# Structure functions in electron-proton scattering

• Kara386
In summary: We can rewrite the integrals in terms of the PDFs with the subscript ##v##:##\int_0^{1} F^p_2(x)dx = \int_0^{1} x(\frac{4}{9}u^p_v(x) + \frac{1}{9}d^p_v(x))dx = 0.18####\int_0^{1} F^n_2(x)dx = \int_0^{1} x(\frac{4}{9}u^n_v(x) + \frac{1}{9}d^n_v(x))dx =
Kara386

## Homework Statement

In electron proton scattering,

##\int_0^{1} F^p_2(x)dx = 0.18##

For the neutron in electron deuteron scattering,

##\int_0^1F^n_2(x)dx = 0.12##

Therefore determine the ratio ##\frac{\int_0^1xu^p_v(x)dx}{\int_0^1xd^p_v(x)dx}##.

## The Attempt at a Solution

The answer is 2. Unfortunately, I don't know how to show that.
I know that ##F_2^{ep}(x) = x(\frac{4}{9}u^p(x)+\frac{1}{9}d^p(x)+\frac{4}{9}\overline{u}^p(x)+\frac{1}{9}\overline{d}^p(x))##.

Based on that, I think
##F_2^{n}(x) = x(\frac{4}{9}u^n(x)+\frac{1}{9}d^n(x)+\frac{4}{9}\overline{u}^n(x)+\frac{1}{9}\overline{d}^n(x))##
And because a proton is essentially a neutron with up and down swapped, ##u^n(x) = d^p(x)##, so that can be substituted in:
##F_2^{n}(x) = x(\frac{4}{9}d^p(x)+\frac{1}{9}u^p(x)+\frac{4}{9}\overline{d}^p(x)+\frac{1}{9}\overline{u}^p(x))##

##= x(\frac{4}{9}d(x)+\frac{1}{9}u^p(x)+\frac{4}{9}\overline{d}^p(x)+\frac{1}{9}\overline{u}^p(x))##

But I couldn't explain why, I've just replaced the superscript from the first expression with n. I've tried using the above expressions to get a ratio of the integrands but it doesn't work, and I don't know what the subscript ##v## means in the ratio I'm supposed to calculate. Any help is much appreciated, I really have no idea what to do!

Thank you for your question. It seems like you are on the right track in your attempt to solve the problem. Let me guide you through the steps to show the ratio ##\frac{\int_0^1xu^p_v(x)dx}{\int_0^1xd^p_v(x)dx}##.

First, let's start by writing out the expressions for the integrals in terms of the parton distribution functions (PDFs):

##\int_0^{1} F^p_2(x)dx = \int_0^{1} x(\frac{4}{9}u^p(x) + \frac{1}{9}d^p(x))dx = 0.18##

##\int_0^{1} F^n_2(x)dx = \int_0^{1} x(\frac{4}{9}u^n(x) + \frac{1}{9}d^n(x))dx = 0.12##

Next, let's substitute in the relation between the PDFs for the neutron and proton, as you correctly pointed out:

##u^n(x) = d^p(x)##

##d^n(x) = u^p(x)##

Now, we can rewrite the expressions for the integrals in terms of the PDFs for the proton:

##\int_0^{1} F^p_2(x)dx = \int_0^{1} x(\frac{4}{9}u^p(x) + \frac{1}{9}u^p(x))dx = \frac{5}{9}\int_0^{1} xu^p(x)dx = 0.18##

##\int_0^{1} F^n_2(x)dx = \int_0^{1} x(\frac{4}{9}d^p(x) + \frac{1}{9}d^p(x))dx = \frac{5}{9}\int_0^{1} xd^p(x)dx = 0.12##

Now, we can take the ratio of the two integrals:

##\frac{\int_0^1xu^p(x)dx}{\int_0^1xd^p(x)dx} = \frac{0.18}{0.12} = 1.5##

However, this is not the final

## 1. What are structure functions in electron-proton scattering?

Structure functions in electron-proton scattering refer to the mathematical functions used to describe the internal structure of the proton. These functions are derived from experiments that measure the scattering of electrons off of protons, providing insights into the distribution of quarks and gluons within the proton.

## 2. How are structure functions measured in electron-proton scattering experiments?

Structure functions are measured by analyzing the energy and angle of the scattered electrons in an electron-proton scattering experiment. By comparing the measured data to theoretical predictions, scientists can determine the values of the structure functions and gain a better understanding of the proton's internal structure.

## 3. What is the significance of structure functions in understanding the proton?

The structure functions in electron-proton scattering experiments provide valuable information about the distribution of quarks and gluons within the proton. This helps scientists understand the strong nuclear force and the fundamental building blocks of matter, as well as providing insights into the behavior of protons in high-energy collisions.

## 4. How do structure functions differ for different types of particles?

The structure functions in electron-proton scattering experiments are specific to the proton and cannot be directly applied to other types of particles. However, similar experiments can be performed on other particles, such as neutrons and nuclei, to determine their respective structure functions and gain a deeper understanding of their internal structures.

## 5. How have structure functions in electron-proton scattering contributed to our understanding of the Standard Model of particle physics?

Structure functions in electron-proton scattering experiments have played a crucial role in confirming the predictions of the Standard Model of particle physics. By providing precise measurements of the proton's internal structure, scientists can test the theory and look for any discrepancies that may lead to new discoveries or improvements in the model.

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