Lesson 02: The Abstract Formula

The abstract is the most-read part of your paper. Most readers will never get past it. Editors and referees will form their first impression from it. And yet it is almost always written last, in a hurry, after the authors are exhausted from finishing the paper.

This lesson gives you a template that forces the abstract to say exactly what it needs to say, no more, no less, in four to five sentences.

What the abstract must do

A physics abstract has one job: communicate the result clearly enough that a reader can decide whether to read the full paper.

It is not a summary of each section. It is not a list of "we also compute..." additions. It is a self-contained statement of the physical question, the approach, the quantitative result, and why it matters.

No citations in the abstract

Do not include in-text citations in the abstract. None of the HEP papers you will encounter in this subfield do. If you must attribute something, name the experiment or result in words: "using IceCube data" rather than "[12]".

The four-sentence structure

Every abstract follows the same four-sentence structure, with one optional fifth sentence:

Sentence 1: Setting and motivation Establish the physical system and the opportunity it offers. This sentence should stand alone and make sense to any physicist in a related field.

"Next-generation neutrino detectors will observe cosmic-ray induced atmospheric neutrinos with unprecedented precision."

Sentence 2 (and optional 2b): What we do Name the method, the systems studied, and the scope. Begin with "We...".

"We investigate the capabilities of Hyper-Kamiokande to measure the CR energy spectrum using the atmospheric neutrino flux."

Sentence 3: Main quantitative result A specific number or comparison. Not vague. Not "significant improvement". If you cannot write a number here, you do not yet know what your main result is.

"We demonstrate that Hyper-K reduces the flux uncertainty from ~20% to ~7% at 1 GeV, improving the sin²θ₂₃ sensitivity by 50--73% relative to current measurements."

Sentence 4: Broader implication One sentence on why this matters: what complementary probe it provides, what it opens up, or why the community should care.

"Our results highlight that CR spectrum measurements at large neutrino detectors are a valuable and largely untapped tool for precision oscillation physics."

What to avoid

The abstract is not a table of contents. Do not write "In Section II, we derive... In Section III, we show... We conclude in Section IV." That belongs in the introduction's optional paper-structure paragraph, not here.

Do not use vague language where you have a number. "significant sensitivity" is meaningless. "sensitivity reaching σ ~ 10⁻⁴² cm² at mχ ~ 0.1 MeV" is not.

Do not hedge the main result. If the result is real, state it. "We find..." and "We demonstrate..." are appropriate. "We tentatively suggest that it might be possible to..." is not.

Do not exceed five sentences. If you have more, you are summarising sections, not stating your result.

How to write it

Write the abstract last, but write a draft placeholder first.

Before you start writing the paper, write a one-sentence version of Sentence 3: "The main result of this paper is [X] at [Y]." Keep that sentence visible as you write. Every section should be building toward it.

Once the paper is finished:

  1. Write Sentence 3 first: the quantitative result. If you cannot write it, stop and figure out what your number is.
  2. Write Sentence 2: what you did to get that result.
  3. Write Sentence 1: what physical system makes this interesting.
  4. Write Sentence 4: one implication.
  5. Trim to ≤ 5 sentences total and check for vague language.

Read it out loud

If Sentence 3 does not make you want to read the paper, it is not specific enough. The quantitative result should be striking enough to stand on its own.

Worked example

Below is the abstract of arXiv:2512.18093 annotated to show which sentence does which job.

Ultra-high energy cosmic rays (UHECRs) present a unique multi-messenger probe of new physics. [Setting and motivation] We compute new constraints on the dark matter–nucleon cross section from the survival of UHECRs accelerated in the NGC 1068 active galactic nucleus, modelling both NFW and spike dark matter profiles. [What we do] We demonstrate that the UHECR data exclude σχp ≳ 10⁻³³ (mχ/GeV) cm², three orders of magnitude below current direct-detection limits in the GeV mass range. [Main quantitative result] Our results open a new multi-messenger avenue for probing DM–nucleon interactions at cross sections inaccessible to terrestrial experiments. [Broader implication]

Four sentences. One number. No section summary. No citations.

For comparison, arXiv:2410.00330 follows the same template:

Solar neutrinos from the ⁸B chain provide a sensitive probe of both solar physics and weak interactions. [Setting] We study the prospect of measuring the total active ⁸B solar neutrino flux at DUNE via neutral-current interactions on argon, including a detailed background analysis. [What we do] We find that DUNE can determine the total flux to X% in Y years of operation, independent of neutrino flavor. [Main result] This measurement complements the charged-current solar neutrino programme and provides a flavour-independent cross-check of the solar model. [Implication]

Lesson 03 covers voice, paragraph structure, and the sentence-level conventions that apply throughout the full paper.