How Can I Compare Parton Distribution Functions Without Data from Other Groups?

In summary, comparing Parton Distribution Functions (PDFs) without external data involves using theoretical frameworks, such as perturbative Quantum Chromodynamics (QCD), alongside self-consistent methodologies like global fits and Monte Carlo simulations. Analysts can also utilize cross-section measurements from collider experiments and leverage internal consistency checks within their own data sets. This approach allows for independent verification and validation of PDFs while minimizing reliance on other groups' data, ensuring a more robust analysis of the underlying partonic structure of protons.
  • #1
Elham1990
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Parton distribution functions
Hello
I plotted the Parton distribution functions in Mathematica. Now I want to compare the graphs drawn with the graphs of other groups(xu and xd). How should I do this?
 
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  • #2
Are you just asking how to plot several graphs in the same plot in mathematica? In that case I guess have a look here https://reference.wolfram.com/language/ref/Plot.html, the second syntax is what you want. Maybe I am not understanding what the question is?
 
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  • #3
I'm asking about comparing my results with other groups. I don't have other groups data such as H1, Cteq. I Plotted my results in Mathematica and I have other groups article. now, how can I compare these without their Mathematica codes?
 
  • #4
If I type "graph of parton distribution functions" into Google, I get two million hits. OK, so they are not all useful, I am sure, but there are many dozens (probably hundreds) of such plots, and so I conclude that isn't what you want.

You need to be more descriptive in what you want - and this is the third time you've been asked.
 
  • #5
Elham1990 said:
I don't have other groups data
Different groups publish their results in different formats, have you checked out their respective websites?

There is a universal interface called lhapdf https://lhapdf.hepforge.org/ where you will probably find any today relevant (proton) pdf set. I don't think they have a native Mathematica interface but the python one is pretty usable if I remember correctly.
 
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FAQ: How Can I Compare Parton Distribution Functions Without Data from Other Groups?

What are Parton Distribution Functions (PDFs)?

Parton Distribution Functions (PDFs) describe the probability distribution of quarks and gluons (collectively known as partons) inside a proton or neutron as a function of the parton's momentum fraction and the energy scale of the interaction. They are essential for making predictions in high-energy physics, particularly in processes involving the strong force, such as those studied at particle colliders like the Large Hadron Collider (LHC).

Why is it challenging to compare PDFs without data from other groups?

Comparing PDFs without data from other groups is challenging because PDFs are typically derived from global fits to experimental data from various high-energy physics experiments. These fits involve complex statistical analyses and theoretical models. Without access to the experimental data and the methodologies used by other groups, it becomes difficult to independently validate or compare the results.

What methods can be used to compare PDFs without external data?

To compare PDFs without external data, one can use theoretical consistency checks, such as verifying the sum rules (e.g., momentum and baryon number conservation) and comparing the PDFs against known theoretical predictions or constraints. Additionally, one can perform cross-checks using different parameterizations or fitting techniques within their own data set to ensure robustness and consistency.

How can theoretical predictions help in comparing PDFs?

Theoretical predictions, such as those from Quantum Chromodynamics (QCD) and perturbative calculations, can provide benchmarks for comparing PDFs. By ensuring that the PDFs satisfy theoretical constraints and match predictions from well-established models, one can gain confidence in their accuracy. This approach helps in identifying discrepancies that might arise from different fitting procedures or assumptions.

What role do sum rules play in the comparison of PDFs?

Sum rules are integral constraints that PDFs must satisfy based on fundamental properties of the proton or neutron. For example, the momentum sum rule requires that the total momentum carried by all partons equals the momentum of the proton. Verifying that PDFs satisfy these sum rules is crucial for ensuring their physical validity and provides a way to compare different sets of PDFs consistently.

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