Influence of Confinement on Barriers for Alkoxide …

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Formation Lengths:
Hadron Formation Lengths:
Hadron
QCD Confinement in Forming Systems
QCD Confinement in Forming Systems

Will Brooks
Will Brooks
Jefferson Lab
Jefferson Lab

Electrons
Workshop on Intersections of Nuclear Physics with Neutrinos and Electrons
Workshop on Intersections of Nuclear Physics with Neutrinos and
May 5, 2006
May 5, 2006

Main Focus
Main Focus

(cid:132)(cid:132) Space

Space–time characteristics of
hadronization
time characteristics of hadronization
–– Formation lengths, production lengths for several

Formation lengths, production lengths for several hadron

species:
hadron species:

How do hadrons form, and how long does it take?””
““How do hadrons form, and how long does it take?

Quark energy loss and multiple scattering
(cid:132)(cid:132) Quark energy loss and multiple scattering
–– How big is the energy loss, and how does it behave? E.g., an ans

How big is the energy loss, and how does it behave? E.g., an answer for
wer for
normal nuclear density and temperature might be:
normal nuclear density and temperature might be:

/fm at 5 fm, proportional to distance squared””
100 MeVMeV/fm at 5 fm, proportional to distance squared
““100

Numerous other studies: correlations, associated photons
Numerous other studies: correlations, associated photons

Steps: How Does Confinement Assemble Hadrons?
Steps: How Does Confinement Assemble Hadrons?

Step 1: Isolate correct interaction mechanisms — physical picture
physical picture
Step 1: Isolate correct interaction mechanisms

–– ModelsModels
Lattice studies require technical development, not happening soonn
–– Lattice studies require technical development, not happening soo
variable studies needed
, multi–variable studies needed
–– MultiMulti–hadron

hadron, multi

ncies
Step 2: Extract characteristic parameters and functional dependencies
Step 2: Extract characteristic parameters and functional depende

Length scales
–– Length scales
Flavor dependence, size dependence
–– Flavor dependence, size dependence
Energy loss
–– Energy loss
Correlation functions
–– Correlation functions

Interaction mechanisms
Interaction mechanisms

(cid:132)(cid:132) Ubiquitous sketch of

Ubiquitous sketch of hadronization

process: string/color flux tube
hadronization process: string/color flux tube

(cid:132)(cid:132) Confinement process isn

Confinement process isn’’t finished yet, these are

t finished yet, these are colored

pairs:
colored pairs:

How do we get to colorless systems?
(cid:132)(cid:132) How do we get to colorless systems?
Is the above picture reality, or just a nice story?(!)
(cid:132)(cid:132) Is the above picture reality, or just a nice story?(!)

Interaction mechanisms
Interaction mechanisms

(cid:132)(cid:132) An alternative mechanism:

An alternative mechanism: ““gluon

gluon bremsstrahlung

bremsstrahlung modelmodel””: :

GY

RG

All hadron color explicitly resolved in this picture

Experimentally, it is completely unknown what the dominant mechanism is

Experimental Studies: ““Hadron
Experimental Studies:

Attenuation””
Hadron Attenuation

(cid:132)(cid:132) We can learn about

We can learn about hadronization
reaction mechanisms from nuclear DIS
reaction mechanisms
from nuclear DIS

hadronization distance scales

distance scales and
and

(cid:132)(cid:132) Nucleus acts as a spatial analyzer for outgoing

hadronization
Nucleus acts as a spatial analyzer for outgoing hadronization
products
products

formation lengths:
Hadron formation lengths:
Hadron
magnitude expectations
order–ofof–magnitude expectations
order

(cid:132)(cid:132) Given

hadron size

size RRh, can build color field of
Given hadron
. In lab frame this is boosted:
less than t0 ~~RRh/c/c. In lab frame this is boosted:
less than t

, can build color field of hadron

in its rest frame in time no
hadron in its rest frame in time no

t =
f

R
h

E
m

If take, e.g., the pionpion mass, radius 0.66 fm, E = 4
If take, e.g., the

mass, radius 0.66 fm, E = 4 GeVGeV, then

, then ttf ~ 20 fm
~ 20 fm..

Slightly more sophisticated, if gluon emission time dominates
(cid:132)(cid:132) Slightly more sophisticated, if gluon emission time dominates

t

f

≈

)

2
1(
E
z
−
h
2
2
mk
+
T
h

,

k
T

Λ≈

QCD

≈

2.0

GeV

If take, e.g., pionpion mass, mass, zz = = EEhadron
If take, e.g.,

hadron//νν = 0.5, E

= 0.5, Eh = 4 = 4 GeVGeV, then

~ 13 fm
, then ttff ~ 13 fm

matched to nuclear dimensions!
WellWell–matched to nuclear dimensions!

Time scales for hadron
Time scales for

formation
hadron formation

(cid:132)(cid:132) Can identify multiple time scales? E.g., isolate the

production length
Can identify multiple time scales? E.g., isolate the production length
formation length?
and the formation length?
and the

Formation length tf
Time required to produce
fully-developed hadron
Signaled by interactions with
known hadron cross sections
No gluon emission

Production length tp
Time required to produce
“colorless pre-hadron”
or “colorless dipole”
Signaled by medium-stimulated
energy loss via gluon emission

It is essentially unknown what these time scales are