The 4th Dimension The 4th Dimension of the Proton of the Proton - PowerPoint PPT Presentation

The 4th Dimension The 4th Dimension of the Proton of the Proton Andrea Bianconi Università Di Brescia, INFN Pavia, Italy Egle Tomasi-Gustafsson CEA,IRFU,SPhN, Université Paris-Saclay (France) PANDA LIX COLLABORATION MEETING, GSI, 5-9 XII 2016 Andrea BIANCONI, Egle TOMASI-GUSTAFSSON GSI, 6-XII-2016 1

The Time-like Region 1 p F GE=GM 1 1 − − 10 Expected QCD scaling (q 2 ) 2 10 2 − 10 4 6 8 10 3 − 10 10 20 30 40 2 2 q [GeV ] Andrea BIANCONI, Egle TOMASI-GUSTAFSSON GSI, 6-XII-2016 2

Proton TL EM Form Factors p F (a) 0.3 Periodic structures recently discovered 0.2 in TL region 0.1 - Hadron creation from vacuum 0.04 (b) (Resonances?) 0.02 D 0 -0.02 -0.04 0 1 2 3 p [GeV] A. Bianconi, E. T-G. Phys. Rev. Lett. 114,232301 (2015), PRC 93, 035201 (2016) Andrea BIANCONI, Egle TOMASI-GUSTAFSSON GSI, 6-XII-2016 3

Oscillations : regular pattern in P Lab The relevant variable is p Lab associated to the relative motion of the final hadrons. p F (a) 0.3 0.2 0.1 0.04 (b) 0.02 A: Small perturbation B: damping D 0 C: r < 1fm D=0: maximum at p=0 -0.02 Simple oscillatory behaviour -0.04 Small number of coherent sources 0 1 2 3 p [GeV] A. Bianconi, E. T-G. Phys. Rev. Lett. 114,232301 (2015), PRC 93, 035201 (2016) Andrea BIANCONI, Egle TOMASI-GUSTAFSSON GSI, 6-XII-2016 4

Fourier Transform 3 3 M (r) (1/fm ) M(r) (1/fm ) 0 0.15 2 10 10 0.1 F 0 = = 1 0.05 -1 10 -2 10 0 -3 10 -0.05 -4 10 0.6 0.8 1 1.2 1.4 1.6 0 0.5 1 1.5 2 r (fm) r (fm) Rescattering processes • Large imaginary part • Related to the time evolution of the charge density? • (E.A. Kuraev, E. T.-G., A. Dbeyssi, PLB712 (2012) 240) Consequences for the SL region? • Data from BESIII confirm the structure • Expected from PANDA • Andrea BIANCONI, Egle TOMASI-GUSTAFSSON GSI, 6-XII-2016 5

Definition of TL-SL Form Factors In SL- Breit frame (zero energy transfer): In TL-(CMS): : distribution in time of the qqbar pair formation E.A. Kuraev, A. Dbeyssi, E. T-G., PLB 712, 240 (2012) Andrea BIANCONI, Egle TOMASI-GUSTAFSSON GSI, 6-XII-2016 6

Definition of TL-SL Form Factors e e’ space-time distribution of the electric charge in the space-time volume SL p’ p SL photon ‘sees’ a charge density time _ _ TL - e+ TL photon can NOT test a space TL+ + p p e distribution. How to connect and understand e p p e the amplitudes? time time Andrea BIANCONI, Egle TOMASI-GUSTAFSSON GSI, 6-XII-2016 7

Definition of TL-SL Form Factors represent projections of the same distribution in orthogonal subspaces Andrea BIANCONI, Egle TOMASI-GUSTAFSSON GSI, 6-XII-2016 8

Charge: photon-charge coupling Fourier transform of a stationary charge and current distribution Amplitude for creating charge-anticharge pairs at time t. Charge distribution => distribution in time of p p p p X 2 The simplest picture: qq pair + g compact di-quark X q q X 1 γ * γ * Resolved Unresolved representation Andrea BIANCONI, Egle TOMASI-GUSTAFSSON GSI, 6-XII-2016 9

Amplitudes p P A q γ * FF P _ B p forbidden leads to imaginary part of F(q) even if F(x) is real affects only phases (T-conservation) Andrea BIANCONI, Egle TOMASI-GUSTAFSSON GSI, 6-XII-2016 10

Implementing causality X (TL) => q(TL) Fock state of N constituents p p p p X 2 g X q q weights related to the masses X 1 γ * γ * Andrea BIANCONI, Egle TOMASI-GUSTAFSSON GSI, 6-XII-2016 11

Examples time X 2 x time 2 X 0 space Causality implies t 1 <t 2 X 1 x 1 Unresolved pair created space at t 1 =0, implies t<0 p p p p Assuming independent probability of creating a (anti)proton (in LC): X 2 g X q q X 1 γ * γ * Andrea BIANCONI, Egle TOMASI-GUSTAFSSON GSI, 6-XII-2016 12

Examples - Homogeneous distribution for positive times: - Exponential damping ( a is finite): Andrea BIANCONI, Egle TOMASI-GUSTAFSSON GSI, 6-XII-2016 13

Examples: Monopole-like shape F(x) is non zero in past and future LC. Annihilation and creation processes are time symmetric. Differ by a phase. Summing two terms with the same phase: 1/a has the meaning of a formation time. For large t, R(t) is very small. Either the second pair is formed within 1/a or the system evolves differently. => zero mass resonance of width a Andrea BIANCONI, Egle TOMASI-GUSTAFSSON GSI, 6-XII-2016 14

Examples: Lorentzian resonance Replacing q->q-M : one obtains poles By Fourier transform: Response of a classical damped oscillator to an instantenous external force Negative energy states are allowed by particle- antiparticle symmetry. To each pole q 0 =M+ia corresponds a pole q 0 =-(M +ia) Positive poles => creation process Negative poles=> annihilation process Andrea BIANCONI, Egle TOMASI-GUSTAFSSON GSI, 6-XII-2016 15

Examples: Breit-Wigner A Breit-Wigner probability contains all four poles: R(t) cos(5*x)*exp(-abs(2*x)) 1 M=1 GeV, Γ =0.1-1 GeV 0.8 The combination: 0.6 retarded (t < 0) advanced (t > 0) 0.4 proton-antiproton proton-antiproton creation annihilation 0.2 corresponds to 0 -0.2 -3 -2 -1 0 1 2 3 t (fm/c) Retarded response of a classical bound and damped oscillator to a external perturbation Andrea BIANCONI, Egle TOMASI-GUSTAFSSON GSI, 6-XII-2016 16

Several spectators: dipole and asymptotics (t) δ R (t- ) τ 2 Use FT properties of convolutions F F Chain of two oscillators, 1 2 one directly connected to the photon The second is a decaying correlation R ( ) τ 1 R * R ( t ) between active quark and spectator 1 2 R(t) 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -3 -2 -1 0 1 2 3 t (fm/c) Andrea BIANCONI, Egle TOMASI-GUSTAFSSON GSI, 6-XII-2016 17

More complicated examples Three quark-antiquarks pair in the intermediate state. Sum of two contributions of equal shape: periodic modulation Andrea BIANCONI, Egle TOMASI-GUSTAFSSON GSI, 6-XII-2016 18

Conclusion • New understanding of Form Factors in the Time-like region: time distribution of quark-antiquark pair creation vertices • The distributions tested by the virtual photon are projections in orthogonal 1 and 3-dim spaces of the function F(x): and R(t) 1 0.8 • Simple functions R(t) 0.6 0.4 0.2 0 • Origin of oscillatory phenomena -0.2 -0.4 -3 -2 -1 0 1 2 3 t (fm/c) Andrea BIANCONI, Egle TOMASI-GUSTAFSSON GSI, 6-XII-2016 19