Limits based on Mandelstam Variables - Revision history

Vanwdani at 19:07, 1 January 2019

2019-01-01T19:07:09Z

2019-01-01T19:06:46Z

2018-05-15T18:49:37Z

2017-06-16T18:20:51Z

2017-06-14T01:56:23Z

Limits based on Mandelstam Variables

2017-06-14T01:50:23Z

Limits based on Mandelstam Variables

2017-06-14T01:45:13Z

Limits based on Mandelstam Variables

2017-06-14T01:43:26Z

Limits based on Mandelstam Variables

2017-06-13T22:22:10Z

Limits based on Mandelstam Variables

2017-06-13T22:17:02Z

Limits based on Mandelstam Variables

@@ Line 3: / Line 3: @@
 [[U-Channel|<math>\vartriangleleft </math>]]
 [[VanWasshenova_Thesis#Moller_Scattering|<math>\triangle </math>]]
-[[https://wiki.iac.isu.edu/index.php/Limit_of_Energy_in_Lab_Frame|<math>\vartriangleright </math>]]
+[[Limit_of_Energy_in_Lab_Frame|<math>\vartriangleright </math>]]
 </center>
@@ Line 153: / Line 153: @@
 [[U-Channel|<math>\vartriangleleft </math>]]
 [[VanWasshenova_Thesis#Moller_Scattering|<math>\triangle </math>]]
-[[https://wiki.iac.isu.edu/index.php/Limit_of_Energy_in_Lab_Frame|<math>\vartriangleright </math>]]
+[[Limit_of_Energy_in_Lab_Frame|<math>\vartriangleright </math>]]
 </center>

@@ Line 3: / Line 3: @@
 [[U-Channel|<math>\vartriangleleft </math>]]
 [[VanWasshenova_Thesis#Moller_Scattering|<math>\triangle </math>]]
-[[Initial_Lab_Frame_4-momentum_components|<math>\vartriangleright </math>]]
+[[https://wiki.iac.isu.edu/index.php/Limit_of_Energy_in_Lab_Frame|<math>\vartriangleright </math>]]
 </center>
@@ Line 153: / Line 153: @@
 [[U-Channel|<math>\vartriangleleft </math>]]
 [[VanWasshenova_Thesis#Moller_Scattering|<math>\triangle </math>]]
-[[Initial_Lab_Frame_4-momentum_components|<math>\vartriangleright </math>]]
+[[https://wiki.iac.isu.edu/index.php/Limit_of_Energy_in_Lab_Frame|<math>\vartriangleright </math>]]
 </center>

@@ Line 1: / Line 1: @@
-<center><math>\textbf{\underline{Navigation}}</math>
+<center><math>\underline{\textbf{Navigation}}</math>
 [[U-Channel|<math>\vartriangleleft </math>]]
@@ Line 149: / Line 149: @@
-<center><math>\textbf{\underline{Navigation}}</math>
+<center><math>\underline{\textbf{Navigation}}</math>
 [[U-Channel|<math>\vartriangleleft </math>]]

@@ Line 3: / Line 3: @@
 [[U-Channel|<math>\vartriangleleft </math>]]
 [[VanWasshenova_Thesis#Moller_Scattering|<math>\triangle </math>]]
-[[Limits_based_on_Mandelstam_Variables|<math>\vartriangleright </math>]]
+[[Initial_Lab_Frame_4-momentum_components|<math>\vartriangleright </math>]]
 </center>
@@ Line 142: / Line 142: @@
 <center><math>cos\ \theta=1-\frac{-2t}{s-4m^2}</math></center>

← Older revision		Revision as of 01:56, 14 June 2017
Line 133:		Line 133:


−	~~<center><math>\frac{s(s-4m^2)}{4s}= \vec p \ ^{*2}</math></center>~~

		+	<center><math>t=-2 p \ ^{*2}(1-cos\ \theta)=\frac{-2(s-4m^2)}{4}(1-cos\ \theta)</math></center>

−	<center><math>t=-~~2 p \~~ ^{*2}(1-cos\ \theta)=\frac{-~~2s(~~s-4m^2~~)}{4s~~}~~(1-cos\ \theta)~~</math></center>	+
		+
		+	<center><math>\frac{-2t}{s-4m^2}=(1-cos\ \theta)</math></center>
		+
		+
		+	<center><math>cos\ \theta=1-\frac{-2t}{s-4m^2}</math></center>

← Older revision		Revision as of 01:50, 14 June 2017
Line 129:		Line 129:


−	<center><math>\frac{s-4m^2}{4}= \vec p \ ^{*2})</math></center>	+	<center><math>\frac{s-4m^2}{4}= \vec p \ ^{*2}</math></center>
		+
		+
		+
		+	<center><math>\frac{s(s-4m^2)}{4s}= \vec p \ ^{*2}</math></center>
		+
		+
		+	<center><math>t=-2 p \ ^{*2}(1-cos\ \theta)=\frac{-2s(s-4m^2)}{4s}(1-cos\ \theta)</math></center>

← Older revision		Revision as of 01:45, 14 June 2017
Line 126:		Line 126:


−	<center><math>s=~~4(m~~^2+\vec p \ ^{2})=~~(2E~~^~~)^{~~2}</math></center>	+	<center><math>s=4m^2+4 \vec p \ ^{*2})</math></center>
		+
		+
		+	<center><math>\frac{s-4m^2}{4}= \vec p \ ^{*2})</math></center>

@@ Line 110: / Line 110: @@
-In the lab frame,
+In the center of mass frame of reference,
-<center><math>s \equiv \left({\mathbf P_1}+ {\mathbf P_2}\right)^2</math></center>
+<center><math>E_1^*=E_2^*=E^* \quad and \quad \vec p \ _1^*=-\vec p \ _2^*= \vec p \ ^*</math></center>
-<center><math>s \equiv \mathbf P_1^{2}+2 \mathbf P_1 \mathbf P_2+ \mathbf P_2^{2}</math></center>
+<center><math>s \equiv 2m^2+2(E_1^{*2}+\vec p \ ^{*2} )</math></center>
-<center><math>s \equiv 2m^2+2E_1E_2+2 \vec p \ _1 \vec p \ _2</math></center>
+Using the relativistic energy equation
-<center><math>s \equiv 2m^2+2E_1E_2</math></center>
+<center><math>s=4(m^2+\vec p \ ^{*2})=(2E^*)^{2}</math></center>

← Older revision		Revision as of 22:22, 13 June 2017
Line 125:		Line 125:


−	<center><math>s \equiv 2m^2+~~2E_2E_2~~</math></center>	+	<center><math>s \equiv 2m^2+2E_1E_2</math></center>

@@ Line 115: / Line 115: @@
-<center><math>s \equiv \mathbf P_1^{2}-2 \mathbf P_1 \mathbf P_2^+ \mathbf P_2^{2}</math></center>
+<center><math>s \equiv \mathbf P_1^{2}+2 \mathbf P_1 \mathbf P_2+ \mathbf P_2^{2}</math></center>
-<center><math>s \equiv 2m^2-2E_1E_2+2 \vec p \ _1 \vec p \ _2</math></center>
+<center><math>s \equiv 2m^2+2E_1E_2+2 \vec p \ _1 \vec p \ _2</math></center>
@@ Line 125: / Line 125: @@
-<center><math>t \equiv 2m^2-2E_2E_2</math></center>
+<center><math>s \equiv 2m^2+2E_2E_2</math></center>