#### Theory of leading twist nuclear shadowing and predictions

The light front quantization [1] [2] [3] of quantum field theories provides a useful alternative to ordinary equal-time quantization. In particular, it can lead to a relativistic description of bound systems in terms of quantum-mechanical wave functions. The basic formalism is discussed elsewhere.

There are many applications of this technique, some of which are discussed below. Essentially, the analysis of any relativistic quantum system can benefit from the use of light-front coordinates and the associated quantization of the theory that governs the system. The light-front technique was brought into nuclear physics by the pioneering papers of Frankfurt and Strikman.

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This sub-section focuses on only a few examples. Calculations of deep inelastic scattering from nuclei require knowledge of nucleon distribution functions within the nucleus. Nuclear wave functions have been best determined using the equal-time framework. It therefore seems reasonable to see if one could re-calculate nuclear wave functions using the light front formalism.

There are several basic nuclear structure problems which must be handled to establish that any given method works. It is necessary to compute the deuteron wave function, solve mean-field theory basic nuclear shell model for infinite nuclear matter and for finite-sized nuclei, and improve the mean-field theory by including the effects of nucleon-nucleon correlations.

Much of nuclear physics is based on rotational invariance, but manifest rotational invariance is lost in the light front treatment. Thus recovering rotational invariance is very important for nuclear applications. The simplest version of each problem has been handled. A light-front treatment of the deuteron was accomplished by Cooke and Miller, [7] [8] which stressed recovering rotational invariance. Quark effects are needed. Most of these developments are discussed in a review by Miller.

There is a new appreciation that initial and final-state interaction physics, which is not intrinsic to the hadron or nuclear light-front wave functions, must be addressed in order to understand phenomena such as single-spin asymmetries, diffractive processes, and nuclear shadowing. Standard scattering theory in Hamiltonian frameworks can provide valuable guidance for developing a LFQCD-based analysis of high-energy reactions.

One of the most important areas of application of the light-front formalism are exclusive hadronic processes. Exclusive processes provide a window into the bound-state structure of hadrons in QCD as well as the fundamental processes which control hadron dynamics at the amplitude level.

The natural calculus for describing the bound-state structure of relativistic composite systems, needed for describing exclusive amplitudes, is the light-front Fock expansion which encodes the multi-quark, gluonic, and color correlations of a hadron in terms of frame-independent wave functions. In hard exclusive processes, in which hadrons receive a large momentum transfer, perturbative QCD leads to factorization theorems [22] which separate the physics of hadronic bound-state structure from that of the relevant quark and gluonic hard-scattering reactions which underlie these reactions.

At leading twist, the bound-state physics is encoded in terms of universal "distribution amplitudes", [23] the fundamental theoretical quantities which describe the valence quark substructure of hadrons as well as nuclei. A basic feature of the gauge theory formalism is color transparency", [24] the absence of initial and final-state interactions of rapidly moving compact color-singlet states. Exclusive processes place important constraints on the light-front wave functions of hadrons in terms of their quark and gluon degrees of freedom as well as the composition of nuclei in terms of their nucleon and mesonic degrees of freedom.We determine the spatial impact parameter dependence of nuclear parton distribution functions nPDFs using the A -dependence of the spatially independent averaged global fits EPS09 and EKS We work under the assumption that the spatial dependence can be formulated as a power series of the nuclear thickness functions T A.

To reproduce the A -dependence over the entire x range we need terms up to [ T A ] 4. We also discuss the implementation of these into the existing calculations. With our results, the centrality dependence of nuclear hard-process observables can be studied consistently with the globally fitted nPDFs for the first time.

In particular, we show that our results are compatible with the PHENIX mid-rapidity data within the overall normalization uncertainties given by the experiment. Download to read the full article text. Collins, D. Soper and G. High Energy Phys. Google Scholar. CTEQ collaboration, R. Brock et al. Gribov and L. Lipatov, Deep inelastic e p scattering in perturbation theorySov. Altarelli and G. Lai et al. D 82 [ arXiv Martin, W. Stirling, R. Thorne and G.

C 63 [ arXiv Ball et al. B [ arXiv Eskola, V. Kolhinen and C. Salgado, The Scale dependent nuclear effects in parton distributions for practical applicationsEur. Hirai, S. Kumano and M.

Miyama, Determination of nuclear parton distributionsPhys. Kumano and T. Nagai, Nuclear parton distribution functions and their uncertaintiesPhys. Sassot, Nuclear parton distributions at next-to-leading orderPhys. Nagai, Determination of nuclear parton distribution functions and their uncertainties in next-to-leading orderPhys. C 76 [ arXiv Eskola, H. Paukkunen and C. Schienbein et al. D 80 [ arXivIn the coherent channel, a large reduction of the coherent cross section—approximately by a factor of three—as compared to the impulse approximation has been reported.

The aim of this paper is twofold. The following channels can be studied: i one of the nuclei emits at least one neutron while its partner does not— 0nXn ; ii both nuclei emit neutrons in opposite directions— XnXniii neither of the nuclei emits neutrons— 0n0n.

This paper is organized as follows. In Sect. The earliest model for production of vector mesons off nuclei is the vector meson dominance model based on hadronic degrees of freedom [ 8 ].

In Eq. Note that in the first and second terms in Eq.

The main issue with Eqs. In a more general case [ 16 ], i. In this respect, the situation is similar to the VMD case considered above. In contrast to the dipole formalism, one can use the leading twist framework of QCD factorization theorems, which enables one to apply Eq.

Applying Eq. The leading twist theory of nuclear shadowing [ 6 ] is based on the space-time picture of the strong interaction at high energies, the generalization of the Gribov—Glauber theory of nuclear shadowing in soft hadron—nucleus scattering [ 1021 ] to hard processes with nuclei, and the QCD collinear factorization theorems for the total and diffractive cross sections of deep inelastic scattering DIS.

The approach allows one to make predictions for the leading twist shadowing correction to nuclear parton distributions nPDFsstructure functions and cross sections, which are given as a series in the number of simultaneous interactions with the target nucleons the multiple scattering series.

The structure of each term in the series is unambiguously given by the Gribov—Glauber theory supplemented by Abramovsky—Gribov—Kancheli AGK cutting rules [ 2223 ] and the QCD factorization theorems. The multiple scattering series of Fig. The Gribov result on the inelastic shadowing correction in hadron—nucleus scattering can be conveniently implemented using the formalism of cross section fluctuations [ 24 ]. In this approach, the interaction of a high-energy projectile with a nucleus is a two-step process.

Second, these fluctuations interact with the nucleus. The first term in Eq. The second term in Eq. In particular, the third term in Eq. This contribution cannot in general be expressed only in terms of diffractive distributions of the proton and needs to be modeled.

Exactly this was assumed in Eq. With this input, the multiple scattering series in Eq. Note that in Eq.

It is important to note that unlike the case of the color dipole formalism, the shadowing correction in Eq. Note that Eq. Generalizing the standard expression for the incoherent quasielastic nuclear cross section [ 9 ] to include cross section fluctuations, we obtain in the high-energy limit:.

Note also that in Eq. In the last line of Eq.The light-front quantization of QCD provides an alternative to lattice gauge theory for computing the mass spectrum, scattering amplitudes, and other physical properties of hadrons directly in Minkowski space.

Nonperturbative light-front methods for solving gauge theory and obtaining light-front wavefunctions, such as discretized light-front quantization, the transverse lattice, and light-front resolvents are reviewed.

In the case of hard inclusive reactions, the effects of final-state interactions must be included in order to interpret leading-twist diffractive contributions, nuclear shadowing, and single-spin asymmetries. Spontaneous symmetry breaking is represented by the appearance of zero modes of the Higgs field, leaving the light-front vacuum equal to the perturbative vacuum. Presented at the.

Documents: Advanced Search Include Citations. Abstract The light-front quantization of QCD provides an alternative to lattice gauge theory for computing the mass spectrum, scattering amplitudes, and other physical properties of hadrons directly in Minkowski space. Powered by:.Google ranks this article in the top 3.

**SCP: The Paradox of Disbelief — SCP Foundation Series**

Click the links to see below the documentation for the BB's fifteen failures listed here. Trust in the big bang's predictive ability has been misplaced when compared to the actual astronomical observations, most of which were made in hopes of affirming the theory. So here is RSR's list of the big bang's extensive poor predictions track record BB Nucleosynthesis : The failure of BB nucleosynthesisas indicated above and summarized here, to account for the origin of most of the universe, including dark matter, dark radiation, dark energy, inflatons, etc.

Click Play for Part 2 on the three main predictions The big bang theory failed in its erroneous antimatter prediction. A nd the theory never predicted the origin of dark matter see belowa probably-non-existent material needed to explain a big bang universe.

If the big bang has actually occurred, transforming vast energy into all of the matter of the universe, then that would have created as much antimatter as matter. When supercolliders form matter from energy, as expected from the laws of particle physics, equal parts of matter and antimatter form; and if they come into contact, they annihilate one another.

For a creationist and a secular explanation of this problem, see creation. Yet many of the most extensive scientific observations ever made suggest otherwise, and they don't give a ringing endorsement to the Copernican principle either.

If you're interested in helping RSR research this topic further, please see below, Research Questions. If the age of the universe could be wrong by a sixthfake news could continue to claim "precision cosmology", but an objective scientist couldn't. The centrality of this failure is explained below.

Thus the big bang theory and its stellar nucleosynthesis have not done a good job at explaining the origin of the stuff of the universe. Continued extensive observations do not bode well for the existence of dark matter. Peebles' assessment here prohibits the use of the vast majority of the claimed matter of the universe in support of Lawrence Krauss' marketing claim that, "All evidence overwhelmingly supports the big bang.

However, problems multiply for even the theoretical underpinning of the existence of dark energy.

### Black hole’s shadow boosts Einstein’s general theory of relativity

For example, a reduction in galaxy surface brightness with distance from the Earth is a long-standing fundamental prediction of an expanding universe. This is so very precise that if the entire universe had as much additional mass as exists in a single grain of sand, the whole cosmos would collapse upon itself.

That is, if a big bang actually formed our universe, and if it created a miniscule additional amount of mass than it is claimed to have created, then no planets, stars, or galaxies could exist. Conversely, if the universe had less mass, by that same quantity, it would be expanding so rapidly that matter would never have coalesced to become planets, stars, and galaxies, and again, we would not exist.

The many arguments against dark energy, etc. Without them, there would be a fatal contradiction between the observations made by astronomers and the predictions of the big bang theory. In no other field of physics would this continual recourse to new hypothetical objects be accepted as a way of bridging the gap between theory and observation.

It would, at the least, raise serious questions about the validity of the underlying theory. But the big bang theory can't survive without these fudge factors. For Wilson admitted :. The first confirmation of the microwave cosmic background that we knew of, however, came from a totally different, indirect measurement. This measurement had, in fact, been made thirty years earlier by [Mount Wilson Observatory's] Adams and Dunhan [ see Wilson's references, dated ] McKellar [ reference ] using Adams' data This rotational transition occurs at 2.

So even though Wilson, the accidental laureatemade it clear on the record that this "prediction" really could only be a retrodiction because published empirical observations first began to detect it a decade prior to its "prediction" see next quotethe canonical BB narrative insists on a revisionist twist.

This was indeed measured with tremendous accuracy The accurate measurement of its shape was another important test of the Big Bang theory. The prediction though was of what was already known to exist.

The theorists in were merely conforming the model to data already collected from to So even after the data from the Mount Wilson observatory reported a temperature very close to actual, leading theorists were making some predictions [or retrodictions] that were close to the actual temperature, and others that were off by a factor of more than 10 universes.

Click Play to see the big bang's CMB story unravelThank you for registering with Physics World If you'd like to change your details at any time, please visit My account. Their results set the stage for even more stringent tests of general relativity in the near future. For over a century, general relativity has had an excellent track record in explaining observations of the universe. As a result, physicists are looking for subtle flaws in general relativity that could lead to the development of a more complete theory.

Initially, these tests used objects in the solar system — famously the motion of Mercury. More recently, gravitational waves created by merging black holes and observed by the LIGO—Virgo collaboration have enabled tests in the gravitational fields of objects as heavy as solar masses.

To test this, Psaltis and colleagues considered alternative models of gravity that modify the general theory of relativity. The new constraints are similar to those derived from gravitational wave observations. The research is described in Physical Review Letters. Close search menu Submit search Type to search. Topics Astronomy and space Atomic and molecular Biophysics and bioengineering Condensed matter Culture, history and society Environment and energy Instrumentation and measurement Materials Mathematics and computation Medical physics Optics and photonics Particle and nuclear Quantum.

Sign in Register. Enter e-mail address Show Enter password Remember me. Enter e-mail address This e-mail address will be used to create your account. Reset your password. Please enter the e-mail address you used to register to reset your password Enter e-mail address. Registration complete. Supermassive test: this simulation of the region around M87 shows the motion of plasma as it swirls around the black hole.

The bright thin ring that can be seen in blue is the edge of the shadow. Want to read more?On general quantum mechanical grounds, the high energy outgoing jet can only lose a nite amount of energy so that the fragmentation function still factorizes in leading twist even though the quark transits the nucleus [6]. More recently, Baier et al. Bjorken has also discussed the predictions for rapidity gaps in deep inelastic electron-nucleus collisions [1].

In contrast, the leading-twist contribution to the longitudinal structure function F L x; Q 2 A derives from the interaction of a approximately symmetric qq component of the virtual photon wavefunction with relative impact separation b? The speci c nuclear e ects at low x then re ect the interactions of a small-color singlet system, thus leading to decreasing nuclear absorption with increasing Q 2: Thus the study of shadowing as a function of photon polarization and Q 2 can illuminate the basic mechanisms underlying short-distance QCD processes.

It is also interesting to measure the shadowing of the charm and bottom cross section.

### Light-front quantization applications

The basic underlying subprocess at low x is photon-gluon fusion. Thus the nuclear dependence of the heavy quark structure functions measures the shadowing of the gluon distribution in the. Documents: Advanced Search Include Citations.

Abstract through the nucleus. Powered by:.

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