# What is the meaning of chiral-odd/chiral-even functions

• A
• joly
In summary, the conversation discusses quark distribution functions in the nucleon and their chiral properties. Chirality refers to the behavior of a state under a specific operator, and in this case, it affects the sign of the distribution function. Chiral-odd functions switch signs when the right and left handed quarks are switched, while chiral-even functions retain their sign. It is recommended to refer to course notes and texts for a better understanding of distribution functions.

#### joly

I read about quark distribution functions in the nucleon that are chiral-odd or chiral-even functions (Sivers function, Boer-Mulders function and other distribution function related to nucleon transversity). What is the definition of chirality for functions? Does this mean they are odd or even under the transformation (t,x,y,z) -> (t,-x,-y,z) ?

Thanks!

Thank you. So in better terms than what I used, it means that when one switches the right handed quarks in a nucleon with the left handed ones, a chiral-odd distribution function switches its sign while a chiral-even one retains its sign. Is that correct?

Off the top of my head, that would be what I'd expect.
I'm thinking you should relate this to your course-notes and text here though... I may not have the same idea of a "distribution function" that your prof has.

joly

## What is the meaning of chiral-odd/chiral-even functions?

Chiral-odd and chiral-even functions are mathematical expressions used to describe the symmetry properties of particles and their interactions in physics. They refer to the behavior of a function under a specific type of transformation, known as chiral symmetry.

## What is chiral symmetry?

Chiral symmetry is a type of symmetry that describes the behavior of a system under the transformation of left-handed and right-handed components. It is an important concept in particle physics and is related to the fundamental properties of matter.

## How are chiral-odd and chiral-even functions different?

The main difference between chiral-odd and chiral-even functions is their behavior under chiral symmetry. Chiral-odd functions change sign under a chiral transformation, while chiral-even functions do not. This difference has significant implications for the interactions and properties of particles.

## What are some examples of chiral-odd and chiral-even functions?

Some common examples of chiral-odd functions include the sine and tangent functions, which change sign under a chiral transformation. Chiral-even functions include the cosine and cotangent functions, which do not change sign under a chiral transformation.

## Why are chiral-odd and chiral-even functions important in physics?

Chiral-odd and chiral-even functions play a crucial role in understanding the fundamental properties of particles and their interactions. They are used in various theoretical models and calculations in particle physics, and their behavior under chiral symmetry provides important insights into the structure of matter.