Les Houches 2023 -- Physics at TeV Colliders: Report on the Standard Model Precision Wishlist

This report reviews recent progress in fixed-order computations, essential ingredients like parton distribution functions and subtraction methods, and identifies necessary higher-order corrections for Standard Model processes to match anticipated LHC experimental precision, continuing the biennial Les Houches tradition.

The Gist

Imagine the Large Hadron Collider (LHC) as the world's most powerful, high-speed camera. It takes billions of pictures of particles smashing into each other every second. Physicists are trying to figure out if the "Standard Model"—the rulebook of how the universe works at a tiny scale—is perfect, or if there are cracks in the foundation that hint at new, mysterious physics.

To do this, they need two things to match perfectly:

1. The Photographs: The actual data from the LHC experiments (which are getting sharper and clearer every year).
2. The Blueprint: The theoretical calculations that predict exactly what the camera should see if the rulebook is correct.

This paper is a "Wishlist" for the people who draw the Blueprints. It was written by a team of theoretical physicists who met at a famous workshop in Les Houches, France. They are saying, "Our experimental friends are taking incredibly precise photos now. To make sure we aren't missing anything, we need to upgrade our Blueprints to match that precision."

Here is a breakdown of what they are asking for, using some everyday analogies:

1. The "Blurry Photo" Problem (Higher-Order Corrections)

Imagine you are trying to predict the path of a car driving down a bumpy road.

• The Old Way (Leading Order): You draw a straight line. It's close, but it misses all the bumps.
• The Better Way (NLO/NNLO): You add the bumps. Now it's pretty good.
• The Wishlist Way (N3LO and beyond): The road is actually covered in tiny pebbles, wind gusts, and temperature changes. The experimental photos are so sharp they can see those pebbles. The theorists need to calculate the effect of every single pebble to match the photo.

The paper lists hundreds of specific particle collisions (like making a Higgs boson, a top quark, or a pair of W bosons) and says, "We have calculated the bumps, but we need to calculate the pebbles and the wind gusts too."

2. The "Recipe Book" (Parton Distribution Functions)

To predict what happens when two protons smash together, you need to know what's inside the proton. A proton isn't a solid ball; it's a bag of smaller particles called quarks and gluons (like a bag of marbles).

• The Analogy: Imagine trying to bake a cake, but you don't know exactly how much flour or sugar is in the bag you bought. You have to guess.
• The Problem: If your guess is slightly off, your cake (the prediction) won't taste right.
• The Wishlist: The authors are asking for a more precise "recipe" (PDFs) that accounts for the fact that the bag of marbles changes depending on how hard you squeeze it. They need to know the exact mix of ingredients to predict the collision perfectly.

3. The "Subtraction" Puzzle (Infrared Subtraction)

When particles collide, they sometimes spit out extra, invisible "ghost" particles (soft radiation) that are hard to detect but mess up the math.

• The Analogy: Imagine trying to weigh a feather on a scale that is also being blown by a fan. The fan (the extra particles) makes the scale wobble.
• The Solution: You need a special mathematical "fan-remover" (subtraction method) to cancel out the wobble so you can see the true weight of the feather.
• The Wishlist: For simple collisions, we have a good fan-remover. But for complex collisions with many particles flying out, the fan-remover breaks. The paper asks for new, more robust fan-removers that work for the most chaotic collisions.

4. The "Higgs Boson" (The Star of the Show)

The Higgs boson is the particle that gives other particles mass. It's the most important character in the story.

• The Wishlist: They want to know everything about the Higgs.
  • How often does it appear?
  • How does it decay (fall apart)?
  • What happens when it appears with other particles (like a top quark or a jet of particles)?
  • The Goal: If the experimental photo shows the Higgs behaving slightly differently than the Blueprint predicts, it might mean there is a "New Physics" character hiding in the background. But we can only find that new character if our Blueprint is perfect.

5. The "Top Quark" (The Heavyweight)

The top quark is the heaviest known particle. It's like the heavyweight champion of the particle world.

• The Wishlist: Because it's so heavy, it interacts strongly with the Higgs. The paper asks for ultra-precise calculations of top quark collisions. If we get these calculations right, we can use the top quark as a magnifying glass to look for cracks in the Standard Model.

Why Does This Matter?

Think of the Standard Model as a map of a city.

• Ten years ago: The map was good enough to get you from Point A to Point B.
• Today: The experimentalists have GPS satellites that can tell you your location within a millimeter.
• The Problem: If the map says "Turn left at the bakery," but the GPS says "You are actually 5 meters to the right of the bakery," you have a problem. Is the bakery moved? Is the GPS broken? Or is there a secret tunnel we didn't know about?

This paper is the team of cartographers saying: "We need to redraw the map with millimeter precision. If we do that, and the GPS still doesn't match, then we know for sure we've discovered a secret tunnel (New Physics)."

Summary

This document is a to-do list for the world's smartest mathematicians. They are telling the experimentalists: "Keep taking those amazing photos! We are working hard to make our calculations just as sharp. Once we match the precision of your photos, we will finally be able to see if the universe is playing by the rules we think it is, or if it's hiding a surprise."

Technical Summary

Technical Summary: Les Houches 2023 - Report on the Standard Model Precision Wishlist

1. Problem Statement
The Large Hadron Collider (LHC) and its future High-Luminosity (HL-LHC) upgrade are generating experimental data with unprecedented precision. To fully exploit this data for testing the Standard Model (SM) and searching for New Physics, theoretical predictions must match this experimental accuracy. A significant gap exists between the precision of experimental measurements (often reaching the few-percent level) and the available fixed-order theoretical calculations for many complex processes. This report addresses the need to systematically identify these gaps, review recent progress in fixed-order computations (specifically NNLO and N3LO), and outline the "wishlist" of calculations required to achieve theoretical uncertainties commensurate with future experimental capabilities.

2. Methodology
The report adopts a structured review approach, building upon the previous 2021 Les Houches wishlist. The methodology involves:

• Categorization: Processes are grouped into four main categories: Higgs boson associated processes, Jet final states, Vector-boson associated processes, and Top-quark associated processes.
• State-of-the-Art Assessment: For each process, the authors summarize the current theoretical status (e.g., LO, NLO, NNLO, N3LO) regarding QCD and Electroweak (EW) corrections, including mixed QCD-EW corrections.
• Technique Review: The report details the underlying computational techniques enabling these advances, including:
  • Parton Distribution Functions (PDFs): Review of global fits (CT18, MSHT20, NNPDF4.0) and the transition toward approximate N3LO PDFs.
  • Amplitude & Loop Techniques: Advances in integration-by-parts (IBP) reduction, finite field methods, and the calculation of multi-loop amplitudes (e.g., 2-loop 5-point amplitudes, 3-loop 2→2 amplitudes).
  • Subtraction Methods: Evaluation of infrared subtraction schemes (Antenna, Sector-improved residue, $q_T$-subtraction, N-jettiness) required for differential cross-sections at NNLO and N3LO.
• Gap Analysis: For each process, the authors identify missing higher-order corrections (e.g., missing N3LO QCD, missing NLO EW, or missing mixed QCD-EW) and specific ingredients (like massive quark effects or off-shell descriptions) needed to reduce theoretical uncertainties.

3. Key Contributions
The report provides a comprehensive roadmap for the theoretical community, highlighting specific achievements and remaining challenges:

• Advancements in Fixed-Order Calculations:

  • Higgs Boson: Confirmation of N3LO QCD results for inclusive gluon-fusion production ($gg \to H$) and significant progress in differential distributions. The report highlights the need for full N3LO differential results and better treatment of finite top/bottom mass effects.
  • Drell-Yan ($V$): Achievement of N3LO QCD accuracy for inclusive $W$ and $Z$ production, including mixed QCD-EW corrections.
  • Jet Production: Completion of NNLO QCD for dijet production and the first NNLO calculations for $2 \to 3$processes (e.g.,$H+j$,$V+j$) without leading-color approximations.
  • Top Quarks: Completion of fully differential NNLO QCD for $t\bar{t}$ production and significant steps toward N3LO (e.g., top decay width at N3LO).

• Electroweak and Mixed Corrections:

  • Emphasis on the necessity of including NLO EW corrections and mixed QCD-EW corrections ($O(\alpha_s \alpha)$) for high-precision observables, particularly in the tails of distributions and for processes involving massive gauge bosons.
  • Progress in automated tools for NLO EW calculations (e.g., OpenLoops, RECOLA, MadLoop).

• PDF and Luminosity Updates:

  • Discussion of the PDF4LHC21 combination and the development of approximate N3LO PDFs (MSHT20xNNPDF40).
  • Identification of tensions between different PDF sets in the gluon distribution at N3LO, necessitating further benchmarking.

• Specific Wishlist Items (Selected):

  • Higgs: Full N3LO differential predictions for $H+j$ and $H+2j$; NNLO QCD for $t\bar{t}H$; N3LO for $t\bar{t}$.
  • Vector Bosons: Full NLO QCD for loop-induced $gg \to ZZ$ and $gg \to WW$; NNLO for $V+2j$ and $V+b\bar{b}$.
  • Top Quarks: NNLO for $t\bar{t}+j$ and $t\bar{t}+b\bar{b}$; full off-shell NLO/NNLO for $t\bar{t}V$ and $t\bar{t}t\bar{t}$.

4. Results

• Current Status: The field has moved from an "industrial" production of NNLO results for $2 \to 2$processes to tackling complex$2 \to 3$and$2 \to 4$processes. However, a saturation point was reached due to the unavailability of 2-loop amplitudes for higher multiplicities, which has recently been broken by the first hadron collider$2 \to 3$ NNLO results.
• Uncertainty Reduction: The inclusion of higher-order corrections (e.g., N3LO for Drell-Yan, NNLO for $t\bar{t}$) has significantly reduced scale uncertainties, often bringing them below the percent level.
• Experimental vs. Theoretical Mismatch: For many processes (e.g., $t\bar{t}H$, $V+j$, $HH$), the experimental uncertainty is projected to drop below the current theoretical uncertainty (often dominated by missing higher orders) by the HL-LHC era.
• Technical Bottlenecks: The primary bottlenecks identified are the calculation of multi-loop amplitudes with massive particles, the complexity of infrared subtraction for high-multiplicity final states, and the computational cost of generating differential predictions for global PDF fits at N3LO.

5. Significance
This report serves as a critical strategic document for the high-energy physics community:

• Guidance for Theory: It directs theoretical efforts toward the most impactful calculations, prioritizing processes where experimental precision is highest or where New Physics sensitivity is greatest (e.g., Higgs self-coupling via $HH$ production, top mass extraction via $t\bar{t}$).
• Enabling Precision Physics: By identifying the missing ingredients (e.g., specific loop amplitudes, subtraction methods), it accelerates the development of tools necessary to interpret HL-LHC data.
• Bridging Experiment and Theory: It highlights the interplay between theoretical predictions and experimental analyses, such as the need for specific jet algorithms (flavor-tagging) and the treatment of fiducial cuts to avoid linear power corrections that destabilize perturbative convergence.
• Foundation for Future Colliders: The methodologies and precision targets established here lay the groundwork for physics at future colliders (FCC, CEPC, ILC), where theoretical precision will be even more stringent.

In summary, the paper confirms that while the "Standard Model Precision Wishlist" has seen substantial progress since 2021, significant work remains to reach the theoretical precision required to fully exploit the HL-LHC dataset and probe the limits of the Standard Model.