arXiv subjects

Wolfgang Schäfer

Publications and source records attributed to Wolfgang Schäfer.

At least 37 records · Page 2Linked to original sources

arXiv2022

Unintegrated gluon distributions from the color dipole cross section in the BGK saturation model

We evaluate the unintegrated gluon distribution of the proton starting from a parametrization of the color dipole cross section including DGLAP evolution and saturation effects. To this end, we perform the Fourier-Bessel transform of $σ(x,r)/α(r)$. At large transverse momentum of gluons we match the so-obtained distribution to the logarithmic derivative of the collinear gluon distribution. We check our approach by calculating the proton structure function $F_L(x,Q^2)$ finding good agreement with HERA data.

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arXiv2022

Exclusive production of $ρ$ meson in gamma-proton collisions: $d σ/dt$ and the role of helicity flip processes

We calculate the differential cross section $dσ/dt$ for the diffractive photoproduction process $γp \to ρp$ and compare to recent data extracted by the CMS collaboration from ultraperipheral proton-lead collisions. Our model is based on two-gluon exchange in the nonperturbative domain. We take into account both helicity conserving and often neglected helicity-flip amplitudes in the $γ\to V$ transition. The letter can contribute at finite $t$. The shape of the differential cross section as well as the role of helicity flip processes is strongly related to the dependence of the unintegrated gluon distribution on transverse momenta in the nonperturbative region.

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arXiv2022

Production of $e^{+} e^{-}$ in proton-lead collision: photon-photon fusion

We analyze the photon-initiated processes for production of $ e ^ + e ^- $ pairs in proton-nucleus collisions at LHC energy, taking into account both elastic processes and proton dissociations in the low-mass region (LMR) and intermediate-mass region (IMR) as defined by the ALICE collaboration. The calculations are performed within the $k_{\rm T}$-factorisation approach, including transverse momenta of intermediate photons. We discuss several differential distributions in invariant mass of both the leptons $M_{ll}$, pair rapidity $Y_{ll}$ and transverse momenta of the lepton pair $p_{t,ll}$. In addition, we present the two-dimensional distributions in $\log_{10} x_{Bj}$ and $\log_{10} Q^{2}$ and ($\log_{10} W,\log_{10} Q^{2}$) the arguments of the deep-inelastic structure functions. All presented results were obtained with modern parametrizations of proton structure functions. Limiting to small invariant masses of dielectrons one tests structure functions in the nonperturbative region of small $Q^2$ and/or small $W$. We quantify difference for different parametrizations from the literature.

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arXiv2022

Exclusive emissions of polarized $ρ$ mesons at the EIC and the proton content at low $x$

We present a new study on helicity amplitudes and cross sections for the exclusive production of $ρ$ mesons at the EIC in high-energy factorization. In this framework the analytic expression of amplitudes takes the form of a convolution between an off-shell impact factor, depicting the ($γ^* \to ρ$) transition, and a nonperturbative density, known as Unintegrated Gluon Distribution (UGD) that encodes information about the proton structure at low $x$ and evolves according to the BFKL equation. We come out with an evidence that observables sensitive to the polarizations of the incoming virtual photon and of the emitted meson allow us to discriminate among different UGD models and to gather quantitative information on the proton content at high energies.

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arXiv2022

Light-front approach to axial-vector quarkonium $γ^* γ^*$ form factors

In this work, we perform a detailed study of transition form factors for axial-vector meson production via the two-photon fusion process $γ^* γ^* \to 1^{++}$, with space-like virtual photons in the initial state and a $P$-wave axial-vector quarkonium in the final state. In this analysis, we employ the formalism of light-front quarkonium wave functions obtained from a solution of the Schrödinger equation for a selection of interquark potentials for $Q \bar Q$ interaction. We found the helicity structure and covariant decomposition of the matrix elements that can be generically applied for any $q \bar q$ axial-vector meson $γ^* γ^* \to 1^{++}$ transition, while our numerical results are given for the phenomenologically relevant charmonium $χ_{c1}$ state. We present the helicity form factors as functions of both photon virtualities. We also obtain, that $Q F_{\rm LT}(Q^2,0)/F_{\rm TT}(Q^2,0) = {\rm const.}$

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arXiv2022

Structure and production mechanism of the enigmatic $X(3872)$ in high-energy hadronic reactions

We calculate the total cross section and transverse momentum distributions for the production of enigmatic $χ_{c,1}(3872)$ (or X(3872)) assuming different scenarios: $c \bar c$ state and $D^{0*} {\bar D}^0 + D^0 {\bar D}^{0*}$ molecule. The derivative of the $c \bar c$ wave function needed in the first scenario is taken from a potential model calculations. Compared to earlier calculation of molecular state we include not only single parton scattering (SPS) but also double parton scattering (DPS) contributions. The latter one seems to give smaller contribution than the SPS one. The upper limit for the DPS production of $χ_{c,1}(3872)$ is much below the CMS data. We compare results of our calculations with existing experimental data of CMS, ATLAS and LHCb collaborations. Reasonable cross sections can be obtained in either $c \bar c$ or molecular $D {\bar D}^*$ scenarios for $X(3872)$. Also a hybrid scenario is not excluded.

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arXiv2022

Hadron structure at small-x via unintegrated gluon densities

Inclusive as well as exclusive emissions in forward and central directions of rapidity are widely recognized as excellent channels to access the proton structure at small-x. In this regime, to describe nucleons structure, it is necessary to use kT-unintegrated distributions. In particular, at large transverse momenta, the x-evolution of the so-called unintegrated gluon distribution is driven by the Balitsky-Fadin-Kuraev-Lipatov equation, within the framework of the high-energy factorization (HEF). Recent analyses on the diffractive electroproduction of ρmesons have corroborated the underlying assumption that the small-size dipole scattering mechanism is at work, thus validating the use of the HEF formalism. Nonetheless, a significant sensitivity of polarized cross sections to intermediate values of the meson transverse momenta, where, in the case of inclusive emissions, a description at the hand of the transverse momentum dependent (TMD) factorization starts to be the most appropriate framework, has been observed. In this work, we will review the formal description of the UGD within the BFKL approach and present some UGD models that have been proposed, then we will describe the state of the art of some recent phenomenological analyses.

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arXiv2021

From Wigner distributions of photons to dilepton production in semicentral heavy ion collisions

We present a formalism how to calculate differential distributions for dilepton production in semicentral heavy ion collisions. In this new approach, the differential cross section is calculated using the complete polarization density matrix of photons resulting from the Wigner distribution formalism. The formalism is used to calculate different distributions of the invariant mass, dilepton transverse momentum and acoplanarity for different regions of centrality. The results of the calculation are compared with recent experimental data. We also study the contribution from different parts of impact parameter space.

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arXiv2021

Exclusive production of $ρ$-mesons in high-energy factorization at HERA and EIC

We calculate cross sections for the exclusive diffractive leptoproduction of $ρ$-mesons, $γ^*~p~\to~ρ~p$, within the framework of high-energy factorization. Cross sections for longitudinally and transversally polarized mesons are shown. We employ a wide variety of unintegrated gluon distributions available in the literature and compare to HERA data. The resulting cross sections strongly depend on the choice of unintegrated gluon distribution. We also present predictions for the proton target in the kinematics of the Brookhaven EIC.

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arXiv2021

Coherent photoproduction of $J/ψ$ in nucleus-nucleus collisions in the color dipole approach- an update

We discuss the role of $c \bar c g$-Fock states in the diffractive photoproduction of $J/ψ$-mesons. We build on our earlier description of the process in the color-dipole approach, where we took into account the rescattering of $c \bar c$ pairs using a Glauber-Gribov form of the dipole-nucleus amplitude. We compare the results of our calculations to recent data on the photoproduction of $J/ψ$ by the ALICE and LHCb collaborations.

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arXiv2021

Central exclusive production of $η_c$ and $χ_{c0}$ in the light-front k$_{\perp}$-factorization approach

We study the exclusive production of $J^{PC}=0^{++}, 0^{--}$ charmonium states in proton-proton collisions at the LHC energies The $pp \to ppη_c$ reaction is discussed for the first time. We observe a substantial contribution from the nonperturbative domain of gluon virtualities, especially for $η_c$ production. To model the nonperturbative region better, we utilize models of the unintegrated gluon distribution based on parametrizations of the color dipole cross-section.

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arXiv2021

Prompt hadroproduction of C-even quarkonia in the light-front $k_T$ -factorization approach

We present a new approach for the prompt production of quarkonia which is based on the $k_T$-factorization method. The production of even C-parity quarkonia proceeds via the fusion of two (off-shell) gluons. Especially in the kinematics of the LHCb experiment these processes are thus expected to be a sensitive probe of the small-$x$ gluon distribution. We calculate the relevant off-shell matrix elements in terms of the light-front wave functions of the quarkonium states. We present our results for scalar and pseudoscalar charmonia and discuss photon transition form factors as well as cross sections for prompt hadroproduction. We compare our results for the $η_c$ to recent LHCb data.

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arXiv2020

Centrality dependence of dilepton production via $γγ$ processes from Wigner distributions of photons in nuclei

We propose a new complete method, based on the Wigner distributions of photons, how to calculate differential distributions of dileptons created via photon-photon fusion in semicentral ($b<2R_A$) $AA$ collisions. The formalism is used to calculate different distributions of invariant mass, dilepton transverse momentum and acoplanarity for different regions of centrality. The results of calculation are compared with recent STAR, ALICE and ATLAS experimental data. Very good agreement with the data is achieved without free parameters and without including additional mechanisms such as a possible rescattering of leptons in the quark-gluon plasma.

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arXiv2020

Production of $η_{c}(1S,2S)$ in $e^+ e^-$ and $pp$ collisions

We derive the light-front wave function (LFWF) representation of the $γ^{\star} γ^{\star} \to η_{c} (1S),η_{c}(2S)$ transition form factor $F(Q^2_1,Q^2_2)$ for two virtual photons in the initial state. For the LFWF, we use different models obtained from the solution of the Schrödinger equation for a variety of $c\bar{c}$ potentials. We compare our results to the BaBar experimental data for the $η_{c}(1S)$ transition form factor, for one real and one virtual photon. We observe that the onset of the asymptotic behaviour is strongly delayed and discuss applicability of the collinear and/or massless limit. In addition, we present a thorough analysis of $η_{c}(1S,2S)$ quarkonia hadroproduction in $k_{\perp}$-factorisation in the framework of the light-front potential approach for the quarkonium wave function. The off-shell matrix elements for the $g^{\star} g^{\star} \to η_{c} (1S,2S)$ vertices are derived. We discuss the importance of taking into account the gluon virtualities. We present the transverse momentum distributions of $η_c$ for several models of the unintegrated gluon distributions. Our calculations are performed for four distinct parametrizations for the $c\bar{c}$ interaction potential consistent with the meson spectra. We compare our results for $η_{c}(1S)$ to measurements by the LHCb collaboration and present predictions for $η_{c}(2S)$ production.

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arXiv2020

Central exclusive production of scalar and pseudoscalar charmonia in the light-front $k_T$-factorization approach

We study exclusive production of scalar $χ_{c0}\equiv χ_c(0^{++})$ and pseudoscalar $η_c$ charmonia states in proton-proton collisions at the LHC energies. The amplitudes for $gg \to χ_{c0}$ as well as for $gg \to η_c$ mechanisms are derived in the $k_{T}$-factorization approach. The $p p \to p p η_c$ reaction is discussed for the first time. We have calculated rapidity, transverse momentum distributions as well as such correlation observables as the distribution in relative azimuthal angle and $(t_1,t_2)$ distributions. The latter two observables are very different for $χ_{c0}$ and $η_c$ cases. In contrast to the inclusive production of these mesons considered very recently in the literature, in the exclusive case the cross section for $η_c$ is much lower than that for $χ_{c0}$ which is due to a special interplay of the corresponding vertices and off-diagonal UGDFs used to calculate the cross sections. We present the numerical results for the key observables in the framework of potential models for the light-front quarkonia wave functions. We also discuss how different are the absorptive corrections for both considered cases.

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arXiv2020

On the mechanism of $T_{4c}(6900)$ tetraquark production

We discuss the production mechanism of a new state, a putative fully charm tetraquark, observed recently by the LHCb at M = 6.9 GeV in the $J/ψJ/ψ$ channel. Both single parton scattering (SPS) and double parton scattering (DPS) mechanisms are considered. We calculate the distribution in the invariant mass of the four-quark system $M_{4c}$ for SPS and DPS production of $c c \bar c \bar c$ in the $k_t$-factorization approach with modern unintegrated gluon distribution functions (UGDFs). The so-calculated contribution of DPS is almost two orders of magnitude larger than the SPS one, but the tetraquark formation mechanism is unknown at present. Imposing a mass window around the resonance position we calculate the corresponding distribution in $p_{t,4c}$ -- the potential tetraquark transverse momentum. The cross section for the $J/ψJ/ψ$ continuum is calculated in addition, again including SPS (box diagrams) and DPS contributions which are of similar size. The formation probability is estimated trying to reproduce the LHCb signal-to-background ratio. The calculation of the SPS $g g \to T_{4c}(6900)$ fusion mechanism is performed in the $k_T$-factorization approach assuming different spin scenarios ($0^+$ and $0^-$). The $0^+$ assignment is preferred over the $0^-$ one by the comparison of the transverse momentum distribution of signal and background with the LHCb preliminary data assuming the SPS mechanism dominance. There is no reliable approach for the DPS formation mechanism of tetraquarks at present as this is a complicated multi-body problem.

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arXiv2020

Hadroproduction of scalar $P$-wave quarkonia in the light-front $k_T$-factorization approach

In this work, we present a thorough analysis of scalar $P$-wave $χ_{Q0}$, $Q=c,b$ quarkonia electromagnetic form factors for the $γ^* γ^* \to χ_{Q0}$ couplings, as well as their hadroproduction observables in $k_\perp$-factorisation using the light-front potential approach for the quarkonium wave function. The electromagnetic form factors are presented as functions of photon virtualities. We discuss the role of the Melosh spin-rotation and relativistic corrections estimated by comparing our results with those in the standard nonrelativistic QCD (NRQCD) approach. Theoretical uncertainties of our approach are found by performing the analysis with two different unintegrated gluon densities and with five distinct models of the $Q\bar Q$ interaction potentials consistent with the meson spectra. The results for the rapidity and transverse momentum distributions of $χ_{Q0}$ produced in high-energy $pp$ collisions at $\sqrt{s} = 13 \, \rm{TeV}$ are shown.

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arXiv2019

Prompt hadroproduction of $η_c(1S,2S)$ in the $k_T$-factorization approach

In this work, we present a thorough analysis of $η_c(1S,2S)$ quarkonia hadroproduction in $k_\perp$-factorisation in the framework of the light-front potential approach for the quarkonium wave function. The off-shell matrix elements for the $g^* g^* η_c(1S,2S)$ vertices are derived. We discuss the importance of taking into account the gluon virtualities. %We discuss the role of relativistic corrections, the Melosh spin-rotation and theoretical uncertainties by comparing our results with the standard NRQCD approach. We present the transverse momentum distributions of $η_c$ for several models of the unintegrated gluon distributions. Our calculations are performed for four distinct parameterisations for the $c\bar c$ interaction potential consistent with the meson spectra. We compare our results for $η_c(1S)$ to measurements by the LHCb collaboration and present predictions for $η_c(2S)$ production.

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