Purpose of the Analysis Report

In this final step you turn your ROOT work into a clear, readable scientific story. The report is not just a dump of plots and numbers. It explains what you did, why you did it, what you found, and how confident you are in the result. Even for a small training project, getting used to this structure prepares you for real analysis notes, theses, and publications.

A short analysis report for this course can usually be between 3 and 8 pages, including key figures and tables. Focus on clarity, traceability, and a logical flow from data to final conclusions.

Recommended Structure

A simple and effective structure for your report is:

1. Title and author
2. Abstract
3. Introduction and physics motivation
4. Data and event selection
5. Analysis method
6. Results
7. Systematic checks and limitations
8. Conclusions
9. Appendix with technical ROOT details (optional)

You can merge some of these sections if your project is very small, but keep the logical order. Start from context, move through methods, then present results and conclusions.

Title, Author, and Abstract

Begin with a descriptive title that tells the reader what you measured or studied. For example, “Measurement of the Lifetime of a Simulated Unstable Particle with ROOT” or “Energy Spectrum of Gamma Rays from a Calibration Source using ROOT.”

List your name, date, and possibly course information.

The abstract is a short paragraph, typically 5 to 7 sentences. It should contain:

What was analyzed: for example, “We analyzed a sample of N events of XYZ collisions / detector signals.”
What was measured: for example, “We determined the mean energy, the width of a resonance, or an efficiency.”
Key methods: for example, “Data were selected using cuts on variable A and B, and histograms were fitted with a Gaussian plus linear background.”
Main numerical results: for example, a final value with its uncertainty, such as $m = (91.2 \pm 0.3)\,\text{GeV}$.
Very brief conclusion: for example, “The measured value is consistent with the nominal parameter within uncertainties.”

Introduction and Physics Motivation

In the introduction, explain what physical quantity or observable you are studying and why it matters. For a training dataset, you can still give a short physics context.

Describe the physical process or detector signal in simple terms. For instance, if you studied an invariant mass peak, say which particle or resonance it corresponds to. If you analyzed a decay time distribution, explain what lifetime means physically.

State your main analysis goals explicitly. Examples:

Measure the peak position and width of a mass distribution.
Determine the efficiency of a selection cut.
Estimate the signal yield after background subtraction.
Compare an experimental spectrum to a simulated one.

You do not need to reproduce detailed theoretical formulas unless they are directly used in your analysis. If a specific formula is essential, introduce it briefly and explain which parameter you will extract.

For example, if you fitted an exponential decay, you might write that the expected time distribution is
$$
N(t) = N_0 e^{-t/\tau},
$$
and that your goal is to determine the lifetime parameter $\tau$ from the data.

Data Sample and Event Selection

In this section, describe clearly what data you used and how you selected events. This part connects your dataset to the histograms and fits that appear later in the report.

Begin with a short description of the input data:

Specify the source: simulated file provided by the course, a ROOT file in a public repository, or real detector data if applicable.
State the format: for example, “Events are stored in a TTree named ‘Events’ in the file data.root.”
List the most important branches that you use, with a short explanation of what they represent.

A small table can help to summarize key branches:

Next, describe your selection cuts. State each cut clearly, in physics terms and then in ROOT terms if useful. For example, you might say that you require the transverse momentum to be above a certain threshold, or that you restrict a time window to reduce noise.

If you applied multiple cuts, explain them in the order they are applied. You can summarize them in text or in a compact table:

Explain briefly why each cut is used, for example to remove unphysical values, reduce background, define a fiducial volume, or select a signal region.

If you estimated or reported event counts, mention the number of events before and after your main cuts. This makes your selection transparent and reproducible.

Analysis Method

Here you explain how you used ROOT to move from selected events to physics results. You do not need to paste long code listings, but you should describe the key analysis steps and the reasoning behind them.

Start by describing how you transformed raw variables into the observables you studied. For example:

If you computed an invariant mass, write the formula,
$$
m^2 = E^2 - |\vec{p}|^2,
$$
and explain which branches you used for $E$ and $\vec{p}$. If you used a TLorentzVector in ROOT, you can state that without showing the full code.
If you defined a derived variable, for example a ratio or difference, write it explicitly and explain its physical meaning.

Then describe how you filled histograms or graphs. For instance, “We filled a TH1D histogram of the invariant mass with 200 bins between 60 and 120 GeV, using one entry per event.” Justify important choices like bin numbers and ranges if they are not obvious. If your project includes 2D histograms or profiles, describe what quantities are on each axis and what the histogram represents.

If you used fits, explain the chosen fit function and free parameters. For example, if you fitted a peak with a Gaussian plus linear background, you can write that the model is
$$
f(x) = A \exp\left(-\frac{(x - \mu)^2}{2\sigma^2}\right) + (p_0 + p_1 x)
$$
with parameters $A$, $\mu$, $\sigma$, $p_0$, and $p_1$. Indicate the fit range and whether any parameters were fixed.

If your analysis involves efficiencies, define them clearly as
$$
\epsilon = \frac{N_{\text{selected}}}{N_{\text{total}}},
$$
and state how $N_{\text{selected}}$ and $N_{\text{total}}$ were counted in ROOT.

For any averages or simple statistics, briefly state the formula you are using, such as the sample mean and standard deviation,
$$
\bar{x} = \frac{1}{N} \sum_{i=1}^{N} x_i, \qquad
s = \sqrt{\frac{1}{N-1} \sum_{i=1}^{N} (x_i - \bar{x})^2}.
$$

End this section with a short summary of the workflow. For example, “After applying the selection cuts, we filled histograms of the invariant mass and applied a Gaussian fit to extract the peak position and width. We also computed the signal selection efficiency and its statistical uncertainty.”

Presenting Results

This section contains your numerical results and your main plots. The key rule is that every result must be easy to understand and trace back to the method described earlier.

Present your most important histograms and graphs with clear captions. A plot caption should say what is being shown, what selection was applied, and what features are important. For example, “Invariant mass distribution of selected events after all cuts, with a Gaussian plus linear background fit in the range 80 to 100 GeV.”

Discuss each figure in the text. Do not just insert plots without explanation. Describe the main features: the peak position, the width, the background shape, or any unexpected structures.

When you quote fit parameters, present them with uncertainties. For example,

$$
\mu = (91.3 \pm 0.2)\,\text{GeV}, \qquad \sigma = (2.4 \pm 0.3)\,\text{GeV}.
$$

If possible, group related results in a table, especially if you have several bins, categories, or comparative measurements:

If you compared different datasets or different selection cuts, show both sets of results and comment on the differences. For example, comparing efficiencies when tightening a cut, or comparing a data histogram to a simulation with normalization.

Include, where relevant, simple numerical summaries such as the mean, RMS, or maximum of a distribution. Explain briefly whether these values are consistent with expectations.

Uncertainties and Interpretation

You have already encountered statistical uncertainties in earlier parts of the course, for example from histogram bin errors or fit parameter uncertainties. In the report you should briefly explain how you treat uncertainties and how they affect your conclusions.

Begin with statistical uncertainties. State that they arise from the finite number of events and that they are estimated by ROOT from counting statistics or from fits. For counting measurements where you count $N$ independent events, you can write that the statistical uncertainty is
$$
\sigma_N = \sqrt{N}.
$$

If you compute an efficiency $\epsilon = N_{\text{sel}} / N_{\text{tot}}$, you can mention that the statistical uncertainty can be approximated as
$$
\sigma_\epsilon = \sqrt{\frac{\epsilon (1 - \epsilon)}{N_{\text{tot}}}},
$$
and explain that you used this expression or ROOT tools to estimate it.

When you quote fit parameter uncertainties, explain briefly that they correspond to one standard deviation estimates from the fit, which are associated with a certain confidence level under standard assumptions.

If your project includes obvious sources of systematic uncertainty, describe them qualitatively even if you do not compute them precisely. Examples include the choice of fit range, the form of the background model, the binning of histograms, or small shifts in calibration constants.

You can illustrate the impact of a systematic effect by repeating a key result under slightly different conditions, such as changing a fit range or tightening a cut, and then comparing the outputs.

Finally, interpret your main results in physical terms. For example, say whether a measured parameter agrees with a known reference value within uncertainties, or whether the shape of a distribution matches the expected model. Make sure the interpretation is consistent with the level of precision and limitations of your dataset.

Figures, Tables, and ROOT Outputs

Because your project uses ROOT, you will have many plots and numeric outputs. In the report, use them selectively and organize them clearly.

For figures:

Export plots from ROOT in a vector format such as PDF or SVG for best quality. If not available, PNG with sufficient resolution is acceptable for this course.
Make sure axis titles, labels, and legends are readable and accurate before exporting.
Include units in axis titles, for example “Energy [MeV]” or “Time [ns].”
Keep the style consistent across figures. Use similar fonts, line widths, and colors.

For tables:

Use tables for compact presentation of numerical results, cut flows, or comparison of variants.
Label each table and refer to it in the text.

You might include a small “cut flow” table that shows how many events remain after each selection step:

If you want to show example ROOT commands or short macros, you can place them in an appendix so that the main text remains focused on physics and results.

Conclusions

End the report with a concise conclusion section that answers the questions you posed in the introduction. Summarize:

What you measured or determined.
The main numerical results with uncertainties.
Whether the results are consistent with expectations or reference values.
What you learned about using ROOT and the analysis technique.

You can also mention possible improvements or extensions, such as using more data, refining the selection, improving the background model, or including additional observables.

Keep this section focused and brief. The reader should finish it with a clear understanding of what was achieved and how reliable the result is.

Keeping the Report Reproducible

Although the report itself is short, it should be possible in principle for someone else to reproduce your results from your description and your ROOT code.

You can help reproducibility by:

Clearly describing the input data and selection cuts.
Explicitly stating formulas and fit functions.
Referring to your main macro or script names, for example “analysis.C” or “analysis.py.”
Keeping your version of ROOT and key settings recorded in a short note or footnote.

If you use version control for your macros, mention this briefly, for example that the analysis code is kept in a Git repository with a particular tag that corresponds to the final results.

Even for a student project, treating your analysis as something that another person could repeat is a valuable habit and prepares you for larger scientific collaborations later.

With these elements, your short analysis report will not only show that you can use ROOT, but also that you can present scientific results in a clear, structured, and professional way.

Views: 13