monopole production and rapid decay of gauge fields n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Monopole production and rapid decay of gauge fields PowerPoint Presentation
Download Presentation
Monopole production and rapid decay of gauge fields

Loading in 2 Seconds...

play fullscreen
1 / 27

Monopole production and rapid decay of gauge fields - PowerPoint PPT Presentation


  • 68 Views
  • Uploaded on

Monopole production and rapid decay of gauge fields. A iichi Iwazaki Nishogakusha University. High energy heavy ion collisions. Generation of color electric a nd magnetic fields according to a model of color glass condensate. High energy density o f the color gauge fields ~.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Monopole production and rapid decay of gauge fields' - shada


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
monopole production and rapid decay of gauge fields

Monopole production and rapid decay of gauge fields

AiichiIwazaki

Nishogakusha University

slide2

High energy heavy ion collisions

Generation of color electric

and magnetic fields

according to a model of

color glass condensate

slide3

High energy density

of the color gauge fields

~

decay time

< <1fm/c

(~0.5fm/c ?)

Quarks and gluons are produced

by the rapid decay of the gauge fields

We have not yet found

the rapid decay mechanism

of the gauge fields.

Hirano, Nara

2004

thermalized

quark gluon plasma

We wish to propose a rapid decay mechanism of the gauge fields.

slide4

Characteristics of the gauge fields

Homogeneous in longitudinal direction

width of

flux tube

Ensemble of

Z2 vortices ?

Dumitru,Nara

Petreska, 2013

saturation

momentum

field strength

( RHIC or LHC )

The gauge fields are unstable.

slide5

Exponential growth of

fluctuations around

the gauge fields

|A(pL=p,t)/A(pL=p,t=0|2

J. Berges, S. Scheffer and D. Sexty, 2008

Exponential growth of the distance

between nearby gauge fields at t=0

Kunihiro, Muller, Ohnishi, Schafer,

Takahashi, Yamamoto (2010, 2013)

B B’ t=0

slide6

Exponential growth of

longitudinal pressure of

fluctuations around

the gauge fields in expanding

glasma (τ,ηcoordinates )

Romatschke and Venugopalan 2006

Fukushima and Gelis 2011

It has been found that

these instabilities do not

lead to sufficiently rapid decay

of the gauge fields for QGP to be

realized within 1fm/c.

They have been discussed to

be Nielsen-Olesen instabilities.

slide7

Nielsen-Olesen instability

Nielsen and Olesen

1978,

Iwazaki 2008,

classical instability in SU(2) gauge theory

Itakura, Fujii, 2008

(charged vector fields

are fluctuations around

the gauge fields)

(Electromagnetic fields

represent the background

gauge fields)

The term can be positive or negative

for arbitrary magnetic field B

slide8

HomogeneousB

Nielsen-Olesenunstable modes

occupying lowest Landau level

negative potential

growth rate

Eq. of motion

Negative potential

forhomogeneous B

Bound states in the Lowest Landau level

-2gB

growth rate

Potential for

inhomogeneous B

Bound states exist with

We may represent these bound states by using effective magnetic field

slide9

Numerical results ( nonexpanding glasma )

J. Berges, S. Scheffer and D. Sexty, 2008

Kunihiro, Muller, Ohnishi, Schafer,

Takahashi, Yamamoto (2010, 2013)

growth rate

A roughly

estimated decay time

of the background fields

saturation

momentum

When we represent the growth rate

by using effective homogeneous

magnetic field such as ,

we find

slide10

Effective Lagrangian of describing the instability

under inhomogeneousmagnetic fields is given such

that using effective homogeneous magnetic field

small effective mass

( imaginary )

small growth rate

long decay time

slide11

Using the effective Lagrangian, we calculate the back reaction of the unstable modes

on the background gauge fields and show how fast the fields decay.

Similarly, we wish to calculate the back reaction of magnetic monopoles on the background gauge fields

by using an effective Lagrangian of the monopoles.

The monopoles are such objects whose condensation gives rise to “quark confinement” in QCD.

We show that the monopole production leads to much more

rapid decay of the gauge fields than the production of

Nielsen-Olesen unstable modes

slide12

Effective Lagrangian of magnetic monopoles

describing quark confinement

describes dual superconductors

larger than

for

magnetic charge

‘tHooft

Mandelstam

1976

Koma, Suzuki

2003

dual gauge fields

monopole field

slide13

We calculate the decay time of background color

electric (magnetic ) fields by using the effective

Lagrangianof Niesen-Olesenunstable modes

(magnetic monopoles ) in expanding glasma

(τ,ηcoordinates )

Note that

the monopoles occupy Landau levels under

background electric field, while Nielsen-Olesen

modes occupyLandau levels under magnetic field.

slide14

Our assumptions

Relevant monopoles occupy only

the lowest Landau level

Their distribution is almost homogeneous in

transverse plain so that magnetic field affected by

the monopoleproductionis almost homogeneous.

The similar assumptions for Nielsen-Olesen

unstable modes are adopted.

slide15

Effective Lagrangian of Nilesen-Olesen

(N-O) unstable modes in τ,ηcoordinates

Assuming homogeneous

distribution of N-O modes

in transverse plain, the dynamical

variable is left.

( wave functions of

the lowest Landau level )

slide16

Effective Lagrangian of magnetic monopoles

in the lowest Landau level

Nielsen-Olesen monopole

wave functions of

the lowest Landau level under

slide17

Equations of motion of Nielsen-Olesen modes

Maxwell eq.

homogeneous in

The equations describe how the electric field

decays via the production of Nielsen-Olesen unstable modes

We assume that

background magnetic field decreases

with the expansion

slide18

initial conditions

We use the initial conditions given by Dusling, Gelis, and Venugopalan

2011, 2012

That is, we include next to

leading order of quantum

effects on the evolution

of the background gauge

fields.

τ→0

Whittaker function

Without taking average of initial values

after obtaining the time evolution of we take the initial value,

τ→0

slide19

asτ→0

Positive energy solutions of the equation with the parameters,

Whittaker function

slide20

For simplicity, we take the simple initial conditions,

τ→0

This initial condition comes from the average,

τ→0

with the use of the formulae,

τ→0

Similar procedures of initial conditions even in the case of the magnetic monopoles are assumed.

slide21

tentative results

Decay of the electric field

producing Nielsen-Olesen

modes

We should note how

the gauge field rapidly

decays producing

the magnetic

monopoles.

fm/c

1 fm/c

Decay of the magnetic field

producing magnetic monopoles

ten times more rapid decay

fm/c

0.1fm/c

slide22

Initial amplitude of Nielsen-Olesen unstable modes

Initial amplitude of magnetic monopoles

The initial amplitude is

10 times larger than the

amplitude ofNielsen-

Olesen unstable modes

slide23

Pair creations of magnetic monopoles under

magnetic fields by Schwinger mechnism

production rate of monopoles

Compare the production rate of the monopoles

with that of Nielsen-Olesen unstable modes

production rate of N-O modes

Tanji and Itakura, 2012

The production rate of the monopoles

is about 10 times larger than that

of Nielsen-Olesen unstable modes.

conclusions
conclusions

We have shown that the gauge fields generated after

high energy heavy ion collisions decay much more rapidly

producing magnetic monopoles than Nielsen-Olesen

unstable modes.

Although our calculation does not properly take into

account precise initial conditions so that the result is

preliminary, it shows that the role of the magnetic

monopolesin the realization of thermalized QGP is

important.

slide26

Numerical simulations

exponential growth of

the fluctuations

time

J. Berges, S. Scheffer and D. Sexty, 2008

slide27

Numerical simulations

Exponential growth of the distance

between nearby gauge fields

t

( in our notations )

B B’ t=0

Kunihiro, Muller, Ohnishi, Schafer, Takahashi, Yamamoto (2010, 2013)