Gluon Exchange Research Articles

Low and moderate x gluon contribution to exclusive Compton scattering processes

Abstract We revisit the high energy semi-classical description of the exclusive processes DVCS, TCS, and Double DVCS by explicitly keeping track of the Feynman x dependence in both the hard and the hadronic matrix elements. This is achieved by a modification of the standard shock wave approximation to derive the effective Feynman rules, which leads to a generic expression on which we then perform a partial twist expansion to get rid of quantities suppressed by the proper physical scales. We obtain a compact factorized master formula that can be used to investigate the Bjorken limit at leading twist. In particular, we recover the full one-loop result in the collinear limit for pure gluon exchange with the target. Finally, we discuss the subtleties in taking the simultaneous collinear and small x limit.

T-odd transverse momentum dependent gluon fragmentation functions in a spectator model

We present a model calculation of the T-odd transverse momentum dependent (TMD) gluon fragmentation functions for a spin-1/2 hadron. Our model is based on the postulation that a time-like off-shell gluon can fragment into a hadron and a single spectator particle, which is considered to be on-shell. We consider the effect of the gluon exchange to calculate all necessary one-loop diagrams for the gluon-gluon correlation functions. Two out of four one-loop diagrams give sizeable contributions to the fragmentation functions. We obtain analytical expressions for the four T-odd TMD fragmentation functions of the gluon. We also provide numerical results on the z-dependence and kT-dependence of the fragmentation functions.

Hadronic spectrum in the chiral large Nc extension of quantum chromodynamics

We study quantum chromodynamics in the chiral large Nc limit which contains a left-handed Weyl fermion in the fundamental representation, a left-handed Weyl fermion in the two index antisymmetric representation and (Nc−3) left-handed Weyl fermions in the antifundamental representation of the SU(Nc) gauge group. We construct gauge singlet composite operators and study their masses and correlation functions at large Nc. It is shown that all hadron masses scale as ∼Nc0nq where nq is the number of constituent quarks in the hadron. In addition by simple gluon exchange considerations it is seen that scattering amplitudes between hadrons have the same Nc scaling as the mass of the lightest hadron involved. This is the case provided the hadrons in the scattering amplitude share a sufficiently large number of constituent quarks. The chiral large Nc extension also allows for other nontrivial processes. For instance we consider two different baryonium states that are unique to this extension and that decay via emissions of two- and three-quark hadrons. Also other nontrivial scattering processes are considered. Finally, we study composites made of a mix of left- and right-handed fields. We categorize multiple groups of hadrons within the full spectrum according to their flavor structure. Within these groups all n-point functions scale the same. Published by the American Physical Society 2024

Theoretical overview on heavy flavor physics at LHCb

Precise prediction of the heavy hadrons decay amplitudes is of great importance in the determination of the parameters of KM matrix and searching for new physics signals beyond the standard model. Due to the high accuracy of the B meson decay constants, the structure dependent QED corrections should be taken into account for B→μ+μ− decays due to the power enhancement, but this effect is numerically negligible for B→τ+τ−. The radiative leptonic decays and double radiative decays are the best channels to determine the B meson distribution amplitudes, but one should systematically deal with the power corrections to reduce the uncertainty. The heavy-to-light form factors is one of the most important nonperturbative quantities, and an improved method to improve the theoretical accuracy is to fit the form factors using combined data from Lattice and light-cone sum rules which works well at large recoil region. The power suppressed weak annihilation contribution is phenomenologically important in the nonleptonic decays, and the previously neglected hard-collinear gluon exchange diagrams have the potential to cancel the endpoint singularity arising from the hard gluon exchange. Therefore, more endeavors need to be paid to this topic.

Bootstrapping M-theory orbifolds

We analyze correlation functions of SU(k) × SU(2)F flavor currents in a family of three-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 superconformal field theories, combining analytic bootstrap methods with input from supersymmetric localization. Via holographic duality, we extract gluon and graviton scattering amplitudes of M-theory on AdS4 × S7/ℤk which contains a ℂ2/ℤk orbifold singularity. From these results, we derive aspects of the effective description of M-theory on the orbifold singularity beyond its leading low energy limit. We also determine a threshold correction to the holographic correlator from the combined contribution of two-loop gluon and tree-level bulk graviton exchange.

Mixed NNLO QCD × electroweak corrections to single-Z production in pole approximation: differential distributions and forward-backward asymmetry

Radiative corrections in pole approximation, which are based on the leading contribution in a systematic expansion of amplitudes about resonance poles, naturally decompose into factorizable corrections attributed to the production or decay of the resonance and non-factorizable corrections induced by soft photon (or gluon) exchange between those subprocesses. In this paper we complete an earlier calculation of mixed QCD × electroweak corrections of \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{O}\\left({\\alpha }_{{\ ext{s}}}\\alpha \\right)$$\\end{document} to the neutral-current Drell-Yan cross section in pole approximation by including the previously neglected corrections that are solely related to the Z-boson production process. We present numerical results both for differential distributions and for the forward-backward asymmetry differential in the lepton-pair invariant mass, which is the key observable in the measurement of the effective weak mixing angle at the LHC. Carefully disentangling the various types of factorizable and non-factorizable corrections, we find (as expected in our earlier work) that the by far most important contribution at \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{O}\\left({\\alpha }_{{\ ext{s}}}\\alpha \\right)$$\\end{document} originates from the interplay of initial-state QCD corrections and electroweak final-state corrections.

Sound velocity peak and conformality in isospin QCD

We study zero temperature equations of state (EOS) in isospin QCD within a quark-meson model which is renormalizable and hence eliminates high density artifacts in models with the ultraviolet cutoff (e.g., Nambu-Jona-Lasinio type models models). The model exhibits a crossover transition of pion condensations from the Bose-Einstein-Condensation regime at low density to the Bardeen-Cooper-Schrieffer regime at high density. The EOS stiffens quickly and approaches the quark matter regime at density significantly less than the density for pions to spatially overlap. The squared sound velocity cs2 develops a peak in the crossover region, and then gradually relaxes to the conformal value 1/3 from above, in contrast to the perturbative QCD results which predicts the approach from below. In the context of QCD computations, this opposite trend is in part due to the lack of gluon exchanges in our model, and also due to the nonperturbative power corrections arising from the condensates. We argue that with large power corrections the trace anomaly can be negative. Our EOS reproduces the qualitative trend of the lattice results from the BEC to the BCS regime, implying that the quark-meson model captures relevant effective degrees of freedom. The BCS gap in our model is Δ≃300 MeV in the quark matter domain, and naive application of the BCS relation for the critical temperature Tc≃0.57Δ yields the estimate Tc≃170 MeV, in good agreement with the lattice data. Published by the American Physical Society 2024

Approximate bound state solutions of the fractional Schr\"{o}dinger equation under the spin-spin-dependent Cornell potential

In this work, the approximate bound state solutions of the fractional Schr\"{o}dinger equation under a spin-spin-dependent Cornell potential are obtained via the convectional Nikiforov-Uvarov approach. The energy spectra are applied to obtain the mass spectra of the heavy mesons such as bottomonium, charmonium and bottom-charm. The masses for the singlet and triplet spin numbers increase as the quantum numbers increase. The fractional Schr\"{o}dinger equation improves the mass spectra compared to other theoretic masses. The bottomonium masses agree with the experimental results where percentage errors for fractional parameters of $\beta =1,\alpha =0.97$ and $\beta =1,\alpha =0.50$ were found to be 0.67\% and 0.49\% respectively. The respective percentage errors of 1.97\% and 1.62\% for fractional parameters of $\beta =1,\alpha =0.97$ and $\beta =1,\alpha =0.50$ were obtained for charmonium meson. The results indicate that the potential curves coupled with the fractional parameters account for the short-range gluon exchange between the quark-antiquark interactions and the linear confinement phenomena which is associated with the quantum chromo-dynamic and phenomenological potential models in particle and high-energy physics.

Quantum Chromodynamics of the Nucleon in Terms of Complex Probabilistic Processes

Despite the obvious progress made by the Feynman, Ravndal, and Kislinger relativistic model in describing the internal motion of a system with confinement of quarks in a nucleon, it turned out to be insufficiently realistic for a number of reasons. In particular, the model does not take into account some cornerstone properties of QCD, namely, gluon exchange between quarks, the influence of the resulting quark sea on valence quarks, and the self-interaction of colored gluons. It is these phenomena that spontaneously break the chiral symmetry of the quark system and form the bulk of the nucleon. To eliminate the above shortcomings of the model, the problem of self-organization of a three-quark dynamical system immersed in a colored quark–antiquark sea is considered within the framework of complex probabilistic processes that satisfy the stochastic differential equation of the Langevin–Kline–Gordon–Fock type. Taking into account the hidden symmetry of the internal motion of a dynamical system, a mathematically closed nonperturbative approach was developed, which makes it possible to construct the mathematical expectation of the wave function and other parameters of the nucleon in the form of multiple integral representations. It is shown that additional subspaces arising in a representation characterized by a noncommutative geometry with topological features participate in the formation of an effective interaction between valence quarks against the background of harmonic interaction between them.

Bilocal Field Theory for Composite Scalar Bosons.

We give a bilocal field theory description of a composite scalar with an extended binding potential that reduces to the Nambu-Jona-Lasinio (NJL) model in the pointlike limit. This provides a description of the internal dynamics of the bound state and features a static internal wave function, ϕ(r→), in the center-of-mass frame that satisfies a Schrödinger-Klein-Gordon equation with eigenvalues m2. We analyze the "coloron" model (single perturbative massive gluon exchange) which yields a UV completion of the NJL model. This has a BCS-like enhancement of its interaction, ∝Nc the number of colors, and is classically critical with gcritical remarkably close to the NJL quantum critical coupling. Negative eigenvalues for m2 lead to spontaneous symmetry breaking, and the Yukawa coupling of the bound state to constituent fermions is emergent.

Unpolarized transverse-momentum dependent distribution functions of a quark in a pion with Minkowskian dynamics

The unpolarized twist-2 (leading) and twist-3 (subleading), T-even, transverse-momentum dependent quark distributions in the pion are evaluated for the first time by using the actual solution of a dynamical equation in Minkowski space. The adopted theoretical framework is based on the 4D homogeneous Bethe–Salpeter integral equation with an interaction kernel given by a one-gluon exchange, featuring an extended quark-gluon vertex. The masses of quark and gluon as well as the interaction-vertex scale have been chosen in a range suggested by lattice-QCD calculations, and calibrated to reproduce both pion mass and decay constant. The sum rules to be fulfilled by the transverse-momentum dependent distributions are carefully investigated, particularly the leading-twist one, that has to match the collinear parton distribution function, and hence can be scrutinized in terms of existing data as well as theoretical predictions. Noteworthy, the joint use of the Fock expansion of the pion state facilitates an in-depth analysis of the content of the pion Bethe–Salpeter amplitude, allowing to calculate the gluon contribution to the quark average longitudinal fraction, that results to be ∼6%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim 6\\%$$\\end{document}. The current analysis highlights the role of the gluon exchanges through quantitative analysis of collinear and transverse-momentum distributions, showing, e.g. for both leading and subleading-twists, an early departure from the widely adopted exponential fall-off, for |k⊥|2>m2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\ extbf{k}_\\perp |^2> m^2$$\\end{document}, with the quark mass ∼ΛQCD\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim {\\varLambda }_{QCD}$$\\end{document}.

Revisiting ΞQ-ΞQ′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Xi _{Q}-\\Xi _{Q}^{\\prime }$$\\end{document} mixing in QCD sum rules

In this work, we perform a QCD sum rules analysis on ΞQ-ΞQ′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Xi _{Q}-\\Xi _{Q}^{\\prime }$$\\end{document} mixing. Contributions from up to dimension-6 four-quark operators are considered. However, it turns out that only dimension-4 and dimension-5 operators contribute, which reveals the non-perturbative nature of mixing. In particular, we observe that only the diagrams with the two light quarks participating in gluon exchange contribute to the mixing. Our results indicate that the mixing angle θc=(1.2∼2.8)∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta _{c}=(1.2\\sim 2.8)^{\\circ }$$\\end{document} for the Q=c\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q=c$$\\end{document} case and θb=(0.28∼0.34)∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta _{b}=(0.28\\sim 0.34)^{\\circ }$$\\end{document} for the Q=b\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q=b$$\\end{document} case. Our prediction of θc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta _{c}$$\\end{document} is consistent with the most recent Lattice QCD result within error. Such a small mixing angle seems unlikely to resolve the tension between the recent experimental measurement from Belle and Lattice QCD calculation for the semileptonic decay Ξc0→Ξ-e+νe\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Xi _{c}^{0}\\rightarrow \\Xi ^{-} e^{+}\ u _{e}$$\\end{document}.

Quark-antiquark states of the lightest scalar mesons within the Nambu-Jona-Lasinio model with flavor-dependent coupling constants

The quark-antiquark components of the U(3) lightest scalar meson nonet are investigated by considering the Nambu-Jona-Lasinio model with flavor-dependent coupling constants that were derived by considering (non-perturbative) gluon exchange. The strange quark effective mass () is varied such that the strangeness content of these scalar mesons can be analyzed further. The neutral states S 0, S 8, and S 3 are adopted as the most relevant quark-antiquark components, respectively, of the σ(500), f 0(980) and mesons. As a result, the mass hierarchy between states S 0 and S 8, and mesons, can be, respectively, inverted and corrected for quite low values of the strange quark constituent mass. In addition, for some particular values of , the masses of σ(500) and f 0(980) can also be obtained by considering the mixing coupling constant G 08. However, the masses of all the nine mesons are not described simultaneously in a self-consistent procedure and this goes along with the need of non-quark-antiquark states to completely describe their masses. A neutral-meson mixing matrix is defined and the leading mixing angle is found by fitting a correct value of the σ(500) − f 0(980) mass difference. Two different estimates for the strengths of the mixings and are proposed, leading to somewhat different behaviors. First by assuming leading transitions to intermediary flavor eigenstates and second by considering a dynamical evolution. The results may be in good agreement with experimental values from BESS-III depending on the value of the strange quark effective mass.

Bootstrapping Witten diagrams via differential representation in Mellin space

We explore the use of the differential representation of AdS amplitudes to compute Witten diagrams. The differential representation expresses AdS amplitudes in terms of conformal generators acting on contact Witten diagrams, which allows us to construct differential equations for Witten diagrams. These differential equations can then be transformed into difference equations in Mellin space, which can be solved recursively. Using this method, we efficiently re-computed scalar four-point amplitudes and obtained new results for scalar six-point amplitudes mediated by gluons and scalars, as well as two examples of scalar eight-point amplitudes from gluon exchange.

Production of strangeonium phi (1680) state in electromagnetic probe-driven scatterings and hadron–hadron ultraperipheral collisions

In this work, the gamma prightarrow phi (1680) p reaction is systematically studied based on the two gluon exchange model and the pomeron model. The calculation results show that the total cross section of phi (1680) photoproduction can reach more than 80 nb near the center-of-mass energy W=4 GeV, so it is suggested that JLab and other experiments carry out relevant measurements. Moreover, under the framework of the vector meson dominance assumption, the scattering length of phi (1680) and proton interaction is estimated as 0.07pm 0.01 fm from the cross sections predicted by the theoretical models, which is on the same order of magnitude as the phi (1020)-p scattering length. In addition, the total cross section, number of events and rapidity distribution of phi (1680) production are predicted at Electron-Ion colliders (EICs) and ultra-peripheral collisions (UPCs) by using eSTARlight and STARlight code. The study of phi (1680) and relevant properties is of enlightening significance in better understanding the strangeonium family spectrum, and provides necessary data support for the future experiment of EICs and UPCs.

Shedding new light on weak annihilation B-meson decays

We identify a novel leading-power contribution to the pure weak annihilation non-leptonic B-meson decay amplitudes, which arises from the hard-collinear gluon exchange between the light quark of the bottom meson and the final-state active partons. This interesting observation is naturally expected to shed new light on deciphering rapidity divergences in the convolution integrals of the soft-collinear factorization formulae. Subsequently we explore an intriguing enhancement mechanism due to the penguin contractions of the current-current operators from the weak effective Hamiltonian, which yields the significant impacts on the CP violating observables.

First extraction of the proton mass radius and scattering length $$\vert\alpha_{\rho^{0}p}\vert$$ from ρ0 photoproduction

As it involves the lightest physical states excited from the vacuum by the vector quark current, near-threshold ρ0 photoproduction is considered a possible way to research the proton radius and the absolute value of the scattering lengths of the ρ0-proton interaction. In this study, under the assumption of a scalar form factor of dipole form, the value of the proton mass radius is calculated as (0.85 ± 0.06) fm by fitting the differential cross section of the γp → ρ0p reaction at near-threshold energy. For light vector meson photoproduction, because the exchange of a scalar quark-antiquark pair is not suppressed and should dominate the scalar gluon exchange, the radius we extract from ρ0 photoproduction is likely to represent the quark radius of the proton. This fact may explain why the value obtained in this study is very near the proton charge radius. Moreover, the absolute value of the ρ0-proton scattering length $$\vert\alpha_{\rho^{0}p}\vert=(0.31 \pm 0.06)$$ fm is obtained for the first time within the vector meson dominance model. This result disobeys the rule that the absolute value of the vector meson and proton scattering length $$\vert\alpha_{V_{p}}\vert$$ increases with the meson’s mass, which can be attributed to treating the ρ0 meson as a point in the analysis. These results provide useful theoretical information for an in-depth understanding of proton structure and the proton-vector meson interaction.

Stronger C -odd color charge correlations in the proton at higher energy

The non-forward eikonal scattering matrix for dipole-proton scattering at high energy obtains an imaginary part due to a $C$-odd three gluon exchange. We present numerical estimates for the perturbative Odderon amplitude as a function of dipole size, impact parameter, their relative azimuthal angle, and light-cone momentum cutoff $x$. The proton is approximated as $\psi_\mathrm{qqq}|qqq\rangle + \psi_\mathrm{qqqg}|qqqg\rangle$, where $\psi_\mathrm{qqq}$ is a non-perturbative three quark model wave function while the gluon emission is computed in light-cone perturbation theory. We find that the Odderon amplitude increases as $x$ decreases from 0.1 to 0.01. At yet lower $x$, the reversal of this energy dependence would reflect the onset of universal small-$x$ renormalization group evolution.

J/ψ Near-Threshold Photoproduction off the Proton and Neutron with CLAS12

Near-threshold J/ψ photoproduction is a key aspect of the physics program at the Thomas Jefferson National Accelerator Facility (JLab) 12 GeV upgrade due to the wealth of information it has to offer. J/ψ photoproduction proceeds through the exchange of gluons in the t-channel and is expected to provide unique insight about the nucleon gravitational form factors and the nucleon mass radius. The JLab based CLAS Collaboration, which uses the CEBAF Large Acceptance Spectrometer (CLAS12), aims to measure the J/ψ near threshold photoproduction cross section using both a proton and a deuteron target, from threshold up to 10.6 GeV. The deuteron target further offers the possibility of comparing the proton and neutron gluonic form factors and mass radii in a first measurement of the cross sections off a proton or neutron within the deuteron target. The analysis towards these measurements is ongoing and well advanced, with machine learning based techniques for particle identification already designed and validated with CLAS12 data.

Radiative corrections to stop-antistop annihilation into gluons and light quarks

We present the full one-loop supersymmetry-QCD corrections to stop-antistop annihilation into gluons and light quarks within the Minimal Supersymmetric Standard Model including Sommerfeld enhancement effects from the exchange of multiple gluons between the incoming particles. These corrections are important as stop (co)annihilation becomes the dominant contribution to the relic density for scenarios with a small mass difference between the neutralino and the stop which are less constrained by current LHC searches and consistent with the observation of a 125 GeV SM-like Higgs boson. We discuss important technical details of our one-loop, real emission, and resummation calculations where we pay particular attention to the cancellation of infrared divergences and the associated application of the dipole formalism for massive initial scalars. The corrections have been implemented in the dark matter precision tool dm@nlo which allows us to study numerically the impact of these corrections on the annihilation cross section. We find that for the chosen reference scenario the dominant correction comes from the Sommerfeld effect and that the pure NLO correction is below 3%. The inclusion of these radiative corrections is still large enough to decrease the relic density by more than 10% and shift the cosmologically preferred parameter region by a few GeV relative to the standard micromegas result. Therefore, the inclusion of these corrections is mandatory if the experimental errors are taken as upper and lower bounds of the theory value.