# 3-Point 1-Loop Integral with 1 Mass

• Hepth
In summary, the conversation is about trying to get an analytic result for an integral of the form ##\int d^{d}l \frac{1}{l^2 (l+q-p)^2 ((l-p)^2-m^2)}##, which should be convergent in 4 dimensions. The speaker mentions the possibility of using a lookup table or working in "d" to avoid divergences. They also mention the integral being equivalent to a passarino-veltman C0 and suggest looking in the qcd loop repository for helpful integrals. The other person suggests using a nice interface for finding integrals in d dimensions and offers to send an analytic formula in a mathematica nb if needed.

#### Hepth

Gold Member
I'm trying to get an analytic result, but can't seem to get it. Does anyone know of a lookup table or another way to get it? The Integral I need is of the form:

##\int d^{d}l \frac{1}{l^2 (l+q-p)^2 ((l-p)^2-m^2)}##

It should be convergent in 4 dimensions I believe, but without some regulators for the masses, which I DONT want, it might be best to work in "d" and absorb any divergences there.

This is equivalent to a passarino-veltman C0. I find results for other cases, but not this one. If I do it myself I can't find a favorable way to regulated the divergences that appear.

Have you tried qcd loop repository?

There is a nice interface to find all the integrals you might need. These are d dimensions for the divergent ones.

Did you find what you needed? If not, pm me and I can send you the analytic formula in a mathematica nb or something.

## 1. What is a 3-Point 1-Loop Integral with 1 Mass?

A 3-Point 1-Loop Integral with 1 Mass is a type of mathematical calculation used in theoretical physics to describe the behavior of particles and their interactions. It involves integrating over three points in space with one of the particles having a non-zero mass.

## 2. Why is this type of integral important in theoretical physics?

This type of integral is important because it allows us to calculate the amplitudes of particle interactions, which are fundamental to understanding the behavior of particles and their interactions in the quantum world. It is also used to test and validate theoretical models and predictions.

## 3. How is a 3-Point 1-Loop Integral with 1 Mass calculated?

The calculation involves using Feynman diagrams, which are graphical representations of particle interactions, to determine the mathematical expression for the integral. This expression can then be solved using mathematical techniques such as dimensional regularization or analytic continuation.

## 4. What is the significance of the "1-Loop" in the name?

The "1-Loop" in the name refers to the number of loops or iterations in the Feynman diagram used to calculate the integral. In this case, it means that the calculation involves one loop or one iteration.

## 5. How is the result of a 3-Point 1-Loop Integral with 1 Mass interpreted?

The result of the integral is typically expressed in terms of a mathematical quantity known as the scattering amplitude, which describes the probability of particles interacting with each other. This result can then be used to make predictions and comparisons with experimental data.