Related Experiment Video
Updated: Dec 22, 2025
07:46
Setting Limits on Supersymmetry Using Simplified Models
Published on: November 15, 2013
8.9K
All-Order Amplitudes at any Multiplicity in the Multi-Regge Limit.
V Del Duca1,2, S Druc3, J M Drummond3
1Institute for Theoretical Physics, ETH Zürich, 8093 Zürich, Switzerland.
Physical Review Letters
|May 9, 2020
Summary
We developed a new formula for scattering amplitudes in planar N=4 super Yang-Mills theory. This formula works for all particle numbers and configurations in multi-Regge kinematics, offering broad applicability in theoretical physics research.
Area of Science:
- High-energy physics
- Quantum field theory
- String theory
Background:
- Planar N=4 super Yang-Mills theory is a key model in quantum field theory, exhibiting rich mathematical structures.
- Understanding scattering amplitudes is crucial for predicting particle interactions and testing fundamental theories.
- Multi-Regge kinematics simplifies complex scattering processes by focusing on high-energy, small-angle interactions.
Purpose of the Study:
- To derive an all-loop expression for scattering amplitudes in planar N=4 super Yang-Mills theory.
- To ensure the expression is valid for all multiplicities, helicity configurations, and arbitrary logarithmic accuracy within multi-Regge kinematics.
- To leverage the integrable structure of related collinear limits and advance understanding of theoretical physics.
Main Methods:
- Comparing explicit perturbative results with expectations from the integrable structure of a collinear limit.
- Developing an all-order extension for the central emission vertex, previously computed at next-to-leading logarithmic accuracy.
- Applying the derived all-order formula to analyze the properties of scattering amplitudes.
Main Results:
- An all-loop expression for scattering amplitudes in planar N=4 super Yang-Mills theory in multi-Regge kinematics was successfully proposed.
- The expression is valid for all multiplicities, helicity configurations, and arbitrary logarithmic accuracy.
- It was proven that all amplitudes in this theory under multi-Regge kinematics are single-valued multiple polylogarithms of uniform transcendental weight.
Conclusions:
- The proposed all-loop expression provides a significant advancement in understanding scattering amplitudes in planar N=4 super Yang-Mills theory.
- The findings confirm the deep connection between scattering amplitudes and the integrable structure of the theory.
- This work establishes a new tool for exploring high-energy phenomena and theoretical physics models.
Related Concept Videos
01:02¹H NMR: Interpreting Distorted and Overlapping Signals
1.4K
Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
1.4K
01:15Orders of Magnitude
25.9K
The order of magnitude of a number is the power of 10 that most closely approximates it. Thus, the order of magnitude estimates the scale (or size) of its value. To find the order of magnitude of a number, take the base-10 logarithm of the number and round it to the nearest integer. Then the order of magnitude of the number is simply the resulting power of 10.
The order of magnitude is simply a way of rounding numbers consistently to the nearest power of 10. This makes doing rough mental math...
The order of magnitude is simply a way of rounding numbers consistently to the nearest power of 10. This makes doing rough mental math...
25.9K
01:19Limits with Oscillating Discontinuities
193
An oscillating discontinuity is a type of discontinuity in which a function’s values fluctuate infinitely often as the input approaches a particular point. Unlike jump discontinuities, where the function suddenly shifts between two values, or infinite discontinuities, where the function diverges without bound, an oscillating discontinuity arises from rapid back-and-forth variation. Because the function never stabilizes toward a single value, no finite limit exists at that point.One of the...
193
01:10Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule
2.3K
In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1 triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the...
2.3K
01:13¹H NMR Signal Multiplicity: Splitting Patterns
6.4K
When protons A and X are coupled, their nuclear spin energy levels are slightly modified. This is because the energy required to excite proton A to a spin state parallel to proton X is slightly different from the energy required for it to become anti-parallel to spin X. Consequently, there are two possible excitation frequencies for A (A1 and A2), depending on the spin state of X, and vice versa. The mutual nature of coupling implies that the difference between frequencies A1 and A2, indicated...
6.4K
01:13¹H NMR: Complex Splitting
1.7K
A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied...
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied...
1.7K