1 Introduction
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mydocument.bib \addbibresourcebibtex/bib/ATLAS.bib \addbibresourceacknowledgements/Acknowledgements.bib \AtlasTitleMeasurements of and production in collisions at = 8 TeV with the ATLAS detector \AtlasRefCodeBPHY-2015-03 \PreprintIdNumberCERN-EP-2016-193 \AtlasJournalJHEP \AtlasAbstractDifferential cross sections are presented for the prompt and non-prompt production of the hidden-charm states and , in the decay mode , measured using 11.4 fb of collisions at  TeV by the ATLAS detector at the LHC. The ratio of cross-sections is also given, separately for prompt and non-prompt components, as well as the non-prompt fractions of and . Assuming independent single effective lifetimes for non-prompt and production gives , while separating short- and long-lived contributions, assuming that the short-lived component is due to decays, gives , with the fraction of non-prompt produced via decays for  GeV being . The distributions of the dipion invariant mass in the and decays are also measured and compared to theoretical predictions.

1 Introduction

The hidden-charm state was discovered by the Belle Collaboration in 2003 [belleDisc] through its decay to in the exclusive decay . Its existence was subsequently confirmed by CDF [cdfDisc] through its production in collisions, and its production was also observed by the BaBar [babarDisc] and D0 [d0Disc] experiments shortly after. CDF determined [Abulencia:2006ma] that the only possible quantum numbers for were and . At the LHC, the was first observed by the LHCb Collaboration [lhcbObs], which finally confirmed its quantum numbers to be  [lhcbQN]. A particularly interesting aspect of the is the closeness of its mass,  [PDGBcTau], to the threshold, such that it was hypothesised to be a molecule with a very small binding energy [binding]. A cross-section measurement of promptly produced was performed by CMS [cmsMeas] as a function of , and showed the non-relativistic QCD (NRQCD) prediction [Artoisenet:2009wk] for prompt production, assuming a molecule, to be too high, although the shape of the dependence was described fairly well. A later interpretation of as a mixed state, where the is produced predominantly through its component, was adopted in conjunction with the next-to-leading-order (NLO) NRQCD model and fitted to CMS data, showing good agreement [chidd].

ATLAS previously observed the state while measuring the cross section of prompt and non-prompt meson production in the decay channel with 2011 data at a centre-of-mass energy  [BPHY-2013-06]. ATLAS later performed cross-section measurements for and decaying through the channel at and  [BPHY-2012-02b].

In this analysis, a measurement of the differential cross sections for the production of and states in the decay channel is performed, using fb of proton–proton collision data collected by the ATLAS experiment at the LHC at . The final state allows good invariant mass resolution through the use of a constrained fit, and provides a straightforward way of comparing the production characteristics of and states, which are fairly close in mass. The prompt and non-prompt contributions for and are separated, based on an analysis of the displacement of the production vertex. Non-prompt production fractions for and are measured, and the production ratios are measured separately for prompt and non-prompt components. The non-prompt results show that while the non-prompt data is readily described by a traditional single-effective-lifetime fit, there are indications in the non-prompt data which suggest introducing a two-lifetime fit with both a short-lived and long-lived component. Results are presented here based on both the single- and two-lifetime fit models. In the two-lifetime case, assuming that the short-lived non-prompt component of originates from the decays of mesons, the best-fit fractional contribution of the component is determined. The distributions of the dipion invariant mass in and decays are also measured. Comparisons are made with theoretical models and available experimental data.

2 The ATLAS detector

The ATLAS detector [PERF-2007-01] is a cylindrical, forward-backward symmetric, general-purpose particle detector. The innermost part of the inner detector (ID) comprises pixel and silicon microstrip (SCT) tracking technology for high-precision measurements, complemented further outwards by the transition radiation tracker (TRT). The inner detector spans the pseudorapidity111ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the -axis along the beam pipe. The -axis points from the IP to the centre of the LHC ring, and the -axis points upward. Polar coordinates are used in the transverse plane, being the azimuthal angle around the -axis. The pseudorapidity is defined in terms of the polar angle as , and the transverse momentum is defined as . The rapidity is defined as , where and refer to energy and longitudinal momentum, respectively. range and is immersed in a 2 T axial magnetic field. Enclosing the ID and the solenoidal magnet are the electromagnetic and hadronic sampling calorimeters, which provide good containment of the electromagnetic and hadronic showers in order to limit punch-through into the muon spectrometer (MS). Surrounding the calorimeters, the MS covers the rapidity range and utilises three air-core toroidal magnets, each consisting of eight coils, generating a magnetic field providing 1.5–7.5 Tm of bending power. The MS consists of fast-trigger detectors (thin-gap chambers and resistive plate chambers) as well as precision-measurement detectors (monitored drift tubes and cathode strip chambers).

The ATLAS detector uses a three-level trigger system in order to select 300 Hz of interesting events to be written out from the 20 MHz of proton bunch collisions. This analysis uses a dimuon trigger with the lowest available transverse momentum threshold of  GeV for each muon. The level-1 muon trigger finds regions-of-interest (RoIs) by searching for hit coincidences in layers of the muon trigger detectors inside predefined geometrical windows. The software-based two-stage high-level trigger (HLT) is seeded by the level-1 RoIs, and uses more precise MS and ID information to reconstruct the final muon trigger objects with a resolution comparable to the full offline reconstruction.

3 Event selection

Events used in this analysis are triggered by a pair of muons successfully fitted to a common vertex. The data sample corresponds to an integrated luminosity of 11.4 fb [Aaboud:2016hhf], collected at a proton–proton collision energy . Each muon candidate reconstructed offline is required to have good spatial matching to a trigger object, satisfying . Events where two oppositely charged muon candidates are reconstructed with pseudorapidity and transverse momenta are kept for further analysis only if the invariant mass of the dimuon system falls within of the mass of the meson,  MeV [PDGBcTau].

The two muon tracks are fitted to a common vertex with a loose cut on fit quality, . The dimuon invariant mass is then constrained to the mass, and the four-track vertex fit of the two muon tracks and pairs of non-muon tracks is performed to find candidates. The two non-muon tracks are assigned pion masses, and are required to have opposite charges and to satisfy the conditions  0.6 GeV, . Four-track candidates with fit probability are discarded.

Only combinations with rapidity within the range are considered in this analysis, with most of the contributing tracks measured within the barrel part of the detector where the tracking resolution is optimal. Then the transverse momenta of the candidates are required to be within the range  GeV GeV.

Further selection requirements are applied to the remaining combinations:

(1)

where is the angular distance between the momenta of the dimuon system and each pion candidate, while . Here and are the fitted invariant masses of the and the dipion system, respectively. These requirements are found to be efficient for the signal from and decays, while significantly suppressing the combinatorial background.

The invariant mass distribution of the dimuons contributing to the selected combinations is shown in Figure LABEL:jpsiYield between the dashed vertical lines. The distribution is fitted with the sum of a second-order polynomial background and a double-Gaussian function, which contains about 3.6M candidates. The invariant mass distribution of the candidates selected for further analysis is presented in Figure LABEL:totalYield. The fitted function is the sum of a fourth-order polynomial background and two double-Gaussian functions. The double-Gaussian functions for and contain about 470k and 30k candidates, respectively.

Monte Carlo (MC) simulation is used to study the selection and reconstruction efficiencies. The MC samples with -hadron production and decays are generated with \PYTHIA6.4 [Sjostrand:2006za], complemented, where necessary, with a dedicated extension for production based on calculations from Refs. [Berezhnoy:1995au, Berezhnoy:1996ks, Berezhnoy:1997fp, Berezhnoy:2004gc]. The decays of -hadrons are then simulated with EvtGen [Lange:2001uf]. The generated events are passed through a full simulation of the detector using the ATLAS simulation framework [SOFT-2010-01] based on \GEANT [Agostinelli:2002hh, Allison:2006ve] and processed with the same software as that used for the data.

4 Analysis method

The production cross sections of the and states decaying to are measured in five bins of transverse momentum, with bin boundaries .

The selected candidates are weighted in order to correct for signal loss at various stages of the selection process. Following previous similar analyses [BPHY-2013-06, BPHY-2012-02b] a per-candidate weight was calculated as

(2)

Here, and stand for the transverse momentum and rapidity of the candidate, is the rapidity of the candidate, while and are transverse momenta and pseudorapidities of the respective pions and muons. The trigger efficiency and the muon reconstruction efficiency were obtained using data-driven tag-and-probe methods described in Refs. [BPHY-2012-02b, muonID]. The pion reconstruction efficiency is obtained through MC simulations using the method described in Ref. [BPHY-2013-06].

The acceptance is defined as the probability that the muons and pions comprising a candidate with transverse momentum and rapidity fall within the fiducial limits described in Section 3. The acceptance map is created using generator-level simulation, with small reconstruction-level corrections applied at a later stage (see Ref. [BPHY-2012-02b] for more details). The different quantum numbers of the and ( and , respectively) cause a difference in the expected dependence of the acceptance on the spin-alignments of the two states. The cross sections measured in this paper are obtained assuming no spin-alignment, but appropriate sets of correction factors for a number of extreme spin-alignment scenarios are calculated and presented in Appendix A for each bin, separately for and .

The efficiencies of the reconstruction-quality requirements and the background-suppression requirements described in Section 3 are determined using MC simulations, and the corrections are applied in each of the bins, separately for and . These efficiencies are found to vary between and . The simulated distributions are reweighted to match the data, and values with and without reweighting are used to estimate systematic uncertainties (see Section 6).

In order to separate prompt production of the and states from the non-prompt production occurring via the decays of long-lived particles such as -hadrons, the data sample in each bin is further divided into intervals of pseudo-proper lifetime , defined as

(3)

where is the invariant mass, is the transverse momentum and is the transverse decay length of the candidate. is defined as

(4)

where is the vector pointing from the primary collision vertex to the vertex, while is the transverse momentum vector of the system. The coordinates of the primary vertices (PV) are obtained from charged-particle tracks with  GeV not used in the decay vertices, and are transversely constrained to the luminous region of the colliding beams. The matching of a candidate to a PV is made by finding the one with the smallest three-dimensional impact parameter, calculated between the momentum and each PV.

Based on an analysis of the lifetime resolution and lifetime dependence of the signal, four lifetime intervals were defined:

  • ,

  • ,

  • ,

  • .

In each of these intervals, and for each bin, the invariant mass distribution of the system is built using fully corrected weighted events. These distributions are shown in Figure LABEL:mFit12 for representative bins.

In order to determine the yields of the and signals, the distributions are fitted in each lifetime interval to the function:

(5)

where the threshold mass  MeV. The and signal yields and , coefficients of the second-order polynomial , parameters and , and the normalisation of the background term , are determined from the fits. Signal peaks for and are described by normalised double-Gaussian functions with common means: and are the narrower Gaussian functions with respective widths and , while and are wider Gaussian functions with widths and . The fraction of the narrower Gaussian function is assumed to be the same for and , while the widths and are related by . The parameters and are fixed for the main fits to the values , as determined from a fit applied in the range 16 GeV GeV, which offers a better signal-to-background ratio than the full range, and is varied within these errors in the systematic uncertainty studies. The fit quality is found to be good throughout the range of transverse momenta and lifetimes. The yields extracted from the fits are shown in Table 1 for the and Table 2 for the .

Corrected yields of vs. [GeV]
window 10–12 12–16 16–22 22–40 40–70
Table 1: Fitted yields of in bins of pseudo-proper lifetime and . Uncertainties are statistical only.
Corrected yields of vs. [GeV]
window 10–12 12–16 16–22 22–40 40–70
Table 2: Fitted yields of in bins of pseudo-proper lifetime and . Uncertainties are statistical only.

Once the corrected yields and are determined in each bin, the double differential cross sections (times the product of the relevant branching fractions) can be calculated:

(6)

where stands for or , is the integrated luminosity, while and are widths of the relevant transverse momentum and rapidity bins, with . and are the branching fractions of these respective decays.

5 Lifetime fits

The probability density function (PDF) describing the dependence of and signal yields on the pseudo-proper lifetime is a superposition of prompt (P) and non-prompt (NP) components:

(7)

where is the non-prompt fraction, while stands for either or . The prompt components of and production should not have any observable decay length, and hence is effectively described by the lifetime resolution function , assumed to be the same for and signals. This was verified with simulated data samples. The resolution function is parameterised as a weighted sum of three normalised Gaussian functions with a common mean, with respective width parameters , and . The resolution parameter and the relative weights of the three Gaussian functions are determined separately for each analysis bin, using two-dimensional mass–lifetime unbinned maximum-likelihood fits on the subset of data which contains a narrow range of masses around the peak. The fitted values for are within the range of 32–52 fs, with the weight of the narrowest Gaussian function steadily increasing with from 6 to about 50.

The simplest description of the non-prompt components of the signal PDF is given by a single one-sided exponential smeared with the resolution function, with the effective lifetime determined from the fit. This model, referred to as a ‘single-lifetime fit’, is applied to the and yields from Tables 1 and 2, and the results of the corresponding binned minimum- fits are shown in Figure LABEL:fig:lifetimesNpr.

bin [GeV] [ps] [ps]
10–12
12–16
16–22
22–40
40–70
Table 3: Effective pseudo-proper lifetimes for non-prompt and obtained with the single-lifetime fit model.

Figure LABEL:fig:lifetimes shows the effective pseudo-proper lifetimes for non-prompt and signals in bins of (see also Table 3). While for the fitted values of are measured to be around  ps in all bins, the signal from at low tends to have shorter lifetimes, possibly hinting at a different production mechanism at low \pt.

In Figure LABEL:fig:npr the ratio of non-prompt production cross sections of and , times respective branching fractions, for the single-lifetime fit is plotted as a function of transverse momentum. The measured distribution is compared to the kinematic template, which is calculated as a ratio of the simulated distributions of non-prompt and non-prompt , assuming that the same mix of the parent -hadrons contributes to both signals. The shape of the template reflects the kinematics of the decay of a -hadron into or , with the width of the band showing the range of variation for extreme values of the invariant mass of the recoiling hadronic system. A fit of the measured ratio to this template allows determination of the ratio of the average branching fractions:

(8)

where the systematic uncertainty reflects the variation of the kinematic template. The of the fit is 5.4 for the four degrees of freedom (dof).

An alternative lifetime model, also implemented in this analysis, allows for two non-prompt contributions with distinctly different effective lifetimes (the ‘two-lifetime fit’). The statistical power of the data sample is insufficient for determining two free lifetimes, especially in the case of production, so in this fit model the non-prompt PDFs are represented in each bin by a sum of two contributions with different fixed lifetimes, and a relative weight determined by the fit:

(9)

Here, the labels SL and LL refer to short-lived and long-lived non-prompt components, respectively, and are the short-lived non-prompt fractions for . The PDFs and are parameterised as single one-sided exponential functions with fixed lifetimes, smeared with the lifetime resolution function described above. Any long-lived part of the non-prompt contribution is assumed to originate from the usual mix of mesons and -baryons, while any short-lived part would be due to the contribution of mesons.

Simulations show that the observed effective pseudo-proper lifetime of or from decays depends on the invariant mass of the hadronic system recoiling from the hidden-charm state. Within the kinematic range of this measurement, it varies from about  ps for small masses of the recoiling system to about  ps for the largest ones. The majority of the decays are expected to have masses of the recoiling system between these values, therefore is taken as the mean of the two extremes,  ps.

The effective pseudo-proper lifetime of the long-lived component, , is determined from the two-lifetime test fits to the mass range, with free and allowing for an unknown contribution of a short-lived component with lifetime . Across the \ptbins, is found to be within the range  ps. The effective pseudo-proper lifetimes and are fixed to the above values for the main fits, and are varied within the quoted errors during systematic uncertainty studies.

Figure LABEL:fig:ratios shows the dependence of the ratio of to cross sections (times respective branching fractions), separately for prompt and non-prompt production contributions. The non-prompt production cross section of is further split into short-lived and long-lived components. The short-lived contribution to non-prompt production is found to be not significant (see Table 6 below). The measured ratio of long-lived to long-lived , shown in Figure LABEL:fig:nonprompt_ratio with blue triangles, is fitted with the MC kinematic template described before to obtain

(10)

with . This value of is somewhat lower than the corresponding result in Equation (8) obtained from the same data with the single-lifetime fit model. Either is significantly smaller than the value obtained by using the estimate for the numerator,  [Artoisenet:2009wk], obtained from the Tevatron data, and the world average values for the branching fractions in the denominator: , .

Production of mesons in high-energy hadronic collisions at low transverse momentum is expected to be dominated by non-fragmentation processes [Berezhnoy:2013cda]. These processes are expected to have \ptdependence relative to the fragmentation contribution, while it is the fragmentation contribution which dominates the production of long-lived -hadrons [Cacciari:2012ny].

So the ratio of short-lived non-prompt to non-prompt , shown in Figure LABEL:fig:nonprompt_ratio with red squares, is fitted with a function to find , with . This value of , and the measured non-prompt yields of and states, are used to determine the fraction of non-prompt from short-lived sources, integrated over the range () covered in this measurement, giving:

(11)

where the last uncertainty comes from varying the spin-alignment of over the extreme scenarios discussed in Appendix A. Since production is only small fraction of the inclusive beauty production, this value of the ratio would mean that the production of in decays is strongly enhanced compared to its production in the decays of other -hadrons.

The two-lifetime fits are used for and to obtain all subsequent results in this paper, unless specified otherwise, with the relatively small differences between the results of the single-lifetime and two-lifetime fits being highlighted alongside all other sources of systematic uncertainty.

6 Systematic uncertainties

The sources of various uncertainties and their smallest (Min), median (Med) and largest (Max) values across the bins are summarised in Table 4 for the differential cross sections of and states, and in Table 5 for the measured fractions.

Source of uncertainty Min Med Max Min Med Max
Statistical
Trigger eff.
Muon tracking
Muon reconstruction eff.
Pion reconstruction eff.
Bkgd suppression req.
Mass fit model variation
Short-lifetime variation
Long-lifetime variation
Lifetime resolution model
Total systematic
(2L-fit 1L-fit) / 2L-fit (prompt)
(2L-fit 1L-fit) / 2L-fit (non-prompt)
Table 4: Summary of relative uncertainties for the and cross-section measurements showing the smallest (Min), median (Med) and largest (Max) values across the bins. The last two rows are described in the text. The uncertainty of the integrated luminosity () is not included.
Absolute uncertainty
Source of uncertainty Min Med Max Min Med Max Min Med Max
Statistical
Trigger eff.
Muon tracking eff.
Muon reconstruction eff.
Pion reconstruction eff.
Bkgd suppression req.
Mass fit model variation
Lifetime resolution variation
Short-lifetime variation
Long-lifetime variation
Total systematic
(2L-fit 1L-fit) / 2L-fit
Table 5: Summary of uncertainties for and non-prompt fractions, and short-lived non-prompt fraction for production, showing the smallest (Min), median (Med) and largest (Max) values across the bins. The last row is described in the text.

Uncertainties in the trigger efficiency, and in the muon and pion reconstruction efficiencies are determined using the procedures adopted in Ref. [BPHY-2013-06]. Additional uncertainty of  [BPHY-2012-02b] is assigned to the tracking efficiency of the two muons within the ID, primarily due to its dependence on the total number of collisions per event. The uncertainties in matching generator-level particles to reconstruction-level particles, and in the detector material simulation within the barrel part of the inner detector are found to be the main contributions to the systematic uncertainty of the pion reconstruction efficiency, estimated to be . Such efficiency uncertainties largely cancel in the various non-prompt fractions (Table 5).

The uncertainties in the efficiency of the background suppression requirements (see Section 4), obtained by combining MC statistical errors and systematic errors in quadrature, are in the range . The uncertainties in the mass fits are estimated by varying the values of parameters that were fixed during the main fit, and by increasing the order of the polynomial in the background parameterisation (see Equation (5)). Similarly, the systematic uncertainties of the lifetime fits are determined by varying the values of the fixed lifetimes and the parameters of the lifetime resolution function within their predetermined ranges.

The statistical and individual systematic uncertainties are added in quadrature to form the total error shown in the tables. In general, the results for are dominated by statistical errors, while for statistical and systematic uncertainties are of comparable size.

The last rows in Tables 4 and 5 show the relative differences between the values obtained using the single- and two-lifetime fits, labelled as ‘1L-fit’ and ‘2L-fit’, respectively. For the quantities listed in Tables 4 and 5, these differences were found to be generally fairly small, compared to the combined systematic uncertainty from other sources.

7 Results and discussion

The measured differential cross section (times the product of the relevant branching fractions) for prompt production of is shown in Figure LABEL:prompt_psi2S_XS. It is described fairly well by the NLO NRQCD model [BPHY-2013-01] with long-distance matrix elements (LDMEs) determined from the Tevatron data, although some overestimation is observed at the highest values. The factorisation model [Baranov:2015laa], which includes the colour-octet (CO) contributions tuned to CMS data [Khachatryan:2015rra] in addition to colour-singlet (CS) production, describes ATLAS data fairly well, with a slight underestimation at higher . The NNLO* Colour-Singlet Model (CSM) predictions [Lansberg:2008gk] are close to the data points at low , but significantly underestimate them at higher values. The measured differential cross section for non-prompt production is presented in Figure LABEL:nonprompt_psi2S_XS, compared with the predictions of the FONLL calculation [Cacciari:2012ny]. The calculation describes the data well over the whole range of transverse momenta.

Similarly, the differential cross section for prompt production of is shown in Figure LABEL:prompt_X3872_XS. It is described within the theoretical uncertainty by the prediction of the NRQCD model which, in this case, considers to be a mixture of and a molecular state [chidd], with the production being dominated by the component and the normalisation fixed through the fit to CMS data [cmsMeas]. The measured differential cross section for non-prompt production of is shown in Figure LABEL:nonprompt_X3872_XS. This is compared to a calculation based on the FONLL model prediction for , recalculated for using the kinematic template for the non-prompt ratio shown in Figure LABEL:fig:npr and the effective value of the product of the branching fractions estimated in Ref. [Artoisenet:2009wk] based on the Tevatron data [Bauer:2004bc]. This calculation overestimates the data by a factor increasing with from about four to about eight over the range of this measurement.

The non-prompt fractions of and production are shown in Figure LABEL:compnpfXSexperimentSLTL. In the case of , increases with , in good agreement with measurements obtained with dimuon decays of from ATLAS [BPHY-2012-02b] and CMS [cmsPsi2S2011]. The non-prompt fraction of shows no sizeable dependence on . This measurement agrees within errors with the CMS result obtained at 7 TeV [cmsMeas].

The numerical values of all cross sections and fractions shown in Figures LABEL:fig:ratiosLABEL:compnpfXSexperimentSLTL are presented in Table 6.

range [GeV]
10–12 12–16 16–22 22–40 40–70
Cross sections times branching fractions [pb / GeV]
Fractions
Ratios
Table 6: Summary of and cross-section measurements, fractions and ratios. The subscripts P and NP denote prompt and non-prompt components, while the labels SL and LL stand for short-lived and long-lived non-prompt components, respectively. The first uncertainty is statistical, the second is systematic. Uncertainties from integrated luminosity () and those due to unknown spin-alignment are not included.

8 Dipion invariant mass spectra

The distributions of the dipion invariant mass in the and decays are measured by determining the corrected yields of and signals in narrow bins of . The two additional selection requirements (Equation (1)) used specifically to reduce combinatorial background in the cross-section measurement, are found to bias the distributions and are therefore replaced for this study by requirements on the pseudo-proper lifetime significance, , and the transverse momentum of the candidates,  GeV.

The invariant mass distributions of the corrected candidates selected for this analysis are shown in Figure LABEL:fig:invMassPsi2Smpipi for the mass range around peak and in Figure LABEL:fig:invMassX3872mpipi for .

The interval of allowed values is subdivided into 21 and 11 bins for and , respectively. In each bin, the signal yield is extracted using a fit to the function

(12)

where is the invariant mass of the system, is the yield of the parent resonance, is the normalisation factor of the background PDF, is the world average mass [PDGBcTau] of the parent resonance, and are free parameters. The signals are described by the same double-Gaussian PDFs