nuclear effects in hadronization...bk, j.nemchik, a.schäfer, a.tarasov, 2002 – p. 14/30. cronin...

Nuclear effects

in hadronization

Boris Kopeliovich

UTFSM & U. Heidelberg

– p. 1/30

Nuclear effects

in hadronization

Boris Kopeliovich

UTFSM Valparaiso

– p. 2/30

In-medium hadronizationThe hadronization proces lasts a short time of severalfms, whiledetectors are installed at macroscopic distances, so one cannotaccess many of the details of hadronization dynamics. Nucleiprovide a unique opportunity to place additional detectors, whichare the bound nucleons, next to the origin of the jet.

• Semi-inclusive hadron production in DIS (SIDIS) is probablythe most precise tool for such studies. The typical observable isthe multiplicity ratio,

RA(zh, pT) =dn(γ∗A → hX)/dzhd2pT

A dn(γ∗N → hX)/dzhd2pT

wherezh = p+h /p+

γ∗ ≈ Eh/Eγ∗ .

– p. 3/30

Hadron attenuation

Will Brooks’ collection

– p. 4/30

Data from CLAS

Will Brooks’ collection– p. 5/30

Hadron attenuation in SIDISPerturbative color neutralization

��

��

q

q

q

q

l l fp

h

γ∗ + ++ +

An intuitive (classical) picture of in-medium hadronization.

Two stages ofleadinghadron production:

– p. 6/30


��

��

q

q

q

q

l l fp

h

γ∗ + ++ +



(i) The parton originating from a hard reaction is regeneratingitscolor field via gluon radiation, which leads to vacuum energyloss. Multiple interactions in the medium induce an additionalradiation and energy loss;

– p. 6/30


��

��

q

q

q

q

l l fp

h

γ∗ + ++ +



(i) The parton originating from a hard reaction is regeneratingitscolor field via gluon radiation, which leads to vacuum energyloss. Multiple interactions in the medium induce an additionalradiation and energy loss;(ii) The leading quark picks up a sea antiquark, and the producedcolorless dipole (pre-hadron) attenuates in the medium(absorption). The dipole is forming the hadron wave functionover a path length which considerably exceeds the nuclear size.

– p. 6/30

String modelIn the c.m. ofe+e− annihilation the producedqq string isexpanding linearly with time.

In the target rest frame the string length saturates atLmax = mq/κ ≈ 0.3 fm. Production ofqq pairs fromvacuum split the string and makes it even shorter.

∗��

��

γ

q

q

q

q

q

q

z

p

t

��

��

qq

z

∗γ��

��

��

��

q

q

M

N

−dE/dz=κ

κl = qm

max0.3 fm

– p. 7/30

Production length scaleIf the hadron takes the main fraction of the jet energy,zh → 1,then energy conservation becomes an issue:

lp <Eγ∗(1 − zh)

|dE/dz|

[B.K. & F.Niedermayer, 1984]The main contribution to the rate of energy loss,dE

dz(z is

longitudinal coordinate), comes fromvacuumenergy loss, whichmay have either a nonperturbative origin (string tension),

−dE

dz

∣

∣

∣

∣

vac

≈ 1 GeV/ fm,

or perturbative (color field regeneration),

− dEdz

∣

∣

vac= 2αs

3πQ2, or both.

– p. 8/30

Broadening in a nuclear mediumA parton experiencing multiple interactions in the mediumincreases its meanp2

T linearly with the path lengthL (Brownianmotion). The coefficient was calculated within the dipoleapproach (M.Johnson, B.K., A.Tarasov, 2001),

∆p2T = 2 C(E) ρA L, where C(E) =

∂σqq(rT , E)

∂r2T

∣

∣

∣

∣

rT =0

The dipole cross sectionσqq(rT , E) is fitted to datafor real photoproduction andto F p

2 (x, Q2).

• Thus, the dipole phe-nomenology has a goodpredictive power for themagnitude of broadening.

– p. 9/30

Measuring the saturation scaleIn the nuclear rest frame saturation looks like color filtering for adipole (qq, or gg) of transverse separationrT and energyEpropagating through a nuclear medium. The partial elasticdipole-nucleus amplitude at impact parameterb reads,

fAdip(b) = 1 − e−

12

σNdip(rT ,E) TA(b) = 1 − e−

14

r2T Q2

A(b,E)

Calculation ofQ2A from the first principles looks pretty

hopeless, but one can get it from phenomenology.

A parton propagating through the nucleus experiencesbroadening of transverse momentum, which turns out to beexactly the saturation scale

∆p2T = Q2

A

Dolejsi, Hüfner, B.K. (1993)Johnson, B.K., Tarasov (2001)

– p. 10/30

Measuring broadeningBroadening has been measured in:

• pA (Drell-Yan; E772&E866)∆(pll

T)2 = z2ll∆p2

T

(quarkbroadening)〈zll〉 ≈ 0.9

• J/Ψ andΥ in pA (E772)∆(pll)2 ≈ ∆p2

T × 9/4

(gluonbroadening)

• eA (SIDIS; HERMES&CLAS)∆(ph

T)2 = z2h∆p2

T

(quarkbroadening)10 10

2

A

∆ P

2 T (

GeV

2 )0.0

0.2

0.4

DY E772DY E866J/ψΥ

J/ψ

Υ

DY

– p. 11/30

Probing the production length

Broadening originates mainly fromthe first stage of hadronization.Broadening of the pre-hadron pro-ceeds with a very small elastic crosssection and can be disregarded.• Thus, broadening is a sensi-tive probe for the production length,∆p2

T ∝ lp, which was predicted toshrink for leading hadrons,lp(zh) ∝ (1 − zh)

[B.K., F.Niedermayer, 1984].This is confirmed by HERMES data.

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

∆pt2 [G

eV2 ]

zh

π+ in Xe (HERMES preliminary)π- in Xe (HERMES preliminary)

π+ in Xe calc.π- in Xe calc.

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

∆pt2 [G

eV2 ]

zh

π+ in Kr (HERMES preliminary)π- in Kr (HERMES preliminary)

π+ in Kr calc.π- in Kr calc.

S.Domdey, D.Grünewald, B.K., H.J.Pirner, 2009– p. 12/30

Broadening in DIS at small x

Experimentally known

is zh =p+

h

q+

γ∗

T

hhh(z ,p )

Trγ

q

q1−α

α∗

∆(phT)2 =

z2h ∆p2

T∫

d2rT

∫ 1

0dα|Ψγ∗(rT , α)|2 σdip(rT , x)

×

∫

d2rT

{

1∫

zh

dα

α2

∣

∣Ψγ∗(rT , α, Q2)∣

∣

2σdip(rT , x)Dh/q

(

zh

α, Q2

)

+

1−zh∫

0

dα

(1 − α)2

∣

∣Ψγ∗(rT , α, Q2)∣

∣

2σdip(rT , x)Dh/q

(

zh

1 − α, Q2

)}

Ψγ∗ is known from pQCD;σdip, Dh/q from phenomenology.

– p. 13/30

Cronin effect in pA collisions

Broadening in hadron-nucleus collisions, knownas Cronin effect, canalso be calculated in aparameter free way, i.e.with no fit to the data to beexplained.

BK, J.Nemchik, A.Schäfer, A.Tarasov, 2002

– p. 14/30

Cronin effect at RHIC/LHC

A much weaker Cronin en-hancement∼ 10% was pre-dicted for RHIC. Later wasconfirmed by PHENIX dataondAu collisions.

Due to gluon shadowing evena weaker effect is expected atLHC.

PHENIX

0.8

0.9

1

1.1

1.2

0.8

0.9

1

1.1

1.2

0 2 4 6 8 10 12 14 16

pT (GeV/c)

RA(p

T)

√s−=200 GeV

√s−=5.5 TeV

– p. 15/30

Induced energy lossGetting additional multiple kicks in the medium the partonradiates more than in vacuum and is losing more energy. Thusbroadening results in an induced energy loss, relates as,

dE

dz

∣

∣

∣

∣

ind

=3αs

8∆p2

T (BDMPS, 1994)

Broadening measured in the HERMES experiment is very small,∆p2

T < 0.06 GeV2, several times smaller than measured inDrell Yan reaction at800 GeV. Then the induced energy loss isvanishingly small,−dE/dz|ind ∼< 0.04 GeV/ fm, compared tothe value−dE/dz|ind = 0.5 GeV/ fm (X.N.Wang & E.Wang,

2002) needed to describe HERMES data on nuclear attenuation.• Thus, the brand-new HERMES data on broadening rule outthe energy loss scenario as a dominant mechanism for hadronattenuation observed in the HERMES experiment.

– p. 16/30

Induced energy loss

Induced gluon radiation can be treated as a modification of thesplitting functions in the DGLAP evolution. This leads to amodification of the fragmentation functions in a medium[Wei-tian Wang, Xin-Nian Wang, 2009]

RMh

Ne

Kr(-0.05)

Xe(-0.2)

π+

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8

q=0.016 GeV2/fmq=0.024 GeV2/fmq=0.032 GeV2/fm

z

<E>=10.742 ∼ 18.358 GeV

<Q2>=2.252 GeV2 ∼ 2.655 GeV2

π-

0.0 0.2 0.4 0.6 0.8

– p. 17/30

Induced energy loss

RMh

π+

6 9 12 15 18 21

<z>=0.326 ∼ 0.583<Q2>=1.889 ∼ 2.595 GeV20.2

0.4

0.6

0.8

1.0

E (GeV)

Ne

Kr(-0.05)

Xe(-0.2)

π-

6 9 12 15 18 21 24


Q2 (GeV2)

RMh

π+

Ne

Kr(-0.05)

Xe(-0.2)

<z>=0.380 ∼ 0.399 <E>=14.583 ∼ 15.100 GeV

0.2

0.4

0.6

0.8

1.0

1 3 10


– p. 18/30

Attenuation of pre-hadronsThe propagation of a "breathing" dipole through a medium isdescribed summing up all possible paths of theq andq.Combining with the above evaluation of the production lengththis approach makes a good job predicting nuclear attenuation inSIDIS (B.K., J.Nemchik, E.Predazzi, 1995).

RMπ

ν (GeV)

z > 0.5

0.8

0.9

1

1.1

8 10 12 14 16 18 20 22

RMh/π

z

■ h, ν > 7 GeV❍ π, ν > 8 GeV

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1

Solid curves: KNP-1995; Data: HERMES-2001for nitrogen.

– p. 19/30

Hadron quenching in DIS

– p. 20/30

Hadron quenching in DIS

[B.K., J.Nemchik, E.Predazzi,A.Hayashigaki, 2004]

– p. 20/30

Perturbative fragmentationLeading pion productionγ∗p → πX inBorn approximation results from radiation ofa gluon which splits intoq2q3. The producedcolorless dipoleq1q2 is then projected to thepion wave function (E.Berger, 1980). Fullcalculations includes:(i) normalization;(ii)higher order terms in(1 − zh) expansion;(iii) realistic light-cone pion wave function;(iv) higher-twist terms;(v) effects of nonper-turbative interaction between the partons;(vi)energy loss. The result agrees with the phe-nomenological fragmentation functions fit-ted to data (B.K., H.J.Pirner, I.Potashnikova,I.Schmidt, A.Tarasov, 2007-2009)

πq

q

q

1

2

3

γ∗ q

10-2

10-1

1

10

10 2

0.6 0.7 0.8 0.9z

Dq/

π(z,

Q2 )

E=200 GeV

100 Gev

20 Gev

10 Gev

x103

x102

x10

– p. 21/30

Quantum-mechanics of absorptionThe model of nuclear attenuation dis-cussed above is semi-classical, sincetreats the space-time development prob-abilistically. It is not correct to say thatthe pre-hadron is produced either inside,or outside the medium.[KPPSTV, 2008]

Indeed, the cross section is a product oftwo amplitudes which may have differ-ent coordinates,z2 6= z3, for pre-hadronproduction. Accordingly, the cross sec-tion contains three terms corresponding topre-hadron production in both amplitudesoutside (σ1), or inside (σ2) the nucleus,and the inside-outside interference (σ3).

* q

1

g

π

γ

N

N

N

1

2

A

q

q2

...

3

��

��

��

��

z4

z1

z

’

3z

’

2

’

q

q3

3

2q

1q

1

π

g

g2

q

q

π

8

"pre−hadron"��

��

��

��

– p. 22/30

Quantum-mechanical treatment

-1

0

1

0.6 0.7 0.8 0.9

!1/!

!2/!

!3/!

zh

!i / !

0.6

0.7

0.8

0.9

1

0.6 0.7 0.8 0.9

E=20 GeV

10 GeV

5 GeV

zh

R(z

h)

The relative contributions of inside and outside productions, andtheir interference (σ = σ1 + σ2 + σ3) are of the same order ofmagnitude, however theinterference term is negative.

• The effects of energy loss and non-perturbativeinteraction between partons are to be added.

– p. 23/30

Summary

• The dipole formalism describes well in a parameter free waydata on broadening of partons in nuclear matter observed invariety of processes and in a wide energy range.

– p. 24/30

Summary


• Smallness of broadening observed by HERMES rules outthe explanation of HERMES data on hadron attenuation solelyby induced energy loss.

– p. 24/30

Summary


• Smallness of broadening observed by HERMES rules outthe explanation of HERMES data on hadron attenuation solelyby induced energy loss.

• The semi-classical model which employs a probabilisticdescription for the space-time development of the hadronizationprocess, but describes the quantum-mechanical evolution of thepre-hadron, well explains data on hadron attenuation in aparameter free way.

– p. 24/30

Summary• The rigorous quantum-mechanical description of in-mediumhadroniztion demonstrates that interference between inside andoutside production of the pre-hadron has negative sign and is100% important. It also leads to a nontrivialzh dependence ofnuclear effects.

– p. 25/30

Summary• The rigorous quantum-mechanical description of in-mediumhadroniztion demonstrates that interference between inside andoutside production of the pre-hadron has negative sign and is100% important. It also leads to a nontrivialzh dependence ofnuclear effects.

Outlook: The non-perturbative corrections, interac-tion among the partons and en-ergy loss, must be introduced.The result can be used as a start-ing function for the DGLAP evo-lution to a higher scale to becompared with data.

– p. 25/30

Backups: Time evolution of ahigh-pT jet

The mean time of radiation of a gluon:

〈lc〉 =

Q2∫

Λ2

dk2

1∫

0

dxdn

dx dk2lc(x, k2) =

E

Λ2

1

ln(Q/Λ) ln(QΛ/4E2)

where

lc =2Ex(1 − x)

k2;

dn

dx d2k=

γ

x k2; γ =

3αs

π2

The mean coherence length of gluon radiation is long.

However, this is not the same as production length of a colorlessdipole with largezh > 0.5, which takes the main fraction of thejet energy. In this caseenergy conservationbecomes an issue.

– p. 26/30


How much energy is radiated over path length L?

∆E(L) = E

Q2∫

Λ2

dk2

1∫

0

dx xdn

dx dk2Θ

(

L −2Ex(1 − x)

k2

)

The rate of energy loss is constant for each interval ofk2,

dE

dL dk2=

1

2γ

Radiation of gluons with given transverse momentumk iscontinuing with the constant rateγ/2 until the maximal lengthLmax(k

2) = 2E/k2 is reached.

– p. 27/30


ι

dEdz

L(k)

dk2

2E/ΛE/Q 2

E/k2

L-dependence for the rate of energy loss for different intervals oftransverse momentumk2

i

– p. 28/30


The total energy radiated over this maximal path length is

∆Etot =

Q2∫

Λ2

dk21

2γ

2E

k2= γ E ln

Q2

Λ2

How long does it take to radiate fractionδ of the total emittedenergy?The answer depends on how large isδ. ForQ = E

L = δ4

Eln

E

Λif δ < 1/ ln

(

Q2

Λ2

)

L =2

Ee

(

E

Λ

)2δ

if δ > 1/ ln

(

Q2

Λ2

)

– p. 29/30


The path length needed to radiate fractionδ of the total vacuumenergy loss.

More than a half of the total energy is lost within1 fm !

– p. 30/30

nuclear effects in hadronization...bk, j.nemchik, a.schäfer, a.tarasov, 2002 – p. 14/30. cronin...

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