# Presentation: 142441

## Tracking in ALICE

**OUTLOOK:**
**Requirements**
**History**
**Tracking methods**
**Track finding**
**Tracking efficiency**
**Momentum resolution**
**Double-track efficiency and resolution**
**Track matching with other detectors**
******-mass resolution**
**Conclusions**

## Tracking requirements

**Environment**
**dN/dy up to 8000 charged particle (about 4 times that foreseen for RHICH**
**Requirements**
**good efficiency (above 90%) starting from pt 0.1 GeV/c**
**some efficiency also below (as low as possible)**
**momentum resolution (dp/p) on the level of 1% for low momenta and for high momenta few % at 5 GeV/c**
**good secondary vertexing capability (V0, charm ?)**
**particle identification capabilities, especially for low momentum electrons (which cannot reach other PID)**
**Principal solution**
**silicon tracker at smaller radii (where affordable)**
**beyond a TPC with track length about 1.5 meter (for dE/dx)**

## History of ALICE tracking

**The first ALICE design (1993)**
**Small magnet**
**1 meter diameter**
**1 Tesla magnetic field**
**very thin (10% of X0) superconducting coil**
**Tracking devices**
**5 layers silicon tracker inside the magnet**
**outside the magnet TPC with no field (i.e. return yoke behind the TPC)**
**Two strategies for tracking**
**do everything with silicon detectors**
**search for straight tracks in TPC (assuming a vertex constraint one has an estimate of momentum) then guided track finding through silicon detectors**

## Problems: change the design

**Neither of the methods worked satisfactory**
**we had 90% efficiency above 0.4 - 0.5 GeV/c in pt but below the efficiency dropped drastically**
**magnetic field was to high, the low-pt tracks banded to much and were lost**
**the coil of the small magnet cannot be done thinner than 17 --20% therefore the low-pt tracks suffer from large multiple scattering**
**we try to put inside the magnet additional silicon layer with a marginal improvement**
**We have to change the design**
**large magnet was needed to house both the silicon tracker and the TPC - problem with funding**
**therefore we reuse the largest LEP magnet L3 which has about 12 meter diameter and field up to 0.5 Tesla (we use 0.2 Tesla)**

## ALICE tracking system

**Two tracking detectors (****maybe three ?****)**
**ITS (Inner Tracking System)**
**six layers of silicon detectors**
**2 pixel layers at radii 3.8 cm and 7.4 cm**
**2 silicon drift layers at radii 14 cm and 24 cm**
**2 silicon strip layers at radii 39 cm and 45 cm**
**TPC (Time Projection Chamber)**
**inner radius 88 cm, outer radius 250 cm**
**about 160 pad rows of three sizes**
**4x7.5 ; 6x10 ; 6x15 mm****2**** from inner to outer**
**two different read-out chamber with different pad response function**
**(TRD (Transition Radiation Detector)**
**6 expansion chambers, maybe use for tracking**

## Tracking methods

**Two large groups of algorithms:**
**Local methods**
**Global methods**
**Local methods**
**decision taken step by step, when only partial information is available**
**no need for global track model**
**Global methods**
**can operate directly on raw data**
**decision taken when all information is known **
**needs precise track model**
**We need to track down to p****t**** 100 MeV/c !**

## Prototyping

**Strategy for local method**
**start at outer part of the TPC**
**proceed towards smaller radii**
**extrapolate track to the outer ITS layers (at this step we usually need to use a vertex constraint)**
**proceed layer by layer through ITS**
**reverse the track and extrapolate to outer detectors (TRD, TOF, HMPID)**
**Stand alone tracking in ITS**
**remove the hits assigned at previous step**
**special track finding in ITS only for low pt tracks**
**can work (with low efficiency) down to pt 60 MeV/c for pions and down to 30 MeV/c for electrons**

## Prototypes

**Prototype 0 (1993-1995)**
**simple road tracker in the TPC, using smeared GEANT hits as input (starting from ALEPH TPC reconstruction) **
**merging with the ITS done by forcing vertex constraint when leaving the TPC (into two outer silicon strip layers)**
**Prototype 1 (1996-1997)**
**taken the experience from prototype 0 first `real’ reconstruction program was written (****in C++ !****) **
**still using only smeared hits as input, not a detector response simulation**
**Prototype 2 (1998-2000)**
**TPC crisis (somebody said that TPC will never work for particle densities foreseen)**
**use very detail detector response and digitization**
**see talk by Yu. Belikov**

## Track finding prototype

**We choose and prototype Kalman filter for tracking (see Yu. Belikov talk)**
**no track model needed**
**easy to take into account stochastic processes**
**multiple scattering**
**fluctuations in energy losses**
**gives simultaneous track finding and fitting**
**faster fitting for correlated space-points**
**natural way to connect with other detectors**
**needs cluster finding in advance**
**needs track seeds to start with**
**We had no serious attempt in prototyping of global tracking method (only not serious)**

## Momentum resolution (ITS)

**Momentum resolution from ITS TDR**

**Question:**** ****Why the total error is so large compare to the contributions due to multiple scattering and measurement error ?**
**Because of correlation.**
**Even larger than the linear sum of the two !**
**Only sum of the norm of covariant matrices has to be larger, not a diagonal term.**

## Example of BAD detector

**Imagine detector like this one:**
**detector thickness infinitely small**
**detector thickness infinitely large**

**L**
**N planes**

**L**
**N planes**

**B**

## Total error and contributions

**Total error**
**first half of detector                  ********p/p = ********L**** ******** ********p ****/ (L****2**** ********N)**
**the measurement in two halves are independent !**
**therefore                                    ********T**** = ********L**** / ********2**
**Multiple scattering contribution**
**point error   ********p**** = 0    therefore   ********L**** -> 0**
**m.s. contribution                       ********MS**** = 0 / ********2 = 0**
**Point error contribution**
**thickness of middle plane goes to zero**
**the two halves are correlated    ********p/p = ********PE**** ******** ********p ****/ [(2L)****2**** ********2N)**
**therefore                                     ********PE**** = ********L**** / (4********2)**
**Finally:          ********T**** = 4 (********PE**** + ********MS****) > ********PE**** + ********MS**

## What about real detectors ?

**Formula with quadratic sum of contributions (see PDG) is valid only for uniform distribution of scattering material (bubble chamber formula)**
**For modern detectors it is not more true**
**even for high momenta ! **
**Typical example is ALICE combination of ITS and TPC**
**there is obviously non negligible material in between**
**this material is responsible for loss of correlation !**
**once again: the interface between ITS and TPC is crucial place to be optimized and watched**
**Another example: muon detectors with measurements in front and after absorber**

## Two track efficiency

**Two-track efficiency for ********q -> 0 goes down to ******** 40 %**
**not to 0 ! (here helps multiple scattering in ITS material !) **

## Two-track resolution

******q****long**** and ********q****side**** do not depend on momentum and on charged particle density**
**their resolutions is determined by angular resolutions**
******q****out**** does depend on both momentum and charged particle density**
**its resolution is determined by momentum resolution itself**
**Two-track resolutions in MeV/c:**
**        ****dNch/dy     ********q****long****      ********q****side****                   ********q****out**** **
**                                            ****p****t****(GeV/c)    0.2          0.5          1.0**
**           ****1000        1.0          1.1           3.7       7.4       13**
**           ****6000        1.1          0.5           3.9       9.5       16**
** **

## Track matching with ITS

**Extrapolation of Kalman filter to ITS with tighter**
**vertex constraint (prototype 1)**

## Track matching with TRD

**Extrapolation of TPC tracks to TRD - simple simulation - preliminary estimate (prototype 0)**

## -mass resolution

**Depend on charged particle density**
**Momentum resolution at ‘nominal’ filed (0.2T) is insufficient to achieve ********’ and ********’’ separation**

**We need to increase magnetic field to about ****0.4 T**

## Conclusions

**We have well defined strategy for tracking - maybe we will still do some `global’ prototype**
**Results from TPC prototype 2, see Yu. Belikov talk**
**Two-track efficiency is very good, but**
**‘****out’ component of ********q is worse then required**
**Track matching to other detectors - satisfactory**
****** ****resolution practically within requirements if we increase magnetic field to 0.4 T**
**Finish prototype 2 through the ITS and TRD - end of this year **