Home » PANDA » PandaRoot » Tracking » Helix and FairTrackParH
| Helix and FairTrackParH [message #9038] |
Wed, 22 July 2009 17:37  |
StefanoSpataro
Messages: 2736
Registered: June 2005
Location: Torino
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first-grade participant |
From: *to.infn.it
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Hello,
I would like to understand the helix parameters used in FairTrackParH, which are different from the ones present in the old-style PndTpcLheTrack.
Could somebody write, according to our "standard" definition of helix parameters, how our track is represented?
The helix parameters are: x0, y0, z0, lambda, phi, charge (even if it is q/p in FairTrackParH).
How can I know the following functions?
x = x(s)
y = y(s)
z = z(s)
px = px(s)
py = py(s)
pz = pz(s)
I have checked some tracking papers but without founding this representation. This is very important for fast correlation inside the barrel.
Thanks in advance.
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| Re: Helix and FairTrackParH [message #9047 is a reply to message #9040] |
Thu, 23 July 2009 13:00  |
StefanoSpataro
Messages: 2736
Registered: June 2005
Location: Torino
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first-grade participant |
From: *to.infn.it
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Hello,
thanks for the Wittek paper. I have read it and found the formula for the momenta:
px = p cos(lambda) cos(phi)
py = p cos(lambda) sin(phi)
pz = p sin(lambda)
(which is also present in your tracking report).
But this is just the "static" relation between angles and momentum coordinated in a well defined point. What I need is the coordinated px py pz along the track, starting from the first point up to the last point (where pz remains constant, while px and py rotate). Therefore, this formula does not help me.
In Lia's thesis, page 42 (50 in the pdf), there is the following formula:
x(s) = x0 + Rh[cos(phi0+h s cos(lambda)/Rh) - cos(phi0)]
y(s) = y0 + Rh[sin(phi0+h s cos(lambda)/Rh) - sin(phi0)]
z(s) = z0 + s sin(lambda)
but unfortunately nothing for momenta.
Are those parameters (phi0 lambda R) the same of the ones in FairTrackParH? Is it possible to use this representation as it is with our trackbase code, or maybe x0 y0 z0 are calcualted ina well defined point, phi0 is defined in a different way, and so on?
Thanks in advance to everybody who could answer to my questions.
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| Re: Helix and FairTrackParH [message #9059 is a reply to message #9058] |
Thu, 23 July 2009 19:41 |
Lia Lavezzi
Messages: 291
Registered: May 2007
Location: Torino
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first-grade participant |
From: *47-151.net24.it
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Hi Stefano,
just to clarify the meaning of the different parametrizations:
1) in FairTrackParH you have the 5 parameters: q/p, lambda, phi, yperp, zperp.
q/p is the charge over momentum, lambda and phi are the dip and polar angles which describe the direction of the particle, yperp and zperp are the coordinates of the point in the SC reference frame (the one perpendicular to the momentum). Using the functions of that class you can also get the position and momentum in the master reference frame;
2) in the equations you cited from my thesis, x0, y0, z0 define the starting point of the helix, phi0 is the azimuthal angle of the starting point with respect to the helix axis, lambda is the dip angle and Rh is the radius of curvature of the helix.
So, I don' t think you can directly apply the equations in 2) to the track from 1) since phi and phi0 should be different: in fact phi0 is calculated with respect to the helix axis and so they would coincide only if the helix axis was coincident with the beam.
If you want to apply the x(s), y(s), z(s) equations you should choose as starting point the one you get with GetPosition in FairTrackParH and then apply them, but you have to calculate the corresponding phi0, since it is not directly given by GetPhi in FairTrackParH.
Concerning the momentum calculation I guess that once you have the helix described in the x(s), y(s), z(s) point you can obtain the px and py coordinates by considering the transverse momentum as tangent to the track (a circle) in that point and then projecting it on the x/y directions, can' t you?
If I find the exact equations for the momentum I will post a message!
Ciao,
Lia.
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| Re: Helix and FairTrackParH [message #9060 is a reply to message #9059] |
Thu, 23 July 2009 20:04 |
StefanoSpataro
Messages: 2736
Registered: June 2005
Location: Torino
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first-grade participant |
From: *15-87-r.retail.telecomitalia.it
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| Lia Lavezzi wrote on Thu, 23 July 2009 19:41 |
1) in FairTrackParH you have the 5 parameters: q/p, lambda, phi, yperp, zperp.
q/p is the charge over momentum, lambda and phi are the dip and polar angles which describe the direction of the particle, yperp and zperp are the coordinates of the point in the SC reference frame (the one perpendicular to the momentum). Using the functions of that class you can also get the position and momentum in the master reference frame;
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Let me correct you, in FairTrackParH the parameters are:
/** fLm = Dip angle **/
Double_t fLm;
/**fPhi = azimuthal angle **/
Double_t fPhi;
/** Points coordinates in SC system */
Double_t fX_sc, fY_sc, fZ_sc;
Or at least these are the data members and the parameters used in the helix constructor.
There is no xperp, yperp and phi0, but x_sc, y_sc, z_sc and phi.
Apart from lambda I have no idea on what the other parameters are.
| Quote: |
2) in the equations you cited from my thesis, x0, y0, z0 define the starting point of the helix, phi0 is the azimuthal angle of the starting point with respect to the helix axis, lambda is the dip angle and Rh is the radius of curvature of the helix.
So, I don' t think you can directly apply the equations in 2) to the track from 1) since phi and phi0 should be different: in fact phi0 is calculated with respect to the helix axis and so they would coincide only if the helix axis was coincident with the beam.
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Well, can I consider x_sc y_sx z_sc as the starting point of the helix? In this case can phi be considered as phi0?
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If you want to apply the x(s), y(s), z(s) equations you should choose as starting point the one you get with GetPosition in FairTrackParH and then apply them, but you have to calculate the corresponding phi0, since it is not directly given by GetPhi in FairTrackParH.
...
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For this reason I think it would be good to have written somewhere thh definition of the FairTrackParH parameters, to avoid misunderstanding (such as phi and phi0) and in order to avoid ambiguity.
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| Re: Helix and FairTrackParH [message #9061 is a reply to message #9060] |
Thu, 23 July 2009 22:02 |
Lia Lavezzi
Messages: 291
Registered: May 2007
Location: Torino
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first-grade participant |
From: *47-151.net24.it
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| Quote: |
| Quote: |
1) in FairTrackParH you have the 5 parameters: q/p, lambda, phi, yperp, zperp.
q/p is the charge over momentum, lambda and phi are the dip and polar angles which describe the direction of the particle, yperp and zperp are the coordinates of the point in the SC reference frame (the one perpendicular to the momentum). Using the functions of that class you can also get the position and momentum in the master reference frame;
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Let me correct you, in FairTrackParH the parameters are:
/** fLm = Dip angle **/
Double_t fLm;
/**fPhi = azimuthal angle **/
Double_t fPhi;
/** Points coordinates in SC system */
Double_t fX_sc, fY_sc, fZ_sc;
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Ok, it' s just a matter of names 
If you have a look in the FairTrackParH.h, the comment at the beginning contains the 5 parameters:
q/p, lambda, phi, y_perp, z_perp
In the code the name of the parameters are:
fLm = lambda
fPhi = phi
fX_sc = x_perp
fY_sc = y_perp
fZ_sc = z_perp
Concerning the names of the coordinate, let me explain: usually the SC frame coordinates are marked as "orthogonal" x, "orthogonal" y and "orthogonal" z, just because the SC frame has its yz plane orthogonal to the track momentum.
When you describe the track you need, of the 5 parameters, 1 parameter to describe the momentum magnitude (fQp is a data member of FairTrackPar), 2 to describe the direction (lambda/phi) and 2 to describe the position (y and z... call them _perp or _sc, they are the same thing).
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Well, can I consider x_sc y_sx z_sc as the starting point of the helix? In this case can phi be considered as phi0?
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Actually I don' t think so: phi is given with respect to the z axis, while phi0 is given with respect to an axis which passes through the center of curvature of the helix; you could consider phi = phi0 only if the helix axis was the z axis. At least this is what I understand...
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For this reason I think it would be good to have written somewhere thh definition of the FairTrackParH parameters, to avoid misunderstanding (such as phi and phi0) and in order to avoid ambiguity.
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There is a definition of the parameters in our report on GEANE, since the parameters for both FairTrackParP and FairTrackParH are the ones used there (in GEANE, I mean) in the SD and SC frame. Maybe we can add a link in the code comment to easily get it. Would it be useful?
Ciao,
Lia.
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| Re: Helix and FairTrackParH [message #9069 is a reply to message #9061] |
Fri, 24 July 2009 13:18 |
StefanoSpataro
Messages: 2736
Registered: June 2005
Location: Torino
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first-grade participant |
From: *to.infn.it
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| Quote: |
Ok, it' s just a matter of names
Ok, but you can
If you have a look in the FairTrackParH.h, the comment at the beginning contains the 5 parameters:
q/p, lambda, phi, y_perp, z_perp
In the code the name of the parameters are:
fLm = lambda
fPhi = phi
fX_sc = x_perp
fY_sc = y_perp
fZ_sc = z_perp
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It is a matter of names only if you know what those names mean (not my case)  And once they are also called in a different way, the amount of confusion in my mind increases.
However, it seems I do not need those parameters for my helix, even because all the defnitions are to move from one system to another, but what I need is how the position/momentum variates along the track.
I have found a document in internet that explains what I need, to characterize my track:
center of the helix (to calculate drho, and phi0)
radius of the helix (to calculate drho)
pt (to calculate k)
lambda
Of these 5 params, I have already lambda, pt, and the radius can be calculated from p. I am only missing the center of the helix, that can be calculated with the suggested method of Gianluigi.
I will try and cross my fingers hoping that it will work.
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