meson photoproduction in ultraperipheral heavy ion ... · meson photoproduction in ultraperipheral...

Meson photoproduction inultraperipheral heavy ion

collisions and energetic protonsMagno V.T. Machado

Universidade Estadual do Rio Grande do Sul (UERGS), Unidade de Bento Goncalves

High Energy Phenomenology Group, GFPAE IF-UFRGS, Porto Alegre

http://www.if.ufrgs.br/ magnus/heavyions.html

Seminario de Grupo GFPAE IF-UFRGS, Porto Alegre, May 06th (2005). – p.1

Outline

THE MINUIT PROJECTSEAL

6Matthias Winkler, Fred JamesAPRIL 9, 2003

“ object-oriented re-implementation of MINUIT in C++”

Design in evolution...

ObjectiveFunctionBase MinuitParameter

Chi2BaseLogLikelBase UserDefinedMinimizerErrorAnalyserContours...

GSL interface?

API

MINUIT-ToolKitgetFreeParametersevaluateFunction 1...n

General motivation for studing meson production.

Vector meson photoproduction (Q2 = 0) in γp and γA.

Short introduction to Ultraperipheral Heavy Ion Collisions(UPC’s) and photoproduction on energetic protons;

Photonuclear production of mesons at UPC’s.

Photoproduction of mesons on energetic protons.

Summary.


General Motivation

In γp(A) photoproduction (real photons, Q2 = 0), the scaleof problem is given by the meson mass, mV .

Light meson production (mainly ρ’s) allows to study thephysics of low momentum scale (saturation effects).

Heavy meson production allows to study gluon distributionon target, since it is ∝ [xGp,A(x,m2

V ) ]2.

What is dynamically behind the transition from light to heavymesons (soft phenomenon → pQCD)?

Experimental motivation: high precision measurements inγp at DESY-HERA and STAR Coll. at RHIC released firstdata on coherent ρ production in Au-Au at

√s = 130 GeV.


QCD PHENOMENOLOGYTHE MINUIT PROJECT

SEAL



At the moment:

discuss the C++ API:parametersfunction (“FCN”)MINUIT:

numerics (migrad, minos, etc.)parameters (fix, release, set, etc.)control (tolerance, iterations, precision, etc)

integration with SPI:moving to SEAL CVS repository (done)adding MathLib to Savannahdocumentation using Doxygenconfiguration for development: SCRAM (done)testing, using Oval and CppUnit... VECTOR MESON PHOTOPRODUCTION IN

γp and γA PROCESSES AT VERY HIGHENERGIES


Is there a unified QCD approach ?

Light meson photoproduction is basically a non-perturbativeprocess, whose scale is mV ' 0.77 − 1 GeV.

For this small momentum scale, perturbative methods arenot useful (Regge phenomenology does a good job).

Heavy mesons (J/Ψ and Υ) provide a hard scale mV ≥ 3

GeV, and pQCD can be applied (DLLA approximation).

Color dipole picture provides a unified and an intuitiveapproach for the transition light-heavy mesons.

Physics of transition is built-in on the cross section ofscattering of color dipoles (Fock states of γ∗) on the target(protons or nuclei) - the so called dipole cross-section.


Deep inelastic scattering (DIS)

DIS described in dipole picture as scattering of qq pairs,fluctuation of the γ∗, and their interaction with the target.

At high energies, the interaction is considered as dominatedby gluon exchange in t-channel (then,it depends on detailsof the dynamical evolution of gluon production).

Photon fluctuation described by γ-wavefunction, Ψ(z, r),analytically computed from electrodynamics (QED).

Interaction described by dipole-target cross section,σdip(x, r), which can be computed from QCD evolutionequations or making use of phenomenological ansatz.


Physical picture for DIS

σdipole(x, r )

*γ

W2

Ψ(z,r,Q )2 Ψ*(z,r,Q )2

Q2 z

1−z

r

Photoabsortion γ∗p cross section factorized:

σγ∗p(x, Q2) =∑

T,L

∫ 1

0dz

∫

d2r |ΨT, L(z, r, Q2)|2 σdip(x, r

2)

Transverse size of the color dipole (r) and longitudinalmomentum fraction carried by quark (z). Transversal andlongitudinal polarizations (T,L).


From color transparency to unitaritySaturation scales

dense dense dilute

Qs2

saturationscale

Below saturation scale: dense system of gluons (ρ ∼ 1/αs)Above saturation scale: dilute system of gluons (ρ 1/αs)

Small-x – p.16/19

In the asymptotic limit the total (hadronic) cross sectionmust not growth faster than logarithmically on energy.

σtot ∝ C ln2(s) (s → ∞) Froissart-Martin Bound

Geometrically, black disc limit of the target is reached.

Similar argumentation for photon-target interaction !?

Translated into σdip → 2πR2target below a typical momentum

scale.Seminario de Grupo GFPAE IF-UFRGS, Porto Alegre, May 06th (2005). – p.8

Saturation scale . . .

Rise of the gluon dist. at small x can be naturally tamed bysaturation, circumventing subsequent violation of unitarity.

Q2sat,A(x; A) ∝ xGA(x, Q2

sat)

πR2A

' Aα x−λ , (α ' 1/3, λ ' 0.3)

Energy dependence of Qsat given by the solution of QCDevolutions equations at the border of saturation region.

In the saturation approach, the transition between the dilutesystem to the saturated one (unitarity) is mediated by Qsat.

In dilute system, σdip ∝ r2xG(x, 1/r2) (color tansparency)and towards unitarity σdip ∝ cte = O(π R2).

Several phenomenological models for σdip . . .Seminario de Grupo GFPAE IF-UFRGS, Porto Alegre, May 06th (2005). – p.9

A saturation model (GBW)

Golec-Biernat & Wusthoff model mimics color transparencyand unitarity through an eikonal ansatz (resembles theGlauber-Mueller approach).

Transition is rendered by partonic (gluons) saturation.

σprotondip (x, r

2) = σ0

[

1 − exp

(

− Q2sat(x) r

2

4

)]

Q2sat(x) =

(x0

x

)λGeV2; x = x

(

1 +4m2

f

Q2

)

Saturation scale Qsat defines the onset of the unitarityeffects [Qsat(x ' 10−4) = 1 GeV].

Parameters fitted from small-x DESY-HERA data.Seminario de Grupo GFPAE IF-UFRGS, Porto Alegre, May 06th (2005). – p.10

More about GBW model

0 0.5 1 1.5 2r [fm]

0

5

10

15

20

25

30

35

40

σ [

mb]

GW, Q2 = 2 GeV2

GW, Q2 = 20 GeV2

FKS, W = 75 GeV

GBW dipole cross section (blue) at√

s = Wγp = 75 GeV atQ2 = 2 and 20 GeV2.

If you dont believe in saturation physics, then enjoy theForshaw-Kerley-Shaw (FKS) dipole cross section based onthe two-Pomeron model (black curve).


Nuclear version (Nestor Armesto)

−

q, zγ∗

A

r

. . .

q, 1−z

Glauber-Gribov formalism for scattering on nuclei.

σnucdip (x, r

2, A) = 2

∫

d2b

1 − exp

[

−1

2ATA(b)σproton

dip (x, r2)

]

σnucdip sums up all the multiple elastic rescattering diagrams of

the QQ pair at large coherence length.

Nuclear profile function TA(b) (3-parameter Fermi distr.),where b is the impact parameter of the center of the dipolerelative to the center of the nucleus.


VM production on proton

Photoproduction cross section is given by:

σγp→VMp = R2g

[ImAproton(s, t = 0)]2

16π BV(1 + β2)

ImAproton =∑

h,h

∫

dz d2rΨγ

h,h(z, r, Q2)σproton

dip (x, r)ΨV ∗h,h(z, r)

Ψγh,h

is the meson wavefunction (needs to be modeled).

BV , meson slope (exponential param. for t-dependence).

β = ReA/ImA is the correction for real part of amplitude.

Skewedness effects Rg (important for heavy mesons):

Rg (λeff) =22λeff+3

√π

Γ(

λeff + 52

)

Γ (λeff + 4), λeff =

d log[ImA]

d log s


The photon wavefunction

Explicit forms for normalised photon light-conewavefunctions in the mixed representation (z, r):

ΨLh,h(r, z) =

√

Nc

4πδh,−heef2z(1 − z)Q

K0(εr)

2π

ΨT (γ=±)

h,h(r, z) = ±

√

Nc

2πeef [ie±iθr(zδh±,h∓ − (1 − z)δh∓,h±)∂r

+mfδh±,h±]K0(εr)

2π

Notation, ε2 = z(1 − z)Q2 + m2f , and modified Bessel

function K0(x).

Mass of quark flavour f is mf and its charge is ef .


The meson wavefunctionsVector meson light-cone wavefunctions are not reliablyknown, and then are obtained from models.

In the market: NNPZ (J. Nemchik et al.), DGKP (H.G. Doschet al.), Boosted Gaussian.

They are subject to two constraints. Normalisation condition(assumption that meson is composed only by qq pairs).

∑

h,h

∫

d2k

(2π)2dz |ΨV (λ)

h,h(k, z)|2 =

∑

h,h

∫

d2r dz |ΨV (λ)

h,h(r, z)|2 = 1

Second constraint from electronic decay width,∑

h,h

∫

d2k

(2π)2dz

z(1 − z)(z(1 − z)Q2 + k2 + m2

f )ΨVh,h(k, z)Ψγ∗

h,h(k, z)

= efV MV ε∗γ .εV , where 3MV ΓV →e+e− = 4πα2emf2

V


The DGKP wavefunctionIn photoproduction, the energy dependence is insensitive tothe specific choice for the meson wavefunction.

We consider DGKP wavefunction (analytical simplicity).

ΨV,L

h,h(r, z) = z(1 − z)δh,−h

√πfV

2√

NceffL(z)e−ω2

Lr2/2

ΨV,T (γ=±)

h,h= ±

(

iω2T re±iθr

MV[zδh±,h∓ − (1 − z)δh∓,h±] +

mf

MVδh±,h±

)

×√

πfV√2Ncef

fT (z)e−ω2T r2/2

ef is effective charge from sum over quark flavours.

Function fλ(z) = Nλ

√

z(1 − z)e

−M2V (z−1/2)2

2ω2λ is taken from

Bauer-Stech-Wirbel model.Seminario de Grupo GFPAE IF-UFRGS, Porto Alegre, May 06th (2005). – p.16

VM production on nuclei

Photoproduction cross section is given by:

σγA→VM X = R2g

[ImAnuc(s, t = 0)]2

16π(1 + β2)

∫ ∞

tmin

dt |F (t)|2 ,

ImAnuc =∑

h,h

∫

dz d2rΨγ

h,h(z, r, Q2)σnucleus

dip (x, r)ΨV ∗h,h(z, r)

Photon energy is ω, with tmin = (m2V /2ω)2.

Nuclear form factor is F (t) (Fourier transform of the nucleardensity profile).

Nuclear dependence is given by the interplay between thedipole cross section and the nuclear form factor.


Results on γA → VMX

101 102 103

W [GeV]

10−3

10−2

10−1

100

101

102

σ(γA

−−>ρ

0 A) [

mb]

HERA data (H1 Coll.) HERA data (ZEUS Coll.)

PROTON

Ca

Pb

101 102 103

W [GeV]

10−5

10−4

10−3

10−2

10−1

100

101

σ(γA

−−>J

/ψA

) [m

b]

HERA data (ZEUS Coll. e+e−)HERA data (ZEUS Coll. µ+µ−)HERA data (H1 Coll.)

PROTON

Ca

Pb

Mild energy behavior and good data description on proton(nuclear shadowing stronger for light mesons).

Large values for the cross sections, reaching ≈ 5 mb (for ρ0)and ≈ 200 µb (for J/Ψ) at WγA = 1 TeV for Pb target.


Comparison with other approaches

30 80 130 180 230 280W [GeV]

10−5

10−4

10−3

σ(γp

−−>J

/ψp)

[mb]

HERA data (ZEUS Coll. e+e−)HERA data (ZEUS Coll. µ+µ−)HERA data (H1 Coll.)GLLMNVDM − SOFT DIPOLE POMERONSAT−MOD

PROTON

GLLMN model: uses also dipole approach with numericalsolution of the Balitski-Kovchegov (BK) nonlinear evolutionequation for the dipole-nucleon cross section.

VDM approach: Regge approach with soft dipole Pomeron +vector meson dominance.


QCD PHENOMENOLOGYTHE MINUIT PROJECT

SEAL



At the moment:

discuss the C++ API:parametersfunction (“FCN”)MINUIT:

numerics (migrad, minos, etc.)parameters (fix, release, set, etc.)control (tolerance, iterations, precision, etc)

integration with SPI:moving to SEAL CVS repository (done)adding MathLib to Savannahdocumentation using Doxygenconfiguration for development: SCRAM (done)testing, using Oval and CppUnit... PHOTONUCLEAR MESON PRODUCTION

IN UPC’s AND PHOTOPRODUCTION ONENERGETIC PROTONS


General Motivation

Very high photon luminosity in UPC’s ∝ Z2 (photonuclear) incomparison with current γN collisions.

This high flux provides invariant mass region hithertounexplored experimentally.

Light mesons (π, η, χ, . . .) are copiously produced in RHICenergy in those reactions. Heavy mesons (J/Ψ, Υ) will beproduced in large rates at LHC.

Important opportunity to investigate the QCD dynamics(QCD Pomeron ?) at high invariant mass in the reasonablyclean (so called silent) process, AA(pp) → AA(pp)VM .


γ’s in relativistic nuclei or protons

b>R +R

Z

Z

1 2

Relativistic nuclei (or protons) having strong electromagneticfield, viewed as a cloud of virtual photons.

They obey the condition of coherence, Q2 ≤ 1/R2A (final

state particles with low transverse momenta).

Maximum energy of quasireal photons is ωmax ≈ γL/RA.Examples in heavy-ions: RHIC (γL ≈ 100, ωRHIC

max ≈ 3 GeV);LHC (γL ≈ 3000, ωLHC

max ≈ 80 GeV).Seminario de Grupo GFPAE IF-UFRGS, Porto Alegre, May 06th (2005). – p.22

Weissacker-Williams approximation

1b2

b1

b2

b

bb

a) side view b) head on view

Equivalent photon spectrum for relativistic particle (chargeZe, velocity v, impact parameter b)

Nγ(ω, b) =Z2α

π2 b2

( c

v

)2x2

[

K21 (x) +

1

γ2L

K20 (x)

]

, x =ωb

γLv

The number of equivalent photons:

n (ω) =

∫ ∞

Rmin

d2bNγ(ω, b) , Rmin = RA1 + RA2


Number of equivalent γ’s

Number of equivalent photons on nuclei:

nnucleus (ω) =2Z2α

π ω

[

η K0 (η)K1 (η) +η2

2

(

K21 (η) − K2

0 (η))

]

,

η = 2ω RA/γL , n (ω) ≈ 2Z2 α

πln

(

γL

ω Rmin

)

Number of equivalent photons on energetic protons:

nproton (ω) =αem

2π ωF (ω)

(

ln Ω − 11

6+

3

Ω− 3

2Ω2+

1

3Ω3

)

,

F (ω) =

[

1 +

(

1 − 2ω√SNN

)2]

, Ω ≈ 1 +

(

0.71γ2L

ω2

)


γ-scattering on nuclei or protons

The photonuclear cross section is given by,

σphotonucA A→VMAA(

√sNN ) =

∫

dω

ωnnucleus (ω) σγ A→VM X (ω)

The photoproduction cross section on protons reads,

σphotopp→VM pp(

√spp) =

∫

dω

ωnproton (ω) σγ p→VM X (ω)

Allow to study photoproduction with energies reachingWγN ' 930 GeV at LHC (at DESY-HERA, Wγp ' 200 GeV).

Accurate theoretical predictions for the subprocessesγp(A) → VMX at very high energies are required!


Results for AA → VMAA in UPC’s

50 100 150 200 250WNN [GeV]

101

102

103

104

σ (A

A−−

>ρ0 A

A) [

mb]

STAR DATA

50 100 150 200 250WNN [GeV]

101

102

103

104

CUTS: t < 0.02

|y| < 3

CUTS: t < 0.02

|y| < 1

Coherent ρ0 production in AuAu collisions at RHIC.

Predictions for photonuclear production at LHC.

HEAVY ION J/Ψ(3097) φ (1019) ω (782) ρ (770)

PbPb 41.5 mb 998 mb 1131 mb 10069 mb


Results for pp → VMpp

Results for pp photoproduction at LHC.

VM (mV) J/Ψ(3097) φ (1019) ω (782) ρ (770)

LHC 132 nb 980 nb 1.24 µb 9.75 µb

High rates for light mesons at LHC and RHIC. Openopportunity to study Υ’s production at LHC with larger rates.

As exclusive reaction, NN → VMNN (N = p, A), theseparation of the signal from hadronic background would berelatively clear.

Low pT meson spectra and double rapidity gap pattern.Detection (Roman pots) of the scattered nuclei (or protons)could be useful.


Summary

THE MINUIT PROJECTSEAL



Summary:

no equivalent minimization package w.r. to MINUITwhat physicists want (errors etc.)

first protoypes:learn from it think about C++ APIcome up with an overall design

define next stepsfunctionality vs. release

Reliable estimates for meson production in γp (A), using thecolor dipole picture and saturation physics. Robust input forperipheral collisions and photoproduction on protons.

For UPC’s and energetic protons the rates are large evenafter taking the respective leptonic branching ratios and/oracceptance estimates.

Reasonably clear experimental signal identification.

Light meson production nice place to study processdominated by low-pT momentum (saturation physics).


Related papers

REVIEWS ON UPC’s PHYSICS:

C.A. Bertulani, S.R. Klein, J. Nystrand, Physics of Ultra-Peripheral

Nuclear Collisions, Annual Review of Nuclear and Particle Science, vol.

55 (2005), nuc-ex/0502005.

G. Baur et al., Coherent γγ and γA interactions in very peripheral

collisions at relativistic ion colliders, Phys. Rept. 364 (2002) 359-450.

PAPERS ON VECTOR MESON PRODUCTION:

V. Goncalves, M.V. Machado, Nuclear exclusive vector meson

photoproduction, Eur. Phys. J. C38 (2004) 319-328.

V. Goncalves, M.V. Machado,The QCD Pomeron in Ultraperipheral

Heavy Ion Collisions: IV. Photonuclear Production of Vector Mesons,Eur.

Phys. J. C32 (2004) 501-506 .Seminario de Grupo GFPAE IF-UFRGS, Porto Alegre, May 06th (2005). – p.29

meson photoproduction in ultraperipheral heavy ion ... · meson photoproduction in ultraperipheral...

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