Unpolarized Proton Research Articles

QCD predictions for the azimuthal asymmetry in charm leptoproduction for the COMPASS kinematics

We present the QCD predictions for the azimuthal cos⁡2φ asymmetry in charm leptoproduction for the kinematics of the COMPASS experiment at CERN. The asymmetry is predicted to be large, about 15%. The radiative corrections to the QCD predictions for the cos⁡2φ distribution are estimated to be small, less than 10%. Our calculations show that the azimuthal asymmetry in charm production is well defined in pQCD: it is stable both perturbatively and parametrically, and practically insensitive to theoretical uncertainties in the input parameters. We analyze the nonperturbative contributions to the cos⁡2φ distribution due to the gluon transverse motion in the target and the c-quark fragmentation. Because of the c-quark low mass, the nonperturbative contributions are expected to be sizable, about (30–40)%. We conclude that extraction of the azimuthal asymmetries from available COMPASS data will provide valuable information about the transverse momentum dependent distribution of the gluon in the proton and the c-quark hadronization mechanism. Finally, we discuss the cos⁡2φ asymmetry as a probe of the gluonic analogue of the Boer–Mulders function, h1⊥g, describing the linear polarization of gluons inside unpolarized proton.

Associated production of a dilepton and a ϒ(J/ψ) at the LHC as a probe of gluon transverse momentum dependent distributions

We discuss the impact on the study of gluon transverse momentum dependent distributions (TMDs) of the associated production of a lepton pair and a ϒ (or a J/ψ) in unpolarised proton–proton collisions, pp→Qℓℓ¯X, at LHC energies, where one can assume that such final states are dominantly induced by gluon fusion. If the transverse momentum of the quarkonium–dilepton system – namely, the transverse momentum imbalance of the quarkonium state and the lepton pair – is small, the corresponding cross sections can be calculated within the framework of TMD factorisation. Using the helicity formalism, we show in detail how these cross sections are connected to the moments of two independent TMDs: the distribution of unpolarised gluons, f1g, and the distribution of linearly polarised gluons, h1⊥g. We complete our exhaustive derivation of these general relations with a phenomenological analysis of the feasibility of the TMD extraction, as well as some outlooks.

Production of TeV-class photons via Compton back-scattering on proton beams of a keV high brilliance FEL

Present availability of high brilliance photon beams as those produced by X-ray Free Electron Lasers in combination with intense TeV proton beams like those available at SPS, LHC or in the future at FCC, makes possible to conceive the production of TeV-class photons by Compton back-scattering of keV photons carried by the FEL radiation pulse. We present here the study of spectra and fluxes of the TeV-class photons, which are collimated in the typical 1/γ forward angle with respect to the propagation of the proton beam (γ is the proton beam relativistic factor). Using a room-temperature Linac based X-ray FEL delivering radiation pulses at 100Hz up to 6keV photon energy (implying a Linac electron beam energy in the 5–8GeV range), fluxes of tens photons/s are achievable. It is also shown that a proper control of proton beam emittance and focusing at the interaction point is crucial to assure a reasonable energy spread of the photons emitted within an angle smaller than 1/γ. Moreover, due to the reasonably small proton recoil, the back-scattering is actually in the Thomson regime, therefore the back-scattered photons retain the same polarization of the incident FEL beam (that is typically linear, but can be made circular too) even using unpolarized protons. The life-time of the proton beam circulating in the main ring is not affected at all by the interaction with the FEL beam due to the small number of Compton back-scattering events generated (maximum of 1 per bunch collision).

Linearly polarized gluons in charmonium and bottomonium production in the color octet model

We study the possibility to probe the unpolarized and linearly polarized transverse momentum- dependent gluon distributions in unpolarized pp collision in charmonium and bottomonium produc- tion, employing non-relativistic QCD (NRQCD) based color octet model within transverse momentum dependent (TMD) factorization framework. The transverse momentum (p T ) and rapidity distributions of J/{\psi} and {\Upsilon}(1S) at LHCb, RHIC and AFTER energies are estimated. Significant modulations in transverse momentum spectrum of quarkonium in the low p T region is obtained when contributions of linearly polarized gluons inside an unpolarized proton are taken into account. The results of quarko- nium production in color octet model and color evaporation model are compared.

Measurement of the proton spin polarizabilities at MAMI

The spin polarizabilities of the nucleon are fundamental structure constants which describe the response of the nucleon spin to an incident polarized photon. The most model-independent way to measure the nucleon spin polarizabilities is the Compton scattering with polarization degrees of freedom. Three Compton scattering asymmetries on the proton were measured in the Δ(1232) region using a polarized incident photon beam and a polarized (or unpolarized) proton target at the Mainz Microtron (MAMI). These asymmetries are sensitive to values of the spin polarizabilities. Fits to asymmetry data were performed using a dispersion model calculation, and a separation of all four proton spin-polarizabilities in the multipole basis was achieved. The values of the proton spin polarizabilities are presented.

Determination of the scalar polarizabilities of the proton using beam asymmetry $\Sigma_{3}$ Σ 3 in Compton scattering

The scalar dipole polarizabilities, $\alpha_{E1}$ and $\beta_{M1}$, are fundamental properties related to the internal dynamics of the nucleon. The currently accepted values of the proton polarizabilities were determined by fitting to unpolarized proton Compton scattering cross section data. The measurement of the beam asymmetry $\Sigma_{3}$ in a certain kinematical range provides an alternative approach to the extraction of the scalar polarizabilities. At the Mainz Microtron (MAMI) the beam asymmetry was measured for Compton scattering below pion photoproduction threshold for the first time. The results are compared with model calculations and the influence of the experimental data on the extraction of the scalar polarizabilities is determined.

Exclusive Single Pion Electroproduction off the Proton: Results from CLAS

Exclusive meson electroproduction off protons is a powerful tool to probe the effective degrees of freedom in excited nucleon states at the varying distance scale where the transition from the contributions of both quark core and meson-baryon cloud to the quark core dominance. During the past decade, the CLAS collaboration has executed a broad experimental program to study the excited states of the proton using polarized electron beam and both polarized and unpolarized proton targets. The measurements covered a broad kinematic range in the invariant mass W and photon virtuality \(Q^2\) with nearly full coverage in polar and azimuthal angles in the hadronic CM system. As results, several low-lying nucleon resonance states in particular from pion threshold to \(W < 1.6\,\hbox {GeV}\) have been explored. These include \(\varDelta (1232)\frac{3}{2}^+\), \(N(1440)\frac{1}{2}^+\), \(N(1520)\frac{3}{2}^-\), and \(N(1535)\frac{1}{2}^-\) states. In addition, we recently published the differential cross sections and helicity amplitudes of the reaction \(\gamma ^*p\rightarrow n\pi ^+\) at higher W (1.6–2.0 GeV) which are the \(N(1675)\frac{5}{2}^-\), \(N(1680)\frac{5}{2}^+\), and \(N(1710)\frac{1}{2}^+\) states. These excited states with isospin 1/2 and with masses near 1.7 GeV can be accessed in single \(n\pi ^+\) production as there are no isospin 3/2 states present in this mass range with the same spin-parity assignments. I will briefly discuss these states from CLAS results of the single charged pion electroproduction data.

Two-photon exchange correction to muon–proton elastic scattering at low momentum transfer

We evaluate the two-photon exchange (TPE) correction to the muon-proton elastic scattering at small momentum transfer. Besides the elastic (nucleon) intermediate state contribution, which is calculated exactly, we account for the inelastic intermediate states by expressing the TPE process approximately through the forward doubly virtual Compton scattering. The input in our evaluation is given by the unpolarized proton structure functions and by one subtraction function. For the latter, we provide an explicit evaluation based on a Regge fit of high-energy proton structure function data. It is found that, for the kinematics of the forthcoming muon-proton elastic scattering data of the MUSE experiment, the elastic TPE contribution dominates, and the size of the inelastic TPE contributions is within the anticipated error of the forthcoming data.

Two-photon exchange correction in elastic unpolarized electron-proton scattering at small momentum transfer

We evaluate the two-photon exchange (TPE) correction to the unpolarized elastic electron-proton scattering at small momentum transfer $ Q^2 $. We account for the inelastic intermediate states approximating the double virtual Compton scattering by the unpolarized forward virtual Compton scattering. The unpolarized proton structure functions are used as input for the numerical evaluation of the inelastic contribution. Our calculation reproduces the leading terms in the $ Q^2 $ expansion of the TPE correction and goes beyond this approximation by keeping the full $ Q^2 $ dependence of the proton structure functions. In the range of small momentum transfer, our result is in good agreement with the empirical TPE fit to existing data.

Description and interpretation of DVCS measurements

Having in mind the well-known limitations of certain models of generalized parton distributions (GPDs), we show that the allegedly universal GPDs, describing both deeply virtual Compton scattering (DVCS) and deeply virtual meson production (DVMP) data, fail to describe measurements of deep inelastic scattering. We present a new global DVCS fit that describes reasonably the world data set, which includes now also new measurements from Hall A and CLAS collaborations. We also explicitly illustrate that Compton form factors (CFFs) cannot be unambiguously extracted from photon electroproduction measurements off unpolarized proton alone and we argue that it is more reliable to interpret such measurements in terms of certain CFF combinations, where still some care is needed in order to estimate the propagated error.

Back-to-Back Isolated Photon-Quarkonium Production at the LHC and the Transverse-Momentum-Dependent Distributions of the Gluons in the Proton

The study of isolated heavy quarkonia, such as [Formula: see text] and [Formula: see text], produced in association with a photon in proton-proton collisions at the LHC, is probably the optimal way to get right away a first experimental determination of two gluon transverse-momentum-dependent distribution (TMDs) in an unpolarized proton, [Formula: see text] and [Formula: see text], the latter giving the distribution of linearly polarized gluons. To substantiante this, we calculate the transverse-momentum-dependent effects that arise in the process under study and discuss the feasibility of their measurements.

Studies of Transverse-Momentum-Dependent Distributions with a Fixed-Target ExpeRiment Using the LHC Beams (AFTER@LHC)

We report on the studies of Transverse-Momentum-Dependent distributions (TMDs) at a future fixed-target experiment –AFTER@LHC– using the [Formula: see text] or Pb ion LHC beams, which would be the most energetic fixed-target experiment ever performed. AFTER@LHC opens new domains of particle and nuclear physics by complementing collider-mode experiments, in particular those of RHIC and the EIC projects. Both with an extracted beam by a bent crystal or with an internal gas target, the luminosity achieved by AFTER@LHC surpasses that of RHIC by up to 3 orders of magnitude. With an unpolarised target, it allows for measurements of TMDs such as the Boer-Mulders quark distributions and the distribution of unpolarised and linearly polarised gluons in unpolarised protons. Using polarised targets, one can access the quark and gluon Sivers TMDs through single transverse-spin asymmetries in Drell-Yan and quarkonium production. In terms of kinematics, the fixed-target mode combined with a detector covering [Formula: see text] allows one to measure these asymmetries at large [Formula: see text] in the polarised nucleon.

Gluon TMD studies at EIC

A high-energy Electron-Ion Collider (EIC) would offer a most promising tool to study in detail the transverse momentum distributions of gluons inside hadrons. This applies to unpolarized as well as linearly polarized gluons inside unpolarized protons, and to left-right asymmetric distributions of gluons inside transversely polarized protons, the so-called gluon Sivers effect. The inherent process dependence of these distributions can be studied by comparing to similar, but often complementary observables at LHC.

Dirac coupled-channel analyses of the high-lying excited states at 22Ne(p,p′)22Ne

Dirac phenomenological coupled channel analyses are performed using an optical potential model for the high-lying excited vibrational states at 800 MeV unpolarized proton inelastic scatterings from $^{22}$Ne nucleus. Lorentz-covariant scalar and time-like vector potentials are used as direct optical potentials and the first-order vibrational collective model is used for the transition optical potentials to describe the high-lying excited vibrational collective states. The complicated Dirac coupled channel equations are solved phenomenologically using a sequential iteration method by varying the optical potential and the deformation parameters. Relativistic Dirac coupled channel calculations are able to describe the high-lying excited states of the vibrational bands in $^{22}$Ne clearly better than the nonrelativistic coupled channel calculations. The channel-coupling effects of the multistep process for the excited states of the vibrational bands are investigated. The deformation parameters obtained from the Dirac phenomenological calculations for the high-lying vibrational excited states in $^{22}$Ne are found to agree well with those obtained from the nonrelativistic calculations using the same Woods-Saxon potential shape.

Hyperon polarization from the twist-3 distribution in unpolarized proton-proton collision

We investigate the transverse polarization of a hyperon produced in the high-energy unpolarized proton-proton collision, $pp\to\Lambda^\uparrow X$, based on the collinear twist-3 factorization formalism. We focus on the contribution from the twist-3 distribution in one of the unpolarized proton and the transversity fragmentation function for the final hyperon. Utilizing the "master formula" for the soft-gluon-pole cross section, we clarify the reason for why it receives only the derivative term of the twist-3 distribution. We also present the first computation of the soft-fermion-pole cross section and found that it vanishes. This means that the derivative of the soft-gluon-pole function is the only source for the twist-3 cross section from the unpolarized twist-3 distribution, which provides a useful basis for a phenomenological analysis.

Impact of gluon polarization on Higgs boson plus jet production at the LHC

In this paper we consider Higgs boson plus jet production as a process that is sensitive to the linear polarization of gluons inside the unpolarized protons of the LHC. The leading order expressions for the transverse momentum distribution of the Higgs boson plus jet pair are provided in terms of transverse momentum dependent quark and gluon distributions. This includes both angular independent and azimuthal angular dependent contributions, presented directly in the laboratory frame. Lacking experimental constraints on the linearly polarized gluon distribution, we study its effects on Higgs boson plus jet production using two different models to illustrate the generic features and maximal effects. It is found that the $\mathrm{cos}2\ensuremath{\phi}$ distribution may be the most promising observable, as it is driven by only one initial linearly polarized gluon. The potential advantages of the Higgs boson plus jet process compared to other processes sensitive to the linear polarization of gluons are discussed.

Polarization effects in double open-charm production at LHCb

Double open-charm production is one of the most promising channels to disentangle single from double parton scattering (DPS) and study different properties of DPS. Several studies of the DPS contributions have been made. A missing ingredient so far has been the study of polarization effects, arising from spin correlations between the two partons inside an unpolarized proton. We investigate the impact polarization has on the double open-charm cross section. We show that the longitudinally polarized gluons can give significant contributions to the cross section, but for most of the considered kinematic region only have a moderate effect on the shape. We compare our findings to the LHCb data in the D0D0 final state, identify observables where polarization does have an impact on the distribution of the final state particles, and suggest measurements which could lead to first experimental indications of, or limits on, polarization in DPS.

Dirac phenomenological analyses of unpolarized proton inelastic scattering from 22Ne

Unpolarized 800 MeV proton inelastic scatterings from an s-d shell nucleus $^{22}$Ne are analyzed using phenomenological optical potentials in the Dirac coupled channel formalism. The first-order rotational collective model is used to obtain the transition optical potentials for the low lying excited collective states that belong to the ground state rotational band of the nucleus. The optical potential parameters of Woods-Saxon shape and the deformation parameters of the excited states are varied phenomenologically using the sequential iteration method to reproduce the experimental differential cross section data. The effective central and spin-orbit optical potentials are obtained by reducing the Dirac equations to the Schr\"odinger-like second-order differential equations and the surface-peaked phenomena are observed at the real effective central potentials when the scattering from $^{22}$Ne is considered. The obtained deformation parameters of the excited states are compared with those of the nonrelativistic calculations and another s-d shell nucleus $^{20}$Ne. The deformation parameters for the $2^+$ and the $4^+$ states of the ground state rotational band at the nucleus $^{22}$Ne are found to be smaller than those of $^{20}$Ne, indicating that the couplings of those states to the ground state are weaker at the nucleus $^{22}$Ne compared to those at the nucleus $^{20}$Ne. The multistep channel coupling effect is confirmed to be important for the $4^+$ state excitation of the ground state rotational band at the proton inelastic scattering from the s-d shell nucleus $^{22}$Ne.

Constraining double-parton correlations and interferences

Double parton scattering (DPS) has become very relevant as a background to interesting analyses performed by the experiments at the LHC. It encodes knowledge of correlations between the proton constituents not accessible in single parton scattering. Within perturbative QCD DPS is described in terms of partonic subprocesses and double parton distributions (DPDs). There exists a large number of different DPDs describing the different possible states of two partons inside a proton. They include correlations between the two partons and interferences between the two hard subprocesses. Taking the probability interpretation of the DPDs as starting point, we derive limits on the interference DPDs and thereby constrain the size of correlations between two partons inside an unpolarized proton.

Transverse single-spin asymmetries inp↑p→γXfrom quark-gluon-quark correlations in the proton

We analyze the transverse single-spin asymmetry in direct photon production from proton-proton collisions, denoted ${A}_{N}^{\ensuremath{\gamma}}$, within collinear twist-3 factorization. We provide a calculation of the contribution due to quark-gluon-quark correlations in the unpolarized proton as well as summarize previous studies on those effects in the polarized proton. Both soft-gluon poles and soft-fermion poles are considered. From this complete result we then estimate ${A}_{N}^{\ensuremath{\gamma}}$, including error bands due to uncertainties in the nonperturbative inputs, at kinematics relevant for planned measurements of this observable at the Relativistic Heavy Ion Collider. We find ${A}_{N}^{\ensuremath{\gamma}}$ can allow for a ``clean'' extraction of the Qiu-Sterman function, which could lead to a definitive solution to the so-called ``sign-mismatch'' crisis. Since we use the Sivers function extracted from semi-inclusive deep-inelastic scattering to develop our input for the Qiu-Sterman function, this reaction can also make a statement about the process dependence of the Sivers function.