Tamar Thesis TheoryChapt - Revision history

Didbtama: /* Notes */

2012-12-10T06:47:18Z

Notes

Didbtama: /* Semi Inclusive Deep Inelastic Scattering */

2012-09-14T17:59:48Z

Semi Inclusive Deep Inelastic Scattering

Didbtama: /* Semi Inclusive Deep Inelastic Scattering */

2012-09-14T03:08:39Z

Semi Inclusive Deep Inelastic Scattering

Didbtama: /* Introduction */

2012-09-04T02:46:23Z

Introduction

Didbtama: /* Introduction */

2012-09-04T02:44:44Z

Introduction

Didbtama: /* Introduction */

2012-09-04T02:43:45Z

Introduction

Didbtama: /* Introduction */

2012-09-04T02:43:04Z

Introduction

Foretony: /* Introduction */

2012-06-26T04:54:42Z

Introduction

Didbtama: /* Lattice QCD */

2012-05-11T21:03:34Z

Lattice QCD

Didbtama: /* Lattice QCD */

2012-05-11T20:54:58Z

Lattice QCD

← Older revision		Revision as of 06:47, 10 December 2012
Line 454:		Line 454:

	[[Delta_D_over_D]]		[[Delta_D_over_D]]
		+
		+	[https://wiki.iac.isu.edu/index.php/SIDIS_PionAsym_EG2000 Go Back]

@@ Line 266: / Line 266: @@
 |<math>Q^2 = - {q^2} ^{lab} = 4EE^'\sin^2 \frac{\theta}{2}</math>||Negative squared 4 - momentum transfer
 |-
-|<math>\nu = \frac {p \cdot q}{M}  =^{lab} E - E^'</math>||Energy of the virtual photon
+|<math>\nu = \frac {p \cdot q}{M}  = (E - E^')|_{lab}</math>||Energy of the virtual photon
 |-
 |<math>x = \frac {Q^2}{2 p \cdot q} = \frac {Q^2}{2M \nu}</math>||Bjorken scaling variable
 |-
-|<math>y = \frac{p \cdot q}{Pk} =^{lab} \frac{\nu}{E}</math>||Fractional energy of the virtual photon
+|<math>y = \frac{p \cdot q}{Pk} = \frac{\nu}{E} |_{lab}</math>||Fractional energy of the virtual photon
 |-
 |<math>W^2 = (p + q)^2 = M^2 + 2M\nu - Q^2</math>||Squared invariant mass of the excited nucleon system
@@ Line 276: / Line 276: @@
 |<math>p = (E_h, p)</math>||4 - momentum of a hadron in the final state
 |-
-|<math>z = \frac{p\cdot p_h}{p\cdot q} =^{lab} \frac{E_h}{\nu}</math>||Fractional energy of the observed final state hadron
+|<math>z = \frac{p\cdot p_h}{p\cdot q} =\frac{E_h}{\nu}|_{lab}</math>||Fractional energy of the observed final state hadron
 |}<br>
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@@ Line 272: / Line 272: @@
 |<math>y = \frac{p \cdot q}{Pk} =^{lab} \frac{\nu}{E}</math>||Fractional energy of the virtual photon
 |-
-|<math>W^2 = (p + q)^2 = M^2 + 2M\nu - Q^2</math>||Squared invariant mass of the photon-nucleon system
+|<math>W^2 = (p + q)^2 = M^2 + 2M\nu - Q^2</math>||Squared invariant mass of the excited nucleon system
 |-
 |<math>p = (E_h, p)</math>||4 - momentum of a hadron in the final state

@@ Line 11: / Line 11: @@
 {| border="0" style="background:transparent;"  align="center"
 |-
-|<math>\Delta \Sigma =  \Delta u + \Delta d + \Delta s</math>
+|<math>\Delta \Sigma =  \Delta u + \Delta d + \Delta s + \overline{\Delta u} + \overline{\Delta d} + \overline{\Delta s}</math>
 |}<br>

@@ Line 8: / Line 8: @@
 |-
 |<math>S_{N}=\frac{1}{2} = \frac{1}{2} \Delta \Sigma + \Delta G +L_z</math>
 |}<br>
 {| border="0" style="background:transparent;"  align="center"
 |-
@@ Line 16: / Line 14: @@
 |}<br>
-- is the spin contribution from the quarks, <math>\Delta G</math> - from the gluons and <math>L_z</math> - the orbital angular momentum contribution from the partons(quarks). The spin contribution from each type of quark to the total nucleon spin is following<ref name="EllisKarline"> Ellis, J., & Karline, M.(1965). Determination of  <math>\alpha</math> and the Nucleon Spin Decomposition using Recent Polarized Structure Function Data. Phys. Lett., B(341), pg 397.</ref>:
+where <math>\Delta \Sigma </math>- is the spin contribution from the quarks, <math>\Delta G</math> - from the gluons and <math>L_z</math> - the orbital angular momentum contribution from the partons(quarks). The spin contribution from each type of quark to the total nucleon spin is following<ref name="EllisKarline"> Ellis, J., & Karline, M.(1965). Determination of  <math>\alpha</math> and the Nucleon Spin Decomposition using Recent Polarized Structure Function Data. Phys. Lett., B(341), pg 397.</ref>:
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 |-

@@ Line 7: / Line 7: @@
 {| border="0" style="background:transparent;"  align="center"
 |-
-|<math>\frac{1}{2} = \frac{1}{2} \Delta \Sigma + \Delta G +L_z</math>
+|<math>S_{N}=\frac{1}{2} = \frac{1}{2} \Delta \Sigma + \Delta G +L_z</math>
 |}<br>
-where <math>\Delta \Sigma =  \Delta u + \Delta d + \Delta s</math> - is the spin contribution from the quarks, <math>\Delta G</math> - from the gluons and <math>L_z</math> - the orbital angular momentum contribution from the partons(quarks). The spin contribution from each type of quark to the total nucleon spin is following<ref name="EllisKarline"> Ellis, J., & Karline, M.(1965). Determination of  <math>\alpha</math> and the Nucleon Spin Decomposition using Recent Polarized Structure Function Data. Phys. Lett., B(341), pg 397.</ref>:
+where<br>
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 |-

@@ Line 1: / Line 1: @@
 =Introduction=
-The understanding of the spin structure in the nucleon remains a major challenge for hadron physics. The parton model predicted that quarks carry about (67 <math>\pm</math> 7)% of the total nucleon spin. Experiments performed at the European Organization for Nuclear Research(CERN) by Electromagnetic Compatibility collaboration(EMC) found out that only (31 <math>\pm</math> 7)% of the nucleon spin is carried by the quarks. Other experiments at CERN(spin muon collaboration(SMC)) and SLAC(E142 && E143) did not agree with the naive quark parton model <ref name="EllisKarline"> Ellis, J., & Karline, M.(1965). Determination of  <math>\alpha</math> and the Nucleon Spin Decomposition using Recent Polarized Structure Function Data. Phys. Lett., B(341), pg 397.</ref>. This reduction is assumed to be the caused by a negatively polarized quark sea at low momentum fraction x, which is not considered in quark models. The complete picture of the nucleon spin can be obtained by taking into account the spin contributions from the gluons, the sea quarks and in addition the quarks orbital momentum. So the spin of the nucleon can be written as the sum of the following terms<ref>B. Hommez, Ph.D Thesis, University of Gent (2003).</ref>:
+The understanding of the spin structure in the nucleon remains a major challenge for hadron physics. The parton model predicted that quarks carry about (67 <math>\pm</math> 7)% of the total nucleon spin. Experiments performed at the European Organization for Nuclear Research(CERN) by Electromagnetic
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@@ Line 149: / Line 149: @@
 |}<br>
 The last expression shows that the quarks inside the nucleon carry about <math>50 %</math> of the total momentum. It leads to the question, are quarks the only particles inside the nucleon? In addition to the quarks and antiquarks, there are other components in the nucleon. They cant be seen by using electromagnetic (electron) and weak (neutrino) probe, because they do not carry weak or electric charge.<br>
-The scaling behavior was given by assumption that the nucleon is built by non-interacting pointlike quarks and antiquarks. However, the quarks were found to be charged particles, which concludes that there should be at least electromagnetic interaction between the  nucleon constituents. The spatial and temporal resolution of the target nucleon can be increased with the high four-momentum transferred squared <math>Q^2</math>. Due to the high four momentum transferred square , quarks that at low <math>Q^{2}</math> are seen as a pointlike particles, will be resolved into more partons in the nucleon. One can see that inside the nucleon there are more components then just three charged quarks. <br>
+The scaling behavior was given by assumption that the nucleon is built by non-interacting pointlike quarks and antiquarks. However, the quarks were found to be charged particles, which concludes that there should be at least electromagnetic interaction between the  nucleon constituents. The spatial and temporal resolution of the target nucleon can be increased with the high four-momentum transferred squared <math>Q^2</math>. Using the high <math>Q^{2}</math> , quarks that at low <math>Q^{2}</math> are seen as a pointlike particles, will be resolved into more partons in the nucleon. One can see that inside the nucleon there are more components then just three charged quarks. Due to the scaling violation, the total four momentum of the nucleon is divided over more partons and the average fractional momentum of each parton will decrease Fig. 3.<br>
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 |-