Muon Online & Offline Constant Specifications

1.  Definition of Constant Specifications

2.  Calibration Constants

-   Common Features

-   PDT

-   MDT

-   Scintillator (MSC)

1.  Thresholds

-   Common Features

-   PDT

-   MDT

-   Scintillator (MSC)

1.  Geometry Constants

2.  Alignment Constants

**1. DEFINITION OF CONSTANT SPECIFICATIONS**

-   **Definition:** Define what constants will be provided. Separate by
    geometric constants (where things nominally are); alignment
    constants (corrections that give actual locations); and calibration
    constants.

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-   **Determination:** Define how each type of constant is determined.

-   **Online Use:** Define online application of each type of constant.
    Include timeliness required for each type of constant.
    \"Timeliness\" means: is the constant needed in real time (e.g., as
    for time to distance conversion in DSP, or similar online
    application in L1, L2, L3); is it needed for pass 1 reconstruction;
    will it only be available for re-reconstruction (i.e., something
    that can only be derived from study of reconstructed data)? Define
    which constants are \"absolute\" - i.e., initial determination of
    constant is final (e.g., pedestal, TZero) - and which are
    \"relative\" - those subject to incremental improvement (e.g.,
    energy scale).

-   **Offline Processing:** Define what operations have to be performed
    on calibration data sent to offline group (e.g., conversion of drift
    time to distance).

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-   **Precision:** Define level of precision required for each type of
    constant.

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-   **Size:** Define number of words required for each type of constant
    per calibration/geometry constant set.

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-   **Frequency:** Define how often each type of constant will be
    re-determined.

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-   **Development:** Define strategy for developing/using calibration
    system - what will be developed/needed well before the run; during
    commissioning; during the start of the run; steady state.

**2. CALIBRATION CONSTANTS**

**[FEATURES COMMON TO ALL MUON SUBSYSTEM CALIBRATION
CONSTANTS]{.underline}**

**Offline Processing:**

All thresholds will be downloaded from offline database into front-end
electronics for data-taking via CDAQ system.

All thresholds will be stored offline permanently.

**[PDT]{.underline}**

**TZERO'S**

**Definition:**

The PDT TZero (T0) is defined as the minimum reported time for a given
wire for a relativistic particle emanating from the IP on a given
crossing - i.e., for a track passing very close to the near end of the
wire. A T0 includes particle propagation time (path length) and signal
propagation time through electronics, cables, etc. It does not include
drift time or propagation time along the PDT wire, which varies with the
location of the track. These are used to determine the track's radial
position with respect to the wire and axial position along the wire.
I.e., the T0-subtracted time for a relativistic particle should be zero,
modulo drift time and propagation time along the PDT wire.

The T0 consists of three separate components:

\- The FEB-wise cable length adjustment (PDT_T0_FEB).

\- The channel-wise T0 adjustment (PDT_T0_ADJ).

\- The module-wise T0 offset (PDT_T0_OFF).

The sum of these three components is the T0 to be subtracted from the
measured time.

The PDT_T0_FEB accounts for differences in cable length between the
FEB's and the PDT service cards. These cable lengths will be measured
during commissioning and will in principle never change.

The PDT_T0_ADJ accounts for channel to channel differences in the PDT
analog front-end electronics. A pulse is injected at the near end of
each wire and read out for both wires in a pair. After subtracting the
PDT_T0_FEB from the measured times, these times should all be the same.
The PDT_T0_ADJ for each channel is the time subtracted from each
channel's readout to make all the times equal to some chosen time less
than the shortest measured time.

The PDT_T0_OFF accounts for the offset between the PDT_T0_FEB and
PDT_T0_ADJ adjusted times and the beam crossing time. This offset
includes particle flight time to the PDT and any cable and electronics
delays and offsets. The PDT_T0_OFF is derived from data taken during
dedicated calibration collision running. The PDT_T0_OFF is the leading
edge of a distribution of PDT_T0_FEB and PDT_T0_ADJ adjusted times from
all wires in a module.

+----------+-------------------+-------------------+-------------------+
|          | PDT_T0_FEB        | PDT_T0_ADJ        | PDT_T0_OFF        |
+----------+-------------------+-------------------+-------------------+
| **Pre    | 1 16-bit word     | 1 16-bit word     | 1 16-bit word     |
| cision** |                   |                   |                   |
|          | (units of 0.1 ns) | (units of 0.1 ns) | (units of 0.1 ns) |
+----------+-------------------+-------------------+-------------------+
| **Size** | 1 word/FEB        | 1 word/channel    | 1 word/module     |
|          |                   |                   |                   |
|          | =\> 278 words     | =\> 6768 words    | =\> 94 words      |
+----------+-------------------+-------------------+-------------------+
| **Fre    | Once              | As necessary      | After shutdowns   |
| quency** | (commissioning)   | (very rare: e.g.  | =\> \~ once per 3 |
|          |                   | when electronics  | months            |
|          |                   | replaced)         |                   |
+----------+-------------------+-------------------+-------------------+
| **Online | DSP =\> real time | DSP =\> real time | DSP =\> real time |
| Use**    |                   |                   |                   |
+----------+-------------------+-------------------+-------------------+

**AXIAL TIME TO DISTANCE CONVERSION (PDT_ATDC)**

**Definition:**

The Axial Time to Distance Conversion (PDT_ATDC) is defined as the
relationship between the difference of the T0-subtracted measured times
of a pair of wires and the corresponding axial position of a hit along
the hit wire, with respect to the IP. PDT_ATDC depends on wire length,
but not on electronics variations, which is accounted for in the T0's.
PDT_ATDC will be determined during testing/commissioning and will in
principle never change. PDT_ATDC is the same for all wires in all PDT's
of given length. PDT_ATDC is kept in the form of a lookup table for
conversion between time and distance (\~20 cm resolution over \~20 m =\>
\~100 words per table).

**DRIFT TIME TO DISTANCE CONVERSION (PDT_DTDC)**

**Definition:**

The Drift Time to Distance Conversion (PDT_DTDC) is defined as the
relationship between the measured, T0-subtracted,
axial-position-corrected drift time and the corresponding drift distance
perpendicular to the PDT wire, with respect to the PDT wire position.
PDT_DTDC will be determined during testing/commissioning. PDT_DTDC
depends only on gas composition (HV variations and other factors are
negligible) and will in principle never change. PDT_DTDC is the same for
all PDT's. PDT_DTDC is kept in the form of a lookup table for conversion
between time and distance (\~100 μm resolution over \~5 cm =\> \~500
words per table).

**PAD ADC GAIN (PDT_PAD_GAIN)**

**Definition:**

The PDT Pad ADC Gain (PDT_PAD_GAIN) is defined as the conversion factor
between ADC readout bins and units of charge.

+----------+-------------------+-------------------+-------------------+
|          | PDT_ATDC          | PDT_DTDC          | PDT_PAD_GAIN      |
+----------+-------------------+-------------------+-------------------+
| **Pre    | \~100 16-bit      | \~500 16-bit      | 1 16-bit word     |
| cision** | words/table       | words/table       |                   |
|          |                   |                   | (units of fC/bin) |
|          | (units of cm)     | (units of 100 μm) |                   |
+----------+-------------------+-------------------+-------------------+
| **Size** | 10 different PDT  | 1 table           | 1 word/channel    |
|          | lengths           |                   |                   |
|          |                   | =\> \~500 words   | =\> 6768 words    |
|          | =\> \~1000 words  |                   |                   |
+----------+-------------------+-------------------+-------------------+
| **Fre    | Once              | Once              | After shutdowns   |
| quency** | (commissioning)   | (commissioning)   | =\> \~ once per 3 |
|          |                   |                   | months            |
+----------+-------------------+-------------------+-------------------+
| **Online | DSP, L3 =\> real  | DSP, L3 =\> real  | DSP =\> real time |
| Use**    | time              | time              |                   |
|          |                   |                   |                   |
|          | (also reco?)      | (also reco?)      |                   |
+----------+-------------------+-------------------+-------------------+

**[MDT]{.underline}**

**TZERO'S**

**Definition:**

The MDT TZero (T0) is defined as the minimum reported time for a given
wire for a relativistic particle emanating from the IP on a given
crossing - i.e., for a track passing very close to the near end of the
wire. A T0 includes particle propagation time (path length) and signal
propagation time through electronics, cables, etc. Propagation time of
the signal along the wire is considered negligible. The T0 does not
include drift time, which varies with the distance of the track form the
wire and is used to determine the track's radial position with respect
to the wire. I.e., the T0-subtracted time for a relativistic particle
should be zero, modulo drift time.

The T0 consists of two separate components:

\- The channel-wise T0 adjustment (MDT_T0_ADJ).

\- The module-wise T0 offset (MDT_T0_OFF).

The sum of these two components is the T0 to be subtracted from the
measured time.

The MDT_T0_ADJ accounts for channel to channel differences in the MDT
analog front-end electronics. A pulse is injected at the near end of
each wire and read out. These times should all be the same. The
MDT_T0_ADJ for each channel is the time subtracted from each channel's
readout to make all the times equal to some chosen time less than the
shortest measured time.

The MDT_T0_OFF accounts for the offset between the MDT_T0_ADJ adjusted
times and the beam crossing time. This offset includes particle flight
time to the MDT and any cable and electronics delays and offsets. The
MDT_T0_OFF is derived from data taken during dedicated calibration
collision running. The MDT_T0_OFF is the leading edge of a distribution
of MDT_T0_ADJ adjusted times from all wires in a module (module = 2
octant-planes). Use of a single MDT_T0_OFF per module requires that all
cable lengths between the front-end cards (MDC's) and the MDT's be the
same for a given module.

**DRIFT TIME TO DISTANCE CONVERSION (MDT_DTDC)**

**Definition:**

The Drift Time to Distance Conversion (MDT_DTDC) is defined as the
relationship between the T0-subtracted drift time and the corresponding
drift distance perpendicular to the MDT wire, with respect to the MDT
wire position. MDT_DTDC will be determined during testing/commissioning.
MDT_DTDC depends only on gas composition (HV variations and other
factors are negligible) and will in principle never change. MDT_DTDC is
the same for all MDT's. MDT_DTDC is kept in the form of a lookup table
for conversion between time and distance (\~1 mm resolution over \~1 cm
=\> \~10 words per table).

+----------+-------------------+-------------------+-------------------+
|          | MDT_T0_ADJ        | MDT_T0_OFF        | MDT_DTDC          |
+----------+-------------------+-------------------+-------------------+
| **Pre    | 1 16-bit word     | 1 16-bit word     | \~10 16-bit       |
| cision** |                   |                   | words/table       |
|          | (units of 0.1 ns) | (units of 0.1 ns) |                   |
|          |                   |                   | (units of 100 μm) |
+----------+-------------------+-------------------+-------------------+
| **Size** | 1 word/channel    | 1 word/module     | 1 table           |
|          |                   |                   |                   |
|          | =\> 50016 words   | =\> 24 words      | =\> \~10 words    |
+----------+-------------------+-------------------+-------------------+
| **Fre    | As necessary      | After shutdowns   | Once              |
| quency** | (very rare: e.g.  | =\> \~ once per 3 | (commissioning)   |
|          | when electronics  | months            |                   |
|          | replaced)         |                   |                   |
+----------+-------------------+-------------------+-------------------+
| **Online | DSP =\> real time | DSP =\> real time | DSP =\> real time |
| Use**    |                   |                   |                   |
|          |                   |                   | (also reco?)      |
+----------+-------------------+-------------------+-------------------+

**[SCINTILLATOR (MSC)]{.underline}**

**TZERO'S**

**Definition:**

The MSC TZero (T0) is defined as the mean reported time for a given
pixel for a relativistic particle emanating from the IP on a given
crossing - i.e., for a track passing through the counter near its
center. A T0 includes particle propagation time (path length) and signal
propagation time through electronics, cables, etc. Propagation time of
light through the scintillator and light guides is considered negligible
at this level. A fixed offset is subtracted from the T0 to avoid
handling negative T0-subtracted times. I.e., the T0-subtracted time for
a relativistic particle should be equal to the fixed offset, modulo
light propagation time.

The T0 consists of two separate components:

\- The channel-wise T0 adjustment (MSC_T0_ADJ).

\- The channel-wise T0 offset (MSC_T0_OFF).

The sum of these two components is the T0 to be subtracted from the
measured time.

The MSC_T0_ADJ accounts for channel to channel differences in the MSC
analog front-end electronics. A pulse is injected at the near end of
each wire and read out. These times should all be the same. The
MSC_T0_ADJ for each channel is the time subtracted from each channel's
readout to make all the times equal to some chosen time less than the
shortest measured time.

The MSC_T0_OFF accounts for the offset between the MSC_T0_ADJ adjusted
times and the beam crossing time. This offset includes particle flight
time to the MSC and any cable and electronics delays and offsets. The
MSC_T0_OFF is derived from data taken during dedicated calibration
collision running. The MSC_T0_OFF is given by: the mean of a
distribution of MSC_T0_ADJ adjusted times for a given pixel, minus the
fixed offset.

+---------------+---------------------------+---------------------------+
|               | MSC_T0_ADJ                | MSC_T0_OFF                |
+---------------+---------------------------+---------------------------+
| **Precision** | 1 16-bit word             | 1 16-bit word             |
|               |                           |                           |
|               | (units of 0.1 ns)         | (units of 0.1 ns)         |
+---------------+---------------------------+---------------------------+
| **Size**      | 1 word/channel            | 1 word/channel            |
|               |                           |                           |
|               | =\> 6076 words            | =\> 6076 words            |
+---------------+---------------------------+---------------------------+
| **Frequency** | As necessary (very rare:  | After shutdowns =\> \~    |
|               | e.g. when electronics     | once per 3 months         |
|               | replaced)                 |                           |
+---------------+---------------------------+---------------------------+
| **Online      | DSP =\> real time         | DSP =\> real time         |
| Use**         |                           |                           |
+---------------+---------------------------+---------------------------+

**ADC PEDESTAL (MSC_PED)**

**Definition:**

The scintillator ADC Pedestal (MSC_PED) is defined as the ADC readout
value when there is no signal in the scintillator. The MSC_PED is
determined in the DSP. The DSP reads out each channel during
non-collision "beam crossings" between fills and extracts the mean of a
distribution of ADC values for each channel.

**ADC GAIN (MSC_GAIN)**

**Definition:**

The scintillator ADC Gain (MSC_GAIN) is defined as the conversion factor
between ADC readout bins and units of charge.

**LED ADC BASELINE MEASUREMENT (MSC_LED_BASE)**

**Definition:**

The scintillator LED ADC measurement (MSC_LED_BASE) is defined as the
pedestal-subtracted ADC readout value for a LED scintillator pulse. The
MSC_LED_BASE will be determined in the DSP during dedicated calibration
running. After phototube thresholds and high voltages are set, the DSP
will pulse the LED's and read out each channel during non-collision
"beam crossings" and extract the mean of a distribution of ADC values
for each channel.

+----------+-------------------+-------------------+-------------------+
|          | MSC_PED           | MSC_GAIN          | MSC_LED_BASE      |
+----------+-------------------+-------------------+-------------------+
| **Pre    | 1 16-bit word     | 1 16-bit word     | 1 16-bit word     |
| cision** |                   |                   |                   |
|          | (units of ?)      | (units of fC/bin) | (units of ?)      |
+----------+-------------------+-------------------+-------------------+
| **Size** | 1 word/channel    | 1 word/channel    | 1 word/module     |
|          |                   |                   |                   |
|          | =\> 6076 words    | =\> 6076 words    | =\> 18 words      |
+----------+-------------------+-------------------+-------------------+
| **Fre    | Once per fill     | After shutdowns   | Once              |
| quency** |                   | =\> \~ once per 3 | (commissioning)   |
|          | =\> \~ once per   | months            |                   |
|          | day               |                   |                   |
+----------+-------------------+-------------------+-------------------+
| **Online | DSP =\> real time | DSP =\> real time | DSP =\> real time |
| Use**    |                   |                   |                   |
+----------+-------------------+-------------------+-------------------+

**3. THRESHOLDS**

**[FEATURES COMMON TO ALL MUON SUBSYSTEM THRESHOLDS]{.underline}**

**Determination:**

Thresholds will be determined during bench testing, commissioning, or
from dedicated calibration collision data.

**Online Use:**

All thresholds will be downloaded to front end electronics =\> real-time
use.

**Offline Processing:**

All thresholds will be downloaded from offline database into front-end
electronics for data-taking via CDAQ system.

All thresholds will be stored offline permanently.

**Development:**

All threshold determination (calibration mode) and application
(data-taking mode) will be fully developed before commissioning. CDAQ
delivery system & offline database will be needed during commissioning
(will be developed when?).

**[PDT]{.underline}**

**WIRE DISCRIMINATOR THRESHOLD**

**Definition:**

The threshold for the discriminator that receives the PDT wire signal
and sends a signal to the TMC.

**Frequency:**

Determined once during commissioning.

**[MDT]{.underline}**

**WIRE DISCRIMINATOR THRESHOLD**

**Definition:**

The threshold for the discriminator that receives the MDT wire signal
and sends a signal to the TMC.

**Frequency:**

Determined once during commissioning.

**[SCINTILLATOR (MSC)]{.underline}**

**PHOTOTUBE DISCRIMINATOR THRESHOLD**

**Definition:**

The threshold for the discriminator that receives the MSC phototube
signal and sends a signal to the TMC.

**Frequency:**

Determined once during commissioning. Possibly re-determined if
monitoring indicates phototube gain decay.

+----------+-------------------+-------------------+-------------------+
| **Thre   | PDT Wire          | MDT Wire          | MSC Phototube     |
| sholds** | Discriminator     | Discriminator     | Discriminator     |
+----------+-------------------+-------------------+-------------------+
| **Pre    | 1 16-bit word:    | 1 16-bit word:    | 1 16-bit word:    |
| cision** |                   |                   |                   |
|          | (units of ?)      | (units of ?)      | (units of ?)      |
+----------+-------------------+-------------------+-------------------+
| **Size** | 1 word/channel    | 1 word/channel    | 1 word/channel    |
|          |                   |                   |                   |
|          | =\> 6768 words    | =\> 50016 words   | =\> 6076 words    |
+----------+-------------------+-------------------+-------------------+

**4. GEOMETRY CONSTANTS**

**Definition:**

Nominal, permanent detector geometry coordinates. Three types of
constants:

1\. Reference point coordinates, in global coordinate system (i.e., with
respect to IP). 1-8 per module (module = 1 PDT or 2 MDT octant-planes or
scintillator serviced by one FE crate). These will be surveyed during
the run, and adjustments to the nominal geometry (i.e., alignment
constants) will be expressed in terms of these reference points.

2\. Offsets between reference point coordinates and channel coordinates
(channel = PDT wire or MDT wire or scintillator pixel). These offsets
will allow translation from reference point global coordinates to
channel global coordinates.

3\. Channel dimensions: wire length, scintillator pixel size.

**Online Use:**

Used in L3, one-event display =\> real-time use.

**Development:**

All geometry constant application (data-taking mode) will be fully
developed by the end of commissioning. Geometry constant determination
will be developed during commissioning. Offline database will be needed
during commissioning (will be developed when?).

**Frequency:**

Determined once, during commissioning.

+----------+-------------------+-------------------+-------------------+
| **PDT**  | PDT Reference     | PDT Wire Offsets  | PDT Wire Length   |
|          | Points            |                   |                   |
+----------+-------------------+-------------------+-------------------+
| **Pre    | 5 16-bit words:   | 3 16-bit words:   | 1 16-bit word:    |
| cision** |                   |                   |                   |
|          | global x, y, z;   | ∆x, ∆y, ∆z from   | (units of mm)     |
|          | global θ, φ of    | reference point   |                   |
|          | PDT               | to center of wire |                   |
|          |                   |                   |                   |
|          | (units of mm,     | (units of mm)     |                   |
|          | μrad)             |                   |                   |
+----------+-------------------+-------------------+-------------------+
| **Size** | 1 point/PDT       | 1 offset/channel  | 1 length/PDT      |
|          |                   |                   |                   |
|          | =\> 470 words     | =\> 20304 words   | =\> 94 words      |
+----------+-------------------+-------------------+-------------------+

+----------+-------------------+-------------------+-------------------+
| **MDT**  | MDT Reference     | MDT Wire Offsets  | MDT Wire Length   |
|          | Points            |                   |                   |
+----------+-------------------+-------------------+-------------------+
| **Pre    | 5 16-bit words:   | 3 16-bit words:   | 1 16-bit word:    |
| cision** |                   |                   |                   |
|          | global x, y, z;   | ∆x, ∆y, ∆z from   | (units of mm)     |
|          | global θ, φ of    | reference point   |                   |
|          | MDT module        | to center of wire |                   |
|          |                   |                   |                   |
|          | (units of mm,     | (units of mm)     |                   |
|          | μrad)             |                   |                   |
+----------+-------------------+-------------------+-------------------+
| **Size** | 1                 | 1 offset/channel  | 1 length/channel  |
|          | p                 |                   |                   |
|          | oint/octant-plane | =\> 150048 words  | =\> 50016 words   |
|          |                   |                   |                   |
|          | =\> 240 words     |                   |                   |
+----------+-------------------+-------------------+-------------------+

+----------+-------------------+-------------------+-------------------+
| **MSC**  | MSC Reference     | MSC Pixel Offsets | MSC Pixel Size    |
|          | Points            |                   |                   |
+----------+-------------------+-------------------+-------------------+
| **Pre    | 5 16-bit words:   | 3 16-bit words:   | 12 16-bit words:  |
| cision** |                   |                   |                   |
|          | global x, y, z;   | ∆x, ∆y, ∆z from   | ∆x, ∆y, ∆z from   |
|          | global θ, φ of    | reference point   | pixel center to   |
|          | normal to pixel   | to center of      | corners           |
|          | plane             | pixel             |                   |
|          |                   |                   | (units of mm)     |
|          | (units of mm,     | (units of mm)     |                   |
|          | μrad)             |                   |                   |
+----------+-------------------+-------------------+-------------------+
| **Size** | \~1 point/SFE     | 1 offset/channel  | 1 size per pixel  |
|          |                   |                   | type              |
|          | =\> \~650 words   | =\> 18228 words   |                   |
|          |                   |                   | =\> \~432 words   |
+----------+-------------------+-------------------+-------------------+

**5. ALIGNMENT CONSTANTS**

**Definition:**

Offsets between nominal reference point coordinates (contained in
geometry constants) and actual surveyed reference point coordinates.

**Online Use:**

**Offline Processing:**

**Frequency:**

Re-determined once per access =\> several times per year.

**Development:**

All alignment constant application (data-taking mode) will be fully
developed by the end of commissioning. Alignment constant determination
(calibration mode) will be developed during commissioning. CDAQ delivery
system & offline database will be needed during commissioning (will be
developed when?).

+----------+-------------------+-------------------+-------------------+
| **R      | PDT               | MDT               | MSC               |
| eference |                   |                   |                   |
| Point    |                   |                   |                   |
| O        |                   |                   |                   |
| ffsets** |                   |                   |                   |
+----------+-------------------+-------------------+-------------------+
| **Pre    | 5 8-bit words:    | 5 8-bit words:    | 3 8-bit words:    |
| cision** |                   |                   |                   |
|          | ∆                 | ∆                 | ∆x, ∆y, ∆z        |
|          | x, ∆y, ∆z, ∆θ, ∆φ | x, ∆y, ∆z, ∆θ, ∆φ |                   |
|          |                   |                   | (units of mm)     |
|          | (units of mm,     | (units of mm,     |                   |
|          | μrad)             | μrad)             |                   |
+----------+-------------------+-------------------+-------------------+
| **Size** | 1 point/PDT       | 1                 | \~1 point/SFE     |
|          |                   | p                 |                   |
|          | =\> 470 words     | oint/octant-plane | =\> \~390 words   |
|          |                   |                   |                   |
|          |                   | =\> 240 words     |                   |
+----------+-------------------+-------------------+-------------------+