Stuff From PhD Proposal - Revision history

Oborn at 05:12, 17 January 2010

2010-01-17T05:12:44Z

Oborn at 05:05, 17 January 2010

2010-01-17T05:05:14Z

Oborn at 20:19, 12 November 2009

2009-11-12T20:19:16Z

Oborn at 19:19, 5 November 2009

2009-11-05T19:19:37Z

Oborn at 19:16, 5 November 2009

2009-11-05T19:16:34Z

Oborn at 05:33, 3 October 2009

2009-10-03T05:33:26Z

Oborn at 19:58, 2 October 2009

2009-10-02T19:58:24Z

Oborn: /* Using Fragmentation function */

2009-10-02T19:27:30Z

Using Fragmentation function

Oborn: /* Using Fragmentation function */

2009-10-02T18:52:41Z

Using Fragmentation function

Oborn at 18:47, 2 October 2009

2009-10-02T18:47:06Z

← Older revision		Revision as of 05:12, 17 January 2010
Line 117:		Line 117:

	(Factorization Theorem: The quark fragmentation into the hadrons is independent of long distance effects and particularly of the final hadron identity.)		(Factorization Theorem: The quark fragmentation into the hadrons is independent of long distance effects and particularly of the final hadron identity.)
		+
		+
		+	The mid 1960's were a revolutionary period in the physics of elementary particles in which the field was challenged to explain the list of particles which became known as the "particle zoo". The most successful scheme to explain the "particle zoo" was proposed by the Gell-Mann and Ne'eman, the ansatz scheme. The scheme classified hadrons in group-theoretical terms as multiplets of the special unitary Lie group SU(3), using as the relevant quantum numbers, such as isospin, baryon number and strangeness.
		+	what is the sentence below trying to say?
		+
		+	searching for quarks
		+
		+
		+	However, the ansatz scheme had classified hadrons, which were in the higher dimensional representations of SU(3), the fundamental ones were empty.
		+	In order to solve this problem Gell-Mann Zweig stated that a set of three particles which were the fundamental representations of the SU(3) group should also exist, so called quarks. According to the SU(3) they carry the fractional charge <math>\pm 1/3</math> and <math>\pm 2/3</math>. The quantum numbers of those new particles, which represent their properties, were u(up), d(down) and s(strange). At the time experimental evidence to support their existence was not present.

← Older revision		Revision as of 05:05, 17 January 2010
Line 115:		Line 115:

	Target is placed 50 cm upstream of the standard CLAS target position.		Target is placed 50 cm upstream of the standard CLAS target position.
		+
		+	(Factorization Theorem: The quark fragmentation into the hadrons is independent of long distance effects and particularly of the final hadron identity.)

← Older revision		Revision as of 20:19, 12 November 2009
Line 116:		Line 116:
	Target is placed 50 cm upstream of the standard CLAS target position.		Target is placed 50 cm upstream of the standard CLAS target position.

		+
		+	[http://www.jlab.org/highlights/phys.html]

	[http://wiki.iac.isu.edu/index.php/User_talk:Tamar Go back]		[http://wiki.iac.isu.edu/index.php/User_talk:Tamar Go back]

← Older revision		Revision as of 19:19, 5 November 2009
Line 113:		Line 113:

	Charge conjugation is the replacement of each particle in a process by the corresponding antiparticle. Charge conjugation invariance states that the rate of a process is identical to the rate of a similar process with all particles replaced by their antiparticles. Charge conjugation invariance is true for strong and electromagnetic interactions, but not for weak interactions.		Charge conjugation is the replacement of each particle in a process by the corresponding antiparticle. Charge conjugation invariance states that the rate of a process is identical to the rate of a similar process with all particles replaced by their antiparticles. Charge conjugation invariance is true for strong and electromagnetic interactions, but not for weak interactions.
		+
		+	Target is placed 50 cm upstream of the standard CLAS target position.


	[http://wiki.iac.isu.edu/index.php/User_talk:Tamar Go back]		[http://wiki.iac.isu.edu/index.php/User_talk:Tamar Go back]

← Older revision		Revision as of 19:16, 5 November 2009
Line 105:		Line 105:

	there is a figure of merit which considers max polarization and radiation damage, Li-6 is a competitor		there is a figure of merit which considers max polarization and radiation damage, Li-6 is a competitor
		+
		+
		+	[http://www2.slac.stanford.edu/vvc/theory/chargeconjugation.html]
		+
		+	Charge Conjugation Invariance
		+	Invariances, in particle physics, are relationships between different processes.
		+
		+	Charge conjugation is the replacement of each particle in a process by the corresponding antiparticle. Charge conjugation invariance states that the rate of a process is identical to the rate of a similar process with all particles replaced by their antiparticles. Charge conjugation invariance is true for strong and electromagnetic interactions, but not for weak interactions.
		+

	[http://wiki.iac.isu.edu/index.php/User_talk:Tamar Go back]		[http://wiki.iac.isu.edu/index.php/User_talk:Tamar Go back]

← Older revision		Revision as of 05:33, 3 October 2009
Line 101:		Line 101:

	'''Quark distribution function q(x) is the probability(density) of finding a quark with fraction x of the proton(neutron) momentum.'''		'''Quark distribution function q(x) is the probability(density) of finding a quark with fraction x of the proton(neutron) momentum.'''
		+
		+
		+
		+	there is a figure of merit which considers max polarization and radiation damage, Li-6 is a competitor

	[http://wiki.iac.isu.edu/index.php/User_talk:Tamar Go back]		[http://wiki.iac.isu.edu/index.php/User_talk:Tamar Go back]

← Older revision		Revision as of 19:58, 2 October 2009
Line 98:		Line 98:


		+	[[Media:Semi-inclusive_π_production_tests_for_independent_fragmentation_and_for_polarized_quark_densities.pdf]]
		+
		+	'''Quark distribution function q(x) is the probability(density) of finding a quark with fraction x of the proton(neutron) momentum.'''

	[http://wiki.iac.isu.edu/index.php/User_talk:Tamar Go back]		[http://wiki.iac.isu.edu/index.php/User_talk:Tamar Go back]

← Older revision		Revision as of 19:27, 2 October 2009
Line 81:		Line 81:

	:::::::::::<math>A</math><sup><math>\pi^+ - \pi^-</math></sup> =<math>\frac {\sigma^{\pi^+ - \pi^-}_{1/2} - \sigma^{\pi^+ - \pi^-}_{3/2}} {\sigma^{\pi^+ - \pi^-}_{1/2} + \sigma^{\pi^+ - \pi^-}_{3/2}} </math>		:::::::::::<math>A</math><sup><math>\pi^+ - \pi^-</math></sup> =<math>\frac {\sigma^{\pi^+ - \pi^-}_{1/2} - \sigma^{\pi^+ - \pi^-}_{3/2}} {\sigma^{\pi^+ - \pi^-}_{1/2} + \sigma^{\pi^+ - \pi^-}_{3/2}} </math>
		+
		+
		+	*Extracting <math>\frac{\Delta d(u)}{d(u)}</math>
		+
		+	In the semi inclusive deep inelastic scattering <math>\pi^+</math> and <math>\pi^-</math> production cross section can be written in the following way:
		+
		+	:::::::::<math>\sigma = \frac{x(P+l)^2}{4 \pi \alpha^2} (\frac{2y^2}{1+(1-y)^2})\frac{d^3\sigma}{dxdydz}</math>
		+
		+	and
		+
		+
		+	:::::::::<math>\Delta \sigma = \frac{x(P+l)^2}{4 \pi \alpha^2}(\frac{y}{2-y})[\frac{d^3\sigma_{+-}}{dxdydz} - \frac{d^3\sigma_{++}}{dxdydz}]</math>
		+
		+
		+	P and l are the four momenta of the target and electron. <math>\sigma_{nm}</math> refer to a nucleon of n helicity and a scattering lepton(electron) of helicity m. Rest of the variables are described in Table.1.



	[http://wiki.iac.isu.edu/index.php/User_talk:Tamar Go back]		[http://wiki.iac.isu.edu/index.php/User_talk:Tamar Go back]

@@ Line 76: / Line 76: @@
 '''In inclusive DIS the polarization of the individual quarks(antiquarks) can be extrapolated from the fits to the data, relying on assumptions such as the Bjorken sum rule and SU(3) symmetry for the sea quark.'''
-There is an alternative approach getting the information about the contributions from the individual quarks(antiquarks) using ''semi-inclusive'' Deep Inelastic Scattering instead of inclusive DIS, where in the final state in coincidence with the scattered lepton(in our case electron) hadron is detected too. In SIDIS after lepton scattering off the target emits an energetic virtual photon, which interacts with the quarks inside the nucleon. The energy and momentum transfer from the virtual photon to the quarks is so large that the struck quark is expelled from the nucleon forming the jet of hadrons. Hadrons created from the fragmentation of the expelled quark can be used as an one more method to tag its flavor. "This exploitation of hadrons in SIDIS measurements requires knowledge of the probabilities of the various types h of hadrons emerging from a struck quark of a given flavor q. These probabilities are embodied in the fragmentation function <math>D_q^h(z,Q^2)</math>, where <math>z=E_h/ \nu</math> and <math>\nu</math> and <math>E_h</math> are the energies in the target rest frame of the absorbed virtual photon(th struck quark) and the detected hadron."['''ref: flavor decomposition of the sea quark helicity dist. in the nucleon from SIDIS''']. The correlation between the flavor of the probed quark and the detected hadron in the final state can be obtained from the fragmentation function, which is the probability that a quark of flavor q will fragment into a h type hadron. For instance, the detection of a <math>\pi^-</math> meson in the final state, which is the bound state of <math>\bar{u}</math>(up anti) and d(down) quarks, indicates that either a <math>\bar{u}</math>(up antiquark) or a d(down) quark was probed in the nucleon. In addition, it is know that at high values of <math>X_B</math> the Bjorken Scaling variable the sea quarks(like <math>\bar{u}</math>(up antiquark)) do not have a major contribution in the nucleon.
+There is an alternative approach getting the information about the contributions from the individual quarks(antiquarks) using ''semi-inclusive'' Deep Inelastic Scattering instead of inclusive DIS, where in the final state in coincidence with the scattered lepton(in our case electron) hadron is detected too. In SIDIS after lepton scattering off the target emits an energetic virtual photon, which interacts with the quarks inside the nucleon. The energy and momentum transfer from the virtual photon to the quarks is so large that the struck quark is expelled from the nucleon forming the jet of hadrons. Hadrons created from the fragmentation of the expelled quark can be used as an one more method to tag its flavor. "This exploitation of hadrons in SIDIS measurements requires knowledge of the probabilities of the various types h of hadrons emerging from a struck quark of a given flavor q. These probabilities are embodied in the fragmentation function <math>D_q^h(z,Q^2)</math>, where <math>z=E_h/ \nu</math> and <math>\nu</math> and <math>E_h</math> are the energies in the target rest frame of the absorbed virtual photon(th struck quark) and the detected hadron."['''ref: flavor decomposition of the sea quark helicity dist. in the nucleon from SIDIS''']. The correlation between the flavor of the probed quark and the detected hadron in the final state can be obtained from the fragmentation function, which is the probability that a quark of flavor q will fragment into a h type hadron. For instance, the detection of a <math>\pi^-</math> meson in the final state, which is the bound state of <math>\bar{u}</math>(up anti) and d(down) quarks, indicates that either a <math>\bar{u}</math>(up antiquark) or a d(down) quark was probed in the nucleon. In addition, it is known that at high values of <math>X_B</math> the Bjorken Scaling variable the sea quarks(like <math>\bar{u}</math>(up antiquark)) do not have a major contribution in the nucleon.
 The semi-inclusive pion electro-production asymmetries can be written in terms of the cross sections of produced hadrons in the final state(<math>\pi^-</math> and <math>\pi^+</math>):

← Older revision		Revision as of 18:47, 2 October 2009
Line 44:		Line 44:

	[[Media:HommezPhDThesis.ps]]		[[Media:HommezPhDThesis.ps]]
		+
		+
		+	The polarized cross sections, which are related to the polarized structure function, are not measured directly. However the asymmetry related to them can be easily determined from the measurements:
		+
		+	::::::::::::<math>A_1 = \frac{\sigma_{1/2} - \sigma_{3/2}}{\sigma_{1/2} + \sigma_{3/2}}</math>
		+
		+	where <math>\sigma_{1/2}</math> (<math>\sigma_{3/2}</math>) is the photon absorption cross section ones whose spin is antiparallel(parallel) to the target polarization. The photon of spin 1 is absorbed by only quarks whose spin is in the opposite direction from the photon's spin. Therefore, the polarized structure function can be related to the difference of these cross sections. However, the unpolarized structure function is the some of those two cross sections. The structure functions described above is based on quark parton model, where the contribution from the sea quarks is minimized. The double spin asymmetry can be written in terms of valence quark distribution functions for proton and neutron targets in this kinematic range:
		+
		+	::::::::::::<math>A_{1, p}^{I} = \frac {4\Delta u_v (x) + \Delta d_v (x)} {4 u_v (x) + d_v (x)} </math> (1) <br>
		+	::::::::::::<math>A_{1, n}^{I} = \frac {\Delta u_v (x) + 4\Delta d_v (x)} {u_v (x) + 4d_v (x)} </math> (2)<br>
		+
		+	In inclusive DIS the asymmetry <math>A_{\|\|}</math> of cross sections, which is related to the beam and target polarization, only two measurable and controlled quantities, can be written in the following way:
		+
		+	::::::::::::::<math>A_{meas} = P_B P_T f_D A_{\|\|}</math>
		+
		+	where <math>P_B</math> and <math>P_T</math> are the beam and target polarization respectively and <math>f_D</math> - target dilution factor, the cross section factor caused by polarizable nucleons in the target.
		+
		+	In inclusive DIS the asymmetry of the photon absorption in the nucleon can be expressed in terms of the asymmetry <math>A_{\|\|}</math> of cross sections:
		+
		+	::::::::::::::<math>A_{\|\|} = D(1 + \eta \gamma )A_1</math>
		+
		+	where <math>\eta = \frac{\epsilon \gamma y}{[1- (1-y) \epsilon ]}</math> is a kinematic factor. The degree of polarization transfer from the electron to the virtual photon, so called depolarization factor D is given below:
		+
		+	::::::::::::::<math>D = \frac{1- (1-y) \epsilon}{1 + \epsilon R}</math>
		+
		+	where <math>\epsilon</math> is the polarization parameter of the virtual photon:
		+
		+	:::::::<math>\epsilon = [1 + \frac{2 \vec{q}^2}{Q^2} tan^2 \frac{\theta}{2}]^{-1} = \frac{1 - y -\frac{1}{4} \gamma^2 y^2}{1-y+\frac{1}{4}y^2(\gamma^2+2)}</math>
		+
		+
		+	'''In inclusive DIS the polarization of the individual quarks(antiquarks) can be extrapolated from the fits to the data, relying on assumptions such as the Bjorken sum rule and SU(3) symmetry for the sea quark.'''
		+
		+	There is an alternative approach getting the information about the contributions from the individual quarks(antiquarks) using ''semi-inclusive'' Deep Inelastic Scattering instead of inclusive DIS, where in the final state in coincidence with the scattered lepton(in our case electron) hadron is detected too. In SIDIS after lepton scattering off the target emits an energetic virtual photon, which interacts with the quarks inside the nucleon. The energy and momentum transfer from the virtual photon to the quarks is so large that the struck quark is expelled from the nucleon forming the jet of hadrons. Hadrons created from the fragmentation of the expelled quark can be used as an one more method to tag its flavor. "This exploitation of hadrons in SIDIS measurements requires knowledge of the probabilities of the various types h of hadrons emerging from a struck quark of a given flavor q. These probabilities are embodied in the fragmentation function <math>D_q^h(z,Q^2)</math>, where <math>z=E_h/ \nu</math> and <math>\nu</math> and <math>E_h</math> are the energies in the target rest frame of the absorbed virtual photon(th struck quark) and the detected hadron."['''ref: flavor decomposition of the sea quark helicity dist. in the nucleon from SIDIS''']. The correlation between the flavor of the probed quark and the detected hadron in the final state can be obtained from the fragmentation function, which is the probability that a quark of flavor q will fragment into a h type hadron. For instance, the detection of a <math>\pi^-</math> meson in the final state, which is the bound state of <math>\bar{u}</math>(up anti) and d(down) quarks, indicates that either a <math>\bar{u}</math>(up antiquark) or a d(down) quark was probed in the nucleon. In addition, it is know that at high values of <math>X_B</math> the Bjorken Scaling variable the sea quarks(like <math>\bar{u}</math>(up antiquark)) do not have a major contribution in the nucleon.
		+
		+	The semi-inclusive pion electro-production asymmetries can be written in terms of the cross sections of produced hadrons in the final state(<math>\pi^-</math> and <math>\pi^+</math>):
		+
		+	:::::::::::<math>A</math><sup><math>\pi^+ - \pi^-</math></sup> =<math>\frac {\sigma^{\pi^+ - \pi^-}_{1/2} - \sigma^{\pi^+ - \pi^-}_{3/2}} {\sigma^{\pi^+ - \pi^-}_{1/2} + \sigma^{\pi^+ - \pi^-}_{3/2}} </math>
		+
		+

	[http://wiki.iac.isu.edu/index.php/User_talk:Tamar Go back]		[http://wiki.iac.isu.edu/index.php/User_talk:Tamar Go back]