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---+ Analysis Results for the systematic shift in &phi;

When matching L1MuonParticle information to HO Rec Hits there appears an asymmetry in the matching.

The matching is performed as follows:
   * Take an L1 Object within |&eta;|&lt;1.25 (HO acceptance)
   * Loop over all HORecHits
      * Find a hit that lies within a Grid of +/- one HO tile and shows more than 0.2 GeV (to suppress noise)
      * If another Hit within the range shows more energy than a previously found hit, take the larger energy hit
When plotting &Delta;&eta; vs. &Delta;&phi; between the L1 information and the HORecHit one can observe that the distribution of values tends towards positive &Delta;&phi;. The &Delta;&phi; is calculated by subtracting the L1-&phi; from the HO-&phi;.

The L1Muon coordinates are binned:
   * &phi; bins &asymp; 0.0425, center at 0
   * &eta; bins = 0.1, center at 0.05 and -0.05

There is a shift in counting i&phi; in HO, meaning that Sector 1 consists of i&phi; 71,72,1,2,3,4. But as the analysis is done using the CMS &eta; and &phi; this should not play a role except the calculation detId to phi is wrong.

Possible Sources of the shift:
   * Binning
      * Did several checks with different binnings but the effect did not disappear
   * Charge effect
      * But then it is not clear, why the shift is in the same direction for different charges
   * Alignment
   * &delta;-electrons
      * Did simulations with B-Field set to 0T and the shift was still there. However, the setup for 0T should be checked

The sanity checks with HO and L1 showed that when shooting a 1TeV muon at (&eta;,&phi;) = (0.0435,0.0435) *without magentic field* the L1MuonParticles show mainly a &phi; of 0.
---++ ##. SanityChecks
---+++ Simulation with (&eta;,&phi;) = (0.0435,0.0435)

<img alt="hoCoordinates_043_043.gif" height="472" src="%ATTACHURL%/hoCoordinates_043_043.gif" title="hoCoordinates_043_043.gif" width="696" />

*Fig ##..:* Histogram of the &phi; values occuring at HO.<b><br /></b>

<img alt="l1Coordinates_043_043.gif" height="472" src="%ATTACHURL%/l1Coordinates_043_043.gif" title="l1Coordinates_043_043.gif" width="696" />

*Fig ##..:* Histogram of the &phi; values occuring at L1MuonParticles.
---+++ Simulation with (&eta;,&phi;) = (0.0435,0.087)

<img alt="hoCoordinates_043_087.gif" height="472" src="%ATTACHURL%/hoCoordinates_043_087.gif" title="hoCoordinates_043_087.gif" width="696" />

*Fig ##..:* Histogram of the &phi; values occuring at HO.

<img alt="l1Coordinates_043_087.gif" height="472" src="%ATTACHURL%/l1Coordinates_043_087.gif" title="l1Coordinates_043_087.gif" width="696" />

*Fig ##..:* Histogram of the &phi; values occuring at L1MuonParticles.
---++ ##. Simulation No PU MuMinus
   * N Events: *2167328*
<img align="middle" alt="averageEnergy_NoPUAnalyzed.gif" height="550" src="%ATTACHURL%/averageEnergy_NoPUAnalyzed.gif" title="averageEnergy_NoPUAnalyzed.gif" width="600" />

*Fig ##..:* Average Energy seen in HO around a given L1 Direction. The binning width is HO-Width/2. &asymp; 0.0435, which corresponds in phi to the L1-Muon binning. The bins are centered around zero.
---

<img align="middle" alt="averageEmax_NoPUAnalyzed.gif" height="549" src="%ATTACHURL%/averageEmax_NoPUAnalyzed.gif" title="averageEmax_NoPUAnalyzed.gif" width="600" />

*Fig ##..:* Average E_Max seen in HO tiles around a given L1-Muon direction. The L1-&eta;&phi;-information is taken and in a range of a 5x5 grid, the HORecHit with the largest energy deposit is chosen. The numbers in the bins is the total number of counts in that bin.
---

<img align="middle" alt="eAverageTightMuons_NoPUAnalyzed.gif" height="588" src="%ATTACHURL%/eAverageTightMuons_NoPUAnalyzed.gif" title="eAverageTightMuons_NoPUAnalyzed.gif" width="600" />

<b>Fig ##..: </b>Same plot as Fig. 1.1 but here, only L1Objects were taken into account that were successfully matched to a tight pat::muon. The matching was done by &Delta;R with a maximum cone size of 0.3. The image has a different axis range but the color scale is the same.
---

<img align="middle" alt="eAveragePerWheel_NoPUAnalyzed.gif" height="424" src="%ATTACHURL%/eAveragePerWheel_NoPUAnalyzed.gif" title="eAveragePerWheel_NoPUAnalyzed.gif" width="1136" />

<b>Fig ##..: </b>Same plot as in Fig 1.1 but plotted per Wheel.

<img align="middle" alt="eAveragePerWheelTightMuons_NoPUAnalyzed.gif" height="500" src="%ATTACHURL%/eAveragePerWheelTightMuons_NoPUAnalyzed.gif" title="eAveragePerWheelTightMuons_NoPUAnalyzed.gif" width="1163" />

*Fig ##..:* Same plot as in Fig. 1.3 but plotted per Wheel.
---++ ##. Simulation No PU MuPlus
   * N Events: *200000*
The plots show the same distributions as for the above plots but with a different dataset.
<img alt="averageEnergy_NoPUMuPlus.gif" height="549" src="%ATTACHURL%/averageEnergy_NoPUMuPlus.gif" title="averageEnergy_NoPUMuPlus.gif" width="600" />

*Fig ##..:*

<img alt="averageEmax_NoPUMuPlus.gif" height="549" src="%ATTACHURL%/averageEmax_NoPUMuPlus.gif" title="averageEmax_NoPUMuPlus.gif" width="600" />

*Fig ##..:*

<img alt="eAverageTightMuons_NoPUMuPlus.gif" height="549" src="%ATTACHURL%/eAverageTightMuons_NoPUMuPlus.gif" title="eAverageTightMuons_NoPUMuPlus.gif" width="600" />

*Fig ##..:*

<img alt="eAveragePerWheel_NoPUMuPlus.gif" height="500" src="%ATTACHURL%/eAveragePerWheel_NoPUMuPlus.gif" title="eAveragePerWheel_NoPUMuPlus.gif" width="1163" />

*Fig ##..:*

<img alt="eAveragePerWheelTightMuons_NoPUMuPlus.gif" height="500" src="%ATTACHURL%/eAveragePerWheelTightMuons_NoPUMuPlus.gif" title="eAveragePerWheelTightMuons_NoPUMuPlus.gif" width="1163" />

*Fig ##..:*
---++ ##. Simulation PU 52

---++ ##. 2015D Single Muon Dataset
   * N Events: *2167328*
The plots show the same distributions as for the above plots but with a different dataset.

<img alt="averageEnergy_SingleMuon2015D.gif" height="588" src="%ATTACHURL%/averageEnergy_SingleMuon2015D.gif" title="averageEnergy_SingleMuon2015D.gif" width="600" />

*Fig ##..:*

<img alt="averageEmax_SingleMuon2015D.gif" height="588" src="%ATTACHURL%/averageEmax_SingleMuon2015D.gif" title="averageEmax_SingleMuon2015D.gif" width="600" />

*Fig ##..:*

<img alt="eAverageTightMuons_SingleMuon2015D.gif" height="549" src="%ATTACHURL%/eAverageTightMuons_SingleMuon2015D.gif" title="eAverageTightMuons_SingleMuon2015D.gif" width="600" />

*Fig ##..:*

<img alt="eAveragePerWheel_SingleMuon2015D.gif" height="500" src="%ATTACHURL%/eAveragePerWheel_SingleMuon2015D.gif" title="eAveragePerWheel_SingleMuon2015D.gif" width="1163" />

*Fig ##..:*

<img alt="eAveragePerWheelTightMuons_SingleMuon2015D.gif" height="500" src="%ATTACHURL%/eAveragePerWheelTightMuons_SingleMuon2015D.gif" title="eAveragePerWheelTightMuons_SingleMuon2015D.gif" width="1163" />

*Fig ##..:*
---++ ##. Studies of the &Delta;&phi; = 1 effect
---+++ &eta;&phi; for matches with &Delta;&phi; = 1

<img alt="etaPhiForDeltaPhiOne_SingleMuon2015D.gif" height="919" src="%ATTACHURL%/etaPhiForDeltaPhiOne_SingleMuon2015D.gif" title="etaPhiForDeltaPhiOne_SingleMuon2015D.gif" width="1005" />

*Fig ##..:* &eta;&phi; in L1MuonParticle Coordinates for the matches where &Delta;&phi; is one. There seems to be a structure at negative &phi;.
---+++ &Delta;&phi; vs. pT

<img alt="deltaPhiVsPt_SingleMuon2015D.gif" height="588" src="%ATTACHURL%/deltaPhiVsPt_SingleMuon2015D.gif" title="deltaPhiVsPt_SingleMuon2015D.gif" width="600" />

*Fig ##..:* &Delta;&phi; vs. pT of the matched L1MuonParticle. As the contribution for &Delta;&phi; = 1 gets stronger for lower pT this argues for the fact that it may be a charge-introduced effect.

<img alt="deltaPhiVsPtL1Tight_SingleMuon2015D.gif" height="588" src="%ATTACHURL%/deltaPhiVsPtL1Tight_SingleMuon2015D.gif" title="deltaPhiVsPtL1Tight_SingleMuon2015D.gif" width="600" />

*Fig ##..:* &Delta;&phi; vs. pT of the matched L1MuonParticle for matching with tight L1Muon objects only. As the contribution for &Delta;&phi; = 1 gets stronger for lower pT this argues for the fact that it may be a charge-introduced effect.

-- Main.AndreasKunsken - 2016-02-02

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Topic attachments
I	Attachment	History	Action	Size	Date	Who
gif	averageEmax_NoPUAnalyzed.gif	r1	manage	76.7 K	2016-02-04 - 13:55	AndreasKunsken
gif	averageEmax_NoPUMuPlus.gif	r1	manage	63.4 K	2016-02-04 - 13:53	AndreasKunsken
gif	averageEmax_SingleMuon2015D.gif	r1	manage	81.1 K	2016-02-04 - 14:10	AndreasKunsken
gif	averageEnergy_NoPUAnalyzed.gif	r1	manage	51.7 K	2016-02-04 - 13:55	AndreasKunsken
gif	averageEnergy_NoPUMuPlus.gif	r1	manage	54.4 K	2016-02-04 - 13:53	AndreasKunsken
gif	averageEnergy_SingleMuon2015D.gif	r1	manage	60.0 K	2016-02-04 - 14:10	AndreasKunsken
gif	deltaPhiVsPtL1Tight_SingleMuon2015D.gif	r1	manage	56.9 K	2016-02-05 - 16:51	AndreasKunsken
gif	deltaPhiVsPt_SingleMuon2015D.gif	r1	manage	56.0 K	2016-02-05 - 16:51	AndreasKunsken
gif	eAveragePerWheelTightMuons_NoPUAnalyzed.gif	r1	manage	99.8 K	2016-02-04 - 13:55	AndreasKunsken
gif	eAveragePerWheelTightMuons_NoPUMuPlus.gif	r1	manage	97.1 K	2016-02-04 - 13:53	AndreasKunsken
gif	eAveragePerWheelTightMuons_SingleMuon2015D.gif	r1	manage	99.7 K	2016-02-04 - 14:10	AndreasKunsken
gif	eAveragePerWheel_NoPUAnalyzed.gif	r1	manage	96.2 K	2016-02-04 - 13:55	AndreasKunsken
gif	eAveragePerWheel_NoPUMuPlus.gif	r1	manage	99.2 K	2016-02-04 - 13:53	AndreasKunsken
gif	eAveragePerWheel_SingleMuon2015D.gif	r1	manage	104.2 K	2016-02-04 - 14:10	AndreasKunsken
gif	eAverageTightMuons_NoPUAnalyzed.gif	r1	manage	64.5 K	2016-02-04 - 13:55	AndreasKunsken
gif	eAverageTightMuons_NoPUMuPlus.gif	r1	manage	59.7 K	2016-02-04 - 13:53	AndreasKunsken
gif	eAverageTightMuons_SingleMuon2015D.gif	r1	manage	55.5 K	2016-02-04 - 14:10	AndreasKunsken
gif	etaPhiForDeltaPhiOne_SingleMuon2015D.gif	r1	manage	48.5 K	2016-02-05 - 16:12	AndreasKunsken
gif	hoAndL1Coordinates_043_043.gif	r1	manage	7.9 K	2016-02-10 - 18:30	AndreasKunsken
gif	hoAndL1Coordinates_043_087.gif	r1	manage	8.2 K	2016-02-10 - 18:30	AndreasKunsken
gif	hoCoordinates_043_043.gif	r1	manage	8.1 K	2016-02-10 - 18:30	AndreasKunsken
gif	hoCoordinates_043_087.gif	r1	manage	8.2 K	2016-02-10 - 18:30	AndreasKunsken
gif	l1Coordinates_043_043.gif	r1	manage	6.6 K	2016-02-10 - 18:30	AndreasKunsken
gif	l1Coordinates_043_087.gif	r1	manage	6.6 K	2016-02-10 - 18:30	AndreasKunsken

Topic revision: r8 - 2016-02-10 - AndreasKunsken

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