We investigate the photon emission from the electrosphere of a quark star. It is shown that at temperatures T\sim 0.1-1 MeV the dominating mechanism is the bremsstrahlung due to bending of electron trajectories in the mean Coulomb field of the electrosphere. The radiated energy for this mechanism is much larger than that for the Bethe-Heitler bremsstrahlung. The energy flux from the mean field bremsstrahlung exceeds the one from the tunnel e^{+}e^{-} pair creation as well. We demonstrate that the LPM suppression of the photon emission is negligible.
An algebraic method for evaluating bare nucleon matrix elements of quark operators is proposed. Thereby, bare nucleon matrix elements are traced back to vacuum matrix elements. The method is similar to the soft pion theorem. Matrix elements of two-quark, four-quark and six-quark operators inside the bare nucleon are considered.
When studying tetraquark states using the method of QCD sum rules, we find some tetraquark currents, such as $\bar u_L γ_μd_L~\bar d_L γ^μu_L$ and $\bar u_L γ_μd_L~\bar d_R γ^μu_R$, etc. We calculate their correlation functions using the method of operator product expansion, and find that non-perturbative QCD effects do not contribute much to them. This indicates the possible existence of tetraquark states composed of bare quarks with abnormally small masses. We study the possible assignment of the $X17$ as such a state. We argue that the Atomki experiments might observe a new type of nuclear …
It is generally thought that pion masses vanish when bare light quark masses $m_q$ vanish. The pions are Nambu-Goldstone bosons of chiral $SU_{A}(2)$ symmetry. We discuss a possibility that even when $m_q=0$, the chiral symmetry is explicitly broken in strong coupled QCD, while it is not in weakly coupled QCD. The point is that QCD monopoles are dynamical degrees of freedom in the strong coupled QCD. We show that the monopole quark interactions break the chiral $U_5(1)$ symmetry as well as the chiral $SU_{A}(2)$ symmetry. They are weak relative to the other chiral symmetric interactions of qua…
The reason, we need three terms of `strange', `bare', and `solid' before quark stars, is presented concisely though some fundamental issues are not certain. Observations favoring these stars are introduced.
The discovery of the $D^\ast_{s0}(2317)$ and $D_{s1}(2460)$ resonances in the charmed-strange meson spectra revealed that formerly successful constituent quark models lose predictability in the vicinity of two-meson thresholds. The emergence of non-negligible effects due to meson loops requires an explicit evaluation of the interplay between $Q\bar q$ and $(Q\bar q)(q\bar q)$ Fock components. In contrast to the $c\bar s$ sector, there is no experimental evidence of $J^P=0^+,1^+$ bottom-strange states yet. Motivated by recent lattice studies, in this work the heavy-quark partners of the $D_{s0}…
I reply to A. Mitra's comment on my PRL paper "Bare quark matter surfaces of strange stars and $e^+e^-$ emission". I show that his points of criticism are not correct.
We have investigated the present renormalization prescriptions of Cabibbo-Kobayashi-Maskawa (CKM) matrix. When considering the prescription which is formulated with reference to the case of zero mixing we find it doesn't satisfy the unitary condition of the bare CKM matrix. After added a delicate patch this problem can be solved at one-loop level. In this paper We generalize this prescription to all loop levels and keep the unitarity of the bare CKM matrix, simultaneously make the amplitude of an arbitrary physical process involving quark mixing convergent and gauge independent. We also find t…
Recent achievements of bare strange stars are briefly reviewed. A nascent protostrange star should be bare because of strong mass ejection and high temperature after the supernova detonation flame, and a crust can also hardly form except for a super-Eddington accretion. The magnetosphere of a bare strange star is composed mainly of electron-positron pair plasma, where both inner and outer vacuum gaps work for radio as well as high energy nonthermal emission. A featureless thermal spectrum is expected since no ion is above the quark surface, whilst electron cyclotron lines could appear in some …
Observations to date cannot distinguish neutron stars from self-bound bare quark stars on the basis of their gross physical properties such as their masses and radii alone. However, their surface luminosity and spectral characteristics can be significantly different. Unlike a normal neutron star, a bare quark star can emit photons from its surface at super-Eddington luminosities for an extended period of time. We present a calculation of the photon bremsstrahlung rate from the bare quark star's surface, and indicate improvements that are required for a complete characterization of the spectrum…
We consider the thermal emission of photons and electron-positron pairs from the bare quark surface of a hot strange star. The radiation of high-energy (> 20 MeV) equilibrium photons prevails at the surface temperature T_S > 5 x 10^{10} K, while below this temperature, 8 x 10^8 < T_S < 5 x 10^{10} K, emission of electron-positron pairs created by the Coulomb barrier at the quark surface dominates. The thermal luminosity of a hot strange star in both photons and pairs is estimated.
We consider N=2 SU(2) Seiberg-Witten duality theory for models with N_f=2 and N_f=3 quark flavors. We investigate arbitrary large bare mass ratios between the two or three quarks at the singular points. For N_f=2 we explore large bare mass ratios corresponding to a singularity in the strong coupling region. For N_f=3 we determine the location of both strong and weak coupling singularities that produce specific large bare mass ratios.
In this article, we investigate the under-structures of the $π$ and B mesons in the framework of the Bethe-Salpeter equation with the bare quark-gluon vertex, bare quark propagator and the confining effective potential (infrared modified flat bottom potential) firstly. Although the bare quark propagator can not embody dynamical chiral symmetry breaking and has a mass pole in the time-like region, it can give reasonable results for the values of decay constants $f_π$ and $f_B$ compared with the values of experimental data and other theoretical calculations, such as lattice simulations and QCD s…
We argue that the charge fractionalization in quarks has a hidden topological character related to a broken ${\cal Z}_2$ symmetry between integer-charged bare quarks and leptons. The mechanism is a tunneling process occurring in time between standard field configurations of a pure gauge form with different topological winding numbers associated with integer-charged bare quarks in the far past and future. This transition, which nonperturbatively normalizes local bare charges with a universal accumulated value, corresponds to a specific topologically nontrivial configuration of the weak gauge fi…
Monopoles have recently been discussed to be a dominant component in strong coupled quark gluon plasma ( QGP ) and to play a role for chiral symmetry breaking as well as quark confinement. We analyze monopole quark interactions and show that massless quarks colliding with the monopoles inevitably change their chiralities keeping their flavors. The monopole quark interaction explicitly breaks the chiral symmetry ( SU$_A(2)\times $U$_A$(1) ) just like bare quark masses. It is given by $\bar{q}qΦ^{\dagger}Φ$ with the monopole field $Φ$. The pions are not Nambu-Goldstone bosons even in the vanishi…
We study the structure of the $Λ_c(2595)$ and $Λ_c(2625)$ resonances in the framework of an effective field theory consistent with heavy quark spin and chiral symmetries, that incorporates the interplay between $Σ_c^{(*)}π-ND^{(*)}$ baryon-meson degrees of freedom and bare P-wave $c\bar ud$ quark-model states. We show that these two resonances are not HQSS partners. The $J^P= 3/2^-$ $Λ_c(2625)$ should be viewed mostly as a dressed three quark state, whose origin is determined by a bare state, predicted to lie very close to the mass of the resonance. The $J^P= 1/2^-$ $Λ_c(2595)$ seems to have, …
We show that the Coulomb barrier at the quark surface of a hot strange star may be a powerful source of $e^+e^-$ pairs which are created in an extremely strong electric field of the barrier and flow away from the star. The luminosity in the outflowing pair plasma depends on the surface temperature $T_{_S}$ and may be very high, up to $\sim 3\times 10^{51} ergs/s$ at $T_{_S}\sim 10^{11}$ K. The effect of pair creation by the Coulomb barrier may be a good observational signature of strange stars which can give an answer to the question of whether a compact object is a neutron or strange star.
A topological approach to quark fractional charges, based on charge constraints unexplained by the Standard Model of particle physics, is discussed. Charge fractionalization is related to a tunneling process occurring in time between pure gauge field configurations at the far past and future associated with integer-charged bare quarks, named prequarks. This transition conforms to a topologically nontrivial configuration of the weak gauge fields in Euclidean space-time. In this context, an electroweak $Z_{2}$ symmetry between bare quarks and leptons, named presymmetry, is revealed. It is shown …
The cooling of a young bare strange star is studied numerically by solving the equations of energy conservation and heat transport for both normal and superconducting strange quark matter inside the star. We show that the thermal luminosity from the strange star surface, due to both photon emission and e+e- pair production, may be orders of magnitude higher than the Eddington limit, for about one day for normal quark matter but possibly for up to a hundred years for superconducting quark matter, while the maximum of the photon spectrum is in hard X-rays with a mean energy of ~ 100 keV or even …
We consider a thin ($\sim 10^2-10^3$ fm) layer of electrons (the electrosphere) at the quark surface of a bare strange star, taking into account the surface effects at the boundary with the vacuum. The quark surface holds the electron layer by an extremely strong electric field, generated in the electrosphere to prevent the electrons from escaping to infinity by counterbalancing the degeneracy and thermal pressure. Because of the surface tension and depletion of $s$ quarks a very thin (a few fm) charged layer of quarks forms at the surface of the star. The formation of this layer modifies the …
A novel framework is proposed to extract near-threshold resonant states from finite-volume energy levels of lattice QCD and is applied to elucidate structures of the positive parity $D_s$. The quark model, the quark-pair-creation mechanism and $D^{(*)}K$ interaction are incorporated into the Hamiltonian effective field theory. The bare $1^+$ $c\bar s$ states are almost purely given by the states with heavy-quark spin bases. The physical $D^*_{s0}(2317)$ and $D^*_{s1}(2460)$ are the mixtures of bare $c\bar s$ core and $D^{(*)}K$ component, while the $D^*_{s1}(2536)$ and $D^*_{s2}(2573)$ are alm…
We studied the high energy quark anti-quark elastic scattering with an exchange of a mesonic state in the $t$ channel with $-t/Λ_{QCD}^{2} \gg 1$. Two methods are proposed to eliminate the strong background from bare pomeron, reggized gluon and odderon exchange. The feasibility of measuring mesonic reggeon exchange is discussed.
We analyze the quark spectral function above the critical temperature for deconfinement in quenched lattice QCD using clover improved Wilson fermions in Landau gauge. We show that the temporal quark correlator is well reproduced by a two-pole approximation for the spectral function and analyze the bare quark mass dependence of both poles as well as their residues. In the chiral limit we find that the quark spectral function has two collective modes which correspond to the normal and plasmino excitations. At large values of the bare quark mass the spectral function is dominated by a single pole…
We analyze the spectral properties of the quark propagator above the critical temperature for the deconfinement phase transition in quenched lattice QCD using clover improved Wilson fermions. The bare quark mass dependence of the quark spectral function is analyzed by varying the hopping parameter κin Landau gauge. We assume a two-pole structure for the quark spectral function, which is numerically found to work quite well for any value of κ. It is shown that in the chiral limit the quark spectral function has two collective modes that correspond to the normal and plasmino excitations, while i…
We present the general formalism required to derive generalized parton distributions within a convolution model where the bare nucleon is dressed by its virtual meson cloud. In the one-meson approximation the Fock states of the physical nucleon are expanded in a series involving a bare nucleon and two-particle, meson-baryon, states. The baryon is assumed here to be either a nucleon or a $Δ$ described within the constituent quark model in terms of three valence quarks; correspondingly, the meson, assumed to be a pion, is described as a quark-antiquark pair. Explicit expressions for the unpolari…
On the basis of the decay couplings f_0 -> ππ, K\bar K, ηη, ηη', which had been found before, in the study of analytical (IJ^{PC}=00^{++})-amplitude in the mass range 450-1900 MeV, we analyse the quark-gluonium content of resonances f_0(980), f_0(1300), f_0(1500), f_0(1750) and the broad state f_0(1420 ^{+ 150}_{-70}). The K-matrix technique used in the analysis makes it possible to evaluate the quark-gluonium content both for the states with switched-off decay channels (bare states, f^{bare}_0) and the real resonances. We observe significant change of the quark-gluonium composition in the evo…
We investigate the valence $u$ and $\bar{s}$ quark distribution functions of the $K^+$ meson, $v^{K(u)}(x,Q^2)$ and $v^{K(\bar{s})}(x,Q^2)$, in the framework of the chiral constituent quark model. We judiciously choose the bare distributions at the initial scale to generate the dressed distributions at the higher scale, considering the meson cloud effects and the QCD evolution, which agree with the phenomenologically satisfactory valence quark distribution of the pion and the experimental data of the ratio $v^{K(u)}(x,Q^2)/v^{π(u)}(x,Q^2)$. We show how the meson cloud effects affect the bare d…
Strange quark matter with the density of ~ 5\times 10^{14} g cm^{-3} might exist up to the surface of a strange star. This differs qualitatively from the case of a neutron star and opens observational possibilities to distinguish strange stars from neutron stars. The thermal emission of photons and e^+e^- pairs from the bare (or nearly bare) quark surface of hot strange stars is reviewed. Bare strange stars are reasonable candidates for soft gamma-ray repeaters. The bursting activity of a soft gamma-ray repeater may be explained by fast heating of the bare quark surface of a strange star up to…
We compute the hadronic matrix elements of the four-quark operators relevant for $K^0-{\bar K^0}$ mixing beyond the Standard Model. Our results are from lattice QCD simulations with $n_f=2+1$ flavours of domain-wall fermion, which exhibit continuum-like chiral-flavour symmetry. The simulations are performed at two different values of the lattice spacing ($a\sim0.08$ and $a\sim 0.11 \, \fm $) and with lightest unitary pion mass $\sim 300\, \MeV$. For the first time, the full set of relevant four-quark operators is renormalised non-perturbatively through RI-SMOM schemes; a detailed description o…
A class of phenomenological relativistic models of hadronic systems motivated by QCD that have dual representations as models of mesons and nucleons or quarks and gluons is investigated. These models are designed to provided qualitative insight into the role of sea quarks in hadronic structure and reactions. The model assumption is that the Hamiltonian can be divided into two parts; one that involves degrees of freedom in the same connected local and global color singlet and the remaining interactions that allow the connected local and global color singlets to interact. The first class of inte…
We consider quark-photon correlations that have been proposed as a source for single-spin asymmetries in inclusive deep-inelastic scattering. A new sum rule for these correlators is derived and its phenomenological consequences are discussed. The results are interpreted within the context of an intuitive 'electrodynamic lensing' picture.
We investigate a possible use of direct photon production in association with a heavy quark to test different models of intrinsic heavy quark parton distribution function (PDF) at the Tevatron, at the large hadron collider (LHC) and at RHIC.
Recently, it was found in QED that the generation of a dynamical electron mass in a strong magnetic field is significantly enhanced by the perturbative electron mass. In the present paper, the related question of a possible enhancement of the dynamical quark mass in an external magnetic field and with a bare mass term is investigated in the Nambu--Jona-Lasinio model.
We study the structure of constituent quarks by dressing bare quarks with the Goldstone bosons and its implications for quark distribution functions of hadrons $f_1(x)$, $g_1(x)$ and $h_1(x)$. In particular we discuss effects of the dressing on the nucleon spin structure, and find that contributions to chiral-odd $h_1(x)$ is quite different from those to $g_1 (x)$, which can be measured in the semi-inclusive polarized deep inelastic scattering.
This paper is concerned with a way of thinking about the standard model that explains the existence of three fermion families and the value of the fine structure constant. The main idea is that the ultraviolet divergences that we encounter in the quantum field theories of the standard model, when interpreted appropriately, have a deep physical significance that leads to new relationships between the physical and bare masses quarks and leptons. This interpretation is based on the assumption of a quantum gravity induced ultraviolet cutoff at the Planck scale and a novel approach to mass renormal…
I discuss mechanisms of heavy quark production in (real) photon-nucleon and (real) photon - (real) photon collisions. In particular, I focuse on application of the Saturation Model. In addition to the main dipole-nucleon or dipole-dipole contribution included in recent analyses, I propose how to calculate within the same formalism the hadronic single-resolved contribution to heavy quark production. At high photon-photon energies this yields a sizeable correction of about 30-40 % for inclusive charm production and 15-20 % for bottom production.
We present the next-to-leading-order cross sections of the heavy quark-antiquark pair production in polarized photon-photon collision for the general case of photon polarizations. The numerical results for top-antitop production cross sections together with production asymmetries are obtained for linearly polarized photon-photon collisions, including one-loop QCD radiative corrections.
The observed excess in the diphoton mass spectrum around 750 GeV at the 13 TeV LHC possibly indicates the presence of a photonphilic resonance. We show that the excess can be explained by a scalar of the type involved in Bekenstein's framework for varying electromagnetic coupling theories. The scalar, in our model, couples dominantly to photons and is mainly produced by the quark-quark fusion at the LHC. In addition, it can also be produced in photon-photon fusion. Our model has only two free parameters, the mass of the scalar and the scale of the new physics, which are fixed by the LHC excess…
We probe the top-quark electric dipole moment (EDM) in top-quark pair production via photon-photon fusion at a photon linear collider. We show how linearly-polarized photon beams can be used to extract information on the top-quark EDM without the use of complicated angular correlations of top-quark decay products. If the luminosity of the laser back-scattered photon-photon collisions is comparable to that of the $e^+e^-$ collisions, then the measurement of the top-quark EDM obtained by counting top-quark-production events in photon fusion can be as accurate as the measurement obtained by study…
We study the inclusive production of isolated prompt photons within the framework of the quasi-multi-Regge-kinematic approach, applying the quark Reggeization hypothesis. We describe accurately and without free parameters the transverse momentum and pseudorapidity spectra of prompt photons in the inclusive photoproduction at the HERA Collider. It is shown that the main mechanism of the inclusive prompt photon production in the gamma p collisions is the fusion of a Reggeized quark (antiquark) from the proton and a collinear antiquark (quark) from the photon into a photon, via the effective Regg…
Two-photon decay rates of pseudoscalar, scalar and tensor states of charmonium and bottomonium are calculated in the framework of the relativistic quark model. Both relativistic effects and one-loop radiative corrections are taken into account. The obtained results are compared with other theoretical predictions and available experimental data.
We study numerically the thermal emission of $e^+e^-$ pairs from a bare strange star heated by energy input onto its surface; heating starts at some moment, and is steady afterwards. The thermal luminosity in $e^+e^-$ pairs increases to some constant value. The rise time and the steady thermal luminosity are evaluated. Both normal and colour superconducting states of strange quark matter are considered. The results are used to test the magnetar model of soft gamma-ray repeaters where the bursting activity is explained by fast decay of superstrong magnetic fields and heating of the strange star…
We calculate photon production from a quark-gluon plasma which is anisotropic in momentum space including the Compton scattering and quark/anti-quark annihilation processes. We show that for a quark-gluon plasma which has an oblate momentum-space anisotropy the photon production rate has an angular dependence which is peaked transverse to the beam line. We propose to use the angular dependence of high-energy medium photon production to experimentally determine the degree of momentum-space isotropy of a quark-gluon plasma produced in relativistic heavy-ion collisions.
We study the prospects for probing the quark content of the photon using b tagging at high energy electron-photon colliders. We find that heavy quark tagging provides a sensitive and effective probe of the quark content of the photon. Using a 500 GeV $e^+e^-$\ NLC in electron-photon mode, the cross section for $eb_γ\rightarrow eb$\ can be measured to 10\% with b tagging. This is sufficient to differentiate between the various photon structure functions.
We consider a stationary, spherically outflowing wind consisting of electron-positron pairs and photons. We do not assume thermal equilibrium, and include the two-body processes that occur in such a wind: Moller and Bhaba scattering of pairs, Compton scattering, two-photon pair annihilation, and two-photon pair production, together with their radiative three-body variants: bremsstrahlung, double Compton scattering, and three-photon pair annihilation, with their inverse processes. In the concrete example described here, the wind injection source is a hot, bare, strange star. Such stars are thou…
We compute the photon production rate of a quark-gluon plasma (QGP) at finite quark chemical potential $μ$ using the Braaten-Pisarski method, thus continuing the work of Kapusta, Lichard, and Seibert who did the calculation for $μ=0$.
The possibility and the implications of the idea, that pulsars are born as strange stars, are explored. Strange stars are very likely to have atmospheres with typical mass of $\sim 5\times 10^{-15}M_\odot$ but bare polar caps almost throughout their lifetimes, if they are produced during supernova explosions. A direct consequence of the bare polar cap is that the binding energies of both positively and negatively charged particles at the bare quark surface are nearly infinity, so that the vacuum polar gap sparking scenario as proposed by Ruderman & Sutherland should operate above the cap, rega…
A quark propagating through the quark gluon plasma and scattering off the thermal gluons can radiate photons in states with definite angular momentum and magnetic helicity. These states, known as the Chandrasekhar-Kendall states, are eigenstates of the curl operator and have a non-trivial topology. I compute spectrum of these states in the ultrarelativistic limit and study its properties.
We present a relativistic calculation of two-photon decays for heavy and light mesons in the framework of the Salpeter equation for quark-antiquark states. The meson-photon-photon vertex is computed by reconstructing the Bethe-Salpeter vertex function and evaluating the four-dimensional Feynman diagram with off-shell quark amplitudes. The two-photon width for light and heavy quarkonia up to spin equal six are calculated with different parameter sets taken from the literature thus giving a complete overview on the mesonic two-photon physics. We find that relativistic effects including the negat…
We study the induced photon bremsstrahlung from a fast quark produced in AA-collisions due to multiple scattering in quark-gluon plasma. For RHIC and LHC conditions the induced photon spectrum is sharply peaked at photon energy close to the initial quark energy. In this region the contribution of the induced radiation to the photon fragmentation function exceeds the ordinary vacuum radiation. Contrary to previous analyses our results show that at RHIC and LHC energies the final-state interaction effects in quark-gluon plasma do not suppress the direct photon production, and even may enhance it…
The production of a single top quark in association with an isolated photon probes the electromagnetic coupling structure of the top quark. We investigate the sensitivity of kinematical distributions at the LHC in single-top-plus-photon production in view of a detection of anomalous electric and magnetic dipole moments of the top quark.
The capability of the LHC to study the electromagnetic dipole moments of the top quark is discussed. In particular, the process $pp\to pγγp\to pt\bar{t}p$, which is supposed to be tagged by the forward/backward detectors at the LHC experiments, is used to explore the top quark electric and magnetic moments. We perform analytical calculations and then a numerical analysis on the sensitivity of the total cross section of the top quark pair production in $γγ$ scattering at the LHC to the anomalous top quark couplings with photon. It is shown that improvements in the bounds on the electromagnetic …
We study ep deep inelastic scattering and the inclusive production of prompt photon within the framework of the quasi-multi-Regge-kinematic approach, applying the quark Reggeization hypothesis. We describe structure functions F_2 and F_L supposing that a virtual photon scatters on a Reggeized quark from a proton, via the effective gamma-Reggeon-quark vertex. It is shown that the main mechanism of the inclusive prompt photon production in p \bar p collisions is the fusion of a Reggeized quark and a Reggeized antiquark into a photon, via the effective Regeon-Reggeon-gamma vertex. We describe the…
We investigated top quark effects on virtual photon structure functions by pQCD. We include the top quark mass effects on the virtual photon structure function with the quark parton model and with the operator product expansion up to the next-to-leading order in QCD. We also consider the threshold effect on the running coupling constant in the calculation to the effective photon structure function with a matching condition. The numerical calculations are investigated in the kinematical region expected at the future international linear collider.
Photon emission arising in the course of transition between the states of quark-gluon and hadron plasma has been considered. Single-photon distributions and two-photon correlations in central rapidity region have been calculated for heavy ion collisions at high energies. It has been found that opposite side two-photon correlations can serve as a sign of sharp transitions between the states of strongly interaction matter.
In two-photon collisions at LEP2 and a future $e^+e^-$ linear collider heavy quarks (mainly charm) will be pair-produced rather copiously. The production via direct and resolved photons can be distinguished experimentally via a remnant-jet tag. We study correlations of the heavy quarks at next-to-leading order in QCD in the direct channel, which is free from phenomenological parton densities in the photon. These correlations are therefore directly calculable in perturbative QCD and provide a stringent test of the production mechanism.
The production cross section of heavy quarks in real and virtual photon-photon collisions has been studied. The unintegrated gluon density in the photon was obtained using the full CCFM evolution equation for the first time. The gluon density was implemented in the Monte Carlo generator CASCADE, and cross sections for heavy quark production in $e^+e^-$ collisions were calculated and compared to LEP data. Also, predictions for heavy quark cross sections in $e^+e^-$ and $γγ$ collisions at TESLA energies are given.
Direct photon production in association with a heavy quark can serve as an excellent tool for the study of the heavy quark distributions. Currently it is believed that heavy quarks are produced radiatively inside the nucleon, and so there is no need to take into account heavy quark parameters inside global PDF analyses. Certain models taking into account the possibility of an intrinsic charm component exist. Here we present how these affect the γ+ c cross section. While at pA collisions the potential of this process to constrain the gluon nuclear PDF which is currently largely unconstrained is…
