TWiki> Main Web>TWikiUsers>ChengguangZhu>ZhuCosmics (2008-12-22, ChengguangZhu) EditAttachPDF
-- ChengguangZhu - 15 Dec 2008

muon sagita in ATLAS ID

  • On the transverse plane, a Muon track starting from primary vertex will pass along a curve whose string is 1.5 meters long
  • Bending radius $r=\frac{mv}{qB}=\frac{\gamma\beta m_{0}c}{qB}=0.168\gamma\sqrt{1-\frac{1}{\gamma^2}}$ here $0.168=\frac{m_{0}c}{qB} with B=2 $
  • The sagita is then $s=r(1-\sqrt{1-{(\frac{1.5}{r})}^2})$
  • muon sagita vs $\gamma$
    muon_sagita_vs_gamma.jpg

Alignment of ID and EM calo

Modeling of EM displacement

EM is regid, without internal deformation

  • displacement is modelled by a straight line in 3D
    • $\phi_0; \theta_0 (0<\theta_0<\pi/2); Z_0$ if the straight line cross Z axis.
  • The norminal $\eta$ ($\eta_{cell}$), displaced to $\eta_{track}$
    • On the $\phi_0$ plane, we have $r_{track}sh(\eta_{track}) - r*sh(\eta) = - (r+\frac{D}{2})sin\theta_0=- \Delta Z$ with $D= (r*sh\eta-Z_0)tan\theta_0$
    • On any $\phi$ plane, then $r_{track}=\sqrt{(rsin(\phi-\phi_0))^2+(D+rcos(\phi-\phi_0))^2}$ and $\Delta Z = (\frac{D}{2}+rcos(\phi-\phi_0))sin\theta_0$
    • generally $ sh(\eta_{track}) = \frac{r*sh(\eta) - ((r*sh\eta-Z_0)tan\theta_0/2+rcos(\phi-\phi_0))sin\theta_0}{\sqrt{(rsin(\phi-\phi_0))^2+((r*sh\eta-Z_0)tan\theta_0+rcos(\phi-\phi_0))^2}}$

      straightline_model.jpg

  • The nominal $\phi$, which is $\phi_{cell}$, changes induced by 2 steps, displacement and rotation
    • displacement: $\phi_{tmp} = \phi - \frac{D'sin(\phi-\phi_0)}{r}$ with $D'=Dcos\theta_0$

      phi_displacement.jpg
    • rotation: $tan(\phi_{tmp}-\phi_0) = tan(\phi_{track} - \phi_0)cos\theta_0 $

      phi_rotation.jpg
    • Totally we have $ tan(\phi_{track}-\phi_0)= tan (\phi -\phi_0 - \frac{(r*sh\eta-Z_0)sin\theta_0sin(\phi-\phi_0)}{r} )/cos\theta_0 $
Attachments Attachments
Topic attachments
I Attachment History Action Size Date Who Comment
JPEGjpg muon_sagita_vs_gamma.jpg r1 manage 19.7 K 2008-12-15 - 17:29 ChengguangZhu  
JPEGjpg phi_displacement.jpg r1 manage 19.4 K 2008-12-19 - 00:28 ChengguangZhu  
JPEGjpg phi_rotation.jpg r1 manage 16.6 K 2008-12-19 - 00:08 ChengguangZhu  
JPEGjpg straightline_model.jpg r2 r1 manage 42.2 K 2008-12-18 - 19:51 ChengguangZhu  
Edit | Attach | Watch | Print version | History: r11 < r10 < r9 < r8 < r7 | Backlinks | Raw View | WYSIWYG | More topic actions
Topic revision: r11 - 2008-12-22 - ChengguangZhu
 
    • Cern Search Icon Cern Search
    • TWiki Search Icon TWiki Search
    • Google Search Icon Google Search

    Main All webs login

This site is powered by the TWiki collaboration platform Powered by PerlCopyright &© 2008-2024 by the contributing authors. All material on this collaboration platform is the property of the contributing authors.
or Ideas, requests, problems regarding TWiki? use Discourse or Send feedback