Radiative corrections to e + e + Szymon Tracz Institute of - - PowerPoint PPT Presentation

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Radiative corrections to e + e + Szymon Tracz Institute of - - PowerPoint PPT Presentation

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Motivation NLO corrections to pion pair production Results Conclusions and outlook Radiative corrections to e + e + Szymon Tracz Institute of Physics, University of Silesia Katowice June 20, 2018 Szymon Tracz Radiative

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Motivation NLO corrections to pion pair production Results Conclusions and outlook

Radiative corrections to e+e− → π+π−γ

Szymon Tracz

Institute of Physics, University of Silesia Katowice

June 20, 2018

Szymon Tracz Radiative corrections to e+e− → π+π−γ

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Motivation NLO corrections to pion pair production Results Conclusions and outlook

Outline

1

Motivation

2

NLO corrections to pion pair production

3

Results

4

Conclusions and outlook

Szymon Tracz Radiative corrections to e+e− → π+π−γ

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Motivation NLO corrections to pion pair production Results Conclusions and outlook

KLOE, CMD-2 and SND measurements

  • A. Anastasi et al. [KLOE-2 Collaboration], JHEP 1803 (2018) 173

Szymon Tracz Radiative corrections to e+e− → π+π−γ

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Motivation NLO corrections to pion pair production Results Conclusions and outlook

BaBar, BES and KLOE measurements

  • M. Ablikim et al. [BESIII Collaboration], Phys. Lett. B 753 (2016) 629

Szymon Tracz Radiative corrections to e+e− → π+π−γ

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Motivation NLO corrections to pion pair production Results Conclusions and outlook

BaBar, BES and KLOE measurements

  • A. Anastasi et al. [KLOE-2 Collaboration], JHEP 1803 (2018) 173

Szymon Tracz Radiative corrections to e+e− → π+π−γ

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Motivation NLO corrections to pion pair production Results Conclusions and outlook

dσ(e+e− → hadrons+γisr) = H(Q2, θγ)dσ(e+e− → hadrons)(Q2)

e− e+ γ Q2 hadrons hadronic current radiative corrections

measurement of R(s) over the wide range of energies, from threshold up to √s large luminosity from factories compensate α/π from photon radiation precise measurement involves radiative corrections FSR contribution has to be subtracted Monte Carlo generators needed (Phokhara)

Szymon Tracz Radiative corrections to e+e− → π+π−γ

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Motivation NLO corrections to pion pair production Results Conclusions and outlook

Phokhara Monte Carlo generator

PHOKHARA 9.3: π+π−, µ+µ−, 4π, ¯ NN, 3π, KK, Λ¯ Λ, Pγ, J/ψ, ψ(2s), χc1, χc2

  • ISR at NLO: virtual corrections to one photon events

and two photon emission at tree level

  • FSR at NLO: π+π−, µ+µ−, K +K −, ¯

pp

  • tagged or untagged photon
  • ISR at NNLO for e+e− → hadrons (muons)

Szymon Tracz Radiative corrections to e+e− → π+π−γ

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Motivation NLO corrections to pion pair production Results Conclusions and outlook

NLO corrections for e+e− → µ+µ−γ

  • F. Campanario, H. Czy˙

z, J. Gluza, M. Gunia, T. Riemann, G. Rodrigo and V. Yundin, JHEP 1402 (2014) 114,[arXiv:1312.3610 [hep-ph]]. Szymon Tracz Radiative corrections to e+e− → π+π−γ

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Motivation NLO corrections to pion pair production Results Conclusions and outlook

NLO corrections for e+e− → µ+µ−γ

  • F. Campanario, H. Czy˙

z, J. Gluza, M. Gunia, T. Riemann, G. Rodrigo and V. Yundin, JHEP 1402 (2014) 114,[arXiv:1312.3610 [hep-ph]]. Szymon Tracz Radiative corrections to e+e− → π+π−γ

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Motivation NLO corrections to pion pair production Results Conclusions and outlook

Two photons emission

Szymon Tracz Radiative corrections to e+e− → π+π−γ

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Motivation NLO corrections to pion pair production Results Conclusions and outlook

Virtual corrections

Szymon Tracz Radiative corrections to e+e− → π+π−γ

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Motivation NLO corrections to pion pair production Results Conclusions and outlook

Modeling pion - photon interaction

  • Factorization of the form factor:

= =

Fπ(s) × sQED Fπ(q2) × sQED

  • Real emission proportional to the form factor
  • Form factor:

Fπ(q2) =

  • n

cπ

ρnBWρn(q2)

  • Renormalizable model
  • H. Czyz, A. Grzelinska and J. H. Kuhn, Phys. Rev. D 81 (2010) 094014

Szymon Tracz Radiative corrections to e+e− → π+π−γ

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Motivation NLO corrections to pion pair production Results Conclusions and outlook

Tests of the code

check of the scalar integrals using few different libraries (QCDLOOP, LoopTools) comparison of two independent codes check the stability of the code (soft, collinear limit) - agreement at the level 10−5 test for the independence on the separation parameter between soft and hard part ( below 1 ) cancelation of infrared divergences between soft and virtual part gauge invariance

Szymon Tracz Radiative corrections to e+e− → π+π−γ

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Motivation NLO corrections to pion pair production Results Conclusions and outlook √s = 1.02 GeV Pion tracks: 50o < θπ± < 130o , |pzπ± | > 90 MeV Missing photon angle: | cos θγ | > cos 15o Track mass: mtrk > 130 MeV q2 ∈ (0.35, 0.95) KLOE 2008

  • Q2 [GeV]

dσ(old+penta)−dσ(old) dσ(old)

1 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.002 0.0015 0.001 0.0005 −0.0005 −0.001 −0.0015 −0.002 −0.0025 Szymon Tracz Radiative corrections to e+e− → π+π−γ

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Motivation NLO corrections to pion pair production Results Conclusions and outlook √s = 3.773 GeV Pion tracks: 22.9o < θπ± < 157.1o , |pTπ± | > 300 MeV Minimal photon energy: Eγ > 400 MeV Missing photon angle: | cos θγ | < 0.8 or 0.86 < | cos θγ| < 0.92 q2 ∈ (0.35, 0.95) BES 2016

  • Q2 [GeV]

dσ(old+penta)−dσ(old) dσ(old)

1 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.003 0.002 0.001 −0.001 −0.002 −0.003 −0.004 Szymon Tracz Radiative corrections to e+e− → π+π−γ

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Motivation NLO corrections to pion pair production Results Conclusions and outlook √s = 10.56 GeV Pion tracks: 20o < θπ± < 160o , |pTπ± | > 300 MeV Minimal photon energy: Eγ > 3 GeV Missing photon angle: 20o < θγ < 160o |q1| > 1 GeV (π−) and |q2| > 1 GeV (π+) q2 ∈ (0.35, 0.95) BABAR 2012

  • Q2 [GeV]

dσ(old+penta)−dσ(old) dσ(old)

1 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.015 0.01 0.005 −0.005 −0.01 Szymon Tracz Radiative corrections to e+e− → π+π−γ

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Motivation NLO corrections to pion pair production Results Conclusions and outlook

Leading logarithmic approximation for virtual FSR corrections

KLOE 2008

  • Q2 [GeV]

dσ(full)−dσ(old) dσ(old)

1 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.004 0.002 −0.002 −0.004 −0.006 −0.008 Szymon Tracz Radiative corrections to e+e− → π+π−γ

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Motivation NLO corrections to pion pair production Results Conclusions and outlook

Pion form factor

  • H. Czyz, A. Grzelinska and J. H. Kuhn, Phys. Rev. D 81 (2010) 094014

Szymon Tracz Radiative corrections to e+e− → π+π−γ

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Motivation NLO corrections to pion pair production Results Conclusions and outlook

Conclusions The size of the pentabox contribution is too small to be able to explain discrepancies between KLOE and BABAR data. For KLOE experiment missing virtual FSR corrections may be non negligible but small For BaBar and BES experiment virtual FSR corrections are small due to the behavior of the form factor Forthcoming developments Implementation of the radiative corrections to initial states at two-loop level for the process e+e− → hadrons +γ using leading logarithmic approximation

Szymon Tracz Radiative corrections to e+e− → π+π−γ