Spatial structure of the color field in the SU(3) flux tube · Marshall Baker, Paolo Cea, Volodymyr Chelnokov, Leonardo Cosmai, Francesca Cuteri, Alessandro Papa 23 July 2018 M. Baker,

IntroductionSimulations results

Extracting the nonperturbative confining fieldConclusions and Problems

Spatial structure of the color field in the SU(3)flux tube

Marshall Baker, Paolo Cea, Volodymyr Chelnokov,Leonardo Cosmai, Francesca Cuteri, Alessandro Papa

23 July 2018

M. Baker, P. Cea, V. Chelnokov, L. Cosmai, F. Cuteri, A. Papa Spatial structure of the color field in the SU(3) flux tube



Outline

1 Introduction

2 Simulations results

3 Extracting the nonperturbative confining field

4 Conclusions and Problems




Introduction

The chromoelectric field between static quark-antiquark pair isconcentrated in a flux tube that connects quark and antiquark.This creates a linear potential between quark and antiquark,causing color confinement.

We measure full profile of the flux tube in SU(3) LGT and proposea way of separating the field into short-range perturbative andlong-range nonperturbative parts.




Field operator

W

UP

L (Schwinger line)

t

x

d

xl

xt

ρconnW =

⟨tr(WLUPL

†)⟩〈tr(W )〉

− 1

N

〈tr(UP)tr(W )〉〈tr(W )〉

.




Smearing procedure

For the Monte-Carlo simulations we used the MILC code, modifiedto calculate the relevant observables.To improve the signal-to-noise ratio the smearing procedure wasapplied, which consisted of one HYP smearing step withparameters (1.0, 0.5, 0.5) for the links in time direction, followed bya set of APE smearing steps with parameter αAPE = 0.167.




Field measurements

We have measured all field components using the operator ρconnW

for the following lattice setups:

Table: Summary of the runs performed in the SU(3) pure gauge theory(measurements are taken every 100 upgrades of the lattice configuration).

β lattice distanced

statistics smearingsteps

6.370 484 0.95 fm 1000 806.240 484 1.14 fm 4000 1006.136 484 1.33 fm 16000 120




Ex field, d = 0.95 fm

xl [fm]

0.0

0.5

1.0xt [fm]

0.50.0

0.5

E x [G

eV2 ]

0.8

0.4

0.0

0.4

0.8




Ey field, d = 0.95 fm

xl [fm]

0.0

0.5

1.0xt [fm]

0.50.0

0.5

E y [G

eV2 ]

0.8

0.4

0.0

0.4

0.8




Ez field, d = 0.95 fm

xl [fm]

0.0

0.5

1.0xt [fm]

0.50.0

0.5

E z [G

eV2 ]

0.8

0.4

0.0

0.4

0.8




Bx field, d = 0.95 fm

x l [fm]

0.0

0.5

1.0xt [fm]

0.50.0

0.5

B x [G

eV2 ]

0.004

0.000

0.004




By field, d = 0.95 fm

x l [fm]

0.0

0.5

1.0xt [fm]

0.50.0

0.5

B y [G

eV2 ]

0.004

0.000

0.004




Bz field, d = 0.95 fm

x l [fm]

0.0

0.5

1.0xt [fm]

0.50.0

0.5

B z [G

eV2 ]

0.004

0.000

0.004




Chromoelectric field structure

We expect that the measured chromoelectric field is composedfrom two parts – the perturbative part, which behaves like aCoulomb electrostatic field and the nonperturbative confining partwhich should be purely longitudinal, at least far away from fieldsources.

~E (~r) = ~EC (~r) + ~Enp(~r)




Chromoelectric field structure

The Coulomb part is just sum of the fields of two sources withcharge Q and −Q. To be able to partially explain the behaviour ofthe field close to the sources – specifically that the maximum oflongitudinal field component is located at nonzero distance fromthe sources, we take the field to be the field of a uniformly chargedsphere of a radius R.

~EC (~r) = ~ER(~r − ~r1, q) + ~ER(~r − ~r2,−q)

~ER(r , q) =q~r

max(r3,R3)




Extracting the nonperturbative part

To extract the nonperturbative part, we make a fit of thetransverse field component Ey to the Coulomb field ~EC (~r). Totake into account that the field is measured using a plaquette of afinite size, we take

ρconnW (rl , rt) =

∫ rt+1

rt

~E (rl , y , 0)dy

From the fit we determine the parameters q – ”electrostatic”charge for the quark and antiqark, and R – radius for theperturbative field.




Extracting the nonperturbative part d = 1.14 fm

0.0 0.2 0.4 0.6 0.8 1.0 1.2xt [fm]

0.4

0.3

0.2

0.1

0.0

0.1

0.2

0.3

0.4

E y [G

eV2 ]

xl = 0xl = 2xl = 4xl = 6xl = 8xl = 10xl = 12xl = 14xl = 16




Extracting the nonperturbative part

Table: Results of the fits extracting Coulomb part of the chromoelectricfield

β q R χ2r

6.370 0.26(3) 0.13(3) 6.36.240 0.29(5) 0.161(18) 3.436.136 0.29(17) 0.21(13) 1.09




Nonperturbative field Ey , d = 1.14 fm

xl [fm]

0.0

0.5

1.0xt [fm]

0.50.0

0.5

E y [G

eV2 ]

0.4

0.0

0.4




Nonperturbative field Ez , d = 1.14 fm

xl [fm]

0.0

0.5

1.0xt [fm]

0.50.0

0.5

E z [G

eV2 ]

0.4

0.0

0.4




Nonperturbative field Ex , d = 1.14 fm

xl [fm]

0.0

0.5

1.0xt [fm]

0.50.0

0.5

E x [G

eV2 ]

0.4

0.0

0.4




Conclusions

For four dimensional SU(3) pure gauge model full profile ofchromoelectromagnetic field in presence of two static chargesis measured using Monte Carlo simulations.

All the components of measured chromomagnetic field arecompatible with zero. The chromoelectric field has radialsymmetry.

The transverse components of the electromagnetic field canbe described (when not too close to the sources) by theCoulomb-type field.

After subtracting the Coulomb field the longitudinalcomponent of electric field does not change with longitudinaldisplacement (away from sources).




Thank you for attention


Documents

Spatial structure of the color field in the SU(3) flux tube · Marshall Baker, Paolo Cea, Volodymyr Chelnokov, Leonardo Cosmai, Francesca Cuteri, Alessandro Papa 23 July 2018 M. Baker,