
CLEO, Phys.Rev. D80 (2009) 032002
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Belle model-independent analysis
Belle, Phys.Rev. D85 (2012) 112014
Belle, full bb sample (710 fb-1)
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LHCb model-independent analysis
LHCb, 3 fb-1 (2011+2012)
B → DK
LHCb, JHEP 1410 (2014) 97
B → Dπ (control sample)
D → KSππ
D → KSKK
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LHCb model-independent analysis
LHCb, JHEP 1410 (2014) 97
2γ
LHCb, 3 fb-1 (2011+2012)
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Measurements of mixing
Neutral mesons (B0, Bs, D0, K0) oscillate, e.g. :
Mass eigenstates ≠ flavour eigenstates
Unlike K0 system, width difference ΔΓ is small.
Indirect CP violation, when the amplitudes B0 → f and B0 → f
interfere though B0-B0 mixing
sin2β measured well by B factories in CP-eigenstate B0 → J/ψK0.
This method gives two-fold ambiguity: β ↔ π/2-β
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Measurements of mixing: angle β
B0 → D0π0 in another final state accessible for both B0 and B0
Dalitz-analysis of D → Ksππ as
0
Bondar, Gershon, Krokovny,
Phys.Lett. B624 (2005) 1-10
a function of B0 decay time.
Sensitive to the mixing phase.
Analysis performed by both Belle and BaBar
BaBar, Phys.Rev.Lett. 99 (2007) 231802
Belle, Phys.Rev.Lett. 97 (2006) 081801
cos2β>0 at 86% CL (BaBar)
KS ρ
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K* π
+
-
cos2β>0 at 98% CL (Belle)
K* π
-
+
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Measurements of mixing: charm
Unlike B, oscillations of D mesons are slow.
Belle, Phys.Rev.Lett. 99 (2007) 131803
both << 1
Again, a time-dependent Dalitz plot analysis extracts both
x and y.
Additionally, sensitive to CP violating parameters q/p
Upgraded LHCb: expect
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G. Wilkinson, C. Thomas, arXiv:1209.0172
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B0 → D0K+π−
Neutral B0 decays: larger rB~0.3 (compared to ~0.1 for B± → DK±)
Increased “contrast” of the interference pattern (larger CP violation magnitude)
but lower “brightness” (smaller probability of the decay)
T. Gershon, Phys.Rev. D79 (2009) 051301
Now, the Dalitz plot analysis of B0 → D0Kπ provides useful info
Can extract γ by analysing B → DKπ
with D → Kπ (flavour state, mostly D0)
and D → KK, ππ (CP-eigenstate)
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Bs0 → D0K+π−
LHCb, Phys.Rev.Lett. 113 (2014) 162001
LHCb analysis: start with Bs → D0Kπ:
Mode with higher yield, potential background for B → D0Kπ
Surprising result for charm spectroscopy:
the Ds state around 2.86 GeV is found to be
an admixture of spin-1 and spin-3 states.
First observation of heavy-flavor spin-3 state
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B0 → DKπ, D → KSπ+π− Double Dalitz plot
T. Gershon, A.P., Phys.Rev. D81 (2010) 014025
The method with B0 → DKπ, D → hh is inherently model-dependent.
Can make it model-independent if consider
B0 → DKπ, D → KSπ+π−
Correlated Dalitz plots, both binned. Large interference term
in some regions of B phase space
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Other B → charm states: baryons
Several first observations
LHCb, Phys.Rev. D89 (2014) 3, 032001
Λb→D0pK-
Λb→Λc+K-
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Ξb0→D0pK-
Ξb0→Λc+K-
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Other B → charm states: baryons
LHCb, Phys.Rev. D89 (2014) 3, 032001
Amplitude analysis of Λb → D pπ decay.
Interesting spectroscopy, preparation for Λ b → D0pK (for γ)
0
Λc(2880)
Λc(2940)
Λc(2940): mass very close to m(D*)+m(p). Exotic candidate: molecule/pentaquark
Need to measure quantum numbers. Should be possible with 3 fb -1.
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A nice by-product: new Λb states
Λb → Λcπ signal is so large that allows one to use it for b baryon spectroscopy
Discovery of two excited Λb baryons (Λb*(5912) and Λb*(5920)) decaying to Λbπ+π-.
First observation of orbital excitations of beauty baryons.
18±5 events
5.2σ
53±8 events
10.2σ
Phys. Rev. Lett. 109, 172003 (2012)
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Amplitude analysis tools
All of this is cool and exciting, but doing the amplitude analyses is usually
still a challenge. Need efficient tools.
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Laura++ package (T. Latham et al.)
Dalitz plot fits.
Developed for BaBar, used in many
analyses at LHCb.
Still something to do:
- Principally 2D (only 3-body)
- Only scalar states so far.
Now developing the fit model
for baryonic decays
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EvtGen
Famous generator package,
Warwick took responsibility of.
Many improvements, incl.
ones for amplitude description
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Meerkat: estimation of multidimensional PDFs
A very common problem for amplitude analyses (and not only) is functional representation
of scattered data (PDF estimation). E.g. efficiency from simulated sample, background, etc.
Especially troublesome in multiple dimensions.
For Λb → D0pπ analysis (5D): a technique using kernel density, which can be applied as a
correction to some approximate shape
Hierarchy of PDFs of increasing
dimensionality. Optimise bias/fluctuations,
correct for boundary effects
1D θp
2D Dalitz
1D φp
1D φDK
3D angular
5D full phase space
A.P., arXiv:1411.5528 (to appear in JINST)
http://meerkat.hepforge.org
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What can we expect in the future?
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With 3 fb-1 data at LHCb (Run 1, 2011-2012) , σ(γ)≈10°.
After Run 2, expect 3-4 times larger dataset. Same modes as now
(+ some additional DK*, DKππ), expect σ(γ)≈4°.
Many new possibilities can still to be tried, sensitivity to be determined:
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B → D*K, D* → Dπ0, Dγ (partially or fully reconstructed)
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B baryons
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Four-body D modes (D → KKππ, 4π, KSπππ0)
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Double Dalitz plot analysis B → DKπ, D → Ksππ
Precision of strong-phase parameters from CLEO will start to limit measurement
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BES-III: 4 times larger sample
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cτ-factory projects (Cabibbo lab, Italy; Novosibirsk, Russia)?
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BES-III: preliminary results of Ksππ phase
2.9 fb-1 data sample at e+e- → ψ(3770) → DD
Precision 1.5-2 times better than CLEO-c. Expect similar gain in γ contribution
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Summary
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Amplitude analyses are effective tools that can be used in many
heavy flavour measurements.
Dalitz plot analyses of the neutral D is a very interesting particular case:
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Can be done completely model-independently
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Probes D0-D0 admixture found in many important cases:
–
Measurement of CKM phase γ
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Indirect CP violation with neutral B (angle β)
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Charm mixing and CP violation in mixing
Dalitz analyses of charmed B decays are another interesting area,
both for γ and charm spectroscopy.
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