Dilepton production

Presentation for FYS4530

Atle Jorstad Qviller

What is a dilepton?

• A dilepton is a particle-antiparticle pair of same-flavour leptons.

• Only electron-type dileptons are of interest here

Why look at dileptons?

• αem is small (1/137)

• αs is large

• Dileptons have no color charge, interact weakly with the nuclear medium and escape easily. Quarks are confined and can not escape. Composite hadrons and quarks are strongly attentuated by gluonic bremsstrahlung.

• We can therefore extract information directly from the reaction zone by looking at dileptons

Sources of dileptons

• Dileptons from Drell-Yan processes

• Dileptons from the QGP

• Dileptons from hadron gas/resonances

• Dileptons from decay of charmed particles

• To detect the QGP by dilepton production requires understanding and subtracting away a lot of background from other processes.

Nucleon structure

• Nucleons are composite objects• They consist of partons: valence quarks, virtual

sea quarks and gluons.• The partons carry a fraction of the nucleon’s

momentum determined by structure functions. Gluons carry about 50%.

• A ”hard” parton collision has a high momentum transfer, and is treatable in pQCD (or QED)

Quark momentum distributions

• Quark distribution function

• A are ”constants” depending on Q2

• a is the flavour• P is a smooth function• We must note that q and qbar distributions

are very different

TTaAascA

f daaxGxq ),()( /,

)()1(),( 210 xPxxAQxxq aAAaa aa

Momentum distributions

Digression:Parton ”tyrrany”

• These momentum distributions are a headache for particle physicists

• They limit the effective fraction of the beam energy used for particle production.

• Tevatron (beam energy ~2 TeV) is mostly seeing collisions with CM energy a couple of hundred GeV.

• This is not a problem in heavy ion physics

Hard scattering/parton collision

Hard scattering

• The x’s are the momentum fraction carried by the fusing partons.

• 1-x is carried away by the other constituents. These fragment into a cloud of mostly low momentum pions.

• Worried about the lack of anti-valence quarks at pp/heavy ion collisions? Remember antiquarks in the sea of virtual pairs!

• Hard scattering can be strong or electroweak processes.

Hard scattering

• Gluon fusion is a strong process.

• Drell-Yan processes are electroweak.

• There are lots of other possible cases.

General cross section for hard processes

• Results from chapter 4:

• R is a kinematical factor close to 1• Gb is probability for finding parton b with

momentum fraction x and transverse momentum fraction bt inside nucleon B. Ga similar.

)'(

),(),(|

3

3

//

CXbadC

dE

raxGbxGdadxdbdxE

c

TaAaTbBbTaTbabCXABc

Scattering formula details

• The last part of the formula is the cross section for generating two final states C and X from the fusion of two partons a and b

• For hadronic final states this is not possible to calculate, as it is not a pertubative problem

• For leptonic endstates it is possible!

Digression: Fragmentation

• For hadron end states: We add a fragmentation function G times a fundamentally calculable matrix element to our cross section. It represents the probability of parton c to fragment into final state C

cdbacTCCcTc

TaAaTbBbTaTbabCXABc

dc

dECxGdcdx

raxGbxGdadxdbdxdc

dE

|),(

),(),(|

3

3

/

//3

3

Dileptons from Drell-Yan

• The result of a Drell-Yan process is e+e-,μ+μ- or τ+τ-,a dilepton.

Drell-Yan process

• The virtual vector boson decays into a pair of fermions.

• Cross section is exactly calculable in electroweak theory (in FYS 4560/4170 you learn this)

• Z interference is only significant at high momentum transfer (over 50-60 GeV).

• Most of our procesess have a lot less momentum transfer. We don’t care about Z exchange here.

Drell-Yan process

• We have no fragmentation function as leptons are fundamental.

• Electons and muon pairs are very easy to detect, as they will somewhat anticorrelated in angle and give signal in EM calorimeter/muon chambers.

• Tau’s decay very fast, mostly into jets and also lepton+neutrino. We don’t care about them.

Dilepton kinematics

• Momentum C and invariant mass M

• Feynman x

llC

222 )( llCM

2/s

Cx ZF

Parton momentum fractions:

FF xs

Mxx

22

2,1

4

2

1

Fxxx 21

221 Msxx

Cross sections

)()()()()()(1

21212

21

2

xqxqxqxqe

eM

Ndxdx

df

Af

Bf

Af

BfN

cf

sMx

xqxqxqxq

e

eM

sNdxdM

d

F

fA

fB

fA

fB

fN

cFf

/4

)()()()()()(

122

212122

2

)()()()()(3

81 23

22

xxqxqxxqxxxqe

e

MNNdMdy

df

Af

Bf

Af

BfN

ccf

Glauber model

• Baryon thickness function

• Probability of finding baryon in A at (ba,za)

• Probability for baryon collision for nuclei A,B

1)( dbbt

1),( AAAAA dzdbzb

inBABBBBBAAAAAin bbbtdzdbzbdzdbzbbTP )(),(),()(

Glauber model

• Probability of n baryon baryon collisions

nABin

nin bTbT

n

ABbnP

)(1)(),(

ABinnABin

AB

bTbnPdb

d )(11),(1

Glauber + Drell Yan

• For spherical nuclei colliding head on

• Scales as A to the 4/3

dMdy

dA

rdMdy

dN DYNN

ll

3/4204

3

Dileptons from the QGP

• Considering a Nb=0 QGP• Quark phase space

density:• Quark spatial density:• Number of dileptons

produced in dtd3x:

)()2( 13

133

Efpxdd

gdN qq

)()2( 131

3

3Ef

pdg

xd

dNq

q

122162

31

3

2

2

12

3)()()(

)2(vMEfEf

pdpd

e

eNN

xdtd

dN fNfsc

ll f

Dileptons from the QGP

• The cross section sigma comes from QED• Remember threefold color degeneracy for the

quark pair (and other degeneracies).

)421()4

1()4

1(3

4)(

4

22

2

22

2

1

2

2

2

1

2

2

2

2

M

mm

M

mm

M

m

M

m

MM lqlqlq

Dileptons from the QGP

• For a QGP with Boltzmann statistics

)()4

1()2(2

)(12

2

242

2

12

42 T

MTMK

M

mM

M

e

eNN

xddM

dN qfNfsc

ll f

)()4

1()2(4

)(02

2

242

2

12

422 T

MK

M

mM

M

e

eNN

xddMdM

dNTqfN

fsc

T

ll f

T

E

eEf

)(

Dileptons from a QGP with Bjorken hydrodynamics

• In the Bjorken model, the contracted slabs of nuclear matter pass straight through each other.

• They set up an excited color field between them

• Temperature evolves as:

3

10

0 )()( TT

Dileptons from a QGP with Bjorken hydrodynamics

• We make simplifications for the Bessel function and neglect quark masses

• The reseult: Dileptons arising from qqbar annihilation in the QGP:

)(

0

2

70

0

/

0

30

2222

0

0

)/(

)/()(1

)(23

5~

T

M

T

Mc

c

TMA

ll

ceTMf

TMf

T

T

T

Mfe

T

MTRa

dMdy

dN

Dileptons from hadrons and resonances

• Dileptons are produced in reactions like:

π+π- →μ+μ

• Assume pion gas for simplicity

• Also from decay of hadron resonances:

ρ,Φ,ω, J/ψ

Dileptons from hadrons and resonances

• Pion annihilation is very similar to q-qbar annihilation in the QGP

• Different degeneracies and cross section• Nc → 1 • Nf → 1 • mq → mpi • ef →e• T0 →Ti• Tc →Tf

Dileptons from hadrons and resonances

• This process is NOT fundamental.

• Use this cross section in previous showed formula:

• Where F:• Width and mass of

rho meson

22

2

2

1

22

1

22

2

|)(|)2

1()4

1()4

1(3

4)('

mFM

m

M

m

M

m

MM ll

2222

4

2

)(|)(|

mmM

mmF

Dileptons from hadrons and resonances

• Resonances originate from nucleus-nucleus collision or from collisions in the hadron gas

• J/psi at 3.1 GeV is massive and therefore arises mostly from hard scattering.

Charm production

• Charm quarks are made in reactions like:

q+qbar→g*→c+cbar

g+g→c+cbar

• This state can from charmonium or fragment directly into a D+D- pair.

• Look at figure 14.7

Dileptons from charm decay

• Charmonium can decay directly into a dilepton

c+cbar→μ+μ-

• A pair of D mesons can further decay into a dilepton

• These dileptons have approximately exponential distribution with a ”low” temperature.

Total spectrum

• We must have dilepton yield from the QGP of large enough magnitude.

• M less than 1 GeV: Resonance decays from ρ,Φ,ω dominate. Difficult to see QGP signal

• Continuum (not resonances) over 1.5 GeV: Hadron interactions and charm decay not important.

Total spectrum

• Drell-Yan is dominant at higher temperatures.

• Look at figure 14.8• The QGP is visible in the dilepton

spectrum if it is hot enough, but we do not know. Drell-Yan will mask it if too cold.

• Stefan-Boltzmann: ε = σT4

• The energy density goes as the 4th power of the temperature.

Conclusion

• Dileptons are not a very clean signature of the QGP due to massive pollution from lots of sources, but still useful as a supplement and for extracting information directly from the collision zone.

• The plasma temperature is crucial.• The plasma temperature is linked directly to the

energy density through Stefan-Boltzmann.• Different energy densities will have a big impact

on dilepton production.