Nucleon Spin Structure Studies at COMPASS

WDS'14 Proceedings of Contributed Papers — Physics, 193–198, 2014. ISBN 978-80-7378-276-4 © MATFYZPRESS Nucleon Spin Structure Studies at COMPASS J. Matouˇsek Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic. Abstract. Though the hadron structure has been studied for a long time, open issues still remain. COMPASS is a multi-purpose fixed-target experiment at CERN, aimed at hadron spin structure studies and hadron spectroscopy. A brief introduction of the apparatus as well as a summary of its results and plans concerning hadron structure will be given. A special attention will be paid to a key component — the polarized target and to the first ever polarized DrellYan reaction study starting this autumn. Nucleon Structure It is well known, that among particle interactions the “hard processes,” which are which are characterized by short distances between the interacting particles and large transferred momenta, are well described by the Standard Model. In the case of hadron constituents by perturbative Quantum Chromodynamics (QCD) in particular. On the other hand, the “soft processes,” interactions between particles at larger distances and with small momentum tran fers, are difficult to calculate in QCD. The problem is basically that the QCD coupling gets stronger with distance and can no longer be used as a parameter of perturbative expansion. The predictions have to rely on lattice calculations or models and effective theories like Chiral Perturbation Theory. Due to these problems the hadron structure is still a major puzzle. What can be done from the experimental side is to divide a process involving a hadron into two parts. First, there is a “hard part,” in which partons — quarks and gluons — are the players, and which can be described using perturbative approach. Second, there is a “soft part,” which is described by phenomenological functions. For example one can use Parton Distribution Functions (PDFs), which can be interpreted as probability that a certain parton species with certain fraction of the parent hadron momentum and spin orientation takes part in the interaction. Then one can calculate the parton-something cross section in the standard way, and at the end use Fragmentation Functions (FFs), that give us probabilities of the produced partons “fragmenting” into hadrons that are observed in the final state. Parton distribution functions In the collinear approximation, i.e. when parton transverse momenta are neglected, there are three PDFs in the leading order: The unpolarized PDF f(x), which gives the parton number density as a function of fraction of the parent hadron momentum the parton carries — the Bjorken x. Then there is the helicity PDF g(x) or ∆f(x), giving the difference between number densities of quarks with spin parallel and antiparallel to the longitudinally polarized hadron. Last, there is the transversity h(x) or ∆T f(x), which has the same meaning for a transversely polarized hadron. g(x) = ∆f(x) = f+(x) − f−(x) h(x) = ∆T f(x) = f↑(x) − f↓(x). (1) The unpolarized PDF is quite well known, even for separate parton species including strange quarks and gluons. For example the MSTW 2008 PDFs [Martin et al., 2009] were extracted using calculations up to next-to-next-to-leading order. The helicity PDFs are quite well known too, thought it is still problem to precisely disentangle the quark and antiquark distributions and to measure the gluon helicity PDF ∆g(x). [de Florian et al., 2008]. The transversity is the 193 MATOUSEK:ˇ NUCLEON SPIN STRUCTURE STUDIES AT COMPASS Table 1. Transverse Momentum Dependent PDFs (TMDs) in the leading order.They can be interpreted as correlations of the parton and parent hadron polarization in the following way: Parent hadron polarization Unpolarized Longitudinal Transverse f (x,~k ) f ⊥ (x,~k ) Unpolarized 1 T 1T T (Number density) (Sivers) q (x,~k ) Longitudinal 1 T g (x,~k ) Parton pol. (Helicity) 1T T ⊥ ~ ~ h1 (x, kT ) h1(x, kT ) ⊥ ~ Transverse (Boer–Mulders) h1L(x, kT ) (Transversity) ⊥ ~ h1T (x, kT ) least known of them. The first extraction was done as late as in 2007 [Anselmino et al., 2007], and thought much work has been done, more data is needed to improve the knowledge. Beyond the collinear approximation Hints that the collinear approximation is not the end of the story appeared quite long time ago. For example strong angular modulations of dimuons produced in Drell–Yan process, that violate the so called Lam–Tung rule, were found in the late eighties [Guanziroli et al., 1988]. Transverse polarization of Λ hyperons produced in high energy unpolarized hadron interactions can serve as the second example. There are two ways beyond the collinear approximation. The first one is the Generalized Parton Distribution (GPD) approach. It is suitable to describe effects of relatively large parton transverse momenta. Measurement of GPDs is difficult, but they can help us to address inter- esting questions. First, the Fourier transform of the GPD H dependence on certain variable describes the distribution of the transverse distance of partons from the center of mass of the parent hadron. This is popularly referred to as a “nucleon tomography.” Second, the so called Ji relation, which takes the GPDs H and E as parameters, is the only known way to constrain the total quark angular momentum Jq contribution to the nucleon “spin budget” 1 = J (Q2) + J (Q2). (2) 2 q g q=Xu,d,s The question, what contributes to the nucleon spin, has been attracting much attention since the famous measurement of the EMC experiment [Ashman et al., 1988], which yielded that the contribution of quark spins to the nucleon spin is just (14 ± 9 ± 21)%. This result was a big surprise at that time, because clearly pointed towards nonzero gluon polarization or parton orbital angular momenta. More recent results show [Chýla, 2009] ∆u + ∆d + ∆s = (27 ± 11)%. (3) The second approach is that of Transverse Momentum Dependent PDFs (TMDs). They are analogs of PDFs, but a second variable — the parton transverse momentum ~kT — is added. These functions are easier to measure than the GPDs, have a bit more direct interpretation, and describe well the situations with relatively low |~kT |. The TMDs in the leading order are listed in Table 1. The three TMDs f1, g1 and h1, when integrated over ~kT , yield the standard PDFs f(x), ∆f(x) and ∆T f(x), respectively. The other vanish after the integration. The latter are up to now poorly known or unknown. COMPASS Experiment at CERN COMPASS [COMPASS Col., 2010] is a fixed-target experiment situated at CERN Super Proton Synchrotron (SPS) North Area. It was commissioned in 2001 and from 2011 the second 194 MATOUSEK:ˇ NUCLEON SPIN STRUCTURE STUDIES AT COMPASS ′ h l′ l a l l c − q′ q l c X ¯q ∗ ¯c γ l+ q X h h X hb Figure 1. The Feynman diagrams of (left to right) deep-inelastic scattering, charmed meson production through photon-gluon fusion and Drell–Yan process. The dashed circles denote PDFs, the grey rectangles represent hadronization. On the middle diagram the hadronization is omitted for brevity. phase of the physics program (“COMPASS-II”) is running. For physics data taking it uses either hadron or muon beams1. The beam interacts with a target, which can be polarized. COMPASS detector is a universal spectrometer with good particle tracking and identification capability. It is equipped with two conventional spectrometer magnets, many tracking planes, a ring-imaging Cherenkov detector, both hadronic and electromagnetic calorimeters and a muon detection system. Physics studied at COMPASS As the abbreviation COMPASS COmmon Muon and Proton Apparatus for Structure and Spectroscopy) hints, the experiment is aimed at both nucleon structure studies and hadron spectroscopy. We will focus on the first in this text and mention several results, thought the list will be far from complete. COMPASS publications can be found at http://wwwcompass. cern.ch/compass/publications/papers/. Most of the time COMPASS run with muon beam, that scattered off various targets. 6 Usually NH3 or LiD were used as a polarized proton or deuteron target, respectively. During 2004–2008 COMPASS measured the gluon helicity ∆g by detection of charmed mesons produced in photon-gluon fusion process (Fig. 1, middle), [Alekseev et al., 2009]. Thought more precise results are available from RHIC polarized pp data, this measurement provided an independent and direct check. The core of the COMPASS physics program were studies of Deep/Inelastic Scattering (DIS) and above all Semi-Inclusive DIS (SIDIS). In the DIS process a lepton (muon in the case of COMPASS) is scattered off a target nucleon (Fig. 1, left). Only the final state lepton is observed (e.g. µ + p → µ′ + X). In the case of SIDIS, one hadron from the final state hadrons X is observed in addition (e.g. µ + p → µ′ + h + X). COMPASS measured various single and double spin asymmetries in SIDIS processes with proton and deuteron targets. It thus contributed to the world data that are used for global fitting of e.g. quark and antiquark helicities ∆u, ∆d and ∆s. The measured produced hadron multiplicities helped to improve the knowledge of the Fragmentation Functions (FFs). The so called Collins asymmetry was measured, which is a convolution of the transversity and Collins FF. This, together with a similar measurement from the HERMES Collaboration and Belle experiment data, enabled the first extraction of the transversity distributions ∆T u + ∆T u¯, ∆T d + ∆T d¯ [Anselmino et al., 2007]. Another measurement was performed a few years later to reduce uncertainties [Adolph et al., 2012]. The reason why the transversity was measured much later than the helicity is that it is chiral-odd, while the QCD in massless and collinear approximation preserves helicity.

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