[Paper Review] Instantons in Deep-Inelastic Scattering

A. Ringwald, F. Schrempp|ArXiv.org|Jun 19, 2000

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper evaluates theoretical uncertainties in instanton-induced processes in deep-inelastic scattering (DIS) at HERA, using lattice QCD data to constrain instanton size and separation. It establishes reliable cuts on $ Q'^\prime/\Lambda_{\overline{MS}} \gtrsim 30.8 $ and $ x^\prime \gtrsim 0.35 $, yielding a predicted $ I $-induced cross section of $ 29^{+10}_{-7.5} $ pb with significant sensitivity to $ \Lambda_{\overline{MS}} $, crucial for H1 experiment searches.

ABSTRACT

In view of the new (preliminary) search results for instanton-induced events at HERA from the H1 collaboration, we present a brief discussion of (controllable) theoretical uncertainties, both in the event topology and the calculated rate.

Motivation & Objective

• To assess controllable theoretical uncertainties in instanton-induced events in deep-inelastic scattering at HERA.
• To determine reliable kinematic cuts for $ I $-induced processes based on lattice QCD constraints.
• To quantify the dependence of the $ I $-induced cross section on $ \Lambda_{\overline{MS}} $ and the resulting impact on experimental observables.
• To support H1 experiment searches by providing a robust theoretical framework for event topology and rate predictions.

Proposed method

• Uses lattice QCD simulations to constrain instanton size $ \rho \leq 0.35 \pm 0.05 $ fm and separation $ R/\rho \geq 1.1 \pm 0.05 $, validating the applicability of instanton-perturbation theory.
• Applies a saddle-point relation to translate lattice constraints into minimal cuts on $ Q'^\prime/\Lambda_{\overline{MS}} \gtrsim 30.8 $ and $ x^\prime \gtrsim 0.35 $ in the $ I $-subprocess.
• Employs the Monte Carlo generator QCDINS 2.0 to simulate $ I $-induced DIS events and study final-state observables under varying cut conditions.
• Performs a path-dependent analysis through the allowed $ (Q'^\prime_{\rm min}/\Lambda_{\overline{MS}}, x^\prime_{\rm min}) $ domain to assess shifts in observable distributions while keeping the total rate constant.
• Quantifies the sensitivity of the $ I $-induced cross section to $ \Lambda_{\overline{MS}} $, using updated $ \alpha_s $ values from PDG '96 and '98.
• Compares theoretical predictions with H1 experimental observables, including $ Q'^{\prime 2}_{\rm rec} $, $ E_t^b $, and $ E_t^{\rm jet} $, to assess robustness under cut variations.

Experimental results

Research questions

• RQ1 What are the theoretically controllable uncertainties in the topology and rate of instanton-induced events in DIS at HERA?
• RQ2 How do lattice QCD constraints on instanton size and separation translate into reliable kinematic cuts for $ I $-induced processes?
• RQ3 What is the sensitivity of the predicted $ I $-induced cross section to variations in $ \Lambda_{\overline{MS}} $ and the resulting impact on observable distributions?
• RQ4 How do shifts in minimal cuts $ Q'^\prime_{\rm min}/\Lambda_{\overline{MS}} $ and $ x^\prime_{\rm min} $ affect the shapes of key final-state observables used in H1 analyses?
• RQ5 To what extent does the lack of direct experimental reconstruction of $ x^\prime $ affect the comparison with theoretical predictions?

Key findings

• The instanton-perturbation theory is quantitatively reliable for instantons with size $ \rho \leq 0.35 \pm 0.05 $ fm and separation $ R/\rho \geq 1.1 \pm 0.05 $, as validated by lattice QCD data.
• A one-to-one saddle-point translation of lattice constraints yields minimal cuts $ Q'^\prime/\Lambda_{\overline{MS}} \gtrsim 30.8 $ and $ x^\prime \gtrsim 0.35 $, which are adopted as default in QCDINS 2.0.
• The $ I $-induced cross section at HERA is highly sensitive to $ \Lambda_{\overline{MS}} $, with a value of $ 29^{+10}_{-7.5} $ pb based on PDG '98 $ \alpha_s $, compared to $ 126^{+300}_{-100} $ pb with PDG '96 values.
• For a constant $ I $-induced rate, increasing $ x^\prime_{\rm min} $ leads to substantial shifts in the average values of $ Q'^{\prime 2}_{\rm rec} $ and $ E_t^b $ toward smaller values, indicating sensitivity to cut choices.
• The $ I $-induced rate is robust against missing $ x^\prime $ reconstruction because lattice data show strong suppression of $ I $-effects for $ x^\prime \lesssim 0.35 $, corresponding to $ R/\rho \lesssim 1.1 $.
• The theoretical uncertainty in $ \sigma^{(I)}_{\rm HERA} $ is dominated by $ \Lambda_{\overline{MS}} $, with the cross section decreasing significantly when updated $ \alpha_s $ values are used.