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In the high energy limit of hadron collisions, the evolution of the gluon density in the longitudinal momentum fraction can be deduced from the Balitsky hierarchy of equations or, equivalently, from the nonlinear Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK) equation. The solutions of the latter can be studied numerically by using its reformulation in terms of a Langevin equation. In this paper, we present a comprehensive study of systematic effects associated with the numerical framework, in particular the ones related to the inclusion of the running coupling. We consider three proposed ways in which the running of the coupling constant can be included: "square root" and "noise" prescriptions and the recent proposal by Hatta and Iancu. We implement them both in position and momentum spaces and we investigate and quantify the differences in the resulting evolved gluon distributions. We find that the systematic differences associated with the implementation technicalities can be of a similar magnitude as differences in running coupling prescriptions in some cases, or much smaller in other cases., 21 pages, 18 figures, references updated

We study diffractive scattering cross sections, focusing on the rapidity gap distribution in realistic kinematics at future electron-ion colliders. Our study consists in numerical solutions of the QCD evolution equations in both fixed and running coupling frameworks. The fixed and the running coupling equations are shown to lead to different shapes for the rapidity gap distribution. The obtained distribution when the coupling is fixed exhibits a shape characteristic of a recently developed model for diffractive dissociation, which indicates the relevance of the study of that diffractive observable for the partonic-level understanding of diffraction., Comment: 7 pages, 2 figures; Submission to SciPost, Contribution to the XXVIII International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS2021)

We investigate hysteresis effects in the perturbative solution of renormalisation group equations (RGEs). We present examples for the QCD running coupling and proton's parton distribution functions (PDFs), relevant to precision physics at the Large Hadron Collider (LHC) and future collider experiments. We propose the use of resummation scales to take into account the theoretical uncertainties from the solution of the RGEs. As a case study, we consider the $F_2$ structure function in a region relevant to the extraction of PDFs., 4 pages + references, 6 figures

We study the production of $J/\psi$ vector mesons as a function of charged hadron multiplicity in p+p and p+Pb collisions at LHC energies. We employ the color glass condensate framework, using running coupling Balitsky-Kovchegov evolved dipole amplitudes, to compute gluon and $c\bar{c}$-pair production. We use fragmentation functions to obtain charged hadrons, and explore two different hadronization schemes for the $J/\psi$: non-relativistic quantum chromodynamics and the improved color evaporation model. In our framework, event-by-event multiplicity fluctuations of both hadrons and $J/\psi$ are driven by geometric and saturation scale normalization fluctuations. Studying the correlation between $J/\psi$ and hadron multiplicity, we show that the characteristic difference between forward and backward rapidity in p+Pb collisions is a result of different degrees of saturation probed at different rapidities. We demonstrate that experimental data on heavy-flavor production as a function of event activity provide stringent constraints on the fluctuating proton structure., Comment: 11 pages, 8 figures

Workshop on Naturalness, Hierarchy, and Fine Tuning, Aachen, Germany, 28 Feb 2018 - 2 Mar 2018; Acta physica Polonica / B 52(6-7), 575 - 605 (2021). doi:10.5506/APhysPolB.52.575, I am considering Veltman's 'The Infrared - Ultraviolet Connection' addressing the issue of quadratic divergences and the related huge radiative correction predicted by the electroweak Standard Model (SM) in the relationship between the bare and the renormalized theory, commonly called 'the hierarchy problem' which usually is claimed that this has to be cured. After the discovery of the Higgs particle at CERN, which essentially completed the SM, an amazing interrelation of the leading interaction strengths of the gauge bosons, the top-quark and the Higgs boson showed up amounting that the SM allows for a perturbative extrapolation of the running couplings up to the Planck scale. The central question concerns the stability of the electroweak vacuum, which requires that the running Higgs self-coupling stays positive. Although several evaluations seem to favor the meta-stability within the experimental and theoretical parameter-uncertainties, one should not exclude the possibility that other experiments and improved matching conditions will be able to establish the absolute stability of the SM vacuum in the future. I will discuss the stable vacuum scenario and its impact on early cosmology, revealing the Higgs boson as the inflaton. It turns out that the Standard Model's presumed 'hierarchy problem' and similarly the 'cosmological constant problem' resolve themselves when we understand the SM as a low energy effective tail that is emergent from a cutoff-medium at the Planck scale. 'The Infrared - Ultraviolet Connection' conveyed by the Higgs boson mass renormalization appears in a new light when the energy dependence of the SM couplings is taken into account. The bare Higgs boson mass square then changes sign below the Planck scale where it is activating the Higgs mechanism. At the same time, it reveals that the SM towards the Planck scale is in the symmetric phase, where the Higgs potential provides a high dark energy density triggering inflation, and four heavy Higgs bosons which decay and thereby are reheating the inflated early universe., Published by Inst. of Physics, Jagellonian Univ., Cracow

The 38th International Symposium on Lattice Field Theory, LATTICE2021, Zoom/Gather@Massachusetts Institute of Technology, USA, 26 Jul 2021 - 30 Jul 2021; Proceedings of Science / International School for Advanced Studies (LATTICE2021), 423 (2021). doi:10.22323/1.396.0423, As present and future experiments, on both the energy and precision frontiers, look to identify new physics beyond the Standard Model (BSM), we require more precise determinations of fundamental quantities, like the QED and electroweak couplings at various momenta. These can be obtained either entirely from experimental measurements, or from one such measurement at a particular virtuality combined with the couplings’ virtuality dependence computed within the SM. Thus, a precise, entirely theoretical determination of the running couplings is highly desirable, even more since the preliminary results of the E989 experiment in Fermilab were published. We give results for the hadronic contribution to the QED running coupling $\alpha(Q^{2})$ and weak mixing angle $\sin^{2}\theta_{W}(Q^{2})$ in the space-like energy region (0, 7] GeV$^{2}$ with a total relative uncertainty of2% at energies $Q^{2} \ll 1$ GeV$^{2}$, and 1% at $Q^{2} > 1$ GeV$^{2}$., Published by SISSA, Trieste

We present predictions for the distribution of rapidity gaps in realistic kinematics of future electron-ion colliders, based on numerical solutions of the original Kovchegov-Levin equation and of its next-to-leading extension taking into account the running of the strong coupling. We find that for the rapidities we have considered, the fixed and the running coupling equations lead to different distributions, rather insensitive to the chosen prescription in the running coupling case. The obtained distributions for the fixed coupling framework exhibit a shape characteristic of a recently proposed partonic picture of diffractive dissociation already at rapidities accessible at future electron-ion colliders. The modification of this shape in the running coupling case can also be understood qualitatively from that picture. Our results confirm the relevance of measurements of such observables for the microscopic understanding of diffractive dissociation in the framework of quantum chromodynamics., Comment: 17 pages, 10 figures

We study a puzzle raised recently regarding the running coupling prescription used in the calculation of forward particle production in proton-nucleus collisions at next-to-leading order: using a coordinate space prescription which is consistent with the one used in the high energy evolution of the target leads to results which can be two orders of magnitude larger than the ones obtained with a momentum space prescription. We show that this is an artefact of the Fourier transform involved when passing between coordinate and momentum space and propose a new coordinate space prescription which avoids this problem., Comment: 4 pages, 1 figure. Quark Matter 2018 proceedings

We analyze the possibility of extracting a clear signal of non-linear parton saturation effects from future measurements of nuclear structure functions at the Electron-Ion Collider (EIC), in the small-x region. Our approach consists in generating pseudodata for electron-gold collisions, using the running-coupling Balitsky-Kovchegov evolution equation, and in assessing the compatibility of these saturate pseudodata with existing sets of nuclear parton distribution functions (nPDFs), extrapolated if necessary. The level of disagreement between the two is quantified by applying a Bayesian reweighting technique. This allows to infer the parton distributions needed in order to describe the pseudodata, which we find quite different from the actual distributions, especially for sea quarks and gluons. This tension suggests that, should saturation effects impact the future nuclear structure function data as predicted, a successful refitting of the nPDFs may not be achievable, which would unambiguously signal the presence of non-linear effects., Comment: 16 pages, 5 figures; small detail updated in the summary for clarification and better understanding

We report results of our recent works [1,2] where we where the correlations between the c,b-quark running masses{m}_{c,b}, the gluon condensate and the QCD coupling \alpha_s in the MS-scheme from an analysis of the charmonium and bottomium spectra and the B_c-meson mass. We use optimized ratios of relativistic Laplace sum rules (LSR) evaluated at the \mu-subtraction stability point where higher orders PT and D< 6-8-dimensions non-perturbative condensates corrections are included. We obtain [1] \alpha_s(2.85)=0.262(9) and \alpha_s(9.50)=0.180(8) from the (pseudo)scalar M_{\chi_{0c(0b)}}-M_{\eta_{c(b)}} mass-splittings at \mu=2.85(9.50) GeV. The most precise result from the charm channel leads to \alpha_s(M_\tau)=0.318(15) and \alpha_s(M_Z)=0.1183(19)(3) in excellent agreement with the world average: \alpha_s(M_Z)=0.1181(11)[3,4]. Updated results from a global fit of the (axial-)vector and (pseudo)scalar channels using Laplace and Moments sum rules @ N2LO [1] combined with the one from M_{B_c} [2] lead to the new tentative QCD spectral sum rules (QSSR) average : m_c(m_c)|_average= 1266(6) MeV and m_b(m_b)|_average=4196(8) MeV. The values of the gluon condensate from the (axial)-vector charmonium channels combined with previous determinations in Table 1, leads to the new QSSR average [1]: _average=(6.35\pm 0.35)x 10^{-2} GeV^4. Our results clarify the (apparent) discrepancies between different estimates of from J/\psi sum rule but also shows the sensitivity of the sum rules on the choice of the \mu-subtraction scale. As a biproduct, we deduce the B_c-decay constants f_{B_c}=371(17) MeV and f_{B_c}(2S)< 139(6) MeV., Comment: Review talk presented at QCD19 (2-7 july 2019, Montpellier - FR) and at HEPMAD19 (14-20 october 2019, Antananarivo-MG). 13 pages, 1 Table. To appear in Nucl. Phys. Proceedings (2020). arXiv admin note: substantial text overlap with arXiv:1801.00592

Within the framework of the dipole factorisation, we use a recent collinearly-improved version of the Balitsky-Kovchegov equation to fit the HERA data for inclusive deep inelastic scattering at small Bjorken $x$. The equation includes an all-order resummation of double and single transverse logarithms and running coupling corrections. Compared to similar equations previously proposed in the literature, this work makes a direct use of Bjorken $x$ as the rapidity scale for the evolution variable. We obtain excellent fits for reasonable values for the four fit parameters. We find that the fit quality improves when including resummation effects and a physically-motivated initial condition. In particular, the resummation of the DGLAP-like single transverse logarithms has a sizeable impact and allows one to extend the fit up to relatively large photon virtuality $Q^2$., Comment: 16 pages, 4 figures, 2 tables

We calculate isolated photon production at forward rapidities in proton-nucleus collisions in the Color Glass Condensate framework. Our calculation uses dipole cross sections solved from the running coupling Balitsky-Kovchegov equation with an initial condition fit to deep inelastic scattering data and extended to nuclei with an optical Glauber procedure that introduces no additional parameters beyond the basic nuclear geometry. We present predictions for future forward RHIC and LHC measurements. The predictions are also compared to updated results for the nuclear modification factors for pion production, Drell-Yan dileptons and $J/\psi$ mesons in the same forward kinematics, consistently calculated in the same theoretical framework. We find that leading order, running coupling high energy evolution in the CGC picture leads to a significant nuclear suppression at forward rapidities. This nuclear suppression is stronger for photons than for pions. We also discuss how this might change with next-to-leading order high energy evolution., Comment: 4 pages, 4 figures, talk by T.L. at the Quark Matter 2018 conference

We report on the first computation of the strong running coupling at the physical point (physical pion mass) from the ghost-gluon vertex, computed from lattice simulations with three flavors of Domain Wall fermions. We find $\alpha_{\overline{\rm MS}}(m_Z^2)=0.1172(11)$, in remarkably good agreement with the world-wide average. Our computational bridge to this value is the Taylor-scheme strong coupling, which has been revealed of great interest by itself because it can be directly related to the quark-gluon interaction kernel in continuum approaches to the QCD bound-state problem., Comment: 6 pages, 3 figures, v2: references added

We study the disappearance of the away-side peak of the di-hadron correlation function in p+A vs p+p collisions at forward rapidities, when the scaterring process presents a manifest dilute-dense asymmetry. We improve the state-of-the-art description of this phenomenon in the framework of the Color Glass Condensate (CGC), for hadrons produced nearly back-to-back. In that case, the gluon content of the saturated nuclear target can be described with transverse-momentum-dependent gluon distributions, whose small-$x$ evolution we calculate numerically by solving the Balitsky-Kovchegov equation with running coupling corrections. We first show that our formalism provides a good description of the disappearance of the away-side azimuthal correlations in d+Au collisions observed at BNL Relativistic Heavy Ion Collider (RHIC) energies. Then, we predict the away-side peak of upcoming p+Au data at $~\sqrt[]{s}=200$ GeV to be suppressed by about a factor 2 with respect to p+p collisions, and we propose to study the rapidity dependence of that suppression as a complementary strong evidence of gluon saturation in experimental data., 13 pages; 6 figures

We calculate isolated photon production at forward rapidities in proton-nucleus collisions in the Color Glass Condensate framework. Our calculation uses dipole cross sections solved from the running coupling Balitsky-Kovchegov equation with an initial condition fit to deep inelastic scattering data. For comparison, we also update the results for the nuclear modification factor for pion production in the same kinematics. We present predictions for future forward RHIC and LHC measurements at $\sqrt{s_{NN}}=200$ GeV and $\sqrt{s_{NN}}=8$ TeV., Comment: 8 pages, 7 figures. v2: matches published version

We address and solve a puzzle raised by a recent calculation [1] of the cross-section for particle production in proton-nucleus collisions to next-to-leading order: the numerical results show an un- reasonably large dependence upon the choice of a prescription for the QCD running coupling, which spoils the predictive power of the calculation. Specifically, the results obtained with a prescription formulated in the transverse coordinate space differ by one to two orders of magnitude from those obtained with a prescription in momentum space. We show that this discrepancy is an artefact of the interplay between the asymptotic freedom of QCD and the Fourier transform from coordinate space to momentum space. When used in coordinate space, the running coupling can act as a fictitious potential which mimics hard scattering and thus introduces a spurious contribution to the cross-section. We identify a new coordinate-space prescription which avoids this problem and leads to results consistent with those obtained with the momentum-space prescription., 28 pages, 9 figures, 2 appendices

We report on an instanton-based analysis of the gluon Green functions in the Landau gauge for low momenta; in particular we use lattice results for $\alpha_s$ in the symmetric momentum subtraction scheme (${\rm MOM}$) for large-volume lattice simulations. We have exploited quenched gauge field configurations, $N_f=0$, with both Wilson and tree-level Symanzik improved actions, and unquenched ones with $N_f=2+1$ and $N_f=2+1+1$ dynamical flavors (domain wall and twisted-mass fermions, respectively). We show that the dominance of instanton correlations on the low-momenta gluon Green functions can be applied to the determination of phenomenological parameters of the instanton liquid and, eventually, to a determination of the lattice spacing. We furthermore apply the Gradient Flow to remove short-distance fluctuations. The Gradient Flow gets rid of the QCD scale, $\Lambda_{\rm QCD}$, and reveals that the instanton prediction extents to large momenta. For those gauge field configurations free of quantum fluctuations, the direct study of topological charge density shows the appearance of large-scale lumps that can be identified as instantons, giving access to a direct study of the instanton density and size distribution that is compatible with those extracted from the analysis of the Green functions., Comment: Proceedings of the 35th International Symposium on Lattice Field Theory, Granada, Spain

The high-energy evolution of Wilson line operators, which at leading order is described by the Balitsky-JIMWLK equations, receives large radiative corrections enhanced by single and double collinear logarithms at next-to-leading order and beyond. We propose a method for resumming such logarithmic corrections to all orders, at the level of the Langevin formulation of the JIMWLK equation. The ensuing, collinearly-improved Langevin equation features generalized Wilson line operators, which depend not only upon rapidity (the logarithm of the longitudinal momentum), but also upon the transverse size of the color neutral projectile to which the Wilson lines belong. This additional scale dependence is built up during the evolution, via the condition that the successive emissions of soft gluons be ordered in time. The presence of this transverse scale in the Langevin equation furthermore allows for the resummation of the one-loop running coupling corrections., 24 pages, 1 figure

The gradient flow in QCD is treated perturbatively through next-to-next-to-leading order in the strong coupling constant. The evaluation of the relevant momentum and flow-time integrals is described, including various means of validation. For the vacuum expectation value of the action density, which turns out to be a useful quantity in lattice calculations, we find a very well-behaved perturbative series through NNLO. Quark mass effects are taken into account through NLO. The theoretical uncertainty due to renormalization scale variation is significantly reduced with respect to LO and NLO, as long as the flow time is smaller than about 0.1 fm., Comment: 25 pages, 6 figures, 3 tables. v2: typos fixed; matches published version

20th International Workshop on Deep-Inelastic Scattering and Related Subjects, DIS 2012, Bonn, Germany, 26 Mar 2012 - 30 Mar 2012; Hamburg : Deutsches Elektronen-Synchrotron, DESY 429-432 (2012). doi:10.3204/DESY-PROC-2012-02/97, The proton structure function F2 is studied in the low x regime using BFKL evolution. The next to leading logarithmic (NLL) analysis requires the inclusion of running coupling effects which lead to off-diagonal terms in the evolution kernel. An all-orders resummation is used to improve the collinear behavior of the NLL BFKL result. We emphasize the theoretical uncertainties that appear throughout the analysis and give a comparison to the combined HERA data., Published by Deutsches Elektronen-Synchrotron, DESY, Hamburg