Hadron Elecro-Production with HallD Generator

Rakitha S. Beminiwattha

Department of Physics, Syracuse University

September 11th, 2015

Rakitha S. Beminiwattha SoLID Collaboration Meeting September 11th , 2015 1/16

Outline

Overview

Hall D Generator

Electro-Production Implementation

Initial Results

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Overview

From Last Meeting : Photo-Production Models Compared

Total Photo-production cross sections from hall D

Total Photo-production cross sections from PDG [1]

Wiser Photo-production cross section summed for all the processes [2]

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Hall D Generator

Hall D Photo-Production Generator

Hall D generator uses various experimental data to generatephoto-production cross sections for photon energies below 3 GeV

It uses modified version of PYTHIA to generate photo-production crosssections for photon energies above 3 GeV

I have not looked at PYTHIA generator in details yet.

Following γ + p+ reactions are considered for photon energies below 3 GeV

1. p+ + π0

2. n + π+

3. p+ + π+ + π−(non − res.)

4. p+ + ρ0

5. ∆++ + π−

6. p+ + π0 + π0

7. n + π+ + π0

8. p+ + η0

9. p+ + π+ + π− + π0

10. n + π+ + π+ + π−

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Hall D Generator

Compare Hall D vs. PDG Compared total cross sections from Hall D event generator and PDG

photo-production cross sections on proton For γ momentum less than 3 GeV it uses combination of different models

including SAID For γ momentum greater than 3 GeV it uses PYTHIA

Figure: Black line : Hall D genertor, Red points : PDG

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Hall D Generator

From Photo-Production to Electro-Production

Electro-Production can takes place either from real bremsstrahlung photonradiated in the target or from virtual photon interaction approximated byEquivalent Photon Radiator (EPA) approximation

Wiser generator estimate these two components to compute theelectro-production cross-section

Bremsstrahlung contribution approximated according to MO and TSAI [3] Virtual contribution approximated using the reference [4]

I have implemented electro-production part to the hall D event generator Bremsstrahlung contribution is implemented using equations available at

PDG-2012 [5] and [6] EPA contribution is implemented according to the reference [7]

Next few slide will summarize the electro-production implementation

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Electro-Production Implementation

Electro-Production with Equivalent Photon Approximation

Figure: Electro-Production (a) and Photo-Absorption (b) equivalency [7]

The electro-production cross section for electron energy E using EquivalentPhoton Approximation (EPA),

dσ = σγ(ω) · dn(ω)

dn(ω) =

∫ q2max

q2min

dn(ω, q2) = NEPA(ω)dω

ω

where σγ(ω) is photo-production cross section at photon energy ω and,

NEPA(ω) = α

π

[(

1 −

ω

E+ ω

2

E 2

)

lnq2

max

q2min

−

(

1 −

ω

2E

)2ln

(ω2+q2max )

(ω2+q2min

)−

m2eω

2

E 2q2min

(

1 −

q2min

q2max

)]

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Electro-Production Implementation

Electro-Production with Radiated Real Photons

The Bremsstrahlung cross section for electron of energy E traveling inside amaterial [5]

dσ

dω=

A

X0NAω

(

4

3−

4ω

3E+

4ω2

3E 2

)

The electro-production cross section due to Bremsstrahlung photons,

dσ = σγ(ω) · NBREMS (ω)dω

ω

NBREMS(ω) =d

X0

(

4

3−

4ω

3E+

4ω2

3E 2

)

Where X0 is the radiation length and d = ρ · t where ρ is target density and t istarget thickness

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Electro-Production Implementation

EPA Photon Spectrum

Figure: Photon Spectrum NEPA(ω)

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Electro-Production Implementation

Bremsstrahlung Photon Spectrum

Figure: Photon Spectrum NBREMS(ω)

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Electro-Production Implementation

Complete Photon Spectrum

Figure: Photon Spectrum NEPA(ω) + NBREMS (ω) for electron incident on a proton target

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Electro-Production Implementation

Electro-Production with Hall-D Generator

Photon energy is sampled using electro-production cross section weighteddistribution

11 GeV electron beam (50 µA) is incident into a 40 cm hydrogen target

Figure: Hall D generator now samples the photon energy using electro-production crosssection weighted distribution

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Initial Results

Electro-Production : π0

Figure: π0 Only for θ < 900 and P < 2 GeV . Total cross-section is ∼ 30 µb for thislimited kinematic phase-space

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Initial Results

Pion Background from Different Methods

Figure: Using EPC code (see Michael Paolone’s May 2015 collaboration meeting talk).Total cross section is ∼ 14 µb

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Initial Results

Pion Background from Different Methods

Figure: Using Std. Wiser Generator (see Michael Paolone’s May 2015 collaborationmeeting talk). Total cross section is ∼ 80µb

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Initial Results

Summary

Hall D generator is now configured with electro-production from proton target

Needs to tweakq2

max

q2

min

better : Paul working on this

Initial result match with the EPC code

Cross section to a factor of 2 but not sure EPC results have real photoncontribution

Next immediate step : folding SoLID acceptance into these distribution anddo a rate estimation

Next long term step : implement a proper Geant4 generator based on the hallD generator

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Initial Results

Electro-Production : π0

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Initial Results

Electro-Production : π−

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Initial Results

Electro-Production : π+

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Initial Results

Electro-Production : π0

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Initial Results

Electro-Production : π−

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Initial Results

Electro-Production : π+

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From Last Meeting

Compare Hall D vs. PDG

Compared total cross sections from Hall D low energy event generator and PDGphoto-production cross sections on proton for γ momentum less than 3 GeV

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From Last Meeting

Wiser Photo-Production Cross Section

Wiser cross section,σi(Eγ) is computed for all the processes : π±, K±,P+

and P−

The cross section for π0 is the average of π± cross sections

Then all the cross sections are summed to compute the total wiser crosssection

See slide 27 for steps

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From Last Meeting

Wiser Photo-Production Cross Section

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From Last Meeting

Wiser Photo-Production Cross Section

Figure: Wiser cross section only for 10 deg. to 90 deg.

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Wiser Code Summary

Wiser Code Steps

The main FORTRAN routine returns the differential cross section per

monochromatic photon beam : E′ d3σ

dp′3 /Eγ

Where (E′, p′) is the hadron momentum and Eγ is the incident photon energy

The total cross section for a monochromatic photon beam for ith typeinteraction,

σi(Eγ) =

∫

phase−space

dσi(Eγ)

dp′dΩdp′dΩ

Wheredσi(Eγ)dp′dΩ

= p′2

E′·

(

E′ d3σ

dp′3 /Eγ

)

· Eγ

And subscript i is,

1. i = 0, 1 : π±

2. i = 2, 3 : K±

3. i = 4, 5 : P+ and P−

π0 cross section is the average of π± cross sectionsRakitha S. Beminiwattha SoLID Collaboration Meeting September 11th , 2015 27/16

Wiser Code Summary

K.A. Olive et al.Review of Particle Physics.Chin.Phys., C38:090001, 2014.

S. Riodan, X. Zheng, Z. Zhao, and N. Ton.Comparison between Wiser π− rates calculation and data from transversityand PVDIS experiments.Internal document, 2014.

L. W. MO and Y. S. TSAI.Radiative corrections to elastic and inelastic ep and up scattering.Rev. Mod. Phys., 41:205–235, Jan 1969.

Min-Shih Chen and Peter Zerwas.Equivalent-particle approximations in electron and photon processes ofhigher-order qed.Phys. Rev. D, 12:187–197, Jul 1975.

J. Beringer et al.Review of particle physics.Phys. Rev. D, 86:010001, 2012.

Yung-Su Tsai.

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Wiser Code Summary

Pair production and bremsstrahlung of charged leptons.Rev. Mod. Phys., 46:815–851, Oct 1974.

V.M. Budnev, I.F. Ginzburg, G.V. Meledin, and V.G. Serbo.The two-photon particle production mechanism. physical problems.applications. equivalent photon approximation.Physics Reports, 15(4):181 – 282, 1975.

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