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CP Violation with bhadrons at LHCb
Laurence Carson, University of Edinburghon behalf of the LHCb collaboration
52nd Rencontres de Moriond, 22.03.17
CPV with b Hadrons: Why?β’ Sources of CPV beyond the Standard Model are needed to explain the large
matter/antimatter asymmetry observed in the universe.
β’ Decays of b hadrons are an excellent place to search for new sources of CPV, as there is a rich variety of possible decays, some of which exhibit considerable CPVeven in the SM.
β’ CPV in hadrons can be classified into three distinct types:
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(A) CPV in decay: difference in rate for a process and its charge conjugate, e.g. compare π΅+and π΅βdecays.
(B) CPV in mixing: difference in rate between e.g. π΅π β π΅π mixing vs π΅π β π΅π mixing.
(C) CPV in interference between mixing and decay: typically gives rise to several CPVobservables, requiring a time-dependent analysis of decay rates to disentangle them.
Menu of Results
β’ First measurement of the CP-violating phase ππ using π΅π
0 β π½/ππΎ+πΎβ decays with ππΎπΎ above the π 1020 region
β’ First measurement of the CKM angle Ξ³in the decay π΅β β π·0πΎββ
β’ Updated measurement of Ξ³ using a time-dependent analysis of the decays
π΅π 0 β π·π
Β±πΎβ
β’ Updated time-dependent measurement of CP-violating observables in the decays
π΅π0 β π+πβ and π΅π
0 β πΎ+πΎβ
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NEW!LHCb-PAPER-2017-008 (in preparation)
LHCb-CONF-2016-014
LHCb-CONF-2016-015
LHCb-CONF-2016-018
β’ The SM prediction for ππ , the CP-violating phase in π β π ππ transitions, is:
The CP-Violating Phase ππ
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β’ LHCb also published an amplitude analysis of π΅π 0 β π½/ππΎ+πΎβ decays with ππΎπΎ
above the π 1020 region, using 1/fb of data. However, Οs was not measured in this analysis.
PRD 91 (2015) 073007
Definition of helicity angles forπ΅π 0 β π½/ππΎ+πΎβ
β’ This prediction ignores corrections from penguin (loop) diagrams, which LHCbanalyses have shown to be small.
β’ LHCb has measured ππ using π΅π 0 β π½/ππΎ+πΎβ decays with ππΎπΎ in the π 1020
region, and with π΅π 0 β π½/ππ+πβ decays, yielding a combined value of
ππ = -10Β±39 mrad.
PLB 742 (2015) 38, JHEP 11 (2015) 082
PRL 114 (2015) 041801, PLB 736 (2014) 186
PRD 87 (2013) 072004
New LHCb Measurement of ππ β’ Now, a flavour-tagged, time-dependent amplitude analysis of π΅π
0 β π½/ππΎ+πΎβ
with ππΎπΎ above the π 1020 region has been performed, using the full 3/fb of Run1 data.
β’ Each vector or tensor resonance is allowed to contribute both CP-even and CP-odd decay amplitudes.
β’ Selection combines cut on a BDT classifier (combining kinematic/geometric variables and ΞΌ PID) and cuts on hadron PID.
β’ The reconstruction and selection efficiency vs decay time is measured on data,
using π΅π0 β π½/ππΎβ0(β πΎ+πβ) as a control channel.
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Yield = 33 200 Β± 240
Decay-time efficiency
LHCb-PAPER-2017-008 (in preparation) NEW!
New LHCb Measurement of ππ β’ The fit to π(π½/ππΎ+πΎβ) is used to provide sWeights that are then used in a multi-
dimensional fit to the decay time, ππΎπΎ and helicity angles.
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β’ For ππΎπΎ > 1.05 GeV, we measure ππ = 0.12Β±0.11Β±0.03 rad.
β’ Dominant systematics are from resonance modelling and background subtraction.
β’ Combining this with the previous LHCb measurements using π΅π 0 β π½/ππΎ+πΎβ and
π΅π 0 β π½/ππ+πβ yields ππ = 0.001Β±0.037 rad.
Fit projections in cos ππ½/π and in decay time,
for ππΎπΎ > 1.05 GeV
Fit projection in ππΎπΎ. S-wave is modelled using splines, the rest using Breit-Wigners
Ο(1020)
Ο(1680)f2β(1525)S-wave
Other f2
β’ The flavour tagging uses both opposite-side (OS) and same-side Kaon (SSK) taggers.
β’ Indirect constraints from the other CKM
parameters give πΎ = (65.3β2.5+1.0)Β°.
β’ Measurements of Ξ³ from B decays that are mediated only by tree-level transitions provide a βstandard candleβ for the Standard Model.
β’ This can be compared with Ξ³ values from B decays involving loop-level transitions,
such as π΅π,π 0 β βββ² decays (β = {πΎ, π}).
β’ This is the least well-constrained of the CKM angles. Combining all direct
measurements yields πΎ = (72.1β5.8+5.4)Β°, while the latest LHCb-only combination
(JHEP 12 (2016) 087) gives πΎ = (72.2β7.3+6.8)Β°.
The CKM Angle Ξ³
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β’ Significant difference between these would indicate New Physics contribution to the loop process.
β’ Experimental methods to measure Ξ³ can be classified into time-independent and time-dependent.
( )
CPV in π΅β β π·0πΎββ
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β’ LHCb is always seeking to improve the precision on Ξ³ by including new decay modes beyond the βclassicβ π΅β β π·πΎβ .
β’ Recently, LHCb made the first measurement of the CPV observables in the decay π΅β β π·πΎββ.
β’ The π·0 final states used are πΎβπ+, πΎ+πΎβ, π+πβ and πΎ+πβ (so-called ADS/GLW analysis) and the πΎββ is reconstructed in the πΎπ
0πβ final state.
β’ This analysis uses the full Run1 dataset, plus 1.0/fb of Run2 data (full 2015 dataset plus ~half of the 2016 dataset), giving a total of 4.0/fb.
β’ Time-independent measurements of Ξ³ exploit interference between π β π and π β π’ transitions in π΅β β π·0πΎβdecays. The exact analysis method depends on the D final state (use βDβ to stand for π·0 or π·0) .
LHCb-CONF-2016-014
CPV in π΅β β π·0πΎββ
β’ Geometric, kinematic and isolation variables are combined to create a BDT classifier, used alongside hadron PID cuts.
β’ CP observables are extracted via a simultaneous fit to the different Ddecay modes.
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Run1+2 data, π«π β π²βπ + (favoured decay)
β’ Here, the ratio of suppressed to favoured B(D) decay amplitudes is rB ei(Ξ΄B- Ξ³) (rD eiΞ΄D).
β’ Plan to follow preliminary result with analysis including full 2016 dataset.
β’ Sensitivity to Ξ³ comes from combining D decay modes, such as (ADS case):
Ξ³ from π΅π 0 β π·π
Β±πΎβ
β’ The fact that π΅π 0 and π΅π
0 can each decay to both π·π βπΎ+ and π·π
+πΎβ means that a flavour-tagged, time-dependent analysis of these decays can give access to Ξ³.
β’ LHCb recently updated this measurement of Ξ³, using the full Run1 dataset.
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β’ The π·π β is reconstructed in the πΎβπΎ+πβ, πβπ+πβ and πΎβπ+πβ final states.
β’ The flavour-specific control channel π΅π 0 β π·π
βπ+ is used to determine the decay-time-dependent efficiencies and the flavour-tagging performance, and to train the BDT classifier.
LHCb-CONF-2016-015
β’ A 3-dimensional fit is made to the π·π βπΎ+ mass, the π·π
β mass and the PID likelihood of the companion Kaon.
Ξ³ from π΅π 0 β π·π
Β±πΎβ
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β’ This 3D fit provides sWeights used to subtract the backgrounds in the time-dependent fit for the CPV observables.
β’ The CPV fit constrains Ξπ , ΞΞπ and Ξππ
to their HFAG averages.
β’ Both OS and SSK taggers are used.
π·π βπ+bkg Combinatorial bkgπ·π
Β±πΎβ
Decay-time acceptance
β’ The CPV observables fit gives:
Ξ³ from π΅π 0 β π·π
Β±πΎβ
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β’ From these observables, use e.g.
Can visualise CP asymmetry by comparing (folded) oscillations of π·π
βπΎ+ and π·π +πΎβ:
β’ Here, and πΏ is the strong phase difference.
β’ Compatibility of Ξ³ with the previous combined LHCb measurement is 2.2Ο.
Dominant systematic varies by parameter, e.g. π΄πππ‘ or correlations between observables
to obtain:
π·π +πΎβ π·π
βπΎ+
Ξ³ from π΅π,π 0 β ββ Decays
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β’ A flavour-tagged, time-dependent analysis of these two modes allows CPV observables to be measured:
β’ Decays such as π΅π0 β π+πβ
and π΅π 0 β πΎ+πΎβ receive
contributions from both tree and penguin diagrams.
β’ These CPV observables can then be used to constrain Ξ³ and ππ , under certain assumptions (U-spin symmetry) relating the strong interaction dynamics of the two decays.
β’ LHCb recently updated its measurement of these observables, using the full Run1 dataset.
β’ The control channel π΅π0 β πΎ+πβ is used to calibrate the flavour tagging.
β’ Only opposite-side taggers are used.
PLB 459 (1999) 306
LHCb-CONF-2016-018
Ξ³ from π΅π,π 0 β ββ Decays
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β’ This gives strong evidence (4.7Ο) of CPV in π΅π
0 β πΎ+πΎβ.
β’ Updated analysis is planned that will include same-side taggers and update constraints on Ξ³.
β’ Signal and backgrounds are parameterised in invariant mass, decay time and per-event mistag probability.
β’ In the time-dependent fit Ξπ,π , ΞΞπ,π and Ξππ,π are constrained to their HFAG averages.
π΅π0 β π+πβ π΅π
0 β πΎ+πΎβ
Summary
β’ LHCb has made the first measurement of ππ using π΅π 0 β π½/ππΎ+πΎβ
decays at high ππΎπΎ, giving a new LHCb combined value of ππ = 0.001Β±0.037 rad.
β’ LHCb is producing new results improving the constraints on Ξ³, both from tree-only decays and those involving loops.
β’ Another β3/fb of data will have been collected by the end of LHC Run2 (2018), allowing for more precise CPV measurements in existing channels, and for new channels to be explored for the first time.
β’ LHCb aims to achieve a combined precision on Ξ³ of β4Β° by the end of Run2, and <1Β° by the end of Run4 (2029).
β’ Stay tuned for more results in the near future!β First CPV analyses using Run2 data are starting to appear
β Many many more are in the pipelineβ¦ 15
Backups
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The LHCb Experimentβ’ Forward arm spectrometer, optimised for study of B and D decays.
β’ Collected 1/fb of data at ECM = 7 TeV in 2011, 2/fb at 8 TeV in 2012, and 2/fb at 13 TeV in 2015 & 2016.
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Key capabilities:β’ High trigger efficiency,
including on purely hadronic final states.
β’ Excellent Impact Parameter (IP) and Mass Resolution
β’ Hadronic PID over wide momentum range
Flavour Tagging
β’ Flavour tagging can be opposite side (OS) or same-side (SS).
β’ The tagging efficiency ππ‘ππ and the mistag
rate π are defined as:
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β’ The tagging power is then: ππππ = ππ‘ππ(1 β 2π)2
β’ The statistical uncertainty is proportional to: ππ π‘ππ‘ β1
πππππ
β’ At LHCb, ππππ is typically up to β5%.
The CKM Matrix
β’ The CKM matrix relates the quark flavour eigenstates (πβ², π β², πβ²) to the mass eigenstates π, π , π :
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Wolfenstein parameterisation
β’ The CKM triangle(s) come from the fact that the CKM matrix must be unitary.
β’ The CKM phase is the only source of CPV in (the quark sector of) the SM.
( , )
Efficiencies for π΅π 0 β π½/ππΎ+πΎβ
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β’ The angular and ππΎπΎ efficiencies are determined using simulated phase-space decays of π΅π
0 β π½/ππΎ+πΎβ.
Fit for π΅π 0 β π½/ππΎ+πΎβ
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β’ The sWeights obtained from the π½/ππΎ+πΎβ mass fit are used to perform a 5D fit to the decay time, ππΎπΎ and the three helicity angles.
β’ The PDF is:
with
β’ Here, Ξ© represents the three helicity angles, q is the flavour tag decision (+1, -1, or 0), and π΄π = 1.1 Β± 2.7 % is the π΅π
0 production asymmetry.
Fit for π΅π 0 β π½/ππΎ+πΎβ
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Left: π 1020 region Left: π(1020) regionRight: higher ππΎπΎ region Right: higher ππΎπΎ region
Other Results from π΅π 0 β π½/ππΎ+πΎβ
23
β’ For mKK > 1.05 GeV, we measure
(where π β‘π
π
π΄
π΄):
Results of fit to resonance structure. The dominant systematic is due to the modelling of the resonances themselves.
Fitted phase differences between transversity states (stat. error only)
Systematics for π΅π 0 β π½/ππΎ+πΎβ
24
Time-Integrated Ξ³ Methods
25
β’ Aside from Ξ³, have hadronic unknowns rB(D), Ξ΄B(D), where ratio of suppressed to favoured B(D) decay amplitudes is rB ei(Ξ΄B- Ξ³) (rD eiΞ΄D)
β’ Method to extract these hadronic unknowns (and Ξ³) depends on the D final state.
β’ Three main methods:
β’ GLW: D CP-eigenstate, e.g. pp, KK (Phys. Lett. B 253 (1991) 483, Phys. Lett. B 265 (1991) 172)
β’ ADS: D quasi-flavour-specific state, e.g. Kp, Kppp (Phys. Rev. Lett. 78 (1997) 257, Phys. Rev. D 63 (2001) 036005)
β’ GGSZ: D self-conjugate 3-body final state, e.g. KSpp, KSKK (Phys. Rev. D 68 (2003) 054018, Phys. Rev. D 70 (2004) 072003)
Fits for π΅β β π·0πΎββ
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Correlations & Systematics for π΅β β π·0πΎββ
27
Interpretation for π΅β β π·0πΎββ
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β’ The parameters ππ· and πΏπ· are constrained to their HFAG averages.
β’ The coherence factor π is estimated using a fit to the πΎπ0πβ mass distribution of
selected events, yielding π = 0.95 Β± 0.06.
Relations for π΅π 0 β π·π
Β±πΎβ
β’ These are the time-dependent decay rates.
β’ For decays to π, ππ is replaced
by π π, and π΄π by π΄ π.
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β’ These observables are related to the physics parameters by:
β’ Here, and πΏ is the strong phase difference.
Fits to π΅π 0 β π·π
βπ+
β’ 3D fit to π·π βπ+ mass, π·π
β mass and the PID likelihood of the companion Pion:
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β’ Decay-time fit, to give decay-time
acceptance for π΅π 0 β π·π
Β±πΎβ:
Decay-time acceptance
π΅π 0 β π·π
Β±πΎβ Tagging Calibration
β’ Each event has a predicted mistag probability, π.
β’ A linear calibration function is used:
β’ Calibrate using flavour-specific π΅π 0 β π·π
βπ+:
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Opposite-sideSame-side Kaon
Correlations & Systematics
for π΅π 0 β π·π
Β±πΎβ
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Confidence Levels for π΅π 0 β π·π
Β±πΎβ
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Fits of π΅π,π 0 β ββ
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π΅π 0 β πΎ+πΎβπ΅π
0 β π+πβπ΅π0 β πΎ+πβ
Correlations & Systematics for
π΅π0 β π+πβ and π΅π
0 β πΎ+πΎβ
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Constraints on Ξ³ from π΅π0 β π+πβ
and π΅π 0 β πΎ+πΎβ
β’ The CP observables measured in a time-dependent analysis of π΅π0 β π+πβ and
π΅π 0 β πΎ+πΎβ, using can be related to the physics parameters:
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β’ The parameters d and π are related to the βpenguin to tree ratioβ:
where
β’ To simplify the equations, we also define:
β’ If U-spin symmetry holds, then π = πβ² and π = πβ².
β’ This reduces the number of free parameters, making the system of equations soluble.
Constraints on Ξ³ from π΅π0 β π+πβ
and π΅π 0 β πΎ+πΎβ
β’ A previous LHCb paper derived constraints on Ξ³ using the CP observables measured
in a time-dependent analysis of π΅π0 β π+πβ and π΅π
0 β πΎ+πΎβ, using 1/fb of data.
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PLB 741 (2015) 1, JHEP 10 (2013) 183CP observable results with 1/fb:
βStandardβ analysis:
Extended analysis, incorporating information on
π΅π0 β π0π0 and
π΅+ β π+π0 decays from B-factories:
π = 0.5
π = 0.5
π parameterises the allowed amount of U-spin breaking
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