\section*{Executive Summary} %\addcontentsline{toc}{section}{\numberline{~}\bfseries Executive Summary} \addcontentsline{toc}{section}{\bfseries Executive Summary} \label{sec:exec_summary} \noindent AThe research fields of hadron spectroscopy and hadron structure are closely connected since their very beginnings. In 1964, spin-1/2 quarks were conjectured to be the building blocks of baryons and mesons in order to explain their quantum numbers observed in hadron spectroscopy. In 1969, when interpreting data from first direct studies of the structure of the proton, partons were hypothesised as its internal constituents and soon after identified with quarks. In the early 1970's, Quantum Chromodynamics (QCD) became accepted as the theory of strong interactions, explaining the observed weakening of the interquark forces at short distances or large momentum transfers. QCD not only describes hard processes through perturbative expansions, but also the non-perturbative dynamics of the strong interaction, down to soft and extremely soft processes which are involved in meson spectroscopy and linked to chiral perturbation theory. Parton Distribution Functions (PDFs) describe the structure of the nucleon as a function of the nucleon momentum fraction carried by a parton of a certain species. They are studied primarily in Deeply Inelastic Scattering (DIS) where the longitudinal momentum structure of the nucleon is explored in the collinear approximation, \ie\ neglecting transverse degrees of freedom. Up to now, PDFs were investigated independently from nucleon electromagnetic form factors that are related to ratios of the observed elastic electron--nucleon scattering cross section to that predicted for a structureless nucleon. The recently developed theoretical framework of Generalised Parton Distributions (GPDs) embodies both form factors and PDFs, such that GPDs can be considered as momentum-dissected form factors which provide information on the transverse localisation of a parton as a function of the fraction it carries of the nucleon's longitudinal momentum. Obtaining such a ``3-dimensional picture'' of the nucleon is sometimes referred to as ``nucleon tomography''. In a complementary approach, the subtle effects of intrinsic transverse parton momenta are described by Transverse-Momentum-Dependent PDFs (TMDs). These effects become visible in hadronic Drell--Yan (DY) and Semi-Inclusive DIS (SIDIS) processes. The structure of hadrons can not yet be calculated in QCD from first principles. However, the deformation of the shape of a hadron in an external electromagnetic field, described by polarisabilities, can be predicted by chiral perturbation theory which is a low-energy expansion of the QCD Lagrangian. More than 10 years ago, the \compass\ experiment was conceived as ``COmmon Muon and Proton apparatus for Structure and Spectroscopy'', capable of addressing a large variety of open problems in both hadron structure and spectroscopy. As such, it can be considered as a ``QCD experiment''. By now, an impressive list of results has been published concerning nucleon structure, while the physics harvest of the recent two years of hadron spectroscopy data taking is just in its beginnings. The \compass\ apparatus has been proven to be very versatile, so that it offers the unique chance to address in the future another large variety of newly opened QCD-related challenges in both nucleon structure and hadron spectroscopy, at very moderate upgrade costs. It consists of a high-precision forward spectrometer and either an unpolarised, longitudinally or transversely polarised target. It is located at the unique \cern\ SPS M2 beam line that delivers hadron or naturally polarised $\mu^\pm$ beams in the energy range between 50~GeV and 280~GeV. This proposal lays the ground for a new decade of fascinating QCD-related studies of nucleon structure and in hadron spectroscopy. It details the physics scope and related hardware upgrades for those topics for which data taking can be envisaged to start in 2012. This implies mainly studies of chiral perturbation theory, ``unpolarised'' generalised parton distributions, and transverse-momentum-dependent parton distributions. More distant projects, as the whole complex of future QCD studies using hadron spectroscopy and also studies of ``polarised'' GPDs, will be described later in an addendum to this proposal. All these studies will significantly expand our knowledge on key aspects of hadron structure and spectroscopy which are inaccessible to any other facility existing or under construction. The concept of GPDs attracted much attention after it was shown that the total angular momentum of a given parton species, $J^f$ for quarks ($f=u,d$ or $s$) or $J^g$ for gluons, is related to the second moment of the sum of the two GPDs $H$ and $E$. As of today, it is by far not fully understood how the nucleon spin $\frac{1}{2}$ is shared between the contributions of intrinsic and orbital angular momenta of quarks of various flavors and gluons. Constraining quark GPDs experimentally by measuring exclusive Deeply Virtual Compton Scattering (DVCS), $\mu \,p \rightarrow \mu \, \gamma \, p$, or Deeply Virtual Meson ($M$) Production (DVMP), $\mu \,p \rightarrow \mu \, M \, p$, is the only known way to constrain the quark components of the nucleon's spin budget $\frac{1}{2}=\sum_{f=u,d,s}J^f + J^g$. Such data will also be very important to experimentally validate GPD moments calculated from first principles through QCD calculations on the lattice. In order to ensure exclusivity of DVCS and DVMP events, a new recoil detector will surround a 2.5~m long liquid hydrogen target. The kinematic domain accessible with 160~GeV muon beams cannot be explored by any other facility in the near future. The DVCS cross section will be determined as a function of both the momentum transfer between initial and final nucleons and the fraction of the longitudinal nucleon momentum carried by the struck parton. A new electromagnetic calorimeter (ECAL0) will provide coverage of substantially higher values of this fraction as compared to the existing calorimeters ECAL1 and ECAL2. One key result will be the first, model-independent answer on the question how the transverse nucleon size varies gradually from the gluon/sea-quark region to that dominated by valence quarks. Only \compass\ can explore the kinematic region between the \hone/\zeus\ collider range and the \hermes/\jlab\ fixed-target range, so that particularly important results can be expected from 3-dimensional nucleon ``tomography'' within this kinematic domain. The transverse structure of the nucleon in the \compass\ kinematic range is considered to be important input for background simulations in proton-proton collisions at LHC. The second key result is information on the GPD $H$, obtained by separating the real and imaginary parts of the DVCS amplitude. This will be accomplished by combining data from positive and negative muon beams. The azimuthal dependence of the cross section will be used to isolate the contribution of the GPD $H$, which is of particular importance for the evaluation of the spin sum rule. The measurements with the liquid hydrogen target will mainly constrain $H$. An extension of the programme is envisaged using a transversely polarised target, mainly to constrain $E$. This will be subject of an addendum to this proposal. After completion of data taking, the combined DVCS and DVMP data set of \hone, \zeus, \compass, \hermes\ and \jlab\ will constrain the nucleon-helicity-conserving $u$ and $d$ quark GPDs over a wide kinematic range in parton longitudinal momentum versus parton transverse localisation, and virtual-photon resolution scale. It is expected that ongoing activities towards global fits of GPDs will lead to a reliable determination of total and also orbital quark angular momenta. Simultaneously with the GPD programme, high-statistics data will be recorded on unpolarised semi-inclusive deep inelastic scattering, $\mu \, p \rightarrow \mu \, h \, X$. The pion and kaon multiplicities will be used to extract at leading order $\alpha_s$ (LO) the unpolarised strange quark distribution function $s(x)$ as well as fragmentation functions describing how a quark fragments into a hadron. Presently, the poor knowledge of these quantities is the limiting factor in the determination of the polarisation of strange quarks from SIDIS data. These multiplicities will also represent important input to future global analyses beyond LO. The transverse momentum of partons is a central element in understanding the 3-dimensional structure of the nucleon. From the measured azimuthal asymmetries of hadrons produced in unpolarised SIDIS and DY processes a sizable transverse momentum was derived. When this intrinsic transverse momentum is taken into account, several new functions are required to describe the structure of the nucleon. Transverse spin, in fact, couples naturally to intrinsic transverse momentum, and the resulting correlations are encoded in various transverse-momentum-dependent parton distribution and fragmentation functions. The SIDIS cross section contains convolutions of these two types of functions, while the convolutions in the DY cross section comprise only PDFs and/or TMDs. In spite of the widespread interest in this approach which goes beyond collinear QCD, the field is still in its infancy and only data can sort out which correlations are appreciably different from zero and relevant. Of particular interest are the correlations between quark transverse momentum and nucleon transverse spin, and between quark transverse spin and its transverse momentum in an unpolarised nucleon, which are encoded in the so-called Sivers and Boer--Mulders functions, both (na{\"\i}vely) $T$-odd. The Boer--Mulders function contributes to the azimuthal modulations in the cross sections of unpolarised SIDIS and DY processes which have been observed since many years. We intend to accurately measure such modulations both in DY and in SIDIS (this last measurement in parallel to the GPD programme). % Much attention in the recent years has been devoted to the Sivers function originally proposed to explain the large single-spin asymmetries observed in hadron--hadron scattering. From $T$-invariance arguments, for a long time it was believed to be zero. One of the main theoretical achievements of the recent years was the discovery that the Wilson-line structure of parton distributions, which is necessary to enforce gauge invariance of QCD, implies a sign difference between the $T$-odd distributions measured in SIDIS and the same distributions measured in DY. According to this ``restricted universality'', the Sivers function can be different from zero but must have opposite sign in SIDIS and DY. There is a keen interest in the community to test this prediction which is rooted in fundamental aspects of QCD, and many laboratories are planning experiments just to test it. The Sivers function was recently measured by \hermes\ and \compass\ in SIDIS off transversely polarised targets and shown to be different from zero and measurable. In order to test its sign change, DY experiments with transversely polarised hadrons are required, but none were performed so far. The main goal of our DY programme is to measure for the first time on a transversely polarised target the process $\pi^- p^{\uparrow} \rightarrow \mu^+ \mu^- X$. This will be a unique measurement as at \compass\ energies the virtual photon originates mainly from the fusion of a $\bar{u}$ quark from the pion and a $u$ quark from the nucleon, both in valence-like kinematics. In two years of data taking with the 190~GeV $\pi^-$ beam and the \compass\ spectrometer with the NH$_3$ transversely polarised target, the fundamental prediction for the sign of the $u$ quark Sivers function can be tested for the first time. Measurements of exclusive final states produced by incoming high-energy pions at very small momentum transfer to the recoiling nucleus, explore the Primakoff region where the cross section is dominated by the exchange of a quasi-real photon. The initial $\pi^-\gamma^*$ system may scatter into $\pi^-\gamma$ (Compton reaction), $\pi^-\pi^0$, $\pi^-\pi^0\pi^0$, $\pi^-\pi^+\pi^-$, or final states containing more pions. In QCD, chiral Perturbation Theory (ChPT) predicts the low-energy behaviour for all these reactions at small intermediate-state masses $m^2_{\pi\gamma}$, from threshold to a few pion masses. The chiral expansion of the cross section contains several low-energy constants which describe important physical properties of the pion. For the Compton reaction, the ChPT calculations result in deviations from the QED bremsstrahlung cross section that is exactly calculable for a point-like particle. The first term in the expansion in $m_{\pi\gamma}$ originates from the electric and magnetic dipole polarisabilities of the charged pion, $\alpha_\pi$ and $\beta_\pi$, and is proportional to their difference $\alpha_\pi-\beta_\pi$. In order to resolve these two polarisabilities independently, \ie\ to also determine $\alpha_\pi+\beta_\pi$, it is necessary to measure the cross section differential in the centre-of-momentum scattering angle $\theta_{cm}$, in which the two contributions have a complementary functional dependence. At that level of precision, it is possible (and necessary) to also account for the most relevant combination of the pion quadrupole polarisabilities, $\alpha_2-\beta_2$. Its effect has a similar $\theta_{cm}$ dependence as that of $\alpha_\pi-\beta_\pi$ but is proportional to $m_{\pi\gamma}^4$ instead of $m_{\pi\gamma}^2$. The planned measurements will also allow for the determination of the two combinations $\alpha_\pi+\beta_\pi$ and $\alpha_2-\beta_2$, for the first time. The neutral (electromagnetic) trigger permits at the same time the precise measurement of final states containing one or more $\pi^0$. The threshold behaviour of $\pi^-\pi^0$ determines the chiral anomaly constant $F_{3\pi}$, for which the new data set will allow a new level of experimental precision beyond that of the theoretical prediction of about 1\%. The physics programme described in this proposal covers a period of five years, one year for the tests of chiral perturbation theory and two years each for the GPD and DY programmes. The tentative schedule for the first three years is as follows: \bi \item 2012: Tests of chiral perturbation theory, \item 2013: GPD programme, \item 2014: Drell--Yan programme. \ei On the basis of the results from the 2008 and 2009 hadron runs, an addendum to this proposal aiming at further hadron spectroscopy measurements will be submitted in due time. The schedule of these measurements will be considered together with that of the remaining parts of the proposed GPD and DY programmes, possibly taking into account extensions of the latter as sketched in the proposal.