The COMPASS (COmmon Muon and Proton Apparatus for Structure and Spectroscopy) Collaboration at CERN is the most recent one in pursuing the more than 40-years old objective to experimentally elucidate the nucleon’s internal structure, in particular its spin dependence. It uses the M2 beam line of the SPS, which provides the only high-energy spin-polarized muon beam in the world. The deep-inelastic scattering (DIS) process serves as a tool for studying in-depth the structure of the nucleon in terms of quarks and gluons and to investigate other phenomena like e.g. nucleon electromagnetic form factors and the strangeness content of the nucleon. Using alternatively high-energy pions or kaons delivered by the M2 beam line, a new era was opened to study exclusively produced multi-meson states, which already led to several new results in meson spectroscopy. In particular, 3-pion and Kππ states were studied through partial-wave analyses with unprecedented high-statistics, allowing one to identify and thoroughly analyze the properties of small signals and to search for new states.

In the last four years, the COMPASS Collaboration used their versatile two-stage open-aperture forward spectrometer in EHN2 in combination with different beam and target configurations.

Artistic view of the 60 m long COMPASS spectrometer. The two dipole magnets SM1 and SM2 are indicated in red, electromagnetic and hadron calorimeters in blue.

In 2015 and 2018, the Drell-Yan (DY) process was studied through pion scattering on polarised hydrogen and three types of heavy targets. In 2016 and 2017, the Deeply Virtual Compton Scattering (DVCS) process was investigated using both charge signs of the high-energy polarised muons delivered by the M2 beam line, in conjunction with a 2.5 m-long liquid hydrogen target surrounded by a recoil-proton detector. Over these four years, the COMPASS Collaboration has produced a rich menu of results on polarised quark parton distribution functions (PDFs), transverse-momentum-dependent (TMD) PDFs and Generalized PDFs, as well as DIS multiplicities of pions and kaons. In addition, they published results on the production of exclusive final states using data taken earlier with a pion beam, a proton target and a recoil-proton detector. Also published were new results on the spectroscopy of standard and exotic mesons, which were obtained from data taken in earlier years.

Drell-Yan results

A key component and an unprecedented feature of the COMPASS physics programme is the study of TMD PDFs of the nucleon via the measurement of spin- (in)dependent azimuthal asymmetries in both semi-inclusive DIS (SIDIS) and DY processes. The first ever spin-dependent Drell-Yan measurement was performed in 2015. The measurement of the Sivers asymmetry and all other transverse spin-dependent azimuthal asymmetries was performed at a comparable hard scale in both SIDIS and DY at COMPASS. Comparing the results of these measurements offers the unique possibility to test the predicted universal and process-dependent features of TMD PDFs by using essentially the same experimental setup. The first DY results based on the 2015 data were published in PRL 119 (2017) 112002. The observed Sivers asymmetry is found to be consistent with the QCD TMD-framework prediction. In order to improve the statistical precision of the result, in 2018 the COMPASS data-taking campaign was again devoted to spin-dependent DY measurements and preliminary results have been shown already (see figure below).

In parallel, further analyses have been done and are still ongoing concerning spin-independent DY azimuthal asymmetries, pion-induced DY and charmonium cross sections on nuclear targets including the so-called EMC effect, the pion valence structure, charmonium polarization and the transverse spin-dependence of azimuthal asymmetries.

TMD single-spin asymmetries measured by COMPASS in the first ever spin-dependent Drell-Yan experiment.

A detailed programme to access Generalised Parton Distributions

The long-lasting COMPASS effort to understand the structure of the nucleon has shifted the focus in the last years to also study Generalized Parton Distribution Functions (GPDs). They describe the correlation between transverse position and longitudinal momentum of quarks and gluons that are confined inside a hadron. This method is often referred to as (quasi-3D) nucleon tomography. GPDs are accessible through hard exclusive measurements, such as a virtual Compton scattering (DVCS) and deeply virtual meson production.

The 160 FeV muon beam impinges on a 2.5 m long liquid hydrogen target surrounded by the CAMERA proton recoil detector to ensure the exclusivity of the reaction. The recoil proton is detected in coincidence with the scattered muon, which is emitted together with the produced photon or meson into the COMPASS forward spectrometer.

Following a successful short pilot run in 2012, data was collected in 2016 and 2017. The first result was published in PLB 793 (2019) 118 using data from the 2012 pilot run. COMPASS measured the slope value B=4.3 +/- 0.7 GeV^-2 in the exponential function that describes the dependence of the average of the measured μ⁺ and μ^- cross sections on the momentum transfer t. Although further analysis using the complete 2016-2017 COMPASS data is still required to improve precision, this result already nicely complements earlier ones obtained by H1 and ZEUS at HERA. As can be seen from the figure, a ‘shrinkage’ of the proton appears when the projectile probes the transverse extension of partons in the proton for increasing parton momenta, i.e. when traversing the Bjorken-x range from  the gluon-dominated region over the sea-quark region to the valence-quark region.

Dependence of the cross section t-slope parameter B on Bjorken-x.

Using the same data, the production of mesons as π⁰, ρ, ω, φ, J/ψ is also studied. From the data of the 2012 pilot run, large transverse virtual-photon contributions for exclusive π⁰ production have been observed, and the results are submitted for publication. Also, non-zero values were observed for certain spin-density matrix elements, which indicates a violation of s-channel helicity conservation in exclusive omega production that may be explained by contributions of chiral-odd GPDs.

Hadron spectroscopy, heavy states

The excitation spectrum of hadrons gives information on how the strong interaction works to keep quarks and gluons bound inside hadrons. Precise spectroscopy of hadrons provides important input to our understanding of the strong interaction in a regime where the QCD equations cannot be solved with current techniques. Lattice-QCD simulations have started very recently to reach some predictive power for excited states, so that comparisons with experiment are becoming possible.

COMPASS collected data samples from peripheral (diffractive) collisions of a 190 GeV pion beam from the SPS M2 beam line with a proton target to study short-lived excited mesons consisting of up, down and strange quarks. These data allow one to study the properties of established mesons with unprecedented precision, but also open the possibility to search for new states, in particular the exotic mesons (i.e. states that go beyond the simple quark-antiquark configurations of the quark model such as four-quark states or states with excited gluon fields).

By employing an analysis technique called partial-wave analysis, COMPASS disentangles the produced excited mesons in terms of their quantum numbers. As a very interesting specific result, they recently found a novel  resonance-like state, the a₁(1420), with surprising properties (published in PRL 115 (2015) 082001). In collaboration with theorists from JPAC, COMPASS data confirm the existence of the π₁(1600), a previously disputed state, thereby solving a long-standing puzzle. This state has quantum numbers forbidden for conventional quark-antiquark states. According to QCD predictions, the π₁(1600) could be a new form of hybrid hadronic matter: a quark-antiquark pair with an excited gluon field.

Exploiting the versatility of the M2 beam line, COMPASS also studied the production of mesons containing the heavier charm and anti-charm quarks by scattering 160 GeV and 200 GeV muons off ⁶LiD and NH₃ targets. The production of the elusive X(3872) meson was observed with a significance of 4.1 standard deviations, for the first time in lepton-nucleon interactions. The properties of this meson cannot be explained by the simple quark-antiquark model. The COMPASS result is complementary to  the ones obtained in experiments at the LHC and at e⁺e^- colliders, helping to explain this puzzle.

Deep Inelastic Scattering results from longitudinally polarised muon-nucleon scattering.

The analysis of all DIS data taken with the polarised muon beam and a longitudinally polarised proton or deuteron target is finished and final results were published on the proton and deuteron spin structure functions for Q² > 1 (GeV/c)². The results include a NLO pQCD analysis of polarised quark PDFs and a re-evaluation of the Bjorken sum. For the first time, a significant spin effect was observed at small values of Bjorken-x and four-momentum transfer Q². In addition, a clear positive signal for the gluon contribution to the nucleon spin was measured thanks to an improved analysis of hadron production in deep inelastic scattering, see the following figure. 

Results for Δg/g in three bins of x_gluon compared to the world data on Δg/g extracted in LO pQCD.

Moreover, COMPASS obtained SIDIS results using spin-independent muon-nucleon scattering. For semi-inclusive pion production, fragmentation functions were extracted and published, while for kaon production further investigations are still required at large values of z, i.e. the relative energy transfer to the produced hadron. Using an extended data set, COMPASS studied the K^- to K⁺ (R_K) and antiproton-to-proton (R_p) multiplicity ratio. The comparison with pQCD calculations shows that the experimental results fall below the prediction of 0.5 for both ratios (see figure below), thereby suggesting that the applicability of factorised pQCD in DIS hadron production may need to be revisited.

Comparison of R_p and R_K, as a function of z. The expected lower limit in LO pQCD is the same for p and K at given x and Q², and is about 0.5 for the data shown in the figure.

Transverse Spin Asymmetries and TMD PDFs

New results were obtained on the transverse-spin and transverse-momentum structure of the nucleon using the SIDIS data collected with the 160 GeV muon beam and transversely-polarized and unpolarised targets.

COMPASS measured Collins and Sivers asymmetries in SIDIS on proton targets that are clearly different from zero, thereby confirming the relevance of transverse-spin and transverse-momentum effects at high energy. The corresponding measurements on the deuteron provided asymmetries compatible with zero within the large statistical uncertainties. These proton and deuteron results were used in several extractions of the transversity distribution, the collinear PDFs related to the tensor charge, and the Sivers function that is presently the best studied among the TMD PDF. Indeed, the non-zero values measured by COMPASS for the Sivers asymmetry in SIDIS at large x and large Q² constitute the solid ground to verify the change of sign of the Sivers function when comparing SIDIS to Drell-Yan.

Very recently, COMPASS has extracted for the first time and published in Nucl. Phys. B 940 (2019) 34 results on the transverse-momentum-weighted Sivers asymmetry for positive and negative hadrons using the 2010 SIDIS proton data. The measurement has allowed extracting in a direct way the first transverse moment of the Sivers function   for the u and the d quark, shown in the figure below. The values for the u quark are different from zero, with relatively small statistical uncertainty, and in agreement with previous extractions. The large uncertainties for the d-quark PDF show the need for precise measurements of transverse-spin asymmetries on the neutron or deuteron.

Measured first moments of the Sivers functions for the u-quark (filled red points) and the d-quark (open black points), compared to a previous extraction using all the available Sivers asymmetry measurements.

More precise data are required for any analysis aiming at the extraction of transversity and TMD PDFs. This motivated COMPASS to propose a one-year measurement of transverse-spin asymmetries using a transversely polarised deuteron target. Following approval in June 2018, the data will be taken in 2021. They will balance the world statistics between deuteron and proton data and allow one to improve the knowledge on all d-quark PDFs, in particular transversity, and on the nucleon tensor charge. The results will remain unique until the eventual start of operation of the EIC, and they are complementary to the upcoming JLab12 data.

Values of    (red) and   (black), with the 68% (dark) and 90% (light) confidence bands for the present (left) and projected (right) accuracies of the deuteron data, while using all existing proton data.

Once the 2021 data will have been analysed, COMPASS expects to reduce the uncertainties in the integral of the transversity function from 0.108 to 0.040 for the d-quark and from 0.032 to 0.019 for the u-quark. This will result in a projected uncertainty on the tensor charge of +/- 0.044, i.e. a reduction by a factor of two, as shown in the figure.

New and complementary information on the TMD structure of the nucleon comes from SIDIS measurements using unpolarised targets. In particular, information on the intrinsic transverse momentum in the nucleon can be inferred from transverse momentum distributions, and azimuthal modulations are used to access the Boer-Mulders TMD PDF. These observables were earlier measured by COMPASS using data taken with the LiD target, and they are now being extracted using the high-statistics proton data collected in 2016 and 2017 during the DVCS measurements.