Getting to Higgs

Calculating Higgs Mass
Remember Higgs and W can be produced together, and Higgs decays into 2 Bs which produce jets.

We have provided data from 3000 candidate Higgs events. All of these events contain a W and two jets identified as b quark jets, but most events do not contain a Higgs. The only way to tell if the events contain W and H is to look at the "invariant mass" of the b quark jet pair. If the b jets come from a Higgs, they will make a peak in the invariant mass plot at the value of the Higgs mass.

To calculate the Higgs mass:

1. Get the data. This is observed data with Higgs candidate events. The Excel data file looks like this. Columns C - H give the measured momenta of the two b jets. The equation =SQRT( (SQRT(F2^2+G2^2)+SQRT(I2^2+J2^2))^2 - (F2*COS(H2)+I2*COS(K2))^2 - (F2*SIN(H2)+I2*SIN(K2))^2 - (G2+J2)^2 ) given in I2 calculates the "invariant mass." Fill Down to complete the calculation for all of the events.

 

A

B

C

D

E

F

G

H

I

M

1

Run No.

Event No.

 pt jet 1
GeV/c		 pz jet 1
GeV/c		 φjet1
radians		 pt jet 2
GeV/c		 pz jet 2
GeV/c		 φjet 2
radians		 m from jets GeV/c2

Mass Bins

2

 100237 5128 137.67 -189.42 6.03 51.71 -179.40 4.03 159.3734

 

3

 100474 5251 23.77 -63.15 1.36 18.24 -23.96 4.19

 

 

2. Make a histogram (with bin width 5 GeV) for the Higgs mass + background.

Help with data analysis

3. Plot frequency vs. binned mass.

Your plot shows masses from the background with a peak at the Higgs mass. Notice the "bump" of many events of about the same mass in your plot. What do you think the Higgs mass is from these data?

graphs

Often a mass plot has many particles at low mass and fewer and fewer at larger masses. These data have been cut to eliminate very low mass-energy particles.

4. Subtract the expected background.

Get the data with the expected background events.

Make a histogram of the two-jet mass for the expected background exactly as you did for the observed data.

Copy the histogram frequency column and paste it in column C in your original histogram.

In column D subtact the value in Column C from the value in Column B (observed mass - expected background mass).

Make another column which is error on this value, =SQRT(B2+C2) and Fill Down.

Highlight columns A and D. Plot the frequency versus mass.

You should now have a mass plot which comes from the Higgs contribution to the original observed data. What is the Higgs mass from these data?
Histogram from Step 1: Observed Data

 

A B C D E
1 Bin Frequency (Step 1) Frequency (Step 4) Frequency Step 1 -
Frequency Step 4 		Error
2 5 14 10 4 4.8989

Congratulations, you have done your first high-energy physics data analysis!