J. G. Contreras CTEQ School 2005

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Small x Physics

in Deep Inelastic Scattering

Puebla

May 20, 2005

J. G. Contreras ● Cinvestav Mérida

►Motivation:

Limits of pQCD,

High density pQCD

►The proton at small x:

F2, FL, F2c

►Looking for saturation:

Forward Jets

Geometric Scaling

Heavy ion physics

►Summary: Very exciting field

J. G. Contreras CTEQ School 2005

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Motivation

What are we made of ?

What is the most fundamental structure of matter ?

What is the structure of the proton in terms of quark and gluons?

Long time ago …

Today …

Homework 1: and tomorrow?

J. G. Contreras CTEQ School 2005

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DIS: The basic idea

Need a microscope to see inside the proton

High energy:

►Good resolution (Deep)

►Proton breaks (Inelastic)

An accelerated electron …

… produces light to see

inside a proton

Microscope components:

► Accelerators: Fixed Target, HERA

► Detectors: H1, Zeus, …

J. G. Contreras CTEQ School 2005

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HERA: the only ep collider

► Asymmetric accelerator using superconducting technology► Operating since 1992► 300 GeV CMS energy ► 6.3 Km of circumference ► At DESY in Hamburg

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H1 and Zeus

►Both big universal detectors with excellent tracking and calorimetry ►Built and maintained by large collaborations, each of ~ 350 scientists and around 40 institutes from around the world ►Each with more than 100 articles and several thousand citations ►Taking new data as we speak!

Open detectors

Note the scale

Note the cables

….

J. G. Contreras CTEQ School 2005

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DIS in pQCD and Experiment

incoming electron

outgoing electron

struck quark

collision

proton remnant

incoming proton

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Description of DIS in pQCD

► Proton “=“ Σ free partons (careful with the frame)

► Two variables to describe the process to be choosen from:

x: parton energy (0<x<1)Q2: resolutions: energy of CMSy: inelasticity (0<y<1) W: energy of γ*p process

J. G. Contreras CTEQ School 2005

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The structure of the proton according to DIS/pQCD

LF

yF

yy

QxdxdQ

d 2

2

22

2

2

2 2)

21(

14

),(

),(

2

22

QxxgF

QxpartonsF

L

Experiment

pQCD:

General theory requirements

J. G. Contreras CTEQ School 2005

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The limits of pQCD

Perturbative solution: ►Needs small parameter ►Not all terms considered ►Free partons?

Expansion parameter: ►αs (only QCD parameter) ►Its value depends on a scale (asymptotic freedom) ►In inclusive DIS scale is Q2

Resummation of ►(αs)mlogn(Q2/Qo) (DGLAP)

or ►(αs)mlogn(1/x) (BFKL)

J. G. Contreras CTEQ School 2005

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The Nobel Prizes in DIS and pQCD

DIS: ►1990 to Friedman, Kendall and Taylor Experiments at the end of 60s, early 70s ►Their results motivated the development of the quark model of the strong interaction

pQCD: ►2004 to Gross, Politzer and Wilczek Theoretical work (1973), foundation of pQCD ►Discovery of asymptotic freedom (btw: read Politzer Nobel lecture!)

Homework 2: You are next …

J. G. Contreras CTEQ School 2005

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Where are we? Where are we going? (I)

Where are we? ►Basic idea of DIS and pQCD understood ►Want to explore limits of pQCD, specifically high density of partons and αs small

Where are we going? ►A first look at data ►A closer look at the theory ►A second look at data

J. G. Contreras CTEQ School 2005

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Experiment: phase space in x and Q2

Huge phase space covered: ►x from almost 1 to ≈ 10-6

►Q2 from less than 0.1 to almost 105 GeV2

Several overlapping regions permit cross checks between different accelerators different experiments

Note the correlation between x and Q2 at small x …

… smallest x outside pQCD?

J. G. Contreras CTEQ School 2005

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The first HERA F2 at small x

Before HERA no data at small x

… but many predictions based onextrapolations of existing data

In 1992 the first HERA databecame available:

F2 (~σ) rises at small x …

… and rises quite fast …

lets look at it in some detail …

J. G. Contreras CTEQ School 2005

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Describing F2 behavior with partons

Lots of partons at small x!

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F2(x,Q2) today

Impressive amount of data

Precision better than few %

Perfect agreement between ►Hera and Fix target experiments ►Between Hera experiments

Dramatic violation of Bjorken scaling

Data described by fits based on DGLAP pQCD

J. G. Contreras CTEQ School 2005

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From F2 to pQCD partons

See Stump’s talk!

H1 and Zeus fits agree: ► independent data ► same theory ► different implementation …

Different physics at ► large x: valence quarks ► small x: gluons and sea (note the scale factor!)

Small x: ► rise dominated by gluons ► x small → log(1/x) big …

J. G. Contreras CTEQ School 2005

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pQCD evolution of F2: The basic idea

In pQCD, F2 is computed from perturbative expansion in αs subject to constraints (RGE) → linear integral-differencial equations PDFs:

►DGLAP: log(Q2), but not log(1/x) ►BFKL: log(1/x), but ‘fixed’ Q2

Need a boundary condition to be taken from data.

Given F2 in one point, one gets it at another point in phase space

Both are pQCD, i.e. weak coupling needed, so none of them should work at very small Q2 …

J. G. Contreras CTEQ School 2005

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pQCD evolution of F2 in pictures

Initial structure ← exp

One emission … … and another … and …

BFKL: big steps in x diffusion in Q2

DGLAP: small steps in x big steps in Q2

Structure after emissions

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1

2

2

2

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3

3

We are interested in this region … but there is no scale in plot …

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1

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High gluon density and saturation

Small x, means high gluon density.

The gluons are inside the proton

At some point they start to overlap(the proton ‘saturates’)

When they overlap, they interact, ► they are not ‘free’ anymore ► F2 stops growing ► non linear equation needed

J. G. Contreras CTEQ School 2005

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Where are we? Where are we going? (II)

Where are we? ►free parton (DGLAP) pQCD works even at small x (where are BFKL effects?) ►Small x, means high gluon density and at some point (where?), saturation

Where are we going? ►A second look at data: behavior at small x and Q2

►Look ‘directly’ at the gluon: FL and F2

C

J. G. Contreras CTEQ School 2005

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The Q2 dependence of the rise of F2 At small x pQCD predicts F2~x-λ

... but λ varies from BFKL expectation to those from non-perturbative QCD

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F2 and the limit Q2 → 0

Remember: W2 is energy of γ*p system

At small x: W2~Q2/x → high energy

Remember x and Q2 correlated at HERA

At very small Q2: F2~Q2

But σ γ*p ~ F2/Q2 , so at small Q2:

σ γ*p ~ constant,

i.e. stops growing …

We look for something like this at high Q2

J. G. Contreras CTEQ School 2005

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Extraction of FL : the basic idea

Look at high y

Compare cross section to F2~x-λ

Assign difference to FL(<x>,Q2)

DGLAP pQCD describes data …

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F2c and the gluon

A small x gluon fluctuates intoa charm quark-antiquark

The virtual photon interactswith one of them

The struck charmed parton is kicked out of the proton

It fragments into a charmed hadron, which then decays

Reconstruct the hadron using specific signatures

Extract F2C ~ charm PDF

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F2c : the data

Lots of data

High precision

Big phase space

Strong rise

…

Described byDGLAP pQCD

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Where are we? Where are we going? (III)

Where are we? ►free parton pQCD works also for the gluon at small x ►no real need of BFKL up to now: where are the log(1/x)? ►No real need to go beyond free partons where is saturation?

Where are we going? ►looking for BFKL effects: Forward jets ►looking for high density effects: Geometric scaling

J. G. Contreras CTEQ School 2005

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Forward Jets: the basic idea

► Enhance BFKL: big step in x

► Suppress DGLAP: no step in Q2

► Experimentally look in small x for a jet at high x and with k2 jet =Q2

► i.e. Forward jets

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Forward Jets as seen by the detector

Initial electron and proton

Scattered electron

Emissions along the ladder

Forward Jet

Proton remnant

… very difficult measurement

1

1

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4

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2

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5

J. G. Contreras CTEQ School 2005

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Forward Jets: the data

► DGLAP do not describe the measurement at small x

► ‘BFKL-like’ models describe the data, but …

► Other models also do … ► pure LL-BFKL too steep, but works with smaller ‘intercept’

Furthermore, extending BFKL beyond leading log(1/x) presents some problems …

► Anyway, strong hint of something beyond DGLAP

J. G. Contreras CTEQ School 2005

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Geometric Scaling

From 2 variables to 1 !

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Geometric Scaling and Saturation

Why is geometric scaling interesting?

► It is an impressive phenomena► It happens at small x► Collapse of data points at different scales in a single curve is known to happen in phase transitions at a critical point► Saturation may be thought as something like a phase transition: from free to interacting partons from a low to a high density system► Some of the QCD based nonlinear equations proposed for saturation accept naturally solutions with geometric scaling behavior

J. G. Contreras CTEQ School 2005

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Where are we? Where are we going? (IV)

Where are we? ►Inclusive and exclusive observables point to a world beyond DGLAP ►Hints of BFKL and saturation? Need denser system, still with weak coupling!!

Where are we going?

BEYOND ►Small x physics with nuclei ►A few words on nonlinear equations ►A final look at data

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Small x Physics and Heavy Ions

Looking for a source of very dense (small x) gluons at a sizable Q2

There are many small x gluons in a proton, what about nuclei? (nuclei: lots of p’s and n’s compressed in a tight space)

► Naively expect gluon density to scale as A1/3 (high A=heavy ion) ► If energy high enough, it is possible to reach small x in the pQCD regime ► Need accelerator of ions► Need forward detectors► Need to disentangle all other effects

Is all this possible? … let’s try and see!

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Heavy ions facilities: today and tomorrowRich history of heavy ions accelerators and experiments: AGS and SPS

Today RHIC plus its detector produce beautiful data

PHENIXSTAR

BRAHMSpp2pp

In the near future, at even higher energy, LHC and ALICE

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Color Glass Condensate: The basic idea

It is a classical effective field theory of QCD with quantum evolution

Valence partons act as a static random source of dynamic sea partons(Born-Oppenheimer separation based on their time scales)

Static random source evolves in a time scale much larger than the natural scale like a spin glass. Lots of bosons together condensate. The new degree of freedom is the classical gluon. Gluons are colored, so call it CGC

Add the corresponding RGE:

Get the JIMWLK equations

Limits: DGLAP, BFKL, BK eqs

Phenomenology: F2, geometric scaling and …

J. G. Contreras CTEQ School 2005

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Small x in heavy ion collisions

deuteron gold

b

Centrality = impact parameter

High η = small x in Gold

Many handels:► Ion species► centrality► CMS energy► different x ranges

For each, measure asmany details as possible► Multiplicity► 4-momentum► Type of particle► Correlations► …

Here only a bit of dAu

J. G. Contreras CTEQ School 2005

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x dependence of RdA

RdAu = d2N/dpTd (d+Au)

NColld2N/dpTd (p+p)

Relative measurement ↔ normalization

1 = no change in physics pp vs dAu

Concentrate in the higher pt values

There is a x dependence …

J. G. Contreras CTEQ School 2005

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Rcp: x and centrality dependence

4.0 > pT > 1.5 GeV/c4.0 > pT > 1.5 GeV/c

Rcp=

Normalize central against peripheral events

Study it as a function of rapidity

as a function of centrality at high pt

J. G. Contreras CTEQ School 2005

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Heavy Ion Physics

CGC ideas quantitatively compatible with dAu Rcp data

Much more data (see Seto’s talk!)

CGC seems to be the right way to go, but …

► many other effects are expected to contribute► difficult to disentangle them and► there are some surprises

A bright future at RHIC and then at LHC!

J. G. Contreras CTEQ School 2005

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Where are we? Where are we going? (V)

Where are we? (almost!) at the end of the talk ... ►Small x physics is a very active field of research accelerators producing tons of exciting data NOW theoreticians coming up with lots of attractive ideas ►Many interesting open questions both for theory and experiment alike

Where are we going? ►questions, answers… ►Next talk …

►Dinner … and beyond!

THANK YOU!

HO

ME

WO

RK

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