notes on projects

A brief procedure:

1. Determin the Kinematics. Match QCD to SCET + NRQCD, basically by writing down the gauge-invariant operators (color singlet or octect) and doing the non-relativistic expansion for quark spinors and etc. in QCD case then matching the results ,to get the hard coefficient at hard-scale. A tree level work(but NOT easy at all).

2. Calculate the scattering amplitude at that (hard) scale : factorize, optical theorem. So a loop integral may be needed for singlet case.

3. Use Renormalizatoin Group to run the coefficent to some other scale, by calculating the “vertex” corrections. Also need to take operator-mixing into consideration at this step, but it may seem small in my case. Bunch of integrals here, damned hard piece!!!

4. Interpolating: combine the end-point-result with result away from that. Maybe some structure functions are needed. No one knows whether these functions are physically correct or not. So maybe, two minus mak e a plus….

Feynman(test embedding Youtube)

“all kinds of interesting questions which a science knowledge only adds to the excitement and mystery and the awe of a flower. It only adds. I don’t understand how it subtracts.”

我对理科的兴趣也许真的越来越少了, 不过这不能说明数学啦, 物理啦枯燥无聊; 相反地, 这表现理科是多么有趣:)—–你想, 通过12年”乏味的”初等数理教育, 另外经过4年”惨无人道”的本科高等数理教育, 接着是这些年的研究生生涯, 我依然对理科存有那么一丝丝幻想, 并没有完全泯灭. 可见,”Science”是多么有趣, 且令人激动.

gnuplot, briefly II plot

gnuplot最重要的当然是作图拉.:) 譬如experimental data存在”calibration.dat”里:

the1st, 4th, 2nd,5th columns分别是dL , L, dL的实验误差, L的实验误差. 把L作为x, dL作为y来plot, 并且带上两者的实验误差, 用命令: plot “calibration.dat” usi 4:1:5:2 w xyerr title “L v.s dL” , 其中”usi 4:1:5:2″代表用第四,一,二,五列的数据. (默认x,y,xerr,yerr) “w xyerr”表示用xyerror bar, “title …”用来作legend.

若打算一次作多种图比如在上面的例子里再作gaussian函数图像, 就用,\来分隔 :

plot “calibration.dat” usi 4:1:5:2 w xyerr title “L vs dL” ,\

300*exp(-0.01*(x-200)**2) title “gaussian distribution”

当然, 可以把所需要作的流程, 如set term, plot “file”之类写在一个文件里面,如plot.那么直接在linux下输入gnuplot plot就行了. !!

谈谈著名的gnuplot:), briefly I 设置

大概是linux下最著名的画图程序了. The most important: it’s free. 最新的版本是4.0.

Fortran下面调用gnuplot使用call system”gnuplot filename” 即可; C下, 网上free code下载.
现谈谈设置.gnuplot所有设置都应在作图之前进行, 包括设置输出文件名. 在command line下键入gnuplot,进入程序:

4.0大概提供60多种图形文件输出形式(terminal type), 包括.gif, .png, .jpeg 以及.ps. 键入set term 会显示所安装的版本提供的所有文件格式(press “q”键退出显示). 用set term <filetype>来设置输出文件形式. :

然后用set output “filename” 选择输出文件名.

结束对文件格式的操作, 然后就进行图形的设置, 一般常用有set xrange[xmin:xmax], set xtics <#>(divide x interval with increment #), set mxtics <#> (draw small tics inside the interval), set xlabels “xlabel” (insert x name)以及对应的y轴操作.接着还有set grid(画网格)等等.全部的set命令可以用help set来查看:

懒人的feynman rules

这里是Stewart的ppt关于SCET. 里面的东西应该有对应的文章, 可惜找不到. 所要用的大概就是22页费曼规则. 如果不想自己推导的话, 就直接抄吧. 不过最多只到两夸克两胶子LO相互作用. 另外作为对自己的提醒: 所有传播子里的p_/{perp}, 都是4动量表达形式, 做积分时p_{perp}^2应取负号.

另, SCET里做积分: 一般对np项做柯西积分, 然后对p_/{perp}做常规的重整化式积分, 剩下n^bar p 估计不用积分:).  如此会简化很多.
最近压力大. Bad….:(