Review of recent Heavy Flavour Physics results from the ATLAS experiment

Recent ATLAS B-Physics results at 7 TeV centre-of-mass energy at the Large Hadron Collider (LHC) at CERN include the measurements of B production cross-sections and the angular analyses of the decays Bd → K∗0μ+μ−, Bs → J/ψφ and Λb → Λ0 J/ψ . All measurements done so far are in good agreement with Standard Model predictions.


Introduction
The ATLAS experiment [1] at the Large Hadron Collider (LHC) [2] accelerator at CERN recorded an integrated luminosity of 4.9 fb −1 of pp collisions at a centre-of-mass energy of 7 TeV in 2011.This dataset has been used to measure several B meson and baryon production and decay properties.
Measurements of the b-hadron production cross-section in proton-proton collisions at the LHC provide further tests of QCD calculations for heavy-quark production at higher centre-of-mass energies and in wider transverse momentum (p T ) and rapidity (y) ranges, thanks to the extended coverage and excellent performance of the LHC detectors.In these proceedings we summarise the measurement of the B + production cross-section in pp collisions at √ s = 7 TeV as a function of B + transverse momentum and rapidity, using the decay channel B + → J/ψK + → μ + μ − K + [3].
Within the Standard Model the decay B 0 d → K * 0 μ + μ − occurs via loop diagrams that mediate the transition b → s + − and therefore has a small branching fraction of (1.06 ± 0.1) • 10 −6 .Angular distributions of the 4-particle final state, as well as the decay amplitudes, are sensitive to physics beyond the Standard Model, mainly as a result of the interference of new diagrams with the Standard Model diagrams [4].In thee proceedings we summarise the measurement of the lepton forward-backward asymmetry A FB in bins of the di-muon invariant mass q 2 and compare the results to theoretical predictions [5] .
New phenomena beyond the predictions of the Standard Model (SM) may alter CP violation in B-decays.A channel that is expected to be sensitive to new physics contributions is the decay B 0 s → J/ψφ.CP violation in the B 0 s → J/ψφ decay occurs due to interference between direct decays and decays occurring through B 0 s − B 0 s mixing.The oscillation frequency of B 0 s meson mixing is characterized by the mass difference Δm s of the heavy (B H ) and light (B L ) mass eigenstates.The CPviolating phase φ s is defined as the weak phase difference between the B 0 s − B 0 s mixing amplitude and the b → ccs decay amplitude.In the absence of CP violation, the B H state would correspond exactly to the CP-odd state and the B L to the CP-even state.In the SM the phase φ s is small and can be related to CKM quark mixing matrix elements via the relation φ s −2β s , with β s = arg[−(V ts V * tb )/(V cs V * cb )]; a value of φ s −2β s = −0.0368± 0.0018 rad is predicted in the SM [6].Many new physics models predict large φ s values whilst satisfying all existing constraints, including the precisely measured value of Δm s [7].Another physical quantity involved in B 0 s −B 0 s mixing is the width difference ΔΓ s = Γ L −Γ H of B L and B H which is predicted to be ΔΓ s = 0.087 ± 0.021 ps −1 [8].Physics beyond the SM is not expected to affect ΔΓ s as significantly as φ s .Extracting ΔΓ s from data is nevertheless useful as it allows theoretical predictions to be tested.The ATLAS results on these measurements are published in [9] and summarised here.
The experimental measurement of the parity violating decay asymmetry parameter, α b , for the weak decay Λ 0 b → J/ψ(μ + μ − )Λ 0 (p + π − ) [10] is also summarised here.Several models have been deployed to predict the value of α b .One assumption is that the parameter can be extracted by representing the Λ 0 b → J/ψ(μ + μ − )Λ 0 (p + π − ) as a factorized hard scattering coupled with universal hadron distribution amplitudes.In the kinematic domain of the Λ 0 b produced in the LHC there is a considerable confidence that the hard scattering function can be accurately calculated in perturbative QCD.Models of this type suggest α b values in the vicinity of -0.2 [11].Contrary to this prediction, models based of a Heavy Quark Effective Theory (HQET) give a value near 0.8 [12].

The ATLAS detector
The ATLAS experiment [1] uses a general-purpose detector consisting of an inner tracker, a calorimeter and a muon spectrometer.ATLAS uses a right-handed coordinate system (x, y, z) with its origin at the nominal interaction point.The z-axis is along the beam pipe, the x-axis points to the centre of the LHC ring and the y-axis points upward.Cylindrical coordinates (r, φ) are used in the transverse plane, φ being the azimuthal angle around the beam pipe.The pseudorapidity η is defined as η = − ln[tan(θ/2)], where θ is the polar angle.
The inner detector (ID) directly surrounds the interaction point; it includes a silicon pixel detector (Pixel), a silicon microstrip detector (SCT) and a transition radiation tracker (TRT), and is embedded in an axial 2 T magnetic field.The ID covers the range |η| < 2.5 and is enclosed by a calorimeter system containing electromagnetic and hadronic sections.
The calorimeter is surrounded by a large muon spectrometer (MS) inside an air-core toroidal magnet system that contains a combination of monitored drift tubes (MDTs) and cathode strip chambers (CSCs), designed to provide precise position measurements in the bending plane in the range |η| < 2.7.In addition, resistive plate chambers (RPCs) and thin gap chambers (TGCs) with a coarse position resolution but a fast response time are used primarily to trigger muons in the ranges |η| < 1.05 and 1.05 < |η| < 2.4, respectively.RPCs and TGCs are also used to provide position measurements in the non-bending plane and to improve pattern recognition and track reconstruction.Momentum measurements in the MS are based on track segments formed in at least two of the three stations of the MDTs and the CSCs.
The ATLAS trigger system [13] has three levels: the hardware-based Level-1 trigger and the twostage High Level Trigger (HLT), comprising the Level-2 trigger and Event Filter (EF).At Level-1, the muon trigger searches for patterns of hits satisfying different p T thresholds using the RPCs and TGCs.The region-of-interest (RoI) around these Level-1 hit patterns then serves as a seed for the HLT muon reconstruction, in which dedicated algorithms are used to incorporate information from both the MS and the ID, achieving a position and momentum resolution close to that provided by the offline muon reconstruction.

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This analysis [3] is based on data collected at the LHC during the proton-proton running period in the early 2011 (April-August) with a dimuon trigger that required the presence of at least two opposite sign muon candidates with p T > 4 GeV, an invariant mass compatible with a J/ψ and coming from a common vertex.Selected events are required to have occurred during stable LHC beam conditions and the ID, as well as the MS, must have been fully operational.The collected data correspond to an integrated luminosity of 2.4 fb −1 with an uncertainty of 1.8%.
In the analysis two Monte Carlo (MC) samples are used, which simulate respectively the signal B ± → J/ψ K ± → μ + μ − K ± and the backgrounds from b b production, with b b → J/ψ X → μ + μ − X, which are relevant for the analysis.Both samples were generated with Pythia 6 using the 2011 ATLAS tune.The response of the ATLAS detector was simulated using Geant4.Additional pp interactions in the same and nearby bunch crossings (pile-up) were included in the simulation.
The differential cross-section for B + meson production in pp collisions times branching ratio to the final state is given by where B is the total branching ratio of the signal decay, which is (6.03 ± 0.21) × 10 −5 , obtained by combining the world-average values of the branching ratios for B + → J/ψ K + and J/ψ → μ + μ − , N B + is the number of B + → J/ψ K + signal decays produced, L is the integrated luminosity of the data sample and Δp T , Δy are the widths of p T and y intervals.Assuming that B + and B − mesons are produced in equal numbers, N B + is derived from the average yield of the two reconstructed charged states in a (p T , y) interval, after correcting for detector effects and acceptance, where N B ± reco is the number of reconstructed signal events, obtained from data with a fit to the invariant mass distribution of B ± candidates, A is the acceptance of the kinematic selection of the final-state particles of the signal decay, obtained from MC simulation, and ε B + , ε B − are the reconstruction efficiencies for the B ± signal decays.The reconstruction efficiencies for B + and B − are obtained from MC simulation, corrected using data-driven methods.
The number of reconstructed B ± mesons is obtained using a binned maximum likelihood fit to the invariant mass distribution of the selected candidates.The total number of signal B ± events observed in data in the full p T and y range covered by the analysis, 9 GeV < p T < 120 GeV and |y| < 2.25, before acceptance and efficiency corrections, is about 125600.These events populate four intervals in |y| and eight intervals in p T for the differential cross-section measurement.The acceptance correction, A, has a small dependence on y and ranges from 4% to 85% from the low to the high p T intervals.The efficiency ε B + has a dependence on both y and p T and ranges from 25% to 40%.The relative difference between the efficiencies for reconstructing B + and B − mesons, (ε B + − ε B − )/ε B + , has a dependence on p T and ranges from 5% to 2%.
Various sources of systematic uncertainty on the measurement of the B + production cross-section are considered.In most intervals, the systematic uncertainty dominates.
Using eq. ( 1), the differential cross-section for B + production times the total branching ratio B is obtained as a function of p T and y of the B + meson and the results are shown in figure 1, averaged over each (p T , y) interval.The double-differential cross-section is integrated over p T to obtain the differential cross-section dσ/dy, or over rapidity to obtain dσ/dp T , and results are reported in figure 2. Powheg and MC@NLO predictions are compared with the double-differential cross-section measurement in figure 1.The data are in good agreement with Powheg in all rapidity intervals.MC@NLO, however, predicts a lower production cross-section at low p T and a p T spectrum that is softer than the data for |y| < 1 and harder than the data for |y| > 1.
The FONLL prediction is compared with the measured differential cross-section dσ/dp T in figure 2a.In this figure, the results from CMS for B + meson production as a function of p T , covering the rapidity range |y| < 2.4, are shown for comparison.The FONLL prediction is in good agreement with the data concerning the behaviour in rapidity and p T , within the theoretical uncertainties.All available predictions for dσ/dy are compared with data in figure 2b.The measured cross-section has a small rapidity dependence and is in agreement with the predictions within their uncertainties.The theoretical uncertainties in all cases are large (∼30%) and are similar for the Powheg, MC@NLO and FONLL predictions.
The integrated B + production cross-section in the kinematic range 9 GeV < p T < 120 GeV and |y| < 2.25 is: The FONLL prediction, with its theoretical uncertainty from the renormalisation and factorisation scale and the b-quark mass, is: where f¯b →B + = (40.1 ± 0.8)% is the world-average value for the hadronisation fraction.The corresponding predictions of Powheg and MC@NLO are 9.4 μb and 8.8 μb, respectively, with theoretical uncertainties similar to the FONLL prediction.

EPJ Web of Conferences
00009-p.4The results are reported for B + meson production, but are derived from both charged states, taking into account the different reconstruction efficiencies for B + and B − , under the assumption that in the phase space accessible by this measurement the B + and B − production cross-sections are equal; this assumption is in agreement with the predictions of NLO Monte Carlo generators and is also valid within the precision of the measurement.

Angular analysis of the decay B
The decay B 0 d → K * 0 μ + μ − with K * 0 → K + π − is described by four kinematic variables: one is the invariant mass q 2 of the di-muon system and the other three are angles describing the geometrical configuration of the final state as shown in figure 3: θ L is the angle between the μ + and the direction opposite to the B 0 d in the di-muon rest frame, θ K is the angle between the K + and the direction opposite to the B 0 d in the K * 0 rest frame, and φ is the angle between the plane defined by the two muons and the plane defined by the kaon-pion system in the B 0 d rest frame.In the case of the B 0 d the angles θ L and θ K are defined with respect to the μ − and the K − , respectively.When the amount of data is insufficient to study the 4-differential decay rate, the differential decay rate is projected from the four kinematic variables into the 2-dimensional distributions d 2 Γ/dq 2 dcos θ L and d 2 Γ/dq 2 dcos θ K by integrating over the two other variables.These distributions are binned in intervals of q 2 , and the values of the K * 0 longitudinal polarisation fraction F L and of the lepton forward-backward asymmetry A FB are extracted, averaged in the q 2 bins [5] .This analysis uses 4.9 fb −1 of data from pp-collisions at √ s = 7 TeV collected in 2011.Data are only used if both the ID and MS subsystems were fully operational and the LHC proton beams were stable.
Monte Carlo events have been generated with Pythia for the signal decay channel B 0 d → K * 0 μ + μ − , the resonant background decay channel B 0 d → K * 0 J/ψ and generic b b and cc production with two muons in the final state.Furthermore a sample of Drell-Yan events has been generated.
Given the increasing luminosity during the data taking period, several single-muon and di-muon triggers are used to select the events, with different transverse momentum thresholds.The main triggers select di-muon events requiring both muons to have p T (μ) > 4 GeV, or alternatively p T (μ 1 ) > 6 GeV and p T (μ 2 ) > 4 GeV.The high-rate triggers were prescaled at higher luminosity.Monte Carlo studies show, that the trigger efficiency relative to the offline selection is 96 %.
Each event has to contain at least one reconstructed primary vertex with a minimum of four associated ID tracks with p T > 0.5 GeV, and is required to have at least two muon candidates with opposite charge.The K * 0 /K * 0 → K ± π ∓ candidates are reconstructed from all pairs of oppositely charged particles with p T > 0.5 GeV and |η| < 2.5 that are not identified as muons.For the reconstruction of B 0 d → K * 0 μ + μ − candidates, all combinations of di-muon pairs and K * 0 → K + π − candidates are considered.Using these requirements, a total of approximately 64 • 10 6 candidates are selected in the invariant mass region of 4600 MeV < m(Kπμμ) < 5900 MeV.In order to avoid background from events containing J/ψ and ψ(2S ), regions in di-muon mass are excluded which cover 3σ around the J/ψ → μ + μ − and ψ(2S ) → μ + μ − decay peaks.After removing those events, a total of approximately 23 • 10 6 candidates are selected.
We select events in the mass region 4600 MeV < m(Kπμμ) < 5900 MeV and are left with 4 466 candidates in the full q 2 range, after the optimised selection.The full q 2 range is defined as the three continuous intervals obtained by removing the J/ψ and ψ(2S ) regions as discussed earlier from the interval 1.00 GeV 2 < q 2 < 19.00 GeV 2 .
The values for A FB and F L are extracted by performing a sequential unbinned maximum likelihood fit, where in a first step the invariant Kπμμ mass distribution is fitted, then the resulting parameters are fixed, and in a second step -where the signal and background yields are fixed by the previous fitthe angular distributions are fitted.
The differential decay rate of B 0 d → K * 0 μ + μ − is parametrized by the invariant di-muon mass q 2 and the three helicity angles θ L , θ K and φ in the rest frame of the four particle final state.At a given EPJ Web of Conferences 00009-p.6 including statistical and systematic uncertainties, compared to theoretical predictions calculated for the limits of small and large values of q 2 including theoretical uncertainties [5] .
q 2 the integration of the differential decay rate over θ K and φ gives 1 Γ and the integration of the differential decay rate over θ L and φ yields 1 Γ Fixing the parameters obtained in the invariant mass fit, the likelihood function for the angular distributions is written as where the A's denote the probability density functions of the angular distributions of cos θ K and cos θ L for the signal and the background.The angular distributions of the signal are given by Equations ( 3) and (4).To take into account angular detector efficiencies due to trigger, event reconstruction, detector effects and the selection cuts, the angular signal distributions are weighted by acceptance maps α K and α L , determined for cos θ K and cos θ L , respectively.The parameters A FB and F L are extracted in five q 2 bins from 2.00 GeV 2 to 19.00 GeV 2 and in the wider bin 1.00 GeV 2 < q 2 < 6.00 GeV 2 .The final results of the unbinned maximum likelihood fit including statistical and systematic uncertainties are summarised in Table 1.In figure 4 the results for A FB and F L are compared to Standard Model expectations.The theoretical expectations have been calculated for the limits of small and large vector meson energy; no expectation is given for the central q 2 region.
Table 1.Summary of the fit results for the different bins of q 2 .Number of signal events N sig from the mass fit and its statistical uncertainty, forward backward asymmetry A FB and longitudinal polarisation F L for different bins in q 2 including statistical and systematic uncertainties [5] .

Flavour-tagged time dependent angular analysis of the B 0 s → J/ψφ decay
The data used for this analysis [9] were collected during a period of rising instantaneous luminosity at the LHC, and the trigger conditions varied over this time.The triggers used to select events for this analysis are based on identification of a J/ψ → μ + μ − decay, with either a 4 GeV p T threshold for each muon or an asymmetric configuration that applies a p T threshold beyond 4 GeV p T to one of the muons and accepting the second muon with p T as low as 2 GeV.Monte Carlo simulation is used to study the detector response, estimate backgrounds and model systematic effects.For this study, 12 million simulated B 0 s → J/ψφ events were generated using Pythia tuned with recent ATLAS data.No p T cuts were applied at the generator level.In order to take into account the varying trigger configurations during data-taking, the MC events were weighted to have the same trigger composition as the collected collision data.Additional samples of the background decay B 0 d → J/ψK 0 * as well as the more general bb → J/ψX and pp → J/ψX backgrounds were also simulated using Pythia.
Events passing the trigger and the data quality selections are required to pass the following additional criteria: the event must contain at least one reconstructed primary vertex built from at least four ID tracks and at least one pair of oppositely charged muon candidates.The candidates for φ → K + K − are reconstructed from all pairs of oppositely charged particles with p T > 0.5 GeV and |η| < 2.5 that are not identified as muons.Candidates for B 0 s → J/ψ(μ + μ − )φ(K + K − ) are sought by fitting the tracks for each combination of J/ψ → μ + μ − and φ → K + K − to a common vertex.In total 131k B 0 s candidates are collected within a mass range of 5.15 < m(B 0 s ) < 5.65 GeV used in the fit.The determination of the initial flavour of neutral B-mesons can be inferred using information from the other B-meson that is typically produced from the other b quark in the event, referred to as the Opposite-Side Tagging (OST).To study and calibrate the OST methods, the decays of B ± → J/ψK ± can be used, where flavour of the charge of the B-meson at production is provided by the kaon charge.Events from the entire 2011 run period satisfying the same data quality selections as previously described are used.
An unbinned maximum likelihood fit is performed on the selected events to extract the parameters of the B 0 s → J/ψ(μ + μ − )φ(K + K − ) decay.The fit uses information about the reconstructed mass m, the measured proper decay time t, the measured mass and proper decay time uncertainties σ m and σ t , the tag probability, and the transversity angles Ω of each B 0 s → J/ψφ decay candidate.There are three transversity angles; Ω = (θ T , ψ T , φ T ), which are defined in the rest frames of the final-state particles.

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The x-axis is determined by the direction of the φ meson in the J/ψ rest frame, the K + K − system defines the xy plane, where p y (K + ) > 0. The three angles are defined: • θ T , the angle between p(μ + ) and the xy plane, in the J/ψ meson rest frame • φ T , the angle between the x-axis and p xy (μ + ), the projection of the μ + momentum in the xy plane, in the J/ψ meson rest frame • ψ T , the angle between p(K + ) and −p(J/ψ) in the φ meson rest frame The likelihood function is defined as a combination of the signal and background probability density functions as follows: where N is the number of selected candidates, w i is a weighting factor to account for the trigger efficiency, f s is the fraction of signal candidates, f B 0 is the fraction of peaking B 0 meson background events calculated relative to the number of signal events; this parameter is fixed in the likelihood fit.
The mass m i , the proper decay time t i and the decay angles Ω i are the values measured from the data for each event i. F s , F B 0 and F bkg are the probability density functions (pdf) modelling the signal, the specific B 0 background and the other background distributions, respectively.The full simultaneous maximum likelihood fit contains 25 free parameters.This includes the nine physics parameters: ΔΓ s , φ s , Γ s , |A 0 (0)| 2 , |A (0)| 2 , δ || , δ ⊥ , |A S | 2 and δ S .The other parameters in the likelihood function are the B 0 s signal fraction f s , the parameters describing the J/ψφ mass distribution, the parameters describing the B 0 s meson decay time plus angular distributions of background events, the parameters used to describe the estimated decay time uncertainty distributions for signal and background events, and scale factors between the estimated decay time and mass uncertainties and their true uncertainties.In addition to this there are also 82 nuisance parameters describing the background and acceptance functions that are fixed at the time of the fit.
The number of signal B 0 s meson candidates extracted from the fits is 22670 ± 150.The results for the measured physics parameters of the simultaneous unbinned maximum likelihood fit are given in Table 2.
Table 2. Fitted values for the physical parameters along with their statistical and systematic uncertainties [9].Systematic uncertainties are assigned by considering several effects that are not accounted for in the likelihood fit: Inner Detector alignment, angular acceptance method, trigger efficiency, fit model, signal and background mass model, resolution model, background lifetime and background angles model, B d contribution, tagging uncertainties.For each variable, the total systematic error is obtained adding in quadrature the different contributions.

Parameter Value
The pdf describing the B 0 s → J/ψφ decay is invariant under the following simultaneous transformations: ΔΓ s has been determined to be positive, therefore there is a unique solution.Uncertainties on individual parameters have been studied in details in likelihood scans.Figure 5 shows the likelihood contours in the φ s -ΔΓ s plane.
[rad] Likelihood contours in φ s -ΔΓ s plane.The blue and red contours show the 68% and 95% likelihood contours, respectively (statistical errors only).The green band is the theoretical prediction of mixing-induced CP violation [9].
The behaviour of the amplitudes around their fitted values is as expected, however the strong phases are more complicated.The behaviour of δ ⊥ appears gaussian and therefore it is reasonable to quote δ ⊥ = 3.89 ± 0.47(stat) rad.For δ ⊥ − δ S the likelihood scan shows a minimum close to π, however it is insensitive over the rest of the scan at the level of 4.3σ.Therefore the measured value of the difference δ ⊥ − δ S is only given as 1σ confidence interval [3.02-3.25]rad.δ || shows normal gaussian behaviour around the minimum however the systematic pull plots show unusual behaviour so it is also given in the form of a 1σ confidence interval [3.04-3.23]Due to the parity conservation in the strong interaction, strongly-produced Λ 0 b can only be polarized in a direction n which is perpendicular to the Λ 0 b momentum.The unit vector n is chosen to point in EPJ Web of Conferences the direction of a cross-product of the beam direction and the Λ 0 b momentum.There is an ambiguity in choice of the beam direction, since LHC is a pp collider.This analysis uses the positive z-axis direction of the ATLAS coordinate system for the Λ 0 b candidates and the negative z-axis for Λ0 b (to preserve symmetry between Λ 0 and Λ0 given by the orientation of the ATLAS magnetic field).The Λ 0 b decay, as well as the subsequent decays of Λ 0 and J/ψ, are 2-body decays, and therefore each of them can be parametrized by a polar and azimuthal angle in their respective rest frames.A definition of the decay angles is shown in figure 6. b rest frame.The angles θ 1 and φ 1 are the polar and azimuthal angles of the proton in the Λ 0 rest frame with respect to the Λ 0 direction in the Λ 0 b rest frame.Similarly, θ 2 and φ 2 are polar and azimuthal angles of μ + in the J/ψ rest frame with respect to the J/ψ direction in the Λ 0 b rest frame.The azimuthal angles, φ 1 and φ 2 , are measured in the Λ 0 and J/ψ rest frame right-handed coordinate systems, (x 1 , y 1 , z 1 ) and (x 2 , y 2 , z 2 ), respectively.The z 1,2 -axes are aligned with the direction of Λ 0 and J/ψ, respectively, and the x 1,2 -axes lie in the plane containing n and the Λ 0 or J/ψ momenta.With this definition, the angle φ 1 + φ 2 is actually the angle between the Λ 0 and J/ψ decay planes [10].
Taking λ Λ and λ J/ψ to represent the helicity of Λ 0 and J/ψ, the considered decay can be described by four helicity amplitudes A(λ Λ , λ J/ψ ): ), which should be normalized to unity: The full angular pdf of the decay angles collection Ω = (θ, φ, θ 1 , φ 1 , θ 2 , φ 2 ) is: where f 1i ( A) are bilinear combinations of the helicity amplitudes, A ≡ (a + , a − , b + , b − ), f 2i is one of the following expressions: Pα Λ , P, α Λ or 1, with α Λ being the decay asymmetry parameter for the decay Λ 0 → pπ − , and P is the Λ 0 b polarization.The value of α Λ is known with high precision, α Λ = 0.642 ± 0.013, and α Λ = −0.71± 0.08 for Λ0 → p − π + .Since there is no evidence of CP violation in Λ 0 and Λ0 decay and the parameter for Λ 0 is more precisely determined, the value of −0.642 ± 0.013 is used for Λ0 in this analysis.The minus sign is required by CP conservation.The ICNFP 2013 00009-p.11F i (Ω) are orthogonal functions of the decay angles.The concrete forms of the f 1i ( A) and F i (Ω) functions are given in [10].
If CP is conserved, the pdf's of Λ 0 b and Λ0 b decay have exactly the same form.Therefore, assuming CP conservation, the Λ 0 b and Λ0 b samples are combined to measure the decay asymmetry parameter α b and the helicity amplitudes with better precision.The α b parameter is related to the helicity amplitudes as follows: There are nine unknown parameters with a real value in the pdf: four complex helicity amplitudes, , each with a magnitude and a phase, and polarization P.However, only six out of these eight helicity amplitude parameters are independent, taking into account the normalization constraint and the arbitrariness of the common phase, due to which only the differences between the four phases are relevant.The following five parameters are chosen to define the model: This analysis [10] uses 7 TeV collision data collected in 2011 using single-muon and J/ψ triggers.The corresponding integrated luminosity is 4.6 fb −1 .Since the rate from the low-p T muon triggers was too high, prescale factors were applied to reduce the output rate.The transverse momentum threshold for single muon triggers is 18 GeV.The J/ψ triggers are di-muon triggers which in addition require that the muons have an opposite charge, come from a common vertex and and that the di-muon mass is in the interval 2.5 GeV < m μμ < 4.3 GeV.The majority of the sample was collected by the J/ψ trigger with a p T threshold of 4 GeV applied to both muons, the lowest p T -threshold trigger unprescaled in the 2011 data taking period.Altogether, the used triggers collected muons with p T spectrum peaking at about 5 GeV with minimum p T above 2.5 GeV.
A Monte Carlo sample of 5 million signal events is used to study the effect of the efficiency and acceptance of the detector.The sample is generated using the Pythia6.4MC generator and the events are filtered such that each event contains a signal decay with the muons having transverse momenta above 2.5 GeV.In addition to the Λ 0 b MC samples, B 0 d → J/ψ(μ + μ − )K 0 S (π + π − ) and b b → J/ψ + X MC samples are also generated using Pythia to optimize the selection cuts and understand the sources of background.
The decay Λ 0 b → J/ψ(μ + μ − )Λ 0 (p + π − ) has a cascade topology.The di-muon candidates are accepted if the J/ψ vertex-refitted invariant mass lies in the range 2.8 GeV < m μμ < 3.4 GeV.The di-hadron candidates are accepted if the invariant mass is in the range 1.08 GeV < m pπ < 1.15 GeV.The masses of a proton and a pion are assigned to the tracks when the invariant mass is calculated; pπ − and pπ + combinations are considered so that both Λ 0 and Λ0 candidates are accepted.The muon and hadronic track pairs are then refitted with the constraint of a Λ 0 b → J/ψ(μ + μ − )Λ 0 (p + π − ) topology.After the selection, there are in total 1548 Λ 0 b and Λ0 b candidates (including background) in the signal region.
The helicity amplitudes and the α b parameter are extracted from the expected value of each of the F i variables in the pdf, as described in [10].As the combinatorial background changes linearly with the Λ 0 b mass, its contribution to the measured F i values can be estimated using events in the invariant mass sidebands.Two mass windows define the sidebands: 5400 < m J/ψΛ 0 < 5520 MeV is chosen as the left sideband and 5720 < m J/ψΛ 0 < 5840 MeV as the right one.These two sidebands have almost the same distance to the mass of Λ 0 b and have the same size as the signal mass window, so the background contribution to the F i values in the central region can be simply estimated as an average of the values in the two sidebands.The estimated background contribution is subtracted from the measured value of F i .
The uncertainty of the parameters are calculated by finding the range that satisfies χ 2 − χ 2 min < 1.With the current data statistics, values of the relative phases, Δ + and Δ − , cannot be determined with sufficient precision and are consistent with the entire allowed range, [−π, π].However, it is found that their large uncertainties have a small effect on the determination of α b , k 0 and k 1 .Figure 7 shows the χ 2 min as a function of the assumed α b parameter, under the condition that α b is fixed in the fit.The minimum of this conditional χ 2 min curve gives the central value of α b , α best b , and the corresponding χ 2 value is 3.03.
The absolute values of the helicity amplitudes were calculated from the fitted parameters and the statistical uncertainties were calculated using error propagation: |a + | = 0.17 +0.12 −0.17 in quadrature the statistical and systematic uncertainties, the observed value of α b is consistent with the recent measurement of LHCb at the level of one standard deviation, however, it is not consistent with the expectation from pQCD [α b = −(0.14∼ 0.18)], and HQET (α b = 0.78) at a level of about 2.5 and 2.9 standard deviation, respectively.A more precise determination of α b and of the decay amplitudes will be possible with the sample of data collected by the ATLAS experiment in 2012.

Conclusions
Thanks to its good inner tracking and muon detector systems, as well as the large acceptance triggers, ATLAS is able to contribute significant results in heavy flavour physics.Recent analyses, still based on 2011 data, measured the differential B + production cross-sections and the angular distributions in the decays B 0 d → K * 0 μ + μ − , B 0 s → J/ψφ and Λ 0 b → J/ψ(μ + μ − )Λ 0 (p + π − ).All measurements done so far are in good agreement with Standard Model predictions, or at least, don't show any significant deviation from the predictions.Additional statistics from the 2012 run will soon reduce statistical errors on all results.

Figure 1 .
Figure1.Double-differential cross-section of B + production as a function of p T and y, averaged over each (p T , y) interval and quoted at its centre[3].The data points are compared to NLO predictions from Powheg and MC@NLO.The shaded areas around the theoretical predictions reflect the uncertainty from renormalisation and factorisation scales and the b-quark mass.

Figure 2 .
Figure2.(a) Differential cross-section of B + production vs p T , integrated over rapidity[3].The solid circle points with error bars correspond to the differential cross-section measurement of ATLAS with total uncertainty (statistical and systematic) in the rapidity range |y| < 2.25, averaged over each p T interval and quoted at its centre.For comparison, data points from CMS are also shown, for a measurement covering p T < 30 GeV and |y| < 2.4.Predictions of the FONLL calculation for b-quark production are also compared with the data, assuming a hadronisation fraction of fb →B + of (40.1 ± 0.8)% to fix the overall scale.Also shown is the ratio of the measured cross-section to the predictions of the FONLL calculation (σ/σ FONLL ).The upper and lower uncertainty limits on the prediction were obtained considering scale and b-quark mass variations.(b) Differential cross-section of B + production vs rapidity, integrated over p T .Points with error bars correspond to the differential cross-section measurement with total uncertainty (lines on the error bars indicate the statistical component) in the p T range 9 GeV < p T < 120 GeV, averaged over each rapidity interval and quoted at its centre.Powheg, MC@NLO and FONLL predictions are also given for comparison.The relevant uncertainties of the predictions of Powheg and MC@NLO are of the same order as for FONLL and are not shown.

Figure 4 .
Figure 4. (a) Forward-backward asymmetry A FB and (b) fraction of longitudinally polarised K * 0 mesons, F L , including statistical and systematic uncertainties, compared to theoretical predictions calculated for the limits of small and large values of q 2 including theoretical uncertainties[5] .

Figure 5 .
Figure 5. Likelihood contours in φ s -ΔΓ s plane.The blue and red contours show the 68% and 95% likelihood contours, respectively (statistical errors only).The green band is the theoretical prediction of mixing-induced CP violation[9].

Figure 6 .
Figure 6.Definition of the decay angles.The angle θ is the polar angle of the Λ 0 momentum measured from the normal direction n in the Λ 0 b rest frame.The angles θ 1 and φ 1 are the polar and azimuthal angles of the proton in the Λ 0 rest frame with respect to the Λ 0 direction in the Λ 0 b rest frame.Similarly, θ 2 and φ 2 are polar and azimuthal angles of μ + in the J/ψ rest frame with respect to the J/ψ direction in the Λ 0 b rest frame.The azimuthal angles, φ 1 and φ 2 , are measured in the Λ 0 and J/ψ rest frame right-handed coordinate systems, (x 1 , y 1 , z 1 ) and (x 2 , y 2 , z 2 ), respectively.The z 1,2 -axes are aligned with the direction of Λ 0 and J/ψ, respectively, and the x 1,2 -axes lie in the plane containing n and the Λ 0 or J/ψ momenta.With this definition, the angle φ 1 + φ 2 is actually the angle between the Λ 0 and J/ψ decay planes[10].