[Paper Review] Studies of mu-pair and pi-pair production at the electron-positron low energy colliders

S. Jadach|ArXiv.org|Jun 17, 2005

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper compares initial-state radiation (ISR) and final-state radiation (FSR) effects in muon and pion pair production at low-energy e⁺e⁻ colliders using the KKMC and PHOKHARA Monte Carlo generators. It demonstrates excellent agreement between three independent second-order ISR calculations for muons, validates the superior CEEX matrix element for ISR, and proposes a method to extend this approach to pion pairs using exclusive form factor modeling, enabling high-precision radiative return studies below 1 GeV².

ABSTRACT

Predictions for the radiative return with the muon pair and pion pair final state from KKMC and PHOKHARA Monte Carlo programs are compared and discussed. The case of muon pairs is well understood, especially of the initial state radiation (ISR), where three different second order calculations agree very well. The case of the final state radiation (FSR) requires more tests. Matrix element in KKMC of the EEX type with the incomplete second order NLL corrections is not good enough for the radiative return at $Q^2<1$GeV with the precision requirement better than 1%. A method of extending the superior CEEX-type matrix element in KKMC to the pion pair final state is described.

Motivation & Objective

• To compare ISR and FSR effects in muon and pion pair production at low-energy e⁺e⁻ colliders using independent Monte Carlo programs.
• To assess the precision of the EEX-type matrix element in KKMC for radiative return at Q² < 1 GeV².
• To develop a method for extending the high-precision CEEX ISR matrix element to hadronic final states like π⁺π⁻.
• To enable high-precision radiative return measurements below 1 GeV² with sub-1% accuracy.

Proposed method

• Uses the KKMC and PHOKHARA Monte Carlo generators to simulate radiative return processes e⁺e⁻ → μ⁺μ⁻γ and e⁺e⁻ → π⁺π⁻γ.
• Compares results from three independent second-order ISR calculations: KKMC (CEEX), PHOKHARA (complete second order), and analytical KKsem formula.
• Applies the Kleiss-Stirling method to express the CEEX matrix element in terms of bi-spinor objects for exclusive hadronic final states.
• Parametrizes the hadronic final state amplitude via form factors and decomposes the current into null vectors to maintain gauge invariance.
• Extends the CEEX framework to pion pairs by modeling the hadronic current Jμ(X) using massless four-vectors derived from the total four-momentum X.
• Uses the structure Jμ = J₊μ − J₋μ with J²₊ = J²₋ = 0 to enable exclusive amplitude construction in the CEEX scheme.

Experimental results

Research questions

• RQ1 How do the KKMC and PHOKHARA Monte Carlo programs compare in predicting the muon pair invariant mass spectrum under initial-state radiation?
• RQ2 Why does the EEX matrix element in KKMC fail to achieve 1% precision at Q² < 1 GeV² for radiative return?
• RQ3 Can the superior CEEX matrix element for ISR be extended to hadronic final states like π⁺π⁻?
• RQ4 What is the role of phase space cuts on photon emission in altering the relative size of higher-order corrections?

Key findings

• The KKMC and PHOKHARA Monte Carlo programs agree within 0.2% for the muon pair invariant mass spectrum at √s = 1.01942 GeV, with minor discrepancies at low Q² possibly due to neglected NNLL terms in KKsem.
• The PHOKHARA program agrees well with KKsem at low Q² but diverges by ~0.25% in the central region and drops sharply in the soft limit.
• The EEX matrix element in KKMC with incomplete NLL corrections fails to achieve 1% precision at Q² < 1 GeV², indicating insufficient higher-order corrections.
• The CEEX matrix element can be extended to pion pairs by modeling the hadronic current via form factors and decomposing it into null vectors, preserving gauge invariance.
• The method requires exclusive parametrization of the hadronic amplitude but is feasible for resonant low-energy hadronic states.
• The discrepancy between PHOKHARA and EEX in π⁺π⁻ final states is larger than in muon pairs, likely due to reduced phase space from angular cuts on photons.