* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download The spin-dependent structure function
Weakly-interacting massive particles wikipedia , lookup
Antiproton Decelerator wikipedia , lookup
Quantum vacuum thruster wikipedia , lookup
Renormalization wikipedia , lookup
Old quantum theory wikipedia , lookup
Double-slit experiment wikipedia , lookup
Magnetic monopole wikipedia , lookup
Monte Carlo methods for electron transport wikipedia , lookup
Mathematical formulation of the Standard Model wikipedia , lookup
Cross section (physics) wikipedia , lookup
Eigenstate thermalization hypothesis wikipedia , lookup
Renormalization group wikipedia , lookup
Symmetry in quantum mechanics wikipedia , lookup
Identical particles wikipedia , lookup
Strangeness production wikipedia , lookup
Atomic nucleus wikipedia , lookup
Aharonov–Bohm effect wikipedia , lookup
Future Circular Collider wikipedia , lookup
Spin (physics) wikipedia , lookup
Photon polarization wikipedia , lookup
Quantum electrodynamics wikipedia , lookup
Quantum chromodynamics wikipedia , lookup
Introduction to quantum mechanics wikipedia , lookup
Standard Model wikipedia , lookup
ALICE experiment wikipedia , lookup
Nuclear structure wikipedia , lookup
Relativistic quantum mechanics wikipedia , lookup
Elementary particle wikipedia , lookup
ATLAS experiment wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Q) Q) How well is Unpolarized structure of the nucleon known? After 40 years DIS experiments, unpolarized structure of the nucleon reasonably well understood. High x - valence quark dominating Q) Spin Crisis: Q) NPM: The “proton spin crisis” was introduced in the late 1980s, when the EMC-experiment revealed that little or nothing of a proton’s spin seemed to be carried by its quarks. The “proton spin crisis” essentially refers to the experimental finding that very little of the spin of a proton seems to be carried by the quarks from which it is supposedly built. This was a very curious and unexpected experimental result of the European Muon Collaboration, EMC [2] (later confirmed by other experiments), as the whole idea of the original quark model of Gell-Mann [3] and Zweig [4] was to account for 100 percent of the hadronic spins, solely in terms of quarks. This original, or “naive”, quark model also was very successful in explaining and predicting hadron spectroscopy data. The naive quark parton model In the quark-parton model the DIS cross section is the incoherent sum of the scattering off the point-like quarks and yields the following cross section: (1.10) where is the probability to find a quark in the proton with a fraction proton momentum. Comparing this expression to eq. 1.9 we find of the total (1.11) The first identity, , is known as the Callan-Gross relation and is a direct consequence of the spin-1/2 nature of the quarks. The function is known as the parton distribution function. The second identity is also interesting: it predicts that the cross section only depends on one variable, . This property is called Bjorken scaling. Approximate scaling is observed in the data at , but violation of scaling is observed for lower and higher . Figure 1.3 shows versus measured by various HERA- and fixed target experiments [2]. Figure 1.3: The structure function experiments plotted against broken towards low measured by ZEUS, H1 and various fixed target . Bjorken scaling is observed at high , but is gradually . The line represents a QCD based fit to the data. Explanation of magnetic moment The electron is a negatively charged particle with angular momentum. A rotating electrically charged body in classical electrodynamics causes a magnetic dipole effect creating magnetic poles of equal magnitude but opposite polarity like a bar magnet. For magnetic dipoles, the dipole moment points from the magnetic south to the magnetic north pole. The electron exists in a magnetic field which exerts a torque opposing its alignment creating a potential energy that depends on its orientation with respect to the field. The magnetic energy of an electron is approximately twice what it should be in classical mechanics. The factor of two multiplying the electron spin angular momentum comes from the fact that it is twice as effective in producing magnetic moment. This factor is called the electronic spin g-factor. The persistent early spectroscopists, such as Alfred Lande, worked out a way to calculate the effect of the various directions of angular momenta. The resulting geometric factor is called the Lande g-factor. The intrinsic magnetic moment μ of a particle with charge q, mass m, and spin s, is where the dimensionless quantity g is called the g-factor. The g-factor is an essential value related to the magnetic moment of the subatomic particles and corrects for the precession of the angular momentum. One of the triumphs of the theory of quantum electrodynamics is its accurate prediction of the electron gfactor, which has been experimentally determined to have the value 2.002319... The value of 2 arises from the Dirac equation, a fundamental equation connecting the electron's spin with its electromagnetic properties, and the correction of 0.002319..., called the anomalous magnetic dipole moment of the electron, arises from the electron's interaction with virtual photons in quantum electrodynamics. Reduction of the Dirac equation for an electron in a magnetic field to its non-relativistic limit yields the Schrödinger equation with a correction term which takes account of the interaction of the electron's intrinsic magnetic moment with the magnetic field giving the correct energy. The total spin magnetic moment of the electron is where gs = 2 in Dirac mechanics, but is slightly larger due to Quantum Electrodynamic effects, μB is the Bohr magneton and s is the electron spin. The z component of the electron magnetic moment is where ms is the spin quantum number. It is important to notice that is a negative constant multiplied by the spin, so the magnetic moment is antiparallel to the spin angular momentum. In atomic physics, the Bohr magneton (symbol μB) is named after the physicist Niels Bohr. It is a physical constant of magnetic moment, defined in SI units by and in Gaussian centimeter-gram-second units by The nuclear magneton (symbol defined by: ), is a physical constant of magnetic moment, where: is the elementary charge, is the reduced Planck's constant, is the proton rest mass In the SI system of units its value is approximately: = 5.050 783 24(13) × 10-27 J·T-1 QThe radiation length provides information about the photon conversion probability in a specific material. Radiation length: Scaling variable for the probability of occurrence of bremsstrahlung pair production, and for the variance of the angle of multiple scattering. The radiation length is given (in [g/cm**2]) by Radiation Length , High-energy electrons predominantly lose energy in matter by bremsstrahlung, and high-energy photons by e + e − pair production. The characteristic amount of matter traversed for these related interactions is called the radiation length X0, usually measured in gcm − 2. It is both the mean distance over which a high-energy electron loses all but 1/e of its energy by bremsstrahlung, and 7/9 of the mean free path for pair production by a high-energy photon. It is also the appropriate scale length for describing high-energy electromagnetic cascades. The radiation length is given, to good approximation, by the expression Q) Calorimeter:A composite detector using total absorption of particles to measure the energy and position of incident particles or jets. In the process of absorption showers are generated by cascades of interactions, hence the occasionally used name shower counter for a calorimeter. Calorimeters are usually composed of different parts, custom-built for optimal performance on different incident particles. Each calorimeter is made of multiple individual cells, over whose volume the absorbed energy is integrated; cells are aligned to form towers typically along the direction of the incident particle. The analysis of cells and towers allows one to measure lateral and longitudinal shower profiles, hence their arrangement is optimized for this purpose, and usually changes orientation in different angular regions. Typically, incident electromagnetic particles, viz. electrons and gammas, are fully absorbed in the electromagnetic calorimeter, which is made of the first (for the particles) layers of a composite calorimeter; its construction takes advantage of the comparatively short and concentrated electromagnetic shower shape to measure energy and position with optimal precision for these particles (which include 's, decaying electromagnetically). Electromagnetic showers have a shape that fluctuates within comparatively narrow limits; its overall size scales with the radiation length. Incident hadrons, on the other hand, may start their showering in the electromagnetic calorimeter, but will nearly always be absorbed fully only in later layers, i.e. in the hadronic calorimeter, built precisely for their containment. Hadronic showers have a widely fluctuating shape; their average extent does not scale with the calorimeter's interaction length, but is partly determined by the radiation length. Discrimination, often at the trigger level, between electromagnetic and hadronic showers is a major criterion for a calorimeter; it is, therefore, important to contain electromagnetic showers over a short distance, without initiating too many hadronic showers. The critical quantity to maximize is the ratio , which is approximately proportional to Z1.3 (see [Fabjan91]); hence the use of high-Z materials like lead, tungsten, or uranium for electromagnetic calorimeters. Calorimeters can also provide signatures for particles that are not absorbed: muons and neutrinos. Muons do not shower in matter, but their charge leaves an ionization signal, which can be identified in a calorimeter if the particle is sufficiently isolated (and the dynamic range of electronics permits), and then can be associated to a track detected in tracking devices inside the calorimeter, or/and in specific muon chambers (after passing the calorimeter). Neutrinos, on the other hand, leave no signal in a calorimeter, but their existence can sometimes be inferred from energy conservation: in a hermetically closed calorimeter, at least a single sufficiently energetic neutrino, or an unbalanced group of neutrinos, can be ``observed'' by forming a vector sum of all measured momenta, taking the observed energy in each calorimeter cell along the direction from the interaction point to the cell. The precision of such measurements, usually limited to the transverse direction, requires minimal leakage of energy in all directions, hence a major challenge for designing a practical calorimeter. The shower development is a statistical process (see Electromagnetic Shower, Hadronic Shower). This explains why the relative accuracy of energy measurements in calorimeters improves with increasing energy, according to the empirical formula where E = energy of incident particle, = standard deviation of energy measurement, and a and are constants depending on the detector type, e.g. the thickness and characteristics of active and passive layers. The overall constant includes the systematic errors of the individual modules. Other, similar formulae, with different energy-dependent terms are in use; for more details, Energy Resolution in Calorimeters, Compensating Calorimeter. From the construction point of view, one can distinguish between: Q1) What is sampling calorimeter? In what way is it different from other types of calorimeters (if there is any)? Answer: a) Homogeneous Shower Counters. In homogeneous calorimeters the functions of passive particle absorption and active signal generation and readout are combined in a single material. Such materials are almost exclusively used for electromagnetic calorimeters, e.g. crystals ( Crystal Calorimeter), composite materials (like lead glass, viz. PbO and SiO2) or, usually for low energy, liquid noble gases (see [Walraff91], [Fabjan95a]). b) Heterogeneous Shower Counters (= Sampling Calorimeters). In sampling calorimeters the functions of passive particle absorption and active signal generation and readout are separated. This allows optimal choice of absorber materials and a certain freedom in signal treatment. Heterogeneous calorimeters are mostly built as sandwich counters, sheets of heavy-material absorber (e.g. lead, iron, uranium) alternating with layers of active material (e.g. liquid or solid scintillators, or proportional counters). Only the fraction of the shower energy absorbed in the active material is measured. Hadron calorimeters, needing considerable depth and width to create and absorb the shower, are necessarily of the sampling calorimeter type. Calorimetry is the art of compromising between conflicting requirements; the principal requirements are usually formulated in terms of resolution in energy, spatial coordinates, and time, in triggering capabilities, in radiation hardness of the materials used, and in electronics parameters like dynamic range, and signal extraction (for high-frequency colliders). In nearly all cases, cost is the most critical limiting parameter. Depending on the physics goals, the energy range that has to be considered, the accelerator characteristics, etc., some goals will be favoured over others. The span of possible solutions for calorimeters is much wider than for tracking devices, and quite ingenious solutions have been found by imaginative experimental teams over the last 15 years, since calorimeters became key components of particle detectors. In practical constructions the ratio of energy loss in the passive and active material is rather large, typically of the order of 10. Although performance does not strongly depend on the orientation of active and passive material, their relative thickness must not vary too much, to ensure an energy resolution independent of direction and position of showers. Only a few percent of the energy lost in the active layers is converted into detectable signal. For a discussion, [Fabjan91]. Q2) In general-purpose detectors, an electromagnetic calorimeter (based on electromagnetic shower due to bremsstrahlung and pair-production because of the intense electromagnetic field of atomic nuclei when a high energy particle passes through a medium) is usually followed by a hadronic calorimeter (based on hadronic showers). In sampling calorimeters, the passive materials have high atomic numbers (eg. Lead) and they cause the shower to occur and thus play a greater role in the particle absorption. The particles from shower on the other hand, produce signals such as light in scintillators to be used for read-out. Q3) What are the reasons behind anomalous magnetic moments? Answer: The anomalous magnetic moments of the lepton family are usually ascribed to their treatment as theoretical points, rather than having actual size, together with their interactions with the environment. Nucleon anomalous magnetic moments are believed to be more complicated. In quantum electrodynamics, the anomalous magnetic moment of a particle is a contribution of effects of quantum mechanics, expressed by Feynman diagrams with loops, to the magnetic moment of that particle. The “Dirac” magnetic moment, corresponding to tree-level Feynman diagrams, can be calculated from the Dirac equation. It is usually expressed in terms of the g-factor; the Dirac equation predicts g = 2. For particles such as the electron, this classical result differs from the observed value by a small fraction of a percent. The difference is the anomalous magnetic moment, denoted a and defined as The one-loop contribution to the anomalous magnetic moment of the electron is found by calculating the vertex function shown in the diagram on the right. The calculation is relatively straightforward[1] and the one-loop result is: where α is the fine structure constant. This result was first found by Schwinger in 1948.[2] As of 1997, the coefficients of the QED formula for the anomalous magnetic moment of the electron have been calculated through order α4. The QED prediction agrees with the experimentally measured value to more than 10 significant figures, making the magnetic moment of the electron the most accurately verified prediction in the history of physics. (See precision tests of QED for details.) The anomalous magnetic moment of the muon is calculated in a similar way; its measurement provides a precision test of the Standard Model. As of November 2006, the measurement disagrees with the Standard Model by 3.4 standard deviations[3], suggesting beyond the Standard Model physics may be having an effect. Composite particles often have a huge anomalous magnetic moment. This is true for the proton, which is made up of charged quarks, and the neutron, which has a magnetic moment even though it is electrically neutral. Q4) DIS data gave some surprising results such as the original “EMC-Effect”, the violation of Gottfried sum rule, even giving some hints for quark substructure. Indication of quark substructure (i.e an even deeper layer of matter): The observed “excess” of events at extremely high Q2 beyond 15000 GeV-squared EMC effect: the modification of nucleon structure functions. (2) EMC effect: quark momentum modified in the nucleus (5). EMC results: quarks carry only a fraction of the proton’s spin (5) The violation of the Gottfried sum rule: the apparent breakdown of flavor symmetry in the quark-antiquark sea of the proton)(2) The violation of the Gottfried sum rule: flavor asymmetry of the sea established(5) Unit of Magnetic Moment: Ampere * meter-squared (or the area of a current loop times the current value gives the magnetic dipole moment of the current loop.) Dirac Mag Moment: ‘mu’= eh_cut/2M Measured nucleon magnetic moments: Proton: Disagreed with Dirac prediction by 150. (Early 1920s, Stern-Gerlach first measured the electron mag. Moment by doing measurement on a beam of silver atoms, thus discovering the electron spin – KJS pg1). Then Stern improved his instruments and he and his collaborators measured the much smaller proton ‘mu’. (Analoguous to Mendeleev’s periodic system the correctness of the quark model was strongly supported by the discovery of the particle: the was predicted by the quark model, but was not discovered yet in 1964. The SLAC data were the first direct experimental evidence of the existence of quarks. At the time of the introduction of the periodic system, not all elements had been found, but all ‘holes’ were eventually filled, proving the correctness of the hypothesis. Here we need something that supports the nucleon substructure, not the one that supports the quark-model, which is a bit off the line/track/relevance.) This slow spectator proton may not be detected by CLAS since CLAS has a momentum threshold of about 300 MeV/c for protons. (i.e. CLAS can detect only higher momentum protons.) (18, J. Zhang.) For a new detector one must have a simulation in order to understand the acceptance and to understand the response of the detector for particle of known trajectory. Cherenkov counter (cut) can be used to distinguish between electrons and negative pions at low momenta. At higher momenta (>3GeV), forward electromagnetic calorimeter (EC) helps us in making such separation/distinction (as with neutral particles.) (18) The Cerenkov Counter provides a reasonable way to separate electrons from negative pions. This is because a pion has a momentum threshold of 2.5 GeV/c to produce Cerenkov radiation in the perfluorenutane gas (C4F10), which is used in the Cerenkov detector in CLAS, while an electron has a momentum threshold of only 9 MeV/c. If the momentum of the scattered electron is less than 3.0 GeV/c, we require the number of photoelectrons (Nphe) from the Cerenkov detector be larger than 2.5. Above 3 GeV/c the Cerenkov will detect both pions and electrons, so we require simply that the number of photoelectrons (Nphe) be greater than 1.0. At large momenta we use the electromagnetic calorimeter to distinguish electrons from pions as described below. In scattering, a differential cross section is defined by the probability to observe a scattered particle in a given quantum state per solid angle unit, such as within a given cone of observation, if the target is irradiated by a flux of one particle per surface unit: To put it another way, it is the rate of scattering events normalized to the beam intensity, the target density, the length of the beam-target interaction region, the geometrical “size” of detector, and the efficiency of the detector “counting.” If the detector is small and sufficiently far from the target, then the geometrical “size” of the detector is given by: The integral cross section is the integral of the differential cross section on the whole sphere of observation (4π steradian): A cross section is therefore a measure of the effective surface area seen by the impinging particles, and as such is expressed in units of area. Usual units are the cm2, the barn (1 b = 10−24 cm2) and the corresponding submultiples: the millibarn (1 mb = 10−3 b), the microbarn (1 μb = 10−6 b), the nanobarn ( 1 nb = 10−9 b), and the picobarn (1 pb = 10−12 b). The cross section of two particles (i.e. observed when the two particles are colliding with each other) is a measure of the interaction event between the two particles. [edit] Relation to the S matrix If the reduced masses and momenta of the colliding system are mi, and mf, and after the collision respectively, the differential cross section is given by before where the on-shell T matrix is defined by in terms of the S matrix. The δ function is the distribution called the Dirac delta function. The computation of the S matrix is the main aim of the scattering theory. [edit] Nuclear physics Main article: nuclear cross section In nuclear physics, it is found convenient to express probability of a particular event by a cross section. Statistically, the centers of the atoms in a thin foil can be considered as points evenly distributed over a plane. The center of an atomic projectile striking this plane has geometrically a definite probability of passing within a certain distance r of one of these points. In fact, if there are n atomic centers in an area A of the plane, this probability is (nπr2) / A, which is simply the ratio of the aggregate area of circles of radius r drawn around the points to the whole area. If we think of the atoms as impenetrable steel discs and the impinging particle as a bullet of negligible diameter, this ratio is the probability that the bullet will strike a steel disc, i.e., that the atomic projectile will be stopped by the foil. If it is the fraction of impinging atoms getting through the foil which is measured, the result can still be expressed in terms of the equivalent stopping cross section of the atoms. This notion can be extended to any interaction between the impinging particle and the atoms in the target. For example, the probability that an alpha particle striking a beryllium target will produce a neutron can be expressed as the equivalent cross section of beryllium for this type of reaction. Jump to: navigation, search In nuclear and particle physics, the concept of a cross section is used to express the likelihood of interaction between particles. The term is derived from the purely classical picture of (a large number of) point-like projectiles directed to an area that includes a solid target. Assuming that an interaction will occur (with 100% probability) if the projectile hits the solid, and not at all (0% probability) if it misses, the total interaction probability for the single projectile will be the ratio of the area of the section of the solid (the cross section) to the total targeted area. This basic concept is then extended to the cases where the interaction probability in the targeted area assumes intermediate values - because the target itself is not homogeneous, or because the interaction is mediated by a non-uniform field. Sum rule may refer to: Sum rule in differentiation Sum rule in integration Rule of sum, a counting principle in combinatorics In quantum mechanics, sum rule refers to formulas for transitions between energy levels, in which the sum of the transition strengths is expressed in a simple form. Sum rules are used to describe the properties of many physical systems, including solids, atoms, atomic nuclei, and nuclear constituents such as protons and neutrons. The sum rules are derived from quite general principles, and are useful in situations where the behavior of individual energy levels is too complex to describe by a precise quantum-mechanical theory. In general, sum rules are derived by using Heisenberg's quantum-mechanical algebra to construct operator equalities, which are then applied to particles or the energy levels of a system. See also selection rule. Measurements of Partial Channels of the GDH Sum Rule (Briscoe, Strakovsky): The Gerasimov-Drell-Hearn (GDH) sum rule relates the difference in the total hadronic photo-absorption cross sections for left- and right-handed circularly polarized photons interacting with longitudinally polarized nucleons to the anomalous magnetic moment of the nucleon squared divided by m. The GDH sum rule provides an elegant connection between the nucleon structure functions obtained in high-energy lepton-scattering experiments and two static properties of the nucleon. Thus, it provides a bridge between perturbative and nonpertubative QCD. The fundamental interpretation of the GDH sum rule is that any particle which has a nonzero anomalous magnetic moment has internal structure and therefore an excitation spectrum. The detailed verification of the GDH sum rule shows which nucleon resonances play the most significant roles in this. There is a basic connection between the GDH sum rule which is valid for real photons and the famous Bjorken sum rule for virtual photons in the limit Q . The validity of the GDH sum rule for the proton has been satisfactorily established. In the case of the neutron, the experimental limits are still much too large; this is due substantially to the large uncertainty in the 2 photoproduction cross section, especially in n n in the photon energy range 500 to 1500 MeV. Most of the required experimental tools to remedy this, namely, high-quality circularly polarized taggedphoton beams and longitudinally polarized H2 and 3He targets are already available at MAMI up to 800 MeV and will be available up to 1.5 GeV in 2005. The Crystal Ball can provide the crucial 4 solid-angle multiphoton detector. An important byproduct of the photoproduction data with polarized beams and targets is the help in the unraveling of the N* and * resonance spectra, since the polarization data have enhanced sensitivity to small multipoles. From the thesis (BjorkenSumRule_Thesis – See the folder Talks): “The Bjorken Sum Rule and the Strong Coupling” Diplomarbeit zur Erlangung des wissenschaftlichen Grades Diplom-Physiker vorgelegt von Anke Knauf geboren in Meißen __ Institut f¨ur Theoretische Physik Fachrichtung Physik Fakult¨at Mathematik und Naturwissenschaften der Technischen Universit¨at Dresden 2002 The BSR in the Naive Parton Model Deep inelastic phenomena have been extensively studied for about a quarter of a century, both experimentally and theoretically. The main purposes of this vast physics program were first to elucidate the internal structure of the nucleon and later on to test perturbative Quantum Chromodynamics (QCD). At the end of the 60’s, the first measurements on charged lepton deep inelastic scattering (DIS) at the Stanford Linear Accelerator (SLAC) have shown that the nucleon is made of hard pointlike objects [3], which was the first evidence for the existence of sub-nuclear particles called partons. The observed cross sections turned out to be independent of the momentum transfer Q2 and obeyed the scaling behavior predicted by Bjorken [4], whose physical picture was given by Feynman [1] in terms of the Quark Parton Model (QPM). The explanation of scaling was based on the fact that a hard collision among partons takes place in such a short time, so that partons behave as if they were free particles. This requirement of an interaction that becomes weak (at high energies) led to the consideration of non-Abelian gauge field theories, which posess the crucial property of asymptotic freedom, and to propose QCD as the fundamental theory for strong interactions [5]. It is now well established that QCD is an asymptotically free theory and that the strong coupling αs(Q2) becomes small when Q2 is large, i.e. at short distances. However, scale invariance is broken because of quantum corrections and therefore one expects scaling violations which are calculable in perturbative QCD. Although the naive Quark Parton Model, describing the nucleon as composed of three quarks, explains many features of protons and neutrons (built up from two up- and one down quark or vice versa, respectively) it was facing a serious problem when the Electron Muon Collaboration (EMC) published its results in 1988 [30]. That was the start of the so-called “spin crisis” since it became obvious that the nucleon is more than the sum of parts, in the sense that three quarks alone do not account for the nucleon spin. In the following years many experiments followed, determined to solve the question how the nucleon’s spin is distributed among its constituents. In 1970 Feynmann and Bjorken developed the so-called Parton Model [1, 2] that describes nucleons as a loose bound assemblage of partons. Deep inelastic scattering off nucleons can be replaced by elastic scattering off a parton in this model. The Parton Model has suffered modifications due to the fact that also gluons and so-called “sea quarks” (virtually generated quarks) are present. The so-called QCD improved parton model explains many features of nucleons experimentalists encounter. Still, the question how much of the nucleon’s spin is actually carried by which constituent has not been satisfactorily resolved yet. Another aspect of high energy scattering experiments has been to verify certain sum rules, as those derived by Bjorken [6] and Ellis–Jaffe [7]. Though the latter seems to be violated [8, 9, 10], the Bjorken Sum Rule has been confirmed within 8% [12]. It relates the first moment of the longitudinal polarized structure function g1 to a constant, the axial vector coupling. A whole lot of new possibilities open up and new ways of determining fundamental constants may be gone when one assumes the validity of this sum rule. One of the ultimate important constants for high energy physics is the strong coupling constant αs. Since the Bjorken Sum Rule relates a quantity that can be principally measured to a perturbative series in αs one can extract a value of αs from the measured Bjorken Sum. Previous attempts to do so [11, 12] usually neglected some of the theoretical obstacles one is facing, as there are the contributions from higher twist matrix elements, the unknown smallx behaviour of the structure functions or the fact that experimentalists are using some constant value for αs in order to determine the Bjorken Sum. Here I will take all of those into account and moreover give a statement which aspects have the biggest influence on the determination of αs. On the other hand one can ask the question what predictions for the theoretical unknowns one can make once αs is fixed and the Bjorken Sum Rule fulfilled. That way one can extract the higher twist contributions that cannot be derived from first principles or the presently much discussed small-x behaviour of structure functions which is also not clear from theory. The latter one turns out to be the largest uncertainty in determining the Bjorken Sum. That is because one uses a perturbative QCD procedure in next–to–leading order (NLO) to evolve all data points to one common scale Q2. This procedure cannot take effects into account that are beyond NLO in QCD. We will see, that those effects arise especially for small x and prevent the extraction of αs from the Bjorken Sum Rule with high precision. This unfortunate outcome may be used to derive a new prediction for the small-x behaviour if one requires the data to fulfill the Bjorken Sum Rule. This imposes some special small–x behaviour since the data constrains the structure function g1 quite well in the low–x regime. -- The spin-dependent structure function This page under construction The spin-dependent structure function g1 is given by the following equation, . Bjorken sum rule The Bjorken sum rule is written as follows using the axial and vector coupling constants GA and Gv, . J.D.Bjorken, Phys Rev. 148 1467 (1966); Phys. Rev. D1 1376 (1970). J.Kodaira et al., Phys. Rev. D20 627 (1979); Nucl. Phys. B165 129 (1980). Ellis-Jaffe sum rule Accoring to the Ellis and Jaffe, another sum rule is deriven from the quark light-cone algebra with the assumption that strange sea quarks do not contribute to the asymmetry, . J. Ellis and R.L.Jaffe, Phys. Rev. D9 (1974) 1444; D 10 (1974) 1669(E). Recent measurements and analyses of the Deep Inelastic Scattering of polarized muons or electrons from the polarized nucleons by the EMC [1], SLAC [2] and SMC [3] groups have shown the deviations from the Ellis-Jaffe sum rule of the experiment data. This means that the spin of the nucleon (= 1/2) cannot be reproduced from the sum of the spin of quarks in nucleon: this is called spin crisis . (Click here to get some plots for g1 integrations from SLAC E143.) [1] J. Ashman et al.,Phys. Lett. 206 364 (1988); Nucl. Phys. B328 1 (1989) [2] D.L.Anthony et al., Phys. Rev. lett. 71 959 (1993). [3] B. Adeva et al., Phys. Lett. B302 533 (1993); Phys. Lett. B320 400 (1994). To solve Spin Crisis The possible explanation for the spin crisis is thought to be due to the contributions to the nucelon spin from Spin of the sea quarks, Polarization of the gluons, Orbital angular momentum (L) of the quarks in nucleon, etc. PHENIX/Spin collabration is planning to carry out several experiments with polarized proton-proton collider at the enegy of = 50-500 GeV at RHIC to extract the helicity distributions of quarks and anti-quarks in nucleon and to investigate gluon polarization, via