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

The 4th Dimension

• f the Proton

Andrea BIANCONI, Egle TOMASI-GUSTAFSSON

GSI, 6-XII-2016 1

The 4th Dimension

• f 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

]

2

[GeV

2

q 10 20 30 40

p

F

3 −

10

2 −

10

1 −

10 1

4 6 8 10

1 −

10

Andrea BIANCONI, Egle TOMASI-GUSTAFSSON

2

The Time-like Region

Expected QCD scaling (q2)2

GSI, 6-XII-2016

GE=GM

Andrea BIANCONI, Egle TOMASI-GUSTAFSSON

GSI, 6-XII-2016 3

p

F

0.1 0.2 0.3

(a)

p [GeV] 1 2 3

D

• 0.04
• 0.02

0.02 0.04

(b)

Proton TL EM Form Factors

Periodic structures recently discovered in TL region

• Hadron creation

from vacuum (Resonances?)

• A. Bianconi, E. T-G. Phys. Rev. Lett. 114,232301 (2015), PRC 93, 035201 (2016)

Andrea BIANCONI, Egle TOMASI-GUSTAFSSON

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Oscillations : regular pattern in PLab

p

F

0.1 0.2 0.3

(a)

p [GeV] 1 2 3

D

• 0.04
• 0.02

0.02 0.04

(b)

A: Small perturbation B: damping C: r < 1fm D=0: maximum at p=0

GSI, 6-XII-2016

The relevant variable is pLab associated to the relative motion of the final hadrons.

Simple oscillatory behaviour Small number of coherent sources

• A. Bianconi, E. T-G. Phys. Rev. Lett. 114,232301 (2015), PRC 93, 035201 (2016)

Andrea BIANCONI, Egle TOMASI-GUSTAFSSON

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Fourier Transform

r (fm)

0.5 1 1.5 2

• 4

10

• 3

10

• 2

10

• 1

10 1 10

2

10

)

3

(r) (1/fm M r (fm)

0.6 0.8 1 1.2 1.4 1.6

• 0.05

0.05 0.1 0.15

)

3

M(r) (1/fm

• Rescattering processes
• Large imaginary part
• Related to the time evolution of the charge density?
• Consequences for the SL region?
• Data from BESIII confirm the structure
• Expected from PANDA

(E.A. Kuraev, E. T.-G., A. Dbeyssi, PLB712 (2012) 240)

GSI, 6-XII-2016

F0 ==

Definition of TL-SL Form Factors

Andrea BIANCONI, Egle TOMASI-GUSTAFSSON

GSI, 6-XII-2016 6

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 7

time time time

e e’ p p’ p p

_

p p

_

e e + e+ e SL TL+ TL -

space-time distribution of the electric charge in the space-time volume TL photon can NOT test a space distribution. SL photon ‘sees’ a charge density How to connect and understand the amplitudes?

Definition of TL-SL Form Factors

Andrea BIANCONI, Egle TOMASI-GUSTAFSSON

GSI, 6-XII-2016 8

represent projections of the same distribution in orthogonal subspaces

Definition of TL-SL Form Factors

Andrea BIANCONI, Egle TOMASI-GUSTAFSSON

GSI, 6-XII-2016 9

Amplitude for creating charge-anticharge pairs at time t. Charge distribution => distribution in time

• f

Charge: photon-charge coupling

Fourier transform of a stationary charge and current distribution

p p p p γ* γ*

1

X

2

X X q q g

The simplest picture: qq pair + compact di-quark Resolved representation Unresolved

Andrea BIANCONI, Egle TOMASI-GUSTAFSSON

GSI, 6-XII-2016 10

p p

_

γ* q

A

P

B

P FF

Amplitudes

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 11

p p p p γ* γ*

1

X

2

X X q q g

Implementing causality

X (TL) => q(TL) weights related to the masses Fock state of N constituents

Andrea BIANCONI, Egle TOMASI-GUSTAFSSON

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Examples

time space X

1

X

2

X time space

2

x

1

x

Causality implies t1<t2

p p p p γ* γ*

1

X

2

X X q q g

Unresolved pair created at t1=0, implies t<0 Assuming independent probability

• f creating a (anti)proton (in LC):

Andrea BIANCONI, Egle TOMASI-GUSTAFSSON

GSI, 6-XII-2016 13

Examples

• Homogeneous distribution for positive times:
• Exponential damping (a is finite):

Andrea BIANCONI, Egle TOMASI-GUSTAFSSON

GSI, 6-XII-2016 14

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 15

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 q0 =M+ia corresponds a pole q0 =-(M +ia) Positive poles => creation process Negative poles=> annihilation process

Andrea BIANCONI, Egle TOMASI-GUSTAFSSON

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Examples: Breit-Wigner

A Breit-Wigner probability contains all four poles: The combination: corresponds to

t (fm/c)

• 3
• 2
• 1

1 2 3

R(t)

• 0.2

0.2 0.4 0.6 0.8 1

advanced (t > 0) retarded (t < 0)

proton-antiproton annihilation proton-antiproton creation

Retarded response of a classical bound and damped

• scillator to a external perturbation

M=1 GeV, Γ=0.1-1 GeV

Andrea BIANCONI, Egle TOMASI-GUSTAFSSON

GSI, 6-XII-2016 17

Several spectators: dipole and asymptotics

) τ (

1

R ) τ (t-

2

R (t) δ ( t )

2

* R

1

R

1

F

2

F

t (fm/c)

• 3
• 2
• 1

1 2 3

R(t)

• 0.4
• 0.2

0.2 0.4 0.6 0.8 1

Use FT properties of convolutions Chain of two oscillators,

• ne directly connected to the photon

The second is a decaying correlation between active quark and spectator

Andrea BIANCONI, Egle TOMASI-GUSTAFSSON

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More complicated examples

Sum of two contributions of equal shape: Three quark-antiquarks pair in the intermediate state. periodic modulation

Conclusion

Andrea BIANCONI, Egle TOMASI-GUSTAFSSON

19 GSI, 6-XII-2016

• 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

• Simple functions R(t)
• Origin of oscillatory phenomena

t (fm/c)

• 3
• 2
• 1

1 2 3

R(t)

• 0.4
• 0.2

0.2 0.4 0.6 0.8 1