⚛️ phenomenology

Towards power corrections in the factorization of baryon quasi-distribution amplitudes in LaMET

This paper presents the first systematic analysis of power corrections in the factorization of leading-twist baryon quasi-distribution amplitudes, deriving an exact closed-form relation that resums target-mass corrections to all orders and explicitly constructing next-to-leading-twist operators to quantify these effects for future lattice QCD determinations.

Original authors: Yu-Ji Shi, Jun Zeng

Published 2026-09-01

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CC BY 4.0

Original authors: Yu-Ji Shi, Jun Zeng

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Inside every proton, neutron, and heavier cousin like the Lambda baryon, a complex world of quarks and gluons churns. These particles are not static beads but dynamic clouds of energy, bound together by the strong force. To understand how these particles behave in high-energy collisions or how they decay, physicists need a precise map of how the quarks share the particle's momentum. This map is called a light-cone distribution amplitude. It describes the probability of finding a quark carrying a specific fraction of the total speed of the particle. While scientists have long understood how to map these distributions for simpler particles like mesons, the task becomes significantly harder for baryons, which are made of three quarks. The internal structure of these three-particle systems is far more intricate, involving complex spin and flavor symmetries that have made them difficult to pin down from first principles.

For decades, researchers relied on theoretical models and approximations to guess the shape of these maps. However, a modern framework known as Large-Momentum Effective Theory, or LaMET, has opened a new door. This approach allows scientists to use supercomputers to simulate the strong force directly, calculating a "quasi-distribution" from a boosted particle and then mathematically translating it into the physical map they seek. The challenge is that these computer simulations are never perfect. They are performed with particles moving at finite speeds, and the mass of the particle itself introduces distortions that blur the picture. These distortions, known as target-mass corrections, become especially problematic for heavy baryons, where the particle's mass is comparable to the momentum used in the simulation. Without a way to remove these distortions, the final map remains fuzzy, limiting the precision of predictions for rare particle decays and fundamental tests of the universe's laws.

In this work, researchers have taken a decisive step toward clearing that fog. They have derived the first exact, all-encompassing formula that connects the distorted quasi-distribution calculated on the computer to the true physical distribution. Previous methods could only estimate these corrections order by order, like peeling an onion one layer at a time, which was insufficient for high-precision work. The new derivation provides a complete, closed-form relationship that accounts for the particle's mass effects all at once, regardless of how large the mass is relative to the momentum. This result is not just a theoretical curiosity; it offers a concrete recipe for lattice QCD practitioners to subtract these mass-induced errors from their data before attempting to extract the final physical distribution. By applying this formula, scientists can now isolate the true shape of the baryon's internal structure with much greater confidence.

The team demonstrated the power of this new method by applying it to the Lambda baryon, a particle containing a strange quark. Using existing data from lattice simulations, they numerically assessed how much the target-mass correction altered the distribution. They found that as the momentum of the baryon increases, the correction drops off rapidly. In the regions where the quarks carry very little or very much of the momentum, the correction is almost negligible. However, in the middle range, the effect is significant enough that ignoring it would skew the results. The study confirms that by explicitly removing these mass effects using their new formula, the remaining data can be extrapolated to the infinite momentum limit with a much tighter grip on systematic errors. This is particularly crucial for heavy baryons, where the mass is large and the corrections would otherwise dominate the signal.

Beyond the immediate application to the Lambda baryon, the framework developed here is robust enough to handle other complex scenarios. The researchers showed that the same mathematical structure applies to heavy baryons containing charm or bottom quarks, which are vital for studying CP violation and the matter-antimatter asymmetry of the universe. They also extended the logic to include transverse momentum, a dimension that describes how quarks move sideways within the particle, proving that the mass corrections behave consistently even in these more detailed distributions. Furthermore, the team explicitly constructed the operators that represent the next level of complexity, known as higher-twist contributions. While these are not yet directly calculable on current lattices, identifying them allows future simulations to account for them systematically, ensuring that the final maps of baryon structure are as complete as possible.

The implications of this work extend to the interpretation of experimental data from facilities like the Large Hadron Collider. Precise knowledge of baryon distribution amplitudes is essential for predicting the rates of rare decays, such as the decay of a bottom Lambda baryon into a Lambda baryon and two kaons. Recent observations of CP violation in these decays have highlighted the need for equally precise theoretical inputs. By providing a method to strip away the artificial distortions caused by finite momentum in computer simulations, this research paves the way for more accurate theoretical predictions. It transforms the extraction of baryon structure from a process of statistical guessing into a controlled, systematic procedure. As lattice simulations continue to improve in power and precision, this new tool will ensure that the resulting maps of the subatomic world are clear, reliable, and ready to test the deepest questions of particle physics.

Technical Summary: Towards Power Corrections in the Factorization of Baryon Quasi-Distribution Amplitudes in LaMET

Problem Statement
Light-cone distribution amplitudes (LCDAs) are fundamental non-perturbative inputs for precision phenomenological studies of hard exclusive processes, particularly in heavy-baryon decays where they determine decay amplitudes and CP asymmetries. While Large-Momentum Effective Theory (LaMET) offers a systematic framework to extract these LCDAs from lattice QCD via quasi-distribution amplitudes (quasi-DAs), current extractions face systematic uncertainties. Specifically, the factorization of quasi-DAs involves power-suppressed corrections of order $O(m^2/P_z^2)$ (target-mass corrections) and $O(\Lambda_{QCD}^2/P_z^2)$ (higher-twist corrections). In existing lattice calculations for baryons (such as the $\Lambda$ and heavy $\Lambda_Q$ ), these target-mass corrections are often not explicitly subtracted but rather absorbed into statistical extrapolations. Given that accessible lattice momenta $P_z$ are limited (typically a few GeV) and comparable to the masses of heavy baryons, these corrections are non-negligible. A rigorous, closed-form relation that resums target-mass corrections to all orders is required to isolate and subtract these effects before extrapolating to the physical LCDA.

Methodology
The authors develop a systematic analysis of power corrections for leading-twist baryon quasi-DAs using the following steps:

Local Operator Expansion: The authors define the baryon LCDA and quasi-DA via gauge-invariant, nonlocal three-quark operators. They perform a local operator expansion (Taylor expansion) of these nonlocal operators around the origin, expressing them in terms of local operators involving covariant derivatives.
Moment Relations: By comparing the coefficients of the Taylor expansions, the authors establish a moment relation between the moments of the quasi-DA ( $\tilde{M}_{n_1, n_2}$ ) and the LCDA ( $M_{n_1, n_2}$ ). This relation is derived by projecting the local operators onto the light-cone direction (for LCDA) and the spatial direction (for quasi-DA).
Target-Mass Resummation: The ratio of these moments is calculated exactly, accounting for the finite baryon mass $m_\Lambda$ and the non-zero square of the spatial vector ( $\lambda^2 = -1$ ). This leads to a closed-form expression for the moment ratio $K_N$ that resums target-mass corrections to all orders in $m_\Lambda^2/P_z^2$ .
Inverse Mellin Transformation: The moment relation is inverted using the Mellin transform to derive an exact, closed-form algebraic relation between the quasi-DA $\tilde{\phi}(x_1, x_2; P_z)$ and the LCDA $\phi(x_1, x_2)$ .
Higher-Twist Construction: The authors explicitly construct the next-to-leading-twist (NLT) operators arising from the trace part of the nonlocal quasi-DA operator, which are responsible for the $O(\Lambda_{QCD}^2/P_z^2)$ corrections.
Extension to TMDs: The formalism is extended to quasi-transverse-momentum-dependent distributions (quasi-TMDs) to demonstrate the universality of the target-mass correction structure.

Key Contributions and Results

Exact Closed-Form Relation: The paper derives the first exact closed-form relation (Eq. 2.29) connecting the leading-twist baryon quasi-DA to the LCDA. This relation resums target-mass corrections to all orders in $m_\Lambda^2/P_z^2$ . The relation is given by:
$\tilde{\phi}(x_1, x_2; P_z) = \frac{1}{\sqrt{1+4c}} \left[ \phi\left(\frac{2x_1}{f_+}, \frac{2x_2}{f_+}\right) - \phi\left(\frac{-2x_1}{f_-}, \frac{-2x_2}{f_-}\right) \right]$
where $c = m_\Lambda^2/(4P_z^2)$ and $f_\pm$ are functions of the kinematic variables.
Inverse Relation for Subtraction: An inverse relation (Eq. 2.34) is provided, allowing the physical LCDA to be expressed as a series expansion of the quasi-DA. This enables the explicit subtraction of target-mass effects from lattice data before performing the large-momentum extrapolation.
Universality: The derived moment ratio and resummation formula are shown to be identical to those for nucleon parton distribution functions (PDFs) and meson distribution amplitudes (DAs), despite the baryon operator involving two distinct quark coordinates. The authors demonstrate that this method applies equally to heavy baryons ( $\Lambda_Q$ ) and quasi-TMDs.
Numerical Assessment: Using existing lattice data for the $\Lambda$ baryon, the authors numerically assess the magnitude of the target-mass correction. They find that the target-mass correction decreases rapidly with increasing baryon momentum and is almost negligible in the endpoint regions.
NLT Operator Construction: The authors explicitly construct the NLT operators (Eq. 3.4) that enter the quasi-DA factorization, identifying them as arising from the trace part of the nonlocal operator.

Significance
The authors claim this work represents the first systematic analysis of power corrections for leading-twist baryon quasi-DAs. The primary significance lies in providing a controlled procedure to subtract target-mass corrections from lattice quasi-DA data. By removing these corrections explicitly via the derived closed-form relation, the systematic uncertainty in the extraction of baryon LCDAs is reduced. This is particularly crucial for heavy baryons, where the mass is comparable to the accessible lattice momenta, rendering standard extrapolation methods less reliable. The results serve as a foundational step toward quantifying power corrections in future lattice determinations of both light and heavy baryon LCDAs, thereby improving the precision of theoretical predictions for heavy-baryon decays and CP violation studies.

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