# Presentation: 856207

## Detector and Physics Calibrations

**Nick Hadley**
**The University of Maryland**
**Hadron Collider Physics Summer School**
**Fermilab August 11-12, 2006**

## Acknowledgements

**Many thanks to those who shared their knowledge, figures and slides with me.**
**Also to those who put useful material on the web.**
**Notably: Guennadi Borissov, Adi Bornheim, Oliver Buchmueller, Georgios Daskalakis, ****Yuri Fisyak, Tapio Lampen, Marjorie Shapiro, Jan Stark, Mayda Velasco**

## Calibration and Alignment

**Goal is to get the maximum out of your detector.**
- Design performance or test beam performance is not guaranteed
- Many more channels, often mass produced, conditions not controlled.
**Calibration: what did you measure?**
- ADC to energy, time to distance
**Alignment: or “dude, where is my detector”?**
**Each has a hardware component**
- Lasers, light flashers, survey marks, pulsers, radioactive sources
**And a software component**
- Calibrate and align with data

## Calibration and Alignment Caveat

**Generally considered to be an extremely boring topic.**
- Success = only 50% of the audience is sleeping at the end of the talk

## Calibration and Alignment – motivation

**General Aesthetics**
- With much time and effort, built beautiful detector, won’t achieve maximum performance without calibration
**Practical Considerations**
- Discover Higgs
- Need superb photon resolution
- Discover supersymmetry
- Understand missing Et resolution, most importantly the tails
- Discover high mass states
- Best momentum resolution possible
- Alignment improves tracking efficiency
- Third Generation may be key
- Need excellent displaced vertex identification

## LHC Question #1 - Low Mass Higgs ?

- Is electroweak symmetry broken via the Higgs mechanism ?

**m****H**** = 117****+67**** GeV   (based on 2004 m****T**** = 178 GeV)**

**-45**

## How good an ECAL do we need for H->?

**How good an ECAL do we need for H->********?**

- Cross section 

**Searching for a 10****-10**** branching ratio ! And ..**

**W****+/-****  m = 80.4 GeV  ******** = 2.1GeV**

**Z****0****   m = 91.2 GeV   ******** = 2.5GeV**

**t   m = 178 GeV   ******** ~ 1.5GeV @ Tevatron : ********s = 2 TeV**

**H   m =  150 GeV ? ******** = ~10 MeV @ LHC : ********s = 14 TeV**

**  ****@ SPS : ********s = 0.5 TeV**

- 

- If the Higgs is light ....

## Resolution Required for Low Mass Higgs

**L**** = 10****34 ****cm****2****s****-1**
**Vertex by track finding**
**m****H**** = 100 GeV**

**Benchmark process:    H ******** ******** ******
-               ( limited by interaction vertex measurement)
-     CMS Resolution* : *******E ****/ E = a / ******** E ********  b ******** c/ E**
**Aim:**		           Barrel	End cap
- Stochastic term:	   a  =   2.7%         5.7%
- Constant term:  	   b  =   0.55%       0.55%
- Noise:         Low L**   **c  =  155 MeV   770 MeV
-                    High L**              **210 MeV   915 MeV

**At 100 GeV : 0.27 ******** 0.55 ******** 0.002 ******** 0.6%**

## Higgs Discovery Potential 

**Excellent ECAL performance and calibration is essential.**
**The constant term dominates and calibration will determine the constant term**

**H->******

## Supersymmetry

**Important Discovery Channels**
- Jets + missing Et or trileptons + missing Et
**Cautionary note**
- “Those who cannot remember the past are condemned to repeat it.” George Santayana

## 0 -> e+e- Discovery (??) 1977(0 ->  discovered 1950)

** ********0**** -> e****+****e****- ****“discovered” with BR 4 times modern value of 6.2 x 10****-8**
**5 events seen, 1 background claimed. With modern BR, only 1 event signal expected.**
**Plot shows e+e- mass (x)**
**Resolution tails hard**

## Supersymmetry or ED Discovery (20XX)

**Supersymmetry**
- x = missing Et
**Extra Dimensions**
- x = +- mass
**Essential to understand mean, sigma and non-gaussian tails**

**TeV**

## Calorimeter Calibration

**Will cover calibration first, then alignment.**
**Will focus on CMS and Dzero, but stay general.**
- One crystal and scintillator calorimeter, one LAR.
**For ATLAS, see ATLAS Physics TDR**
- http://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/TDR/access.html
**For CMS, see CMS Physics TDR volume**
- http://cmsdoc.cern.ch/cms/cpt/tdr/

## ECAL Calibration and Alignment

**Goal: approximately 0.5% constant term**
**G = overall gain**
**F = correction function depending on type of particle, position, energy and cluster algorithm used**
**C****i ****= intercalibration constant**
**A****i**** = signal amplitude (ADC) in channel i **

## ECAL Calibration and Alignment

**Calorimeter Alignment: use tracker, typically much better position resolution than calorimeter**
**Calibration problem often factorizes.**
- Overall scale vs stability
- Electronics vs detector (crystals or LAR)
- One changes often, one fixed (more or less)
- Initial calibration vs calibration in situ
**Details are detector specific**

## ECAL Calibration and Alignment

**During construction, often possible to calibrate with radioactive sources (e.g. ****60****Co), pulsers and so on. **
- Design mechanical tolerances for resolution goal.
**Test beams used to get overall gain factor.**
- Test beam conditions (material in front of calorimeter often different, electronics used may not be final, cables almost certainly not final.
- Understand response as function of position
**Cosmic ray muons can be useful.**

## CMS ECAL Calibration & Monitoring

**ECAL Calibration ****(Resolution : ‘Constant Term of the Resolution Formula’)**** : **

**ECAL Stability (<< 0.5%) ,**
**Monitored with Laser Monitoring System****  **

**Transparency Loss Correction,**
**Signal Change under Irradiation ~5%**
**Measured with Laser Monitoring System**

**Raw (uncalibrated) Supermodule : **
**6%-10% ‘Resolution’**
**Spread among channels before calibration**

**Beam Test Precalibration : **
**2 % ‘Resolution’**
**With a ‘fast’ calibration**
**‘****Lab Precalibration’ :**
**4 % ‘Resolution’**

**In-Situ Physics Calibration : **
**0.5 % ‘Resolution’**
**Timescale for calibration : Weeks **

**ECAL Monitoring**** ****(Monitor Stability and Measure Radiation Effects)**** :**

## CMS: Radiation Effects PWO Transparency 

** ****Radiation reduces transparency in the ****blue,**
**  **** ****where PWO emission spectrum peaks**
** ****Effect is ****dose rate dependent****.**
** ****Monitoring ****relative change**** of PWO **
**  ****transparency with pulsed laser light. **
**For CMS barrel (15 rad/hour) :**
**Transparency change at a level of  ~5%.**

**Approx. PWO emission spectrum**

## ECAL Laser Monitoring System

## ECAL Laser Monitoring System

**Transparency of each crystal is measured with a precision of <0.1% every 20 minutes**

**Very stable PN-diodes used as reference system**
**Each Level-1 Fan-out is seen by 2 PN diodes**
**Each PN diode sees 2 Level-1 Fan-out, 10 PN diodes per SM **
**SM are illuminated one half at a time, constraint by data volume**
**Precision pulsing system for electronics calibration**

**APD**

**VPT**

## Testbeam Measurements at CERN SPS

**ECAL Test Area**** **

**Air Conditioning**

**Insulated Hall**

** ****Electrons, pions, muons **
** ****Precisely known energies**
** ****Supermodules on moveable table**
** ****Study of energy resolution, ****      irradiation effects etc.**

**Moveable Table with ECAL Module**

## CMS ECAL Resolution in Test Beam 2004

**CMS ECAL Resolution in Test Beam 2004**

****** ****Design performance achieved in the test beam !**

**(Design resolution as well as noise, stability, ...)**

## Calibration Strategies

- Lab measurements

- 70          80          90           100  GeV

- Reference pre-calibration of few SM with 50/120 GeV electrons in test beam (<2%)

**Finally: calibration to < 0.5% with ****W ******** ********e in few months**

## Cosmic Muon Calibration

**E2 is the second highest energy deposit in the 3x3 matrix (evaluated at the same sample as E1 )**

**Simulation**

**Cosmic Muon Calibration**

- For APD gain (50) cosmic muons are hidden in the noise.
- Run at higher gain (200).

**Relative calibration ~ 2% achievable.**

## CMS ECAL in-situ Calibration Strategies

**Very high precision :**** **
-     0.5 % constant term
-      (Note : this accounts for inter-calibration, stability and  transparency loss correction)
**Hadron Collider at high luminosity :**
-     No “standard candle” or golden events (e.g. Bhabhas), CM energy not fixed,      Pile-up, very high cross-sections, and trigger issues for calibration events
**Perform calibration in a timely manner :**
-     Key physics processes are only (or at least much much easier) accessible at low
-      luminosity (pile up).
-      The performance of the ECAL will degrade over 10 years of LHC running (noise).

## CMS In-situ :  φ-uniformity method

***Idea***:      φ-uniformity of deposited energy              ***Used***:  Min-bias / Level-1 jet trigger events
***               ***in crystals at constant η***              ***
***                                                                             ******Method***: Compare <ET>CRYSTAL with <ET>RING .
***Limitations ***: non-uniformities in φ
-  in-homogeneity of tracker material
-  geometrical asymmetries

**Precision limits **
**assuming no knowledge **
**of tracker material**
**(****~10h , 1kHz L-1 single jet triggers**** )**

***BARREL***

***ENDCAPS***

- 11 million
- Level-1 jet trigger events

***Inter-calibration of ******η ******rings:***
- Ze+e-, Zμ+μ-γ , isolated electrons

## CMS In-situ:  using Ze+e-

- Method:
- Z mass constraint

- Barrel

- Use cases:
-  Inter-calibrate crystals in ECAL regions
-  Inter-calibrate ECAL regions (i.e.rings in φ-symmetry method)
-  Set the absolute energy scale
-  Tune algorithmic corrections for electron reconstruction

- Algorithm:
- Iterative (~10-15), constants are obtained from the peak of   **ε****i**   distribution.

- Events Selection: Low brem electrons.

- Results:
- Assuming 5% mis-calibration between the rings and 2% mis-calibration between the crystals within a ring

**0.6%** ring inter-calibration precision

-                                  *Statistics: ****2.0 fb******-1***

-  2.0 fb-1

- 2.0 fb-1
- Barrel

- σ = 0.6%

## CMS In-situ:  using isolated electrons

**Target**:   **0.5%**   calibration precession

**Sources**:  Weν  (10Hz     HLT @ 2x1033cm-2s-1  ),
- 	Ze+e- (  2Hz     HLT @ 2x1033cm-2s-1 ),                J/Ψe+e-, b/ce, ...

**Method**:        E / P     <width minimization>

**Calibration Constants extraction Techniques**:
-  L3/LEP iterative (~20 iterations),
-  matrix inversion

**Event Selection**:
- We need a narrow E/P  Low brem e
- Variables related to electron bremsstrahlung :
- ECAL         (S3x3/S5x5)
- TRACKER (track valid hits, χ2/n.d.f.,  Pout/Pin)
- Efficiency after HLT: 20-40% Barrel ,
-                                     10-30% Endcaps

- _ECAL_
- E = Σ ciΕi

- 5x5

- _TRACKER_
- electron
- momentum

**Calibration Steps **
-  Calibrate crystals in small η-φ regions
-  Calibrate regions between themselves using tighter electron selection, Ze+e- , Zμ+μ-γ

-          Background: S/B~8
- (isol. electrons from W/QCD)
- Part of it might be useful (b/ce).

## In-situ:  using isolated electrons

- Hγγ

- Tracker Material Budget

- Barrel
- 5 fb-1

- Endcaps
- 7 fb-1

- Precision versus Statistics

- η

- η

- Barrel

- Barrel

- Higgs Boson Mass Resolution

- Calibration Precision versus η

## In-situ:  0 , η

- Method:
- Mass constraint for crystal inter-calibration.
- Unconverted photons are  in-sensitive of the tracker material

- “Common” π0s; can be found in L1 e/m triggers (source: jets or pileup events)

**Selection** :  shower shape cuts per γ,  small γ opening angles (60-90mm)

- Much lower rate after background suppression
- Better mass resolution ~ 3%

**π****0******** ****γγ**:

- Efficiency     ~ **1.4%**
- Level-1 rate : **25kHz**

- ~**2days ****** **1K** ev./crystal             ~ **0.5%**  stat. inter-calibr.

- }

**η**** ******** ****γγ**:

*** ... ******they seem promising ... still under study ... ***

- precision

## ECAL Calibration: Reality Check

**In Monte Carlo, calibration is always easier. Events are clean, weird effects absent.**
**The detector won’t be exactly phi symmetric.**
**It won’t be built exactly as drawn.**
**The trigger will be biased.**
**Full understanding of signal process, from ionization/light production thru the electronics to final storage will likely be necessary.**
- Examples from Dzero.

## Electromagnetic showers

## DØ is a “U/LAr sampling calorimeter”

- EM1

- EM2

- EM4

- EM3

**One “*****di-gap*****” :**

*signal board*

**More detailled view of one CC-EM module :**

- incident particle

- Basically a stack of Uranium plates with liquid Argon in between.
- Shower develops in U and LAr (mainly U); charged shower particles
- ionise the Argon atoms => current in Argon because of HV applied
- across each gap. This current is measurable
- (thanks to electronic charge amplifiers with very large gain).
- EM1, EM2, EM3 and EM4 are read out separately; each one of these
- layers regroups a number of digaps.

- sampling fraction: 15 %

## DØ Basics of the readout

**Preamp/**
**Driver**

**Trig. sum**

**Filter/**
**Shaper**

**x1**

**x8**

**SCA (48 deep)**

**BLS**

**Output**
**Buffer**

**Bank 0**

**Bank 1**

**L2**
**SCA**

**Calorimeter**

- • Detector signal ~ 450 ns long
-       (bunch crossing time: 396 ns)
- • Charge preamplifiers
- • BLS (baseline subtraction) boards
-      • short shaping of ~2/3 of integrated signal
-      • signal sampled and stored every 132 ns in
-        analog buffers (SCA) waiting for L1 trigger
-      • samples retrieved on L1 accept,
-         then baseline subtraction to remove pile-up
-         and low frequency noise
-      • signal retrieved after L2 accept
- • Digitisation

- two gains for
- better dynamic range

## Keep in mind: the CAL is not alone !

- Interaction
- point

- First active layer of
- liquid argon

- about
- 3.7 X0 in
- between !

- 0.9 X0

- 0.3 X0 plus 1 X0 of lead

- cryo walls: 1.1 X0

- inner detector: 0.1 X0

- The preshowers will finally get a
- new readout later this year.

## DØ Samples and weights

- The plot on the right shows the average longitudinal profile
- of a shower with E = 45 GeV. Assuming normal incidence,
- the position of the active parts of the CC are also indicated.
- In the reconstruction, we apply artificially high weights to
- the early layers (especially EM1) in an attempt to partially
- compensate the losses in the dead material:
-     Layer        depth (X0)      weight (a.u.)       weight/X0
-   ------------------------------------------------------------------------
-      EM1	 2.0               31.199              15.6
-      EM2              2.0                 9.399                4.7
-      EM3              6.8               25.716                3.8
-      EM4              9.1               28.033                3.1
-      FH1             40               24.885             0.6
- The lower plot illustrates the situation for the same average
- shower, but this time under a more extreme angle of incidence
- (physics eta = 1). The shower maximum is now in EM1 !

- depth in radiation lengths (X0)

- dE/dX0 (arbitrary units)

- EM1

- EM2

- EM3

- EM4

- FH1

- DEAD

- depth in radiation lengths (X0)

- dE/dX0 (arbitrary units)

- EM1

- EM2

- EM3

- EM4

- DEAD

- eta = 0
- (normal
- incidence)

- eta = 1

## DØ Energy-dependence & fluctuations

- depth in radiation lengths (X0)

- dE/dX0 (arbitrary units)

- EM1

- EM2

- EM3

- EM4

- FH1

- DEAD

- E = 45 GeV
- eta = 0
- (normal
- incidence)

- depth in radiation lengths (X0)

- dE/dX0 (arbitrary units)

- EM1

- EM2

- EM3

- EM4

- FH1

- DEAD

- E = 5 GeV
- eta = 0
- (normal
- incidence)

- The plots on the previous slide show the *average*
- shower profile at E = 45 GeV.
- The plot on the right is basically the same,
- except that it includes typical *shower fluctuations*.
- => The fraction of energy lost in the dead material
-       varies from shower to shower.

- The bottom plot illustrates the situation at a different,
- lower, energy. The position of the shower maximum
- (in terms of X0) varies approximately like ln(E).
- => The average fraction of energy lost in dead material,
-       as well as the relative importance of
-       shower-by-shower fluctuations depend on the
-       energy of the incident electron.

## DØ average response ...

- eta = 0.2

- eta = 1.1

- So we need to apply an energy-loss correction to our reconstructed electron energies to account
- for the energy lost in front of the calorimeter. This correction, as a function of energy and angle (eta)
- is estimated using detailed detector simulations based on Geant.

- This is the energy as reconstructed in the CAL.

- This is the energy
- correction factor
- that gets us back
- to the energy of the
- incident electron.

## DØ fluctuations around the average

**D****Ø**** fluctuations around the average**

- Jan Stark                                             UMD, May 10th, 2006

- 1/sqrt(sin )

- E = 45 GeV

- E/E = 16.4% / sqrt(E)

- E/E = 16.4% / sqrt(E)  +  12.2% / E

- 1/sqrt(E) scaling
- is violated !

- Here we show the impact on the energy resolution for electrons. This is again from a detailled
- detector simulation based on Geant.

- Resolution at normal incidence, as a function
- of electron energy:

- Resolution at E = 45 GeV, as a function of
- the angle of incidence (eta):

- sigma(E)/E   [%]

- for an ideal sampling calorimeter
- (no dead material) one would expect
- this to scale as 1/sqrt(E)

- for an ideal sampling calorimeter
- (no dead material) one would expect
- this to be almost flat

## DØ EM calibration: basic idea

**Factorise (roughly) into two parts:**
-     - calibration of the calorimeter electronics,
-     - calibration of the device itself.
- Electronics calibrated using pulsers.
- Calibration of the device itself:
-     Determine energy scale (i.e. multiplicative correction factor), ideally per cell.
-     Use phi intercalibration to “beat down the number of degrees of freedom”
-     as much as possible.
-     Use Z  e+ e- to get access to the remaining degrees of freedom, as well as
-     the absolute scale.

## Calibration of electronics: pulsers !

**Aim:** 	Pulsers are a powerful tool, both for debugging and calibration of the
-             readout electronics.
- 	Identify technical problems in the electronics, like e.g. dead channels.
- 	Correct for channel-by-channel differences in electronics response.
**Principle:**
- inject known signal into
- preamplifier and see what
- the electronics measures.
- Do this separately for
- gains x8 and x1, optionally
- also separately for the
- two L1 SCAs per channel.
- Among other things, gives handle on the non-linearities in the electronics response,
- which are mainly caused by the analog buffers (SCA).
- Tricky part: the calibration signal is not injected at the cell level, but right before the preamps ....

- DAC (pulser signal)

- ADC (readout)

## Phi intercalibration

- The idea is not new, see e.g. Run I: work by R. Raja, or PhD thesis by Q. Zhu (April 1994), available
- on the DØ web server, and refs therein. The Run II calibration has much finer granularity, though.

- pp beams in the Tevatron are not polarised.
-  Energy flow in the direction transverse to the beams should not have any azimuthal dependence.
-      Any  dependence must be the result of instrumental effects.
**Energy flow method:**
- Consider a given  bin of the calorimeter. Measure the density of calorimeter objects above a
- given ET threshold as a function of . With a perfect detector, this density would be flat in .
- Assuming that any -non-uniformities are due to energy scale variations, the uniformity
- of the detector can be improved by applying multiplicative calibration factors to the energies
- of calorimeter objects in each  region in such a way that the candidate density becomes flat in 
- (“ intercalibration”).
**Trigger:**
- We collect our events using a trigger that was specially designed for this purpose.
- L1:  At least one EM trigger tower, low threshold.
- L3:  Significant EM energy in at least one of the readout towers of the trigger tower that fired L1.
-        The threshold on the readout tower is significantly higher than the threshold on L1 trigger tower.
- So far, have taken these data in dedicated special runs. Plan to collect them continuously at low
- rate during normal running.

## Phi intercalibration: results

- An example of results from phi intercalibration:
- determine one energy correction factor per CAL tower (EM part) at ieta = -5 .

- iphi

- energy correction factor

- module 17 dropped during
- construction in mid 1980’s.
- Optimistic view : “response stable over decades”

- We are exploring
- a ~13 % range here
- ... but typically the
- spread has an RMS
- of the order of 3 %.

## Phi intercalibration: results

- Change in electronics integration time made energy scale
- More sensitive to construction non-uniformities. LAR drift time 400 ns Run 1 shaping time 3 s, Run II shaping time 400 ns. Gap non-uniformities matter now

- One “*di-gap*”:

- Signal from a di-gap
- of ideal geometry:

- Response when we
- move the signal board away
- from the centre of the di-gap:

*signal board*

**In the deformed case:**
-    Infitite integration time (Run I) : We still see all the charge. Nice.
-    Short integration time (Run II) :
-         We see less charge than with perfect geometry. The fraction of the  charge
-         read out depends on the size of the displacement of the signal board.
-         Not good..

- finite integration time

## Phi intercalibration: results

- The ruler in the photograph is 12 inches long.

- This is a photograph of an FH1 signal board. The EM signal boards are almost the same:
- same material, similar length, similar thickness, but roughly half the width.
- Look how “wobbly” it is ! These boards are held in place between the uranium plates by a few platic spacers.
- “Wobbling” with a typical amplitude of 15 % or more of the gap width is not untypical.

## Eta equalisation and absolute scale

- Write reconstructed Z mass as:
- E1 and E2 are the electron energies and  is the opening angle from tracking.
- The electron energies are evaluated as:

- With the raw cluster energy:

- Then determine the set of calibration constants *c*ieta that minimise the experimental resolution on the
- Z mass and that give the correct (LEP) measured value for the Z mass.

- raw energy measurement from the calorimeter

- parameterised energy-loss correction from
- detailed detector simulation

- one (unknown) calibration constant
- per ring in eta

- cell energy after electronics calibration,
- phi intercalibration and layer weights

## Z -> e+e- vs. W -> e

- Black:
-    W->e
- Red:
-    Z-> ee

- At a given physics eta, the spread in energy of electrons from the Z is small. Also, the overlap with the energy spectrum of electrons from the W is small.
- How can we test the quality of our MC predictions for the scaling of the average response and resolution from the Z
- down to the W ? Without any further study and just trying some “reasonable” variations of the Monte Carlo,
- the systematic uncertainty on the W mass would be at least 90 MeV.

- If you need to be concerned at the detail level, using MC to extrapolate from known processes to the one you want to measure (in this case W->e) may not be as straightforward as you expect.

- electron eta

- electron energy (GeV)

- electron energy (GeV)

## Detector and Physics CalibrationsDay 2

**Nick Hadley**
**The University of Maryland**
**Hadron Collider Physics Summer School**
**Fermilab August 11-12, 2006**

## (CMS) HCAL Calibration

**Use charge injection to calibrate ADCs**
**Use sources to calibrate each tile in every *****layer***** of the calorimeter**
**Use testbeam for electrons, pions and muons results to tie all the numbers together**
**Signal seen depends on magnetic field.**
**Must understand shower shape, radiation damage.**
**Have lasers and LEDs for fast monitoring.**

## CMS Longitudinal  Shower Profile for  in HB

***CMS Longitudinal  Shower Profile for ************ in HB***

****** ****300 GeV**

******30 GeV**

_**Initial Calibration Given for the Expected Mean Energy:**_
** ****50   GeV ********’s for ********< 30****o**
** ****100 GeV ********’s for ******** > 30****o**
****** ****This is why muons are not useful for HB/HE Energy Scale... they see all planes**

## WS/-

**3%**

**WS****/********-**

**WS****/********-**

**WS****/********-**

**c)  each tower**

**b)**

****** ****tower number**

**a)**

**a)  Calibration of source with**
**     ****100GeV electron beam.**
**         ******** ****6.98 MeV equivalent**
**              ****date == 2005-01-31**
**b,c)  Comparison with muon beam**

***CMS  “Energy” Calibration for the source is found from the testbeam by ***
***comparing source response to 100 GeV e-***

**GeV**

## HCAL Calibration 

**Important to understand your HCAL in detail.****e/********response, fluctuations, electronics, aging, etc...**
**The important topic of jet energy calibration will be covered by Beate Heinemann in her talk Monday.**

## Alignment Strategy

**Applies to tracking detectors including muon chambers.**
- Then use tracks to align calorimeters as trackers measure position better (usually) than calorimeters
**Typically 3 step process**
- Measure element (e.g. wire, pixel) position during construction of subdetector using coordinate measuring machines and similar devices.
- Measure relative position of subdetectors after assembly using surveying techniques such as lasers.
- Only works for detectors you can see.
- Track based alignment

## Tracker Alignment Concept in a Nutshell

*Challenge: Alignment uncertainties must not degrade intrinsic *
*tracker resolution: *≈20m*     *

**LAS:** Aligns global support structures
- and will monitor relative movements
- at the level of ≈10m

**Mechanical Constraints:**
- Sensors on Modules: ≈10m
- Composted Structures: 0.1-0.5 mm

*First Data Taking:*
* **Laser Alignment *
* ***
*Mechanical Constraints*
*** *≈100m alignment uncertainties

**Sufficient for a first**
**efficient pattern recognition**.

**Final Alignment**: Use Tracks in order to achieve the desired level
- of alignment uncertainties of ≈10m. A combination of track based alignment
- and  laser alignment will insure an accurate monitoring of time dependent
- alignment effects.

## Alignment Concept & Typical Numbers

**Tracker**

**Muon**

- Assembly:

- Hardware
- Alignment:

**+**

- Track Based
- Alignment

**+**

- Strip

- Pixel

- O(mm)

- ~<100m

- ~100m
- (perhaps below)

- 0.1-0.5mm

- <100m

- ~10m

- 50-100 m

- 50-100 m
- (no HA foreseen)

- ~5 m

- Remarks:

- Hardware Alignment
- will provide the operational
- alignment level.
- Track based alignment will
- be a cross check and
- eventually a completion

- Hardware Alignment
- will insure pattern recognition.
- Track Based Alignment must
- provide the final alignment

- Only Track
- based Alignment.
- Nothing else!

## Alignment Concept & Typical Numbers

**Tracker**

**Muon**

- Assembly:

- Hardware
- Alignment:

**+**

- Track Based
- Alignment

**+**

- Strip

- Pixel

- O(mm)

- ~<100m

- ~100m
- (perhaps below)

- 0.1-0.5mm

- <100m

- ~10m

- 50-100 m

- 50-100 m
- (no HA foreseen)

- ~5 m

- Remarks:

- Hardware Alignment
- will provide the operational
- alignment level.
- Track based alignment will
- be a cross check and
- eventually a completion

- Hardware Alignment
- will insure pattern recognition.
- Track Based Alignment must
- provide the final alignment

- Only Track
- based Alignment.
- Nothing else!

***Importance of Track Based Alignment***

***Importance of Hardware Alignment***

## Mis-Alignment: Impact on Physics  (important for Z’, LED)

****** ****Use Z******** to illustrate the impact of mis-alignment on physics**

- Mz

- Mz

- Mz

*First Data Taking*
*<1fb**-1*
* **Laser Alignment *
* ***
*Mechanical Constraints*
- ≈100m alignment
- uncertainties

- Perfect
- Alignment

*Long(er) Term:*
***>1fb**-1*
* **First results of Alignment*
*with tracks*
- ≈20m alignment
- uncertainties

**Alignment**
**with tracks**

- 2.4 GeV

- 3.5 GeV

- 2.9 GeV

- B field and
- material budget
- uncertainties

## CMS Laser System goals and concepts

- External alignment (for joint Tracker+Muon system track fit)
- <= 150 μm measurement of Muon System position w.r.t. Tracker
- <= 30 μrad measurement of Muon System orientation w.r.t. Tracker
- Internal alignment:
- <= 100 μm measurement of sub-detector relative positions for track pattern recognition (between TIB and TEC, between TOB and TEC)
- <= 50 μm for 50% of TEC petals → 70 μm for 50% of TEC modules
- <= 10 μm monitoring of relative sub-detector position stability for track parameter reconstruction
- Main concepts Use Tracker silicon sensors and Tracker DAQ
- No external reference structures
- No precise positioning of LAS beams (redundancy to constrain)
- Minimum impact on Tracker layout and production

## Slide 59

## “Hardware Alignment System”

_***Four important ingredients:***_
-  Internal Muon Alignment Barrel
-  Internal Muon Alignment Endcap
-  Internal Tracker Alignment
-  Alignment of Muon w.r.t Tracker
-   (Link System)

_***Specifications:***_
-  Monitor tracker support structures at ~10m
-  Monitor Muon support structures at ~100m
-  Monitor Muon w.r.t Tracker at ~100m

- Hardware Alignment System monitors only
- global structures of the CMS tracking devices.
- The final alignment of the individual
- measurement units (e.g. silicon sensors) will
- be carried out with tracks!

- Note: Only Strip Tracker and Muon System are included in the Hardware Alignment System.
- The PIXEL detector will be aligned and monitored with tracks only.

## Track Based Alignment

**Basic Alignment problem**
- For each detector determine 6 parametersx0, y0, z0 global position of center and φ, θ, ψ global rotation angles
**In simplest form, a chisquared minimization problem. **
- Can linearize if nearly aligned. Linear least squares problem. All you have to do is invert a matrix.
- Want corrections ***p*** to alignment parameters, ***p***
- Track parameters***, q***
- i = fitted value – measured value

## Aside: Linear least squares 

## Track based Alignment

**Minimize chisquared by taking derivatives.**
- Leads to a matrix equation
**Problem is have of order 15K silicon sensors.**
**Inverting the matrix compute time proportional to N****3****, storage proportional to N****2**
- It’s a sparse matrix, which helps some.
- Lots of nice Computer Science/Applied Math work on such problems.
**Must fix position/orientation of one detector**
**Additional problem, tracks not straight, and the track parameters are unknown (standard candle problem again).**
- Once one detector aligned, easier to align others.

## DØ Tracker Alignment

**D****Ø Tracker Alignment**

## DØ Tracker Alignment

**D****Ø Tracker Alignment**

## DØ Tracker Alignment Procedure

## DØ Tracker Alignment Results

**D****Ø Tracker Alignment Results**

## CMS Complexity of the Problem

**CMS Complexity of the Problem**

- ATLAS study: Matrix inversion

**“****State of the Art Alignment”** requires
- the inversion of large matrices!
- Real challenge for computing

***Rounding precision:***
***Double vs. quadruple:***
- Nmax~15000 for double
- Nmax~50000 for quadruple

**Inversion fails**

**~20000 sensors**
******6x20000********100k **
**alignment parameters**

**Bottom Line: **
- The available computing resources in 2007
- are probably not sufficient for
- a full blown “state of the art” alignment
- of the CMS tracker
*********Need to pursuit new approaches!******  ***

## CMS Data Samples for Alignment

_***The Golden Alignment Channels:***_
- Z  O(20K x 2) per day
- W O(100K) per day

-   Isolated well measured track statistic of one
-  day nominal running should enable us to align
-  all higher lever tracker structures (rod level)

**A dedicated trigger stream for these event types would be very beneficial in order to**
**insure **_***immediate***_** access to the data and, thus, a speedy alignment of the tracker!**

***Bottom Line:***
- Isolated high momentum (pT ~50-100 GeV) muon tracks seem to be the
- first choice for the alignment
********* ******Need special stream for these events!***

**Exploit mass constraint:**
*Properly including the mass constraint for **Z**** (or even** **J/****) will significantly enlarge our capability two align also detectors wrt each other which are not crossed by single collision tracks *

## CMS implementation of Millepede II Algorithm(Millepede see www.desy.de/~blobel)

- Original Millepede method solves matrix eqn. A  x = B, by inverting huge matrix A.This can only be done for < 12000 alignment parameters.
- New Millepede method instead minimises |A x – B|. Is expected to work for our 100000 alignment parameters.
- Both successfully aligned ~12% of Tracker Modules using 2 million Z + - events.Results identical, but new method 1500 times faster !

**Factor 1500 faster!!!!!**

## CMS Kalman Filter

## Kalman Filter alignment

- Alignment of the TIB

- 600 m

- 2 m

- After 100K single muon tracks

## CMS Hits and Impact Points (HIP) Algorithm

**Collect a sample of tracks**
**Align individual sensors independently**
**Reconstruct tracks and iterate**
**Low computational cost, 6 x 6 matrix per sensor**
**Algorithm studied with **_**real data**_**: CRack test beam and cosmic data****(8 genuine alignable strip detectors)**
**Proof of principle for alignment software implementation in CMS software**
**Larger cosmic data sample expected**

- Average
- track 2

- Particularsensor

**manual result**

**CMS Hits and Impact Points (HIP) Algorithm**

## CMS HIP Algorithm 

## CMS PTDR-Section 6.6 – Alignment(https://cmsdoc.cern.ch/cms/cpt/tdr/)

**Initial surveys and starting alignment**** **
- Module mounting precision known from the surveys to about 100 m
- Laser Beams will be able to monitor the *global tracker elements* wrt other subsystems (e.g. Muons) to about 100 m
**Data taking alignment will be done using tracks**
- Two scenarios foreseen
- 1 fb-1
- Pixels will have ~10 micron residuals
- Silicon strip detector ~ 100 micron
- 10 fb-1
- All systems aligned to ~10 micron

**Three methods currently exploited**
- HIP
- 2 based large 6Nx6N matrix inversion, block diagonalized
- Especially suited for pixel alignment
- Millipede
- Based on the inversion of large matrices, including track parameters
- CDF and H1 already used
- New fast version implemented successfully for CMS
- Kalman filter
- Iterative method track-by-track
- Update alignment parameters after each track

## In flux, Google search to get many talks and papers
Good list of alignment references	http://www4.rcf.bnl.gov/~fisyak/star/References.html
HIP Algorithm (CMS-CR-2003/022)
V. Karimaki, T. Lampen (Helsinki), F.-P.S. (CERN)
Robust and straightforward, but no correlations between sensors
Kalman Filter
R. Fruehwirth, W. Adam, E. Widl  (Vienna); also M. Weber(Aachen)
Novel approach, full treatment of correlations, w/o large matrix inv.
V. Blobel’s Millepede (new version of Millepede II will avoid matrix inversion)
M. Stoye/PhD, G. Steinbrueck (Hamburg)
Simulated annealing
A. le Carpentier/PhD, E. Chabanat (Lyon)

**Good list of alignment references****	****http://www4.rcf.bnl.gov/~fisyak/star/References.html**
_**HIP Algorithm**_** ****(CMS-CR-2003/022)**
- V. Karimaki, T. Lampen (Helsinki), F.-P.S. (CERN)
- Robust and straightforward, but no correlations between sensors
_**Kalman Filter**_
- R. Fruehwirth, W. Adam, E. Widl  (Vienna); also M. Weber(Aachen)
- Novel approach, full treatment of correlations, w/o large matrix inv.
_**V. Blobel’s Millepede **__**(new version of Millepede II will avoid matrix inversion)**_
- M. Stoye/PhD, G. Steinbrueck (Hamburg)
_**Simulated annealing**_
- A. le Carpentier/PhD, E. Chabanat (Lyon)

**CMS Track Based Alignment References **

## General References

**ATLAS Physics TDR**
- http://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/TDR/access.html
**CMS Physics TDR**
- http://cmsdoc.cern.ch/cms/cpt/tdr/