U-Channel - Revision history

Vanwdani at 18:49, 15 May 2018

2018-05-15T18:49:17Z

2017-06-09T23:30:52Z

u-Channel

2017-06-09T23:24:01Z

2017-06-09T23:23:29Z

u-Channel

2017-06-09T23:21:58Z

u-Channel

2017-06-09T22:29:34Z

u-Channel

2017-06-09T22:28:41Z

u-Channel

2017-06-08T22:24:08Z

Created page with " =u-Channel="

New page

=u-Channel=

@@ Line 1: / Line 1: @@
-<center><math>\textbf{\underline{Navigation}}</math>
+<center><math>\underline{\textbf{Navigation}}</math>
 [[T-Channel|<math>\vartriangleleft </math>]]
@@ Line 58: / Line 58: @@
-<center><math>\textbf{\underline{Navigation}}</math>
+<center><math>\underline{\textbf{Navigation}}</math>
 [[T-Channel|<math>\vartriangleleft </math>]]

← Older revision		Revision as of 23:30, 9 June 2017
Line 51:		Line 51:


−	<center><math>u \equiv -2 p \ _1^{*2}(1+cos\ \theta)</math></center>	+	<center><math>u \equiv -2 p \ ^{*2}(1+cos\ \theta)</math></center>

@@ Line 1: / Line 1: @@
 <center><math>\textbf{\underline{Navigation}}</math>
 [[T-Channel|<math>\vartriangleleft </math>]]
 [[VanWasshenova_Thesis#Moller_Scattering|<math>\triangle </math>]]
-[[U-Channel|<math>\vartriangleright </math>]]
+[[Limits_based_on_Mandelstam_Variables|<math>\vartriangleright </math>]]
 </center>
@@ Line 63: / Line 62: @@
 [[T-Channel|<math>\vartriangleleft </math>]]
 [[VanWasshenova_Thesis#Moller_Scattering|<math>\triangle </math>]]
-[[U-Channel|<math>\vartriangleright </math>]]
+[[Limits_based_on_Mandelstam_Variables|<math>\vartriangleright </math>]]
 </center>

← Older revision		Revision as of 23:23, 9 June 2017
Line 42:		Line 42:


−	<center><math>t \equiv 2m_1^-2E_1^{2}-2 \|p \|^{*2}cos\ \theta</math></center>	+	<center><math>u \equiv 2m_1^-2E_1^{2}-2 \|p \|^{*2}cos\ \theta</math></center>


Line 52:		Line 52:


−	<center><math>t \equiv -2 p \ _1^{*2}(1+cos\ \theta)</math></center>	+	<center><math>u \equiv -2 p \ _1^{*2}(1+cos\ \theta)</math></center>

← Older revision		Revision as of 23:21, 9 June 2017
Line 27:		Line 27:


		+	In the center of mass frame of reference,
		+
		+	<center><math> E^* \equiv E_1^=E_1^{'} = E_2^=E_2^{'} = E_1^=E_2^</math></center>
		+
		+
		+	and
		+
		+
		+	<center><math>\|p^\| \equiv \| \vec p \ _1^\|=\| \vec p \ _1^{'}\| =\| \vec p \ _2^\|=\| \vec p \ _2^{'*}\|</math></center>
		+
		+
		+	and <math>\theta_1=-\theta_2</math> is the angle between <math>\vec p \ _1^* </math> and <math> \vec p \ _2^{'*}</math>
		+
		+
		+
		+	<center><math>t \equiv 2m_1^-2E_1^{2}-2 \|p \|^{*2}cos\ \theta</math></center>
		+
		+
		+	Using the relativistic term for Energy
		+
		+
		+	<center><math>E^2=\vec p \ ^2+m^2</math></center>
		+
		+
		+
		+	<center><math>t \equiv -2 p \ _1^{*2}(1+cos\ \theta)</math></center>


	----		----
		+

@@ Line 12: / Line 12: @@
 The u quantity is does not have a clear cut interpretation like the s and t channels
-<center><math>s \equiv \left({\mathbf P_1^*}- {\mathbf P_2^{'*}}\right)^2=\left({\mathbf P_2^*}- {\mathbf P_1^{'*}}\right)^2</math></center>
+<center><math>u \equiv \left({\mathbf P_1^*}- {\mathbf P_2^{'*}}\right)^2=\left({\mathbf P_2^*}- {\mathbf P_1^{'*}}\right)^2</math></center>
 <center>[[File:400px-CMcopy.png]]</center>
@@ Line 18: / Line 18: @@
-<center><math>t \equiv\left({\mathbf P_1^*}- {\mathbf P_2^{'*}}\right)^2</math></center>
+<center><math>u \equiv\left({\mathbf P_1^*}- {\mathbf P_2^{'*}}\right)^2</math></center>
-<center><math>t \equiv \mathbf P_1^{*2}-2 \mathbf P_1^* \mathbf P_2^{'*}+ \mathbf P_2^{'*2}</math></center>
+<center><math>u \equiv \mathbf P_1^{*2}-2 \mathbf P_1^* \mathbf P_2^{'*}+ \mathbf P_2^{'*2}</math></center>
-<center><math>t \equiv 2m_1^2-2E_1^*E_2^{'*}+2 \vec p \ _1^* \vec p \ _2^{'*}</math></center>
+<center><math>u \equiv 2m_1^2-2E_1^*E_2^{'*}+2 \vec p \ _1^* \vec p \ _2^{'*}</math></center>

← Older revision		Revision as of 22:28, 9 June 2017
Line 1:		Line 1:
		+
		+	<center><math>\textbf{\underline{Navigation}}</math>
		+
		+	[[T-Channel\|<math>\vartriangleleft </math>]]
		+	[[VanWasshenova_Thesis#Moller_Scattering\|<math>\triangle </math>]]
		+	[[U-Channel\|<math>\vartriangleright </math>]]
		+
		+	</center>
		+

	=u-Channel=		=u-Channel=
		+	The u quantity is does not have a clear cut interpretation like the s and t channels
		+
		+	<center><math>s \equiv \left({\mathbf P_1^}- {\mathbf P_2^{'}}\right)^2=\left({\mathbf P_2^}- {\mathbf P_1^{'}}\right)^2</math></center>
		+
		+	<center>[[File:400px-CMcopy.png]]</center>
		+
		+
		+
		+	<center><math>t \equiv\left({\mathbf P_1^}- {\mathbf P_2^{'}}\right)^2</math></center>
		+
		+
		+	<center><math>t \equiv \mathbf P_1^{2}-2 \mathbf P_1^ \mathbf P_2^{'}+ \mathbf P_2^{'2}</math></center>
		+
		+
		+	<center><math>t \equiv 2m_1^2-2E_1^E_2^{'}+2 \vec p \ _1^* \vec p \ _2^{'*}</math></center>
		+
		+
		+
		+
		+	----
		+
		+
		+	<center><math>\textbf{\underline{Navigation}}</math>
		+
		+	[[T-Channel\|<math>\vartriangleleft </math>]]
		+	[[VanWasshenova_Thesis#Moller_Scattering\|<math>\triangle </math>]]
		+	[[U-Channel\|<math>\vartriangleright </math>]]
		+
		+	</center>