Diapositiva 1

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Puebla May 20, 2005
Small x Physics in Deep Inelastic Scattering
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
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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?
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DIS The basic idea
Need a microscope to see inside the proton
produces light to see inside a
proton
An accelerated electron
High energy ?Good resolution (Deep)
?Proton breaks (Inelastic)
Microscope components ? Accelerators Fixed
Target, HERA ? Detectors H1, Zeus,
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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 .
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DIS in pQCD and Experiment
incoming electron
incoming proton
outgoing electron
proton remnant
collision
struck quark
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Description of DIS in pQCD
? Proton S free partons (careful with
the frame) ? Two variables to describe the
process to be choosen from
x parton energy (0ltxlt1) Q2
resolution s energy of CMS y
inelasticity (0ltylt1) W energy of ?p
process
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The structure of the proton according to DIS/pQCD
Experiment
General theory requirements
pQCD
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The limits of pQCD
Perturbative solution ?Needs small parameter
?Not all terms considered ?Free
partons? Expansion parameter ?as (only QCD
parameter) ?Its value depends on a scale
(asymptotic freedom) ?In inclusive DIS scale is
Q2 Resummation of ?(as)mlogn(Q2/Qo) (DGLAP)
or ?(as)mlogn(1/x) (BFKL)
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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
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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 as
small
Where are we going? ?A first look at data ?A
closer look at the theory ?A second look at
data the data
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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?
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The first HERA F2 at small x
Before HERA no data at small x but many
predictions based on extrapolations of existing
data In 1992 the first HERA data became
available F2 rises at small x and rises
quite fast lets look at it in some detail
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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
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From F2 to pQCD partons
See Stumps 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)
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pQCD evolution of F2 The basic idea
In pQCD, F2 is computed from perturbative
expansion in as subject to constraints (RGE) ?
linear integro-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
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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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2
3
3
2
2
1
1
2
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We are interested in this region but there is
no scale in plot
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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
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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 F2C
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The Q2 dependence of the rise of F2
At small x pQCD predicts F2x-? ... but ?
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 ?p system At small x
W2Q2/x ? high energy Remember x and Q2
correlated at HERA At very small Q2 F2Q2 But
s ?p F2/Q2 , so at small Q2 s ?p
constant, i.e. stops growing We look for
something like this at high Q2
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Extraction of FL the basic idea
Look at high y Compare cross section to
F2x-? Assign difference to FL(ltxgt,Q2)
DGLAP pQCD describes data
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F2c and the gluon
A small x gluon fluctuates into a charm
quark-antiquark The virtual photon
interacts with 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 by DGLAP 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
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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
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4
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Initial electron and proton Scattered
electron Emissions along the ladder Forward
Jet Proton remnant very difficult measurement
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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
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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 strongly 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
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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 ps and ns compressed in a
tight space) ? Naively expect gluon density to
scale as A1/3 (high Aheavy 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? lets try
and see!
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Heavy ions facilities today and tomorrow
Rich history of heavy ions accelerators and
experiments AGS and SPS Today RHIC plus its
detector produce beautiful data
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
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Small x in heavy ion collisions
Many handels ? Ion species ? centrality ? CMS
energy ? different x ranges For each, measure
as many details as possible ? Multiplicity ?
4-momentum ? Type of particle ? Correlations ?
Here only a bit of dA
Centrality impact parameter High ? small x
in Gold
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x dependence of RdA
Relative measurement ? normalization 1 no
change in physics pp vs dAu Concentrate in the
higher pt values There is a x dependence
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Rcp x and centrality dependence
Normalize central against peripheral
events Study it as a function of rapidity
as a function of centrality at high pt
Rcp
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Heavy Ion Physics
CGC ideas quantitatively compatible with dA Rcp
data Much more data (see Setos talk!) CGC
seems to be the right way to go, but ? many
other effects are expected to contribute ?
difficult to disentangle and them ? some surprise
also A bright future at RHIC and then at LHC!
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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!
HOMEWORK 3