The status of R value measurement at BESIII

TL;DR: The data samples for R value measurement and QCD experimental study with BESIII from 2.0 to 4.59 GeV have been collected, the total energy points are 130 and the total integrated luminosity is about 1.3 fb−1.

About: This article is published in Nuclear and Particle Physics Proceedings.The article was published on 2017-06-01 and is currently open access. It has received 3 citations till now.

Summary

1 Introduction

• R value is a basic input parameter for the calculations of the abnormal magnetic moment of muon (g − 2)µ, and the QED running coupling constant α(s).
• BESII ever measured R value between 2-5 GeV.
• To reduce the error of R value is still one of the experimental goals at BESIII.
• This note will focuses on the issue of the initial state radiative corrections and the simulation of hadronic events by the Lund area law generator LUARLW and parameters tuning with BESIII data.

2 Data analysis

• In experiment, R value is measured with following expression: Rexp = Nobshad − Nbg σ0µµL trḡhad(1 + δ) , (1) the meanings of all of these quantities in above formula were explained in references [4–6].
• Huhm@ihep.ac.cn © The Authors, published by EDP Sciences, also known as ∗e-mail.
• This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/).
• The basic physics processes produced in e+e− annihilation in BEPCII energy region are four types: e+e− → l+l−, γγ, e+e−X and hadrons.
• The scheme of event selection in this work are similar to the criteria described in references [4–6].

3 Initial state radiation

• The directly measured hadronic cross section is the observed total cross section, which contains the total contributions of all Feynman diagrams shown in Figure 1: The R value is the Born cross section corresponding to the tree level Feynman diagram of Figure 1(a).
• The Figure 2 (left) shows the numerical ISR factor (1 + δ) calculated by the Feynman diagram scheme Eq.(4) and the structure function scheme[14, 15].
• The numerical results of (1 + δ) calculated by Feynman diagram and structure function schemes agree within 1%.

4 Generator LUARLW

• Figure 2 shows the general picture of e+e− annihilation and hadrons production.
• The nonperturbative hadronization process can be described by the Lund string fragmentation model[8].
• The Lund area law generator LUARLW[9, 10] is built in order to simulate the few-body production processes in BEPC energy region.
• The maximum number of primary hadrons in string fragmentation is six.
• LUARLW simulation contains following constitutes: initial state radiation (ISR), string fragmentation, multiplicity and momentum-energy distributions, decay of unstable hadrons.

4.1 Simulation of ISR return processes

• The Figure 3 shows the number of events distribution with different effective hadronic energies √ s′ in LUARLW sampling.
• The peaks of resonances ρ, φ and J/ψ which with larger Breit-Wigner cross sections are clearly visible.
• Correctly simulating the ISR return processes are important for reducing the systematic error of efficiency ̄had.

4.2.1 Physics picture

• The basic physics picture of LUARLW is the Lund string fragmentation model[8, 9].
• Figure 5 shows that mesons (M) and baryons ( B and B̄) produce at the vertex of light-cone area in string fragmentation processes.
• Single-quark-pair excitation in string fragmentation form mesons, and di-quark-pair excitation form baryons.
• Starting from the Lund area law, one may obtain an approximation expression of poissonlike multiplicity distribution of the preliminary fragmentation hadrons[10]: Pn(s) = µn n! exp[c0 + c1(n − µ) + c2(n − µ)2], (9) where n is the number of the hadrons, and the parameter µ can be understood as the average multiplicity.

4.2.2 Production modes

• The simulations of the continuum states include the lowest and leading order QCD correction: e+e− → γ∗ → { qq̄→ string→ hadrons gqq̄→ 2 strings→ hadrons.
• For the 2-string mode, each string fragments independently according to the Lund area law.
• The energy-momentum distributions are determined by Lund area law[10].
• The decay fractions of these vector mesons to different final states take PDG values, and the polar angles distribution depends on their decay final states[17].
• The production and decay of the charmonium adopt the standard pictures[18, 19].

4.3.2 Scheme B: Pure LUARLW

• LUARLW is used an independent generator.
• The main parameters to be tuned are those about the multiplicity of the preliminary hadrons in Eq.(9) and Eq.(10), and those which determine the ratios of mesons and baryons with different quantum number (S , L, J).
• In LUARLW these parameters are stored in array PARJ(1-20) as did in JETSET[20].

5 Summary

• The data analysis of R value measurement almost has been finished.
• The challenging for the R value measurement is still parameters tuning of LUARLW, which is in progress.
• The goal is MC simulations agreeing BESIII data well, and the error of hadronic efficiency reach a acceptable level, for example 2%.
• The total errors of R value reduce to about 3%.

Figures

Figure 2. Left: the ISR correction factor (1 + δ) calculated by Feynman diagram scheme (Crystalball) and structure function schemes (KureavFadin,Wu). Right: the picture of e+e− annihilation into hadrons.

Figure 5. Left: the Born cross section of e+e− → hadrons below 5 GeV. The black points are the total cross section measured in inclusive method, the red points are the sum of the measured exclusive cross sections. Right: Comparison between data and MC in scheme A at 3.65 GeV. (a) multiplicity of charged track; (b) multiplicity of photon; (c) polar angle cos θ; (d) momentum of charged track.

Figure 1. The Feynman diagrams of e+e− annihilation into hadrons up to one-loop order: (a) the tree level diagram, (b) the bremsstrahlung, (c) electron self-energy, (d) vertex correction and vacuum polarization.

Figure 4. The mesons (M) and baryons (B) production in the string fragmentation processes.

Figure 3. The event distributions of ISR return processes with different effective hadronic energies √ s′.

Frequently asked questions

Q1. What have the authors contributed in "Status of r value measurement at besiii" ?

This paper reviews the present status of R value measurement from 2. 232 to 3. 671 GeV at 14 energy points, especially describes the calculations of initial state radiative correction and the issue of the parameter tuning for the Lund area law generator LUARLW. 

Q2. What is the MC method used to calculate the fraction of the contributions of the higher level processes?

LUARLW simulation contains following constitutes: initial state radiation (ISR), string fragmentation, multiplicity and momentum-energy distributions, decay of unstable hadrons. 

Q3. What are the main parameters to be tuned?

The main parameters to be tuned are those about the multiplicity of the preliminary hadrons in Eq.(9) and Eq.(10), and those which determine the ratios of mesons and baryons with different quantum number (S , L, J). 

Q4. What is the physics of the continuum states?

The vector mesons whose masses smaller than 2 GeV and with quantum number JPC = 1−− can directly couple to virtual photon in ISR return process:e+e− → γ∗ → ρ(770), ω(782), φ(1020) · · · ρ(1700). 

Q5. What is the resonant cross section of the Feynman diagram?

A bremsstrahlung event which with the radiative photon angles (θ, φ) and fraction momentum x can be sampled by the differential cross section:dσHB(x, θ) dxdΩγ = α π2 sin2 θ (1 − a2 cos2 θ)2 1 x (1 − x + x 2 2 )σ0(s′) (7)The values of σ0(s) from 2mπ to 1.8 GeV use experimental values cited in PDG [16], and in the energy region above 1.8 GeV,σ0(s) = σ0µ(s)RpQCD(s) + σBW (s), (8)whereσ0µ(s) is the theoretical di-muon Born cross section, RpQCD(s) the R value of continuous hadronic states predicted by pQCD, σBW (s) the resonant cross section calculated by the BreitWigner formula. 

Q6. What is the definition of R value?

R value is defined as the inclusive e+e− annihilation hadronic production cross section at the tree level Feynman diagram normalized by the theoretical di-muon cross section. 

Q7. What is the important physics picture of the continuum states?

The simulations of the continuum states include the lowest and leading order QCD correction: e+e− → γ∗ → {qq̄→ string→ hadrons gqq̄→ 2 strings→ hadronsFor the 2-string mode, each string fragments independently according to the Lund area law. 

Q8. What is the R value of the data samples?

The data samples at 130 energy points from 2.0 to 4.59 GeV have been collected with BESIII, the total integrated luminosity is about 1.3 fb−1. 

Q9. What is the simplest way to calculate the irr?

Starting from the Lund area law, one may obtain an approximation expression of poissonlike multiplicity distribution of the preliminary fragmentation hadrons[10]:Pn(s) = µnn! exp[c0 + c1(n − µ) + c2(n − µ)2], (9)where n is the number of the hadrons, and the parameter µ can be understood as the average multiplicity. 

Q10. What is the meaning of the residual QED background events?

The numbers of the residual QED background events Nbg in Eq.(1) are statistically subtracted by MC method:Nbg = L[ eeσee + µµσµµ + ττσττ + γγσγγ], (2)where L is the integrated luminosity of data, σee the cross section of Bhabha process, ee the residual efficiency of Bhabha process which passes the hadronic event selection criteria, other symbols have corresponding meanings. 

Q11. What is the probability of an exclusive process?

The probability of an exclusive process e+e− → qq̄(g)→ string(s)→ m1 + m2... + mn can be factorized as:dσn(s) = dσ(e+e− → qq̄) · dPn(qq̄(g)→ m1,m2...mn; s), (11)where dσ(e+e− → qq̄) is the QED cross section, dPn the probability for string fragmentation into n hadrons. 

Q12. What is the purpose of this paper?

This note will focuses on the issue of the initial state radiative corrections and the simulation of hadronic events by the Lund area law generator LUARLW and parameters tuning with BESIII data. 

Q13. What is the fraction contribution of the higher level diagrams in Figure 1?

The fraction contribution of the higher level diagrams in Figure 1(b), (c) and (d) can be calculated by the initial state radiative correction:σtot(s) = (1 + δ)σ0(s), or (1 + δ) = σtot(s) σ0(s) , (3)where σ0(s) is the Born cross section, σtot(s) the total cross section, and (1 + δ) is called the ISR correction factor, which reflects the fraction of the contributions of the higher level processes.