Dipole Amplitude Research Articles

Helicity evolution at small x: quark to gluon and gluon to quark transition operators

We include the quark to gluon and gluon to quark shock-wave transition operators into the small Bjorken-x evolution equations for helicity in the flavor-singlet channel derived earlier in [1–3]. While such transitions do not affect the large-Nc version of the evolution equations for helicity, the large-Nc & Nf equations are affected. (Nc and Nf are the numbers of quark colors and flavors, respectively.) We derive the corresponding corrected large-Nc & Nf equations for the polarized dipole amplitudes contributing to the flavor-singlet quark and gluon helicity distributions in the double-logarithmic approximation (DLA), resumming powers of αs ln2(1/x) with αs the strong coupling constant. We solve these equations iteratively and extract the polarized splitting functions up to four loops. We show that our splitting functions agree with the fixed-order perturbative calculations up to and including the existing three-loops results [4–7]. Similar to the large-Nc helicity evolution in the shock-wave approach [8], our large-Nc & Nf small-x splitting functions agree with those obtained in the infrared evolution equations framework from [9, 10] up to three loops, but appear to slightly disagree at four loops.

Nonlinear country-heterogenous impact of the Indian Ocean Dipole on global economies

A positive Indian Ocean Dipole features an anomalously high west-minus-east sea surface temperature gradient along the equatorial Indian Ocean, affecting global extreme weathers. Whether the associated impact spills over to global economies is unknown. Here, we develop a nonlinear and country-heterogenous econometric model, and find that a typical positive event causes a global economic loss that increases for further two years after an initial shock, inducing a global loss of hundreds of billion US dollars, disproportionally greater to the developing and emerging economies. The loss from the 2019 positive event amounted to US$558B, or 0.67% in global economic growth. Benefit from a negative dipole event is far smaller. Under a high-emission scenario, a projected intensification in Dipole amplitude causes a median additional loss of US$5.6 T at a 3% discount rate, but likely as large as US$24.5 T. The additional loss decreases by 64% under the target of the Paris Agreement.

Probing the cosmological principle using the slope of log N-log S relationship for quasars

We study the dipole signal in the slope x of the log N–log S relationship for quasars using the CatWISE2020 catalog of infrared sources. Here N is the number of sources with flux density greater than S. The slope is extracted by using a maximized log-likelihood method as well as Bayesian analysis. We obtain the value x = 1.579 ± 0.001 for a quasar sample of 1355352 sources. We extract the dipole signal in this parameter by employing χ 2 minimization, assuming a sky model of x up to the quadrupole term. We find that the dipole amplitude |D| is 0.005 ± 0.002 and dipole direction (l, b) in Galactic coordinate system equal to (201.50° ± 27.87°, -29.37° ± 19.86°). The direction of dipole anisotropy is found to be very close to the hemispherical power asymmetry (l, b)=(221°,-27°) in the Cosmic Microwave Background (CMB). The dipole signal is also extracted using Bayesian analysis and found to be in good agreement with that obtained using χ 2 minimization. We also obtain a signal of quadrupole anisotropy which is found to be correlated with the ecliptic poles and can be attributed to ecliptic bias.

Revisiting the implications of Liouville's theorem to the anisotropy of cosmic rays

We present a solution to Liouville's equation for an ensemble of charged particles propagating in magnetic fields. The solution is presented using an expansion in spherical harmonics of the phase space density, allowing a direct interpretation of the distribution of arrival directions of cosmic rays. The results are found for chosen conditions of variability and source distributions. We show there are two conditions for an initially isotropic flux of particles to remain isotropic while traveling through a magnetic field: isotropy and homogeneity of the sources. In case isotropically-distributed sources inject particles continuously in time, a transient magnetic induced dipole will appear. This dipole will vanish if the system reaches a steady-state. The formalism is used to analyze the data measured by the Pierre Auger Observatory, contributing to the understanding of the dependence of the dipole amplitude with energy and predicting the energy in which the quadrupole signal should be measured.

Numerical and Experimental Investigations on the Acoustic Characteristics of a Single-Stage Centrifugal Pump

The acoustic properties of a single-stage centrifugal pump with low specific speed are investigated by means of compressible 3D CFD simulations (URANS) and experiments. In order to determine the pump’s acoustic transmission and excitation characteristics, a four-pole approach in the frequency domain is used. The transmission parameters determined by simulation are compared to experiments in water and air as functions of the Helmholtz number. The results indicate that the acoustic transmission characteristics within the experiments are significantly influenced by the structural compliance of the volute casing in terms of a fluid–structure interaction (FSI). A modelling approach for a one-dimensional representation of the centrifugal pump’s acoustic transmission characteristics in the time and frequency domains is applied to the current pump. As one model parameter, the effective speed of sound in the 1D model needs to be reduced to 607 ms−1 to account for the FSI. The agreement of the simulation results and the experiments underlines the above statement about the influence of the FSI. In a last step, the acoustic excitation parameter, depicted as monopole and dipole amplitudes, at two different blade-passing frequencies (fBP≈[111;169] Hz) are determined for several operating points. Especially for dipole amplitudes, a good agreement between experiments and simulations can be seen. The monopole amplitudes are also of similar orders of magnitude, but show stronger deviations. The cause of discrepancies between the 3D CFD simulations and experiments is believed to be the neglected influence of the FSI and surface roughness as well as the inaccurate reproduction of flow separation at the volute’s tongue due to the use of wall functions. A final important observation made during the numerical investigations is that the excitation mechanisms at the blade-passing frequency are probably independent of the piping system’s acoustic impedance.

Orbital angular momentum at small x revisited

We revisit the problem of the small Bjorken-x asymptotics of the quark and gluon orbital angular momentum (OAM) distributions in the proton utilizing the revised small-x helicity evolution derived recently in [1]. We relate the quark and gluon OAM distributions at small x to the polarized dipole amplitudes and their (first) impact-parameter moments. To obtain the OAM distributions, we derive novel small-x evolution equations for the impact-parameter moments of the polarized dipole amplitudes in the double-logarithmic approximation (summing powers of αs ln2(1/x) with αs the strong coupling constant). We solve these evolution equations numerically and extract the leading large-Nc, small-x asymptotics of the quark and gluon OAM distributions, which we determine to beLq+q¯xQ2~LGxQ2~∆ΣxQ2~∆GxQ2~123.66αsNc2π,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {L}_{q+\\overline{q}}\\left(x,{Q}^2\\right)\\sim {L}_G\\left(x,{Q}^2\\right)\\sim \\Delta \\Sigma \\left(x,{Q}^2\\right)\\sim \\Delta G\\left(x,{Q}^2\\right)\\sim {\\left(\\frac{1}{2}\\right)}^{3.66\\sqrt{\\frac{\\alpha_s{N}_c}{2\\uppi}}}, $$\\end{document}in agreement with [2] within the precision of our numerical evaluation. (Here Nc is the number of quark colors.) We also investigate the ratios of the quark and gluon OAM distributions to their helicity distribution counterparts in the small-x region.

Exclusive production of ground and excited light vector mesons with a holographic wave function model

AbstractThe exclusive photo‐ and electroproduction of light vector mesons like and is studied in collisions within the color dipole formalism with vector meson wave functions obtained using the AdS/QCD holographic approach. This setup provides a good description of the existing data for the ground vector mesons and permits us to make predictions for the corresponding excited states. The results show significant theoretical uncertainties related to modeling the partial dipole amplitude, which can be constrained with upcoming measurements in future hadron colliders.

Hemispherical power asymmetry in intensity and polarization for Planck PR4 data

One of the foundations of the Standard Model of Cosmology is statistical isotropy, which can be tested, among other probes, through the study of the Cosmic Microwave Background (CMB). However, a hemispherical power asymmetry on large scales has been reported for WMAP and Planck data by different works.The statistical significance is above 3σ for temperature, suggesting a directional dependence of the local power spectrum, and thus a feature beyond the ΛCDM model. With the third release of the Planck data (PR3), a new analysis was performed including the E-mode polarization maps, finding an asymmetry at a modest level of significance. In this work, we perform an asymmetry analysis in intensity and polarization maps for the latest Planck processing pipeline (PR4). We obtain similar results to those obtained with PR3, with a slightly lower significance (2.8% for the Sevem method)for the amplitude of the E-mode local variance dipole as well as a significant variability with the considered mask.In addition, a hint of a possible T-E alignment between the asymmetry axes is found at the level of ∼ 5%. For the analysis, we have implemented an alternative inpainting approach in order to get an accurate reconstruction of the E-modes. More sensitive all-sky CMB polarization data, such as those expected from the future LiteBIRD experiment, are needed to reach a more robust conclusion on the possible existence of deviations from statistical isotropy in the form of a hemispherical power asymmetry.

COSMOGLOBE DR1 results

We present COSMOGLOBEData Release 1, which implements the first joint analysis of WMAP andPlanckLFI time-ordered data, processed within a single Bayesian end-to-end framework. This framework directly builds on a similar analysis of the LFI measurements by the BEYONDPLANCKcollaboration, and approaches the cosmic microwave background (CMB) analysis challenge through Gibbs sampling of a global posterior distribution, simultaneously accounting for calibration, mapmaking, and component separation. The computational cost of producing one complete WMAP+LFI Gibbs sample is 812 CPU-h, of which 603 CPU-h are spent on WMAP low-level processing; this demonstrates that end-to-end Bayesian analysis of the WMAP data is computationally feasible. We find that our WMAP posterior mean temperature sky maps and CMB temperature power spectrum are largely consistent with the official WMAP9 results. Perhaps the most notable difference is that our CMB dipole amplitude is 3366.2 ± 1.4 μK, which is 11 μK higher than the WMAP9 estimate and 2.5σhigher than BEYONDPLANCK; however, it is in perfect agreement with the HFI-dominatedPlanckPR4 result. In contrast, our WMAP polarization maps differ more notably from the WMAP9 results, and in general exhibit significantly lower large-scale residuals. We attribute this to a better constrained gain and transmission imbalance model. It is particularly noteworthy that theW-band polarization sky map, which was excluded from the official WMAP cosmological analysis, for the first time appears visually consistent with theV-band sky map. Similarly, the long standing discrepancy between the WMAPK-band and LFI 30 GHz maps is finally resolved, and the difference between the two maps appears consistent with instrumental noise at high Galactic latitudes. Relatedly, these updated maps allowed us for the first time to combine WMAP and LFI polarization data into a single coherent model of large-scale polarized synchrotron emission. Still, we identified a few issues that require additional work, including (1) low-level noise modeling; (2) large-scale temperature residuals at the 1–2 μK level; and (3) a strong degeneracy between the absoluteK-band calibration and the dipole of the anomalous microwave emission component. We conclude that leveraging the complementary strengths of WMAP and LFI has allowed the mitigation of both experiments’ weaknesses, and resulted in new state-of-the-art WMAP sky maps. All maps and the associated code are made publicly available through the COSMOGLOBEweb page.

Probing proton structure with cc¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \ extrm{c}\\overline{\ extrm{c}} $$\\end{document} correlations in ultraperipheral pA collisions

We study the exclusive diffractive cc¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ c\\overline{c} $$\\end{document} photoproduction in ultraperipheral pA collisions. The formalism makes use of off-diagonal generalizations of the unintegrated gluon distribution, the so-called generalized transverse momentum dependent distributions (GTMDs). We present two different formulations. The first one is based directly on gluon GTMD parametrizations in momentum space. Another option is the calculation of the GTMD as a Fourier transform of the dipole-nucleon scattering amplitude N(Y, r→\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overrightarrow{r} $$\\end{document}⊥, b→\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overrightarrow{b} $$\\end{document}⊥). The latter approach requires some extra regularization discussed in the paper. Different dipole amplitudes from the literature are used. Compared to previous calculations in the literature, we integrate over the full phase space and therefore cross sections for realistic conditions are obtained. We present distributions in rapidity of c or c¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{c} $$\\end{document}, transverse momentum of the cc¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ c\\overline{c} $$\\end{document} pair, four-momentum transfer squared as well as the azimuthal correlation between a sum and a difference of the c and c¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{c} $$\\end{document} transverse momenta. The azimuthal correlations are partially due to the so-called elliptic gluon Wigner distribution. Different models lead to different modulations in the azimuthal angle. The modulations are generally smaller than 5%. They depend on the range of transverse momentum selected for the calculation.

Effects of exact kinematics and the Sudakov form factor on the dipole amplitude

We investigate the effects of exact gluon kinematics on the parameters of the Golec-Biernat–Wüsthoff, and Bartels–Golec-Biernat–Kowalski saturation models. The resulting fits show some differences, particularly, in the normalization of the dipole cross section σ0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma _0$$\\end{document}. The refitted models are used for the dijet production process in DIS to describe HERA data and investigate the effects of the Sudakov form factor at the future Electron Ion Collider.

Extending Schottky–Mott rule to van der Waals heterostructures of 2D Janus materials: Influence of intrinsic dipoles

The Schottky–Mott (S–M) limit based on the S–M rule is often used to evaluate the Schottky barrier height (SBH) at metal–semiconductor (MS) van der Waals (vdW) contacts but fails at the polar interfaces. In order to extend the S–M rule to the polar interfaces, we here modify the S–M equation to predict the SBH at vdW interfaces of 2D Janus materials, taking into account the effects of intrinsic and interface dipoles. The modified S–M equation is verified based on the first-principles calculations of the MoSi2As2P2/HTaSe2F vdW interfaces, showing a sharp dependence of SBH on the dipole amplitude and direction. Specifically, n-type Schottky barriers tend to form when a semiconductor contacts with a low-work-function surface of Janus metal or a metal interfaces to the high-electron-affinity surface of Janus semiconductor; otherwise, a p-type one is preferable. Interestingly, the smallest n(p)-type SBH could be attained when both intrinsic dipole directions are the same. This work demonstrates that the S–M rule can be extended to the polar interfaces and dipole engineering is an effective strategy to tune the SBH at the MS interface.

Consistency of Pantheon+ supernovae with a large-scale isotropic universe* *Supported by the National Natural Science Fund of China (12147102, 12275034) and the Fundamental Research Funds for the Central Universities of China (2023CDJXY-048)

We investigate the possible anisotropy of the universe using data on the most up-to-date type Ia supernovae, i.e., the Pantheon+ compilation. We fit the full Pantheon+ data with the dipole-modulated ΛCDM model and find that the data are well consistent with a null dipole. We further divide the full sample into several subsamples with different high-redshift cutoffs . It is shown that the dipole appears at the confidence level only if , and in this redshift region, the dipole is very stable, almost independent of the specific value of . For , the dipole amplitude is , pointing toward , which is approximately away from the CMB dipole. This implies that the full Pantheon+ sample is consistent with a large-scale isotropic universe, but the low-redshift anisotropy could not be purely explained by the peculiar motion of the local universe.

Deciphering Core, Valence, and Double-Core-Polarization Contributions to Parity Violating Amplitudes in 133Cs Using Different Many-Body Methods.

This work examines the accuracy of different many-body methods for the calculations of parity violating electric dipole (E1PV) amplitudes in atomic systems. In the last decade, many different groups claim to achieve its accuracy below 0.5%, for the 6s2S1/2 → 7s2S1/2 transition in the 133Cs atom. One of the major issues in these calculations is the opposite signs among the core correlation contribution from different works. To estimate E1PV of the above transition, various groups have used different many-body methods both in the linear response and sum-over-states approaches. By examining how these methods capture various electron correlation effects, we identify the underlying cause of sign discrepancies in the previously reported results. We also demonstrate how the double-core polarization effects and scaled wave functions influence estimation of the E1PV amplitudes. The comprehensive discussions provided in this work will not only aid in our understanding on the potentials of the employed many-body methods, but it will also serve as a road map for improving the E1PV calculation in the atomic systems further.

Testing the cosmological principle with CatWISE quasars: a bayesian analysis of the number-count dipole

ABSTRACT The Cosmological Principle, that the Universe is homogeneous and isotropic on sufficiently large scales, underpins the standard model of cosmology. However, a recent analysis of 1.36 million infrared-selected quasars has identified a significant tension in the amplitude of the number-count dipole compared to that derived from the cosmic microwave background (CMB), thus challenging the Cosmological Principle. Here, we present a Bayesian analysis of the same quasar sample, testing various hypotheses using the Bayesian evidence. We find unambiguous evidence for the presence of a dipole in the distribution of quasars with a direction that is consistent with the dipole identified in the CMB. However, the amplitude of the dipole is found to be 2.7 times larger than that expected from the conventional kinematic explanation of the CMB dipole, with a statistical significance of 5.7σ. To compare these results with theoretical expectations, we sharpen the ΛCDM predictions for the probability distribution of the amplitude, taking into account a number of observational and theoretical systematics. In particular, we show that the presence of the Galactic plane mask causes a considerable loss of dipole signal due to a leakage of power into higher multipoles, exacerbating the discrepancy in the amplitude. By contrast, we show using probabilistic arguments that the source evolution of quasars improves the discrepancy, but only mildly so. These results support the original findings of an anomalously large quasar dipole, independent of the statistical methodology used.

Theoretical Systematics in Testing the Cosmological Principle with the Kinematic Quasar Dipole

The Cosmological Principle (CP) is part of the foundation that underpins the standard model of the Universe. In the era of precision cosmology, when stress tests of the standard model are uncovering various tensions and possible anomalies, it is critical to check the viability of this principle. A key test is the consistency between the kinematic dipoles of the cosmic microwave background and of the large-scale matter distribution. Results using radio continuum and quasar samples indicate a rough agreement in the directions of the two dipoles, but a larger than expected amplitude of the matter dipole. The resulting tension with the radiation dipole has been estimated at ∼5σ for some cases, suggesting a potential new cosmological tension and a possible violation of the CP. However, the standard formalism for predicting the dipole in the two-dimensional projection of sources overlooks possible evolution effects in the luminosity function. In fact, radial information from the luminosity function is necessary for a correct projection of the three-dimensional source distribution. Using a variety of current models of the quasar luminosity function, we show that neglecting redshift evolution can significantly overestimate the relative velocity amplitude. While the models we investigate are consistent with each other and with current data, the dipole derived from these, which depends on derivatives of the luminosity function, can disagree by more than 3σ. This theoretical systematic bias needs to be resolved before robust conclusions can be made about a new cosmic tension.

Exclusive photo- and electroproduction of excited light vector mesons via holographic model

In this paper, we study total and differential observables of electro- and photoproduction of light rho , omega and phi mesons as functions of the center-of-mass energy of the gamma p collision and momentum transfer squared |t|. The corresponding vector mesons wave functions have been computed in the framework of relativistic AdS/QCD holographic approach. A satisfactory description of all available data on ground-state rho (1S), omega (1S) and phi (1S) mesons production cross sections has been achieved in the color dipole picture. Finally, the key observables of excited rho (2S), omega (2S) and phi (2S) states production in gamma ^{(*)} p collisions have been presented here using a common wave function formalism. This study reveals a large theoretical uncertainty coming from the modeling of the partial dipole amplitude in the nonperturbative kinematical domain. Hence, the latter could benefit from future measurements of photoproduction of the excited states.

BEYONDPLANCK

We present posterior sample-based cosmic microwave background (CMB) constraints fromPlanckLFI and WMAP observations as derived through global end-to-end Bayesian processing within the BEYONDPLANCKframework. We first used these samples to study correlations between CMB, foreground, and instrumental parameters. We identified a particularly strong degeneracy between CMB temperature fluctuations and free-free emission on intermediate angular scales (400 ≲ ℓ ≲ 600), mitigated through model reduction, masking, and resampling. We compared our posterior-based CMB results with previousPlanckproducts and found a generally good agreement, however, with notably higher noise due to our exclusion ofPlanckHFI data. We found a best-fit CMB dipole amplitude of 3362.7 ± 1.4 μK, which is in excellent agreement with previousPlanckresults. The quoted dipole uncertainty is derived directly from the sampled posterior distribution and does not involve any ad hoc contributions forPlanckinstrumental systematic effects. Similarly, we find a temperature quadrupole amplitude of $ \sigma^{TT}_2=229\pm97\,\muup{\rm K}^2 $ , which is in good agreement with previous results in terms of the amplitude, but the uncertainty is one order of magnitude greater than the naive diagonal Fisher uncertainty. Concurrently, we find less evidence of a possible alignment between the quadrupole and octopole than previously reported, due to a much larger scatter in the individual quadrupole coefficients that is caused both by marginalizing over a more complete set of systematic effects – as well as by requiring a more conservative analysis mask to mitigate the free-free degeneracy. For higher multipoles, we find that the angular temperature power spectrum is generally in good agreement with bothPlanckand WMAP. At the same time, we note that this is the first time that the sample-based, asymptotically exact Blackwell-Rao estimator has been successfully established for multipoles up toℓ ≤ 600. It now accounts for the majority of the cosmologically important information. Overall, this analysis demonstrates the unique capabilities of the Bayesian approach with respect to end-to-end systematic uncertainty propagation and we believe it can and should play an important role in the analysis of future CMB experiments. Cosmological parameter constraints are presented in a companion paper.

BEYONDPLANCK

We describe the BEYONDPLANCKproject in terms of our motivation, methodology, and main products, and provide a guide to a set of companion papers that describe each result in more detail. Building directly on experience from ESA’sPlanckmission, we implemented a complete end-to-end Bayesian analysis framework for thePlanckLow Frequency Instrument (LFI) observations. The primary product is a full joint posterior distributionP(ω ∣ d), whereωrepresents the set of all free instrumental (gain, correlated noise, bandpass, etc.), astrophysical (synchrotron, free-free, thermal dust emission, etc.), and cosmological (cosmic microwave background – CMB – map, power spectrum, etc.) parameters. Some notable advantages of this approach compared to a traditional pipeline procedure are seamless end-to-end propagation of uncertainties; accurate modeling of both astrophysical and instrumental effects in the most natural basis for each uncertain quantity; optimized computational costs with little or no need for intermediate human interaction between various analysis steps; and a complete overview of the entire analysis process within one single framework. As a practical demonstration of this framework, we focus in particular on low-ℓCMB polarization reconstruction withPlanckLFI. In this process, we identify several important new effects that have not been accounted for in previous pipelines, including gain over-smoothing and time-variable and non-1/fcorrelated noise in the 30 and 44 GHz channels. Modeling and mitigating both previously known and newly discovered systematic effects, we find that all results are consistent with the ΛCDM model, and we constrained the reionization optical depth toτ = 0.066 ± 0.013, with a low-resolution CMB-basedχ2probability to exceed of 32%. This uncertainty is about 30% larger than the official pipelines, arising from taking a more complete instrumental model into account. The marginal CMB solar dipole amplitude is 3362.7 ± 1.4 μK, where the error bar was derived directly from the posterior distribution without the need of any ad hoc instrumental corrections. We are currently not aware of any significant unmodeled systematic effects remaining in thePlanckLFI data, and, for the first time, the 44 GHz channel is fully exploited in the current analysis. We argue that this framework can play a central role in the analysis of many current and future high-sensitivity CMB experiments, including LiteBIRD, and it will serve as the computational foundation of the emerging community-wide COSMOGLOBEeffort, which aims to combine state-of-the-art radio, microwave, and submillimeter data sets into one global astrophysical model.

Sudakov effects and the dipole amplitude

In this study we incorporate the Sudakov form factor into the dipole factorization formula, where the hard scale of the former is provided by the photon virtuality Q2. We obtain a general formula which we then apply to the well-known GBW and BGK saturation models. Parameters of the above Sudakov-improved models are successfully fitted to the F2 data from HERA. We observe, in particular, that inclusion of the Sudakov factor on top of the GBW model improves description of data at large Q2.