24.6 Create Histograms

Planning Your Histograms

In the final project you already loaded the dataset and explored its structure, so at this stage you should know which physical quantities and event-level variables are available. Before creating any ROOT objects, decide what you want to visualize and why. Each histogram you create must be tied to a clear physics or analysis question, such as understanding the energy response of a detector, checking the distribution of a timing variable, or visualizing an invariant mass peak.

Start by listing the key observables that are central to your project goals. For a typical particle or nuclear physics dataset this might include energies, momenta, angles, hit multiplicities, or calibrated quantities derived from raw measurements. For each observable decide whether you need a one-dimensional distribution, a two-dimensional correlation plot, or both. One-dimensional histograms are usually the first step, since they show the basic shape, range, and possible outliers of each variable. Two-dimensional histograms and profiles become useful once you want to study correlations, such as energy versus angle, or a detector response as a function of position.

At this stage also think about the selection cuts you will later apply. It is common to create both inclusive histograms with minimal cuts to see the full raw distribution, and more selective histograms that focus on signal regions or specific detector conditions. For example, you might plan one energy spectrum with only basic data-quality cuts, and a second one restricted to events in a narrow timing window that is expected to isolate a particular particle species. Planning both versions early will make your later comparisons more systematic.

Finally, make a simple naming and file structure plan for your histograms. Choose a consistent prefix or pattern for related histograms, and think ahead about which ones must be saved to the final ROOT file for later plotting, fitting, or sharing with collaborators. This planning reduces confusion as the number of histograms grows.

Choosing Binning, Ranges, and Types

The choice of binning is one of the most important technical decisions you will make for this project, because it affects both the visibility of structures and the numerical content of each bin. In ROOT you specify a one-dimensional histogram with a number of bins, a minimum, and a maximum, for example with a TH1F object. Your choice should be driven by the physics scale and by the typical statistical uncertainties.

A good way to start is to identify the natural units and rough dynamic range for each variable. If you are plotting an energy between 0 and 5 GeV and your detector resolution is of order tens of MeV, then using thousands of extremely narrow bins is rarely helpful. The bin width should be smaller than the physical resolution so that peaks are not excessively washed out, but not so small that most bins are empty or contain only a few entries. As a rule of thumb, aim for each populated bin to have enough entries that Poisson fluctuations do not dominate the plot, especially for distributions you plan to fit.

You will often iterate on the binning after seeing a first plot. In the context of the final project, it is acceptable to generate trial histograms with a coarse binning to get an overview, then refine the binning once you identify the regions of interest. For example, you might begin with 100 bins over the full range, then create a second histogram focused around a narrow mass peak with much finer bins to resolve the shape.

Choosing the histogram class is also important for numerical precision. TH1F stores bin contents as floating point numbers with single precision, while TH1D uses double precision. For many student projects TH1F is adequate for energies, positions, and counts, but if your dataset is large or you perform many scaling operations, using TH1D can provide better numerical stability. In any case, remain consistent across related histograms so that later combination or comparison is straightforward.

The range of the histogram must cover the physically allowed values, but you should also be aware of underflow and overflow bins. If you expect a small fraction of events to lie far from the main region, such as extreme noise or saturated measurements, decide whether you want to include them in the main range, or let them accumulate in the underflow or overflow for monitoring. In this project it is often useful to set a main range that focuses on the physically meaningful region, then later inspect the underflow and overflow contents as a quality check.

Finally, think about two-dimensional histograms when you want to study correlations between two quantities in more detail than a scatter plot. In ROOT you can use TH2F or TH2D with separate binning definitions for the X and Y axes. Choose binning so that both dimensions have enough resolution to reveal structure, but not so fine that each cell is nearly empty. For smooth trends a TProfile may be a better choice than a full two-dimensional histogram, but the choice depends on your project goals and will be guided by what you discovered in the earlier exploration chapter.

Filling Histograms from Your Data

Once histogram objects are defined, the central task is to fill them with your dataset. In the final project you are expected to use ROOT mechanisms appropriate to how your data are stored, typically a TTree-based ROOT file or a data structure created in earlier project steps. The detailed syntax for TTrees is covered elsewhere in the course, so here you should focus on designing a clear and reproducible filling strategy that implements your event selection and physics logic.

For a TTree-based analysis the standard workflow is to create your histograms before entering the event loop, then iterate over all entries, apply your selection criteria, and call the Fill method for each variable you wish to record. You will usually create one histogram per observable and per category of interest, such as one energy spectrum for all events, and another spectrum for events passing a tighter cut. Inside the loop, when an event passes your selection, you read the needed variables from the tree branches and fill each corresponding histogram.

When your analysis requires two-dimensional distributions, you apply the same event selection and then call the two-dimensional Fill method with both the X and Y values. For example, if you want to study detector energy response as a function of angle, for each selected event you would read the reconstructed energy and the polar angle and fill a TH2 object with those two values. It is good practice to think in terms of which histograms will share the same event selection so that later comparisons are meaningful.

If you are using RDataFrame in your project, you can define histograms in a more declarative way, specifying the column to plot and the binning, then triggering the event loop when you access the result. In this case the logic is similar but expressed through Filter and Histo* calls instead of manual loops. Regardless of the technical method, the conceptual requirement is the same: you must have a clear mapping from physics questions to which events and which quantities are used to fill each histogram.

In many analyses you will also want to fill separate histograms for different subsets of the data, such as signal-like and background-like regions, or events taken under different detector configurations. The simplest approach is to create separate histogram objects with names that encode the selection, and then use conditional statements in your event loop that decide which ones to fill. For instance, if an event falls into a background control region, you fill the background histogram rather than the signal one. This approach will later allow you to compare shapes directly and perform operations like background subtraction.

Finally, be aware of statistical uncertainties while filling. If your analysis uses event weights, you should supply those weights to Fill so that each entry contributes correctly according to its weight, not only as a simple count. In such cases you must also ensure that the histogram is configured to track the squared sum of weights so that bin errors correctly reflect the weighted statistics. That aspect will be particularly important in the later stages of the project where you compare distributions or perform fits.

Checking and Saving Your Histograms

After you have filled your histograms, take time to inspect them carefully before proceeding to the fitting and interpretation stages of the project. Begin by drawing each important histogram on a canvas and examining the overall shape, the position of peaks or structures, and any unexpected features such as long tails, spikes, or sharp cut-offs. Compare what you see with the expectations formed during the dataset exploration phase. If a variable was supposed to be positive but you observe negative values, or if a mass distribution appears shifted from where theory predicts, this is an early sign of a possible bug in your selection, calibration, or filling logic.

Quantitative checks are as important as visual ones. For key histograms, read the number of entries, mean, and RMS, and compare these with simple estimates. If you expect a few hundred thousand events after selection but the histogram contains far fewer or many more entries than anticipated, revisit your selection cuts and loop structure. Pay attention to underflow and overflow contents, since a large number of entries outside the nominal range often indicates that your chosen range is too narrow or that the variable has unexpected extreme values.

Once you are satisfied that your histograms reflect the data correctly, you should save them in a well-structured ROOT file so they can be used later in the project for fitting and for producing final figures. Typically you will open or create a TFile in write or recreate mode at the end of your analysis macro or script, write each histogram object into the file, and then close the file properly. Organize histograms into directories inside the file if appropriate, for example by grouping them according to physics topic or event category, so that navigation remains manageable as the number of objects grows.

It is also good practice to save at least some diagnostic plots in standard image formats such as PNG or PDF for quick reference. Even if you will remake publication-quality figures later, having early versions captured helps you track the evolution of your analysis, and can be useful for debugging regressions if code changes alter the shapes of distributions. For this project you may choose a small set of representative histograms that illustrate the main physics features and save them as images at this stage.

Finally, document your work as you go. Write down which histograms you created, their binning and ranges, and the selection criteria used when filling them. This information will be essential in the later project chapters where you perform fits, estimate uncertainties, and build final plots. It also supports reproducibility, since another person should be able to reproduce your histograms using your description and code alone.

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