Related Experiment Video
Updated: Jun 23, 2026
07:46
Setting Limits on Supersymmetry Using Simplified Models
Published on: November 15, 2013
Chiral logarithms in the massless limit tamed.
Nikolai Kivel1, Maxim V Polyakov, Alexei Vladimirov
1Petersburg Nuclear Physics Institute, Gatchina, St. Petersburg 188350, Russia.
Physical Review Letters
|May 14, 2009
Summary
Researchers developed nonlinear recursion relations to efficiently compute and sum leading chiral logarithms (LLs) in massless theories. This method is applicable to various nonrenormalizable effective field theories, enhancing computational efficiency.
Area of Science:
- Theoretical Physics
- Quantum Field Theory
Background:
- Leading chiral logarithms (LLs) are crucial in massless theories.
- Efficient computation and summation of LLs are significant challenges.
Purpose of the Study:
- To derive novel nonlinear recursion relations for LLs.
- To establish an efficient computational method for LLs.
- To demonstrate the broad applicability of the method.
Main Methods:
- Derivation of nonlinear recursion relations.
- Application to massless theories.
- Computational implementation for LLs.
Main Results:
- A highly efficient method for computing LLs was developed.
- The method allows for rapid calculation of high-loop contributions (e.g., 33-loop in seconds).
- The derived relations facilitate the summation of LLs.
Conclusions:
- The nonlinear recursion relations offer a powerful tool for LL computation and summation.
- The method is broadly applicable to nonrenormalizable effective field theories.
- This approach significantly enhances computational efficiency in theoretical physics.
Related Concept Videos
01:30Laws of Logarithms I
Logarithms are fundamental mathematical operations that serve as the inverse of exponentiation. They provide a means to express how many times a base must be raised to yield a given number. For base 10, often referred to as the common logarithm, the notation is written simply as log. Thus, if 10n = x, then log(x) = n. This relationship makes logarithms especially valuable in simplifying complex calculations involving multiplication, division, and exponentiation.Logarithmic expressions are...
02:30Chirality in Nature
Chirality is the most intriguing yet essential facet of nature, governing life’s biochemical processes and precision. It can be observed from a snail shell pattern in a macroscopic world to an amino acid, the minutest building block of life. Most of the snails around the world have right-coiled shells because of the intrinsic chirality in their genes. All the amino acids present in the human body exist in an enantiomerically pure state, except for glycine - the sole achiral amino acid. The...
02:25Chirality
Chirality is a term that describes the lack of mirror symmetry in an object. In other words, chiral objects cannot be superposed on their mirror images. For example, our feet are chiral, as the mirror image of the left foot, the right foot, cannot be superposed on the left foot.
Chiral objects exhibit a sense of handedness when they interact with another chiral object. For example, our left foot can only fit in the left shoe and not in the right shoe. Achiral objects — objects that have...
Chiral objects exhibit a sense of handedness when they interact with another chiral object. For example, our left foot can only fit in the left shoe and not in the right shoe. Achiral objects — objects that have...
01:28Laws of Logarithms II
Logarithmic laws provide essential tools for simplifying and evaluating exponential expressions, particularly in mathematical and applied settings where powers and repeated multiplication play a central role. Two important rules are the power law and the change-of-base formula, both allowing for transforming expressions into more manageable forms.The power law of logarithms states that the logarithm of a number raised to an exponent equals the exponent multiplied by the logarithm of the base...
01:28Logarithmic Differentiation
When a car’s weight and driving forces act on a tire, they impose an external load on the rubber material. This load is resisted internally by forces distributed throughout the tire structure, which are defined as stress. The resulting deformation of the rubber due to this stress is quantified as strain. The relationship between stress and strain governs how the tire deforms under load and is central to understanding its mechanical response during operation.Rubber exhibits a nonlinear...
02:25Molecules with Multiple Chiral Centers
Molecules that possess multiple chiral centers can afford a large number of stereoisomers. For instance, while some molecules like 2-butanol have one chiral center, defined as a tetrahedral carbon atom with four different substituents attached, several molecules like butane-2,3-diol have multiple chiral centers. A simple formula to predict the number of stereoisomers possible for a molecule with n chiral centers is 2n. However, there can be a lower number where some of the stereoisomers are...