[Paper Review] The Nuts and Bolts of Diffraction

K. Goulianos|arXiv (Cornell University)|Oct 17, 2001

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TL;DR

This paper investigates the breakdown of QCD factorization in hard diffraction processes, proposing that soft diffraction dynamics—governed by renormalized rapidity gap probabilities and unitarity-preserving Regge-based models—explain the observed suppression of diffractive structure functions at the Tevatron relative to HERA. The key contribution is a renormalized gap probability model that preserves unitarity and explains factorization breakdown via energy-independent gap formation, validated by agreement with SD and DD cross sections across energies.

ABSTRACT

Results on soft and hard diffraction are briefly reviewed with emphasis on the interplay among factorization properties, universality of rapidity gap formation and unitarity.

Motivation & Objective

• To understand the breakdown of QCD factorization between HERA and Tevatron data in hard diffraction processes.
• To explain the observed suppression of diffractive structure functions at the Tevatron relative to HERA predictions based on HERA data.
• To establish a unitarity-preserving framework for rapidity gap formation in soft and hard diffraction using renormalized gap probabilities.
• To extend the model to multi-gap diffractive events and predict cross sections for multiple rapidity gaps.

Proposed method

• Uses a renormalized rapidity gap probability derived from Regge theory, with the gap probability normalized to unity to preserve unitarity.
• Applies the parton model amplitude $ \text{Im } f(t,\Delta y) \sim e^{(\epsilon + \alpha' t)\Delta y} $ to model elastic scattering between diffractively excited states.
• Incorporates the Pomeron trajectory $ \alpha(t) = 1 + \epsilon + \alpha' t $, coupling $ \beta(t) $, and triple-Pomeron coupling ratio $ \kappa = g(t)/\beta(0) $.
• For multi-gap events, computes the differential cross section as a product of sub-energy cross sections and normalized gap probabilities, with $ \kappa $ factors for each gap.
• Normalizes the total gap probability $ P_{\text{gap}} $ over phase space to unity, ensuring energy independence and unitarity.
• Applies the model to 4-gap events, showing the normalization factor $ N_{\text{gap}} $ depends only on center-of-mass energy $ s $, not on the number of gaps.

Experimental results

Research questions

• RQ1 Why is the diffractive structure function measured at the Tevatron suppressed by a factor of ~10 compared to predictions from HERA data?
• RQ2 To what extent does QCD factorization hold between HERA and Tevatron data for hard diffraction processes?
• RQ3 How can rapidity gap formation be described in a way that preserves unitarity and explains the observed energy dependence of soft diffraction cross sections?
• RQ4 What is the role of color matching (via $ \kappa $) in determining the probability of multiple rapidity gaps in diffractive events?
• RQ5 Can a unified model explain both single and double diffractive cross sections using a single, renormalized gap probability?

Key findings

• The diffractive structure function measured at the Tevatron is suppressed by a factor of ~10 relative to predictions from HERA data, indicating a breakdown of QCD factorization between the two colliders.
• Factorization holds within HERA data and within single-diffractive data at the Tevatron at the same center-of-mass energy, indicating consistency within each dataset.
• The renormalized rapidity gap probability model successfully explains the energy dependence of single and double diffractive cross sections, in contrast to the $ s^{2\epsilon} $ behavior predicted by standard Regge theory.
• The model predicts that the ratio of double-Pomeron-exchange to single-diffractive cross sections is approximately $ \kappa $, with no additional energy suppression, consistent with unitarity.
• For 4-gap events, the normalization factor $ N_{\text{gap}} $ depends only on $ s $, not on the number of gaps, implying a universal energy dependence for gap probability across multi-gap configurations.
• The model's predictions for SD and DD cross sections agree well with data, as shown in Figs. 3 and 4, validating the renormalization procedure for gap probabilities.