Lecture 7.3: Calibration Example from MINOS and Homework

Lecture 7.3: Calibration Example from MINOS

and Homework Assignment

Prof. Luke A. CorwinPHYS 733

South Dakota School of Mines & Technology

October 11, 2013

L. Corwin, PHYS 733 (SDSM&T) Lecture 7.3: MINOS PMT Calib. October 11, 2013 1 / 16

Outline

1 MINOS PMTsThe MINOS experimentPMTsThe Calibration Method: Light InjectionFrom Calibration Data to Gains

2 Homework Assignment


MINOS PMTs The MINOS experiment

MINOS Data Chain

Reality Muon Neutrino (νµ)↓

Interactions with Medium νµn→ µ−p↓

Signal Particles Scintillator Radiation from µ−

↓Signal in Detectors Electronic cascade in PMTs

↓Detector Output Current from PMTs

↓Data See Following Slide





π-

π+

Target Focusing Horns

2 m

675 m

νµ

νµ

15 m 30 m

Figure : A beam of 120 GeV protons is impinged upon a graphitetarget. The resulting hadrons are focused by two magnetic focusinghorns. The field of the horns can be chosen to select positively ornegatively charged hadrons. The hadrons are then allowed to decay ina decay pipe before. A hadron absorber and rock then remove allremaining particles, except neutrinos, from the beam before it reachesthe near detector.



Figure : The Near detector (left) is 1 km from the target, is immersedin a 1.3 T magnetic field, has a total mass of 1 kton and a fiducial massof ∼ 0.03 kton. The Far Detector (right) is 735 km from the target, isimmersed in a 1.3 T magnetic field, has a total mass of 5.4 kton and afiducial mass of ∼ 4 kton.



Figure : Neutrinos interact with the steel planes, producing chargedparticles as a result. Those particles pass through the scintillator,producing light. The scintillator strips are arranged in alternatingorthogonal planes in order to extract three dimensional positioninformation.




MINOS PMTs PMTs

Figure : Image from Dr. Bai’s Lecture 4. The amount of light emittedby scintillator is correlated with the amount of energy deposited in thescintillator. We want to know how much energy our particles depositand where they deposit it. We need to measure the gain g of the PMT,which is the number of electrons per photon.


MINOS PMTs PMTs

Our measuring instrument is aPMT. What ideas do you have forhow one might calibrate it andwhat standard might be used?


MINOS PMTs The Calibration Method: Light Injection

How it is done

Use LEDs to pulse a PMT with a constant (unknown) light levelfor 10,000 pulses.

Our Data

Current in arbitrary units (x), with x being the mean.

The width of the current distribution σx.

We can also assume the number of photons per pulse n isnormally distributed. Thus, σn =

√n.

We want to know g, where x ≡ gn. It is measured in units ofADC/PE (analog to digital counts per photo electron).


MINOS PMTs The Calibration Method: Light Injection

Figure : Any ideas for how to derive g?L. Corwin, PHYS 733 (SDSM&T) Lecture 7.3: MINOS PMT Calib. October 11, 2013 12 / 16

MINOS PMTs From Calibration Data to Gains

The Answer

x ≡ gn⇒ σx =g

σn

σn =√n⇒ σx = g

√n⇒ g =

σx√n⇒ g2 =

σ2x

n

n =x

g⇒ g2 = σ2

x

g

x

⇒ g =σ2x

x


MINOS PMTs From Calibration Data to Gains

Additional Considerations

We have been assuming that the PMTs had perfectone-electron resolution. If they do not we need to introduce acorrection factor w such that σx → σxw

Each PMT has a different gain and w, so we can eitherrecord each PMTs gain separately and fold that into ouranalysis, or we can take the distribution of gains as asystematic uncertainty (∼ 5% in this case).


Homework Assignment

In-Class Exercise

Find (via http://inspirehep.net/, http://arxiv.org/, etc.) apaper or book section describing the calibration of on an actualexperiment. The experiment must not be MINOS, IceCube,LBNE, or DIANA because we will be covering those in class.


http://inspirehep.net/

http://arxiv.org/

Homework Assignment

Homework Assignment Due Nov. 1

A short presentation (10 min + 5 min. for questions)

Present to the class a calibration example of one instrumentfrom the paper found in the in-class exercise or from yourown work.

Questions to Answer

What is the experiment?

What is the instrument?

To what standard/model was it compared?

What were the results?


Documents

Lecture 7.3: Calibration Example from MINOS and Homework