The dilepton invariant mass spectrum

1

The study of lepton (e+e-, +-) pairs is one of the most important tools to extract information on the early stages of the collision Dileptons do not interact strongly, once produced can cross the system without significant re-interactions (not altered by later stages) Several resonances can be “easily” accessed through the dilepton spectrum

“low” s version

“high” s version

Heavy quarkonium states

2

Quarkonium is a bound state of and q

qwith

Charmonium () family Bottomonium () family

Several quarkonium states exists,distinguished by their quantum numbers (JPC)

Colour Screening

3

At T=0, the binding of the and quarks can be expressed using the Cornell potential:

krr

rV )(

Coulombian contribution, induced by gluonic exchange between and

Confinement term

qq

3

The QGP consists of deconfined colour charges the binding of a pair is subject to the effects of colour screening

What happens to a pair placed in the QGP?

krr

rV )( Dre

rrV /)(

• The “confinement” contribution disappears• The high color density induces a screening of the coulombian term of the potential

qq

..and QGP temperature

Perturbative Vacuum

cc

Color Screening

ccScreening of

strong interactionsin a QGP

• Screening stronger at high T• D maximum size of a bound state, decreases when T increases

Resonance melting

QGP thermometer

• Different states, different sizes

Feed-down and suppression pattern

J/

(3S) b(2P)(2S)

b(1P)

(1S)

(2S)c(1P)

J/

Digal et al., Phys.Rev. D64(2001)

094015

• Due to different dissociation temperature for each resonance, one should observe «steps» in the suppression pattern of measured J/ or (1S)

• Ideally, one could vary T• by studying the same system (e.g. Pb-Pb) at various s• by studying the same system for various centrality classes

Yiel

d(T)

/Yie

ld(T

=0)

• Feed-down process: charmonium (bottomonium) “ground state” resonances can be produced through decay of larger mass quarkonia Effect : ~30-40% for J/, ~50% for (1S)

From suppression to (re)generation At sufficiently high energy, the cc pair multiplicity becomes large

Contrary to the suppression scenarii described before,these approaches may lead to a J/ enhancement

Statistical approach: Charmonium fully melted in QGP Charmonium produced, together with all other hadrons, at chemical freeze-out, according to statistical weightsKinetic recombination: Continuous dissociation/regeneration over QGP lifetime

How quantifying suppression ? High temperature should indeed induce a suppression of the charmonia and bottomonia states How can we quantify the suppression ? Low energy (SPS)

Normalize the charmonia yield to another hard process (Drell-Yan) not sensitive to QGP

At RHIC, LHC Drell-Yan is no more “visible” in the dilepton mass spectrum overwhelmed by semi-leptonic decays of charm/beauty pairs

Solution: directly normalize to elementary collisions (pp), via nuclear modification factor RAA

= If no nuclear effects NP

AA=Ncoll NPNN (binary scaling)

RAA<1 suppressionRAA>1 enhancement

Results: cold nuclear matter also matters….

pA collisions no QGP formation. What is observed ?

NA50, pA 450 GeV

There is suppression of the J/ already in pA! This effect can mask a genuine QGP signal. Needs to be calibrated and factorized out Commonly known as Cold Nuclear Matter Effects (CNM)

Effective quantities are used for their parameterization (, abs, …)

Drell-Yan usedas a reference here!

SPS: the anomalous J/ suppression

After correction for EKS98 shadowing

In-In 158 GeV (NA60)Pb-Pb 158 GeV (NA50)

Results from NA50 (Pb-Pb) and NA60 (In-In) B. Alessandro et al., EPJC39 (2005) 335R. Arnaldi et al., Nucl. Phys. A (2009) 345

Anomaloussuppression

In semi-central and central Pb-Pb collisions there is suppression beyond CNM anomalous J/ suppression

Drell-Yan usedas a reference here!

Maximum suppression ~ 30%. Could be consistent with suppressionof J/ from c and (2S) decays (sequential suppression)

RHIC: first surprises Let’s simply compare RAA (i.e. no cold nuclear effects taken into account)

Qualitatively, very similar behaviour at SPS and RHIC !

RHIC: larger suppression at forward rapidity: favours a regeneration scenario

Do we see (as at SPS) suppression of (2S) and c ? Or does (re)generation counterbalance a larger suppression at RHIC ?

Answer: go to LHC

11

Two main improvements:

1) Evidence for charmonia (re)combination: now or never!

Yes, we can!

(3S) b(2P)(2S)

b(1P)

(1S)

2) A detailed study (for the first time) of bottomonium suppression

Massr0

J/, ALICE vs PHENIX

12

Compare with PHENIX Stronger centrality dependence at lower energy Systematically larger RAA values for central events in ALICE

First possible evidence for (re)combination

Even at the LHC, NO rise of J/ yield for central events, but….

results

13

(2S), (3S) much less bound than (1S) Striking suppression effect seen when comparing Pb-Pb and pp !

Conclusions on quarkonia Very strong sensitivity of quarkonium states to the medium created in heavy-ion collisions

Two main mechanisms at play in AA collisions

1) Suppression by color screening/partonic dissociation2) Re-generation (for charmonium only!) at high s

can qualitatively explain the main features of the results

Cold nuclear matter effects are an important issue (almost not covered here and in these lectures): interesting physics in itself and necessary for precision studies study pA at the LHC

High pT particles (and jet!)suppression,

open heavy quark particles

Their production cross section can be calculated via perturbative QCD approaches

Other hard probes High pT hadrons and jets Mesons and baryons containing heavy quarks (charm+beauty)

Such hard probes come from high pT partons produced on a short timescale (tform ≈ 1/Q2) Sensitive to the whole history of the collisions Can be considered as probes of the medium

But what is the effect of the medium on such hard probes ?

pp and “normal” AA production

)Q(zDQxPDFQxPDF qHqqqabbaHxhh222 ,),(),(

Partoniccross section

Parton Distribution Functionsxa , xb= momentum fractions ofpartons a, b in their hadrons

Cross section for hadronic collisions (hh)

s /2

q

q

H

xa

xb

Q2

s /2

Jet-

Fragmentation ofquark q in the hadron H

In pp collisions, the following factorized approach holds

In AA collisions, in absence of nuclear and/or QGP effects

one should observe binary scalingTppcollTAA pNNpN d/dd/d

Breaking of binary scaling (1)

RAA < 1

RAA = 1

RA

A

Binary scaling for high pT particles can be broken by

Initial state effects (active both in pA and AA) Cronin effect PDF modifications in nuclei

(shadowing)

Breaking of binary scaling (3) Final state effects change in the fragmentation functions due to the presence of the medium: energy loss/jet quenching

E - DE

Parton crossing the medium looses energy via

scattering with partons in the medium (collisional energy loss) gluon radiation (gluonstrahlung)

The net effect is a decrease of the pT of fast partons (produced on short timescales)

Quenching of the high-pT spectrum

Radiative mechanism dominant at high energy

Quenched spectrum

Spectrum in pp

Radiative energy loss (BDMPS approach)

2 ˆ LqCE RsD

Casimir factorTransport coefficient

Energy loss Distance travelled in medium

S = QCD coupling constant (running)CR = Casimir coupling factor

Equal to 4/3 for quark-gluon coupling and 3 for gluon-gluon coupling

q = Transport coefficient Related to the properties (opacity) of the medium, proportional to gluon density and momenta

L2 dependence related to the fact that radiated gluons interact with the medium

^

Transport coefficient

Pion gas

Cold nuclear matter

QGP

4/3 ˆ q

The transport coefficient is related to the gluon density and therefore to the energy density of the produced medium

From the measured energy loss one can therefore obtain an indirect measurement of the energy density of the system

Typical (RHIC) values qhat = 5 GeV2/fm S = 0.2 value corresponding to

a process with Q2 = 10 GeV CR = 4/3 L = 5 fm

GeV40DE

Enormous! Only veryhigh-pT partons can survive(or those produced close tothe surface of the fireball)

Results for charged hadrons and 0

Tpp

TAA

collTAA dpdN

dpdNN

pR//1)(

factor ~5 suppression

Is this striking result due to a final state effect ? Control experiments

pA collisions AA collisions, with particles not interacting strongly (e.g., photons)

d-Au collisions and photon RAA

Both control experiments confirm that we observe a final state effect d-Au collisions observe Cronin enhancement Direct photons medium-blind probe

Angular correlations qqbar pairs produced inside fireball: both partons

hadronize to low pT particles

qqbar pairs produced in the corona: one parton (outward going) gives a high pT hadron (jet), the other (inward going) looses energy and hadronizes to low pT hadron

Study azimuthal angle correlations between a “trigger” particle (the one with largest pT) and the other high-pT particles in the event

At LO, hard particles come from back-to-back jet fragmentation: two peaks at 00 and 1800

23

Near-side peak

Away-side peak

Results on angular correlations

24

Suppression of back-to-back jet emission in central Au-Au collisions Another evidence for parton energy loss

d-Au results confirm this is a final state effect

High-pT particles: results from LHC (1)

Comparison RHIC vs LHC

In the common pT region, similar shape of the suppression (minimum suppression at pT~ 2 GeV/c)

Larger suppression at LHC!

Possibly due to higher energy density (take also into account that pT spectra are harder at the LHC and should give a larger RAA

for the same energy loss)

High-pT particles: results from LHC (2)

Good discriminating power between models at very high pT

Dijet imbalance: clear signal at LHC

2, 12

21

21 D

TT

TTJ EE

EEA

Significant imbalance of jet energies for central PbPb events! Jet studies should tell us more about the parton energy loss and its dynamics (leading hadrons biased towards jets with little interaction)

Pushing to very high pT

Strong jet suppression at LHC, extending to pT = 200 GeV! Radiation is not captured inside the jet cone R But where does the energy go ?

Where does energy go? (1) Calculate projection of pT on leading jet axis and average over selected tracks with pT > 0.5 GeV/c and |η| < 2.4

Define missing pT//

Leading jet definesdirection

0-30% Central PbPb

balanced jets unbalanced jets

excess away from leading

jet

excess towards leading jet

Integrating over the whole event final state the momentum balance is restored

Where does energy go? (2) Calculate missing pT in ranges of track pT

The momentum difference in the leading jet is compensated by low pT particles at large angles with respect to the jet axis

in-cone

out-of-cone

Energy loss of (open) heavy quarkmesons/baryons

The study of open heavy quark particles in AA collisions is a crucial test of our understanding of the energy loss approach

A different energy loss for charmed and beauty hadrons is expected In particular, at LHC energy

Heavy flavours mainly come from quark fragmentation, light flavours from gluons smaller Casimir factor, smaller energy loss Dead cone effect: suppression of gluon radiation at small angles, depending on quark mass

Suppression forq < MQ/EQ

DEg > DEcharm > DEbeauty

RAA (light hadrons) < RAA (D) < RAA (B)

Should lead toa suppression

hierarchy

Heavy-flavor measurements: NPE

g conversion

0 gee

h gee, 30

w ee, 0ee

f ee, hee

r ee

h’ gee

Non-photonic electrons (pioneered at RHIC), based on semi-leptonic decays of heavy quark mesons

Electron identification

Subtract electrons not coming from heavy-flavour decays

ge+e- (main bckgr. source) 0 , h, h’ Dalitz decays r, w, f decays

Indirect measurement, expect non-negligible systematic uncertainties

Sophisticated background subtraction techniques

Converter method Vertex detectors…

Non-photonic electrons - RHIC

RAA values for non-photonic electrons similar to those for hadrons no dead cone ?

No separation of charm and beauty, adds difficulty in the interpretation

Results difficult to explain bytheoretical models, even including high q values andcollisional energy loss

Fair agreement with models including only charm, but clearly not a realistic description

^

Various techniques forheavy-flavor measurements

Direct reconstruction of hadronic decay Pioneered at RHIC, fully exploited at the LHC

Fully combinatorial analysis (build all pairs, triplets,…) prohibitive Use

Invariant mass analysis of decay topologies separated from the interaction vertex (need ~100 m resolution) K identification (time of flight, dE/dx)

LHC results – D-mesons

Good compatibility between various charmed mesons Large suppression! (factor~5)

35

Similar trend vs. pT for D, charged particles and ±

Hint of RAAD > RAA

π at low pT ? Look at beauty

Beauty via displaced J/

36

Fraction of non-prompt J/ from simultaneous fit to +- invariant mass spectrum and pseudo-proper decay length distributions (pioneered by CDF) LHC results from CMS

Background from sideways (sum of 3 exp.) Signal and prompt from MC template

Non-prompt J/ suppression

37

Suppression hierarchy (b vs c) observed, at least for central collisions (note different y range)

Larger suppression at high pT ?

Heavy quark v2 at the LHC

3838

OUTIN

OUTIN

NNNN

Rv

4

1

22

Indication of non-zero D meson v2 (3 effect) in 2<pT<6 GeV/c

A non-zero elliptic flow for heavy quark would imply that also heavy quark thermalize and participate in the collective expansion

Data vs models: D-mesons

39

Consistent description of charm RAA and v2very challenging for models,

can bring insight on the medium transport properties,also with more precise data from future LHC runs

Heavy quark – where are we ?

40

Studies pioneered at RHIC Abundant heavy flavour production at the LHC

Allow for precision measurements Can separate charm and beauty (vertex detectors!)

Indication for RAAbeauty>RAA

charm and RAAbeauty>RAA

light

More statistics needed to conclude on RAAcharm vs. RAA

light

Indication (3) for non-zero charm elliptic flow at low pT

At the end of the journey…..…let’s try to summarize the main findings

Heavy-ion collisions are our door to the study of the properties of strong interaction at very high energy densities A system close to the first instants of the Universe

Years of experiments at various facilities from a few GeV to a few TeV center-of-mass energies provided a lot of results which shows a strong sensitivity to the properties of the medium

This medium behaves like a perfect fluid, has spectacular effects on hard probes (quarkonia, jet,…) and has the characteristics foreseen for a Quark-Gluon Plasma

Even if many aspects are understood, with the advent of LHC we are answering long-standing questions but we face new challenges…. …so QGP physics might be waiting for you!

Also because….

…sagas never end!

Other topics

Low-mass resonances anddilepton continuum

Conceptual difference between study of heavy quarkonia and low-mass resonances

Study of low-mass region: investigate observables related to QCD chiral symmetry restoration

J/ Long-lived meson ( = 93 keV) Decays outside reaction region QGP may influence production

cross section but not its spectral characteristics (mass, width)

r (w, f to a lesser extent) Short-lived meson ( = 149 MeV) Decays to e+e- (+ -) inside the reaction zone QGP directly influences spectral

characteristics may expect mass, width modifications

Chiral symmetry(1) The QCD lagrangian for two light massless quarks is

jjiL g where du

The Lagrangian is unchanged under a rotation of L by any 2 x 2 unitary matrix L, and R by any 2 x 2 unitary matrix R This symmetry of the lagrangian is called chiral symmetry

The quark fields can be decomposed into a left-handed and a right-handed component

g2

1 5L g

21 5

R

It turns out that the non-zero mass for hadrons is generated by a spontaneous breaking of the chiral symmetry (i.e. the ground state does not have the symmetry of the lagrangian)

Chiral symmetry(2) In our world, therefore, the QCD vacuum corresponds to a situation where the scalar field qq (quark condensate) has a non-zero expectation value

The massless Goldstone bosons associated with the symmetry breaking are the pions Contrary to the expectations m 0, due to the non-zero (but very small) bare mass of u,d quarks Pion mass is anyway much smaller than that of other hadrons

Lattice QCD calculations predict that , close to the deconfinement transition, chiral symmetry is (approximately) restored, i.e. qq 0 with consequences on the spectral properties of hadrons

Chiral symmetry restoration and QCD phase diagram

Even in cold nuclear matter effects one could observe effects due to partial restoration of chiral symmetry Strong sensitivity to baryon density too study collisions far from transparency regime Stronger effect in AA than in pA, but interpretation more difficult need to understand the fireball evolution, mesons emitted along the whole history of the collision

Effects on vector mesons In the vector meson sector, predictions around TC are model dependent Some degree of degeneracy between vector and pseudovector states, r and a1 mesons

Dilepton spectrum study vector mesons (JPC=1--)

Brown-Rho scaling hypothesis, hadron masses directly related to quark condensate

qqqq

mm

mm

mm

N

N

****

r

r

Rapp-Wambach broadening scenario

rB /r0 0 0.1 0.7 2.6

Results at SPS energy: NA60

h

wf

In-In collisions, s=17 GeV Highest-quality data on the market w ~ f ~ 20 MeV

Subtract contributions of resonance decays, both 2-body and Dalitz, except r

Investigate the evolution of the resulting dilepton spectrum, which includes r meson plus a continuum possibly due to thermal production

Centrality dependence of r spectral function

A clear broadening ofthe r-meson is

observed, but withoutany mass shift

Brown-Rho scaling clearly disfavored

12 centrality bins

Comparison data vsexpected spectrum

Theory comparisons

Good agreement with broadening models Direct contribution from QGP phase is not dominant 4 interaction sensitive to r-a1 mixing and therefore to chiral symmetry restoration

Dilepton studies at RHIC

Minbias (value ± stat ± sys) Central (value ± stat ± sys)

STAR 1.53 ± 0.07 ± 0.41 (w/o ρ) 1.40 ± 0.06 ± 0.38 (w/ ρ)

1.72 ± 0.10 ± 0.50 (w/o ρ) 1.54 ± 0.09 ± 0.45 (w/ ρ)

PHENIX 4.7 ± 0.4 ± 1.5 7.6 ± 0.5 ± 1.3Difference 2.0 σ 4.2 σ

Clear signal in the low-mass region ! But discrepancy between experiments, not easy to explain… STAR and NA60 results can be described in the broadening approach

Conclusions on low-mass dileptons Chiral symmetry is a property of the QCD lagrangian, when neglecting the (small) light quark mass terms

A spontaneous breaking of the chiral symmetry is believed to be responsible for the generation of the hadron masses, and leads to having a non-zero value for the quark-condensate in the vacuum

At high temperature and baryon density chiral symmetry is gradually restored, leading to qq = 0

Chiral symmetry restoration effects can influence spectral properties of light vector mesons

Several interesting effects observed, clear connection with chiral symmetry still being worked out

Backup

Breaking of mT scaling in AA

55

200 GeV130 GeV130 GeV200 GeV

Average pT increases with particle mass (as a consequence of the increase of Tslope with particle mass)

v1 coefficient: directed flow

56

....2cos2)cos(212)( 21

0 RPRPRP

vvNd

dN

Directed flow

RPv cos1 v1 0 means that there is a difference between the number of particles emitted parallel (00) and anti-parallel (180 0) with respect to the impact parameter

Directed flow represents therefore a preferential emission direction of particles

Probes of the QGP One of the best way to study QGP is via probes, created early in the history of the collision, which are sensitive to the short-lived QGP phase Ideal properties of a QGP probe

Production in elementary NN collisions under control

Not (or slightly) sensitive to the final-state hadronic phase

High sensitivity to the properties of the QGP phase

Why are heavy quarkonia sensitive to the QGP phase ?

Interaction with cold nuclear matter under control

VACUUM

HADRONICMATTER

QGP

RHIC: forward vs central y

58

Comparison of results obtained at different rapidities

Stronger suppression at forward rapidities

Mid-rapidity

Forward-rapidity

Not expected if suppression increases with energy density (which should be larger at central rapidity) Are we seeing a hint of (re)generation, since there are more pairs at y=0? Comparisons with theoretical models tend to confirm this interpretation, but not in a clear enough way. How to solve the issue ?

pT dependence of the suppressionLarge pT: compare CMS with STAR Small pT: compare ALICE with models

(comparison with PHENIX in prev. slide)

At high pT no regeneration expected: more suppression at LHC energies At small pT ~ 50% of the J/ should come from regeneration

What happens to (1S)?

60

Also a large suppression for (1S), increasing with centrality

(1S) compatible with only feed-down suppression ? Complete suppression of 2S and 3S states would imply 50% suppression on 1S

Probably yes, also taking into account the normalization uncertainty

Possibly (1S) dissoc. threshold still beyond LHC reach ? Full energy

(2S) and (3S) are suppressed with respect to (1S). But what about (1S) itself ?

RpA = 1RpA

RpA > 1Cronin

enhancement

TdpdN

Tp

pp spectrum

pA spectrum normalized to Ncoll ≈ A

Cronin effect Multiple scattering

of initial state partons

pT kick Increase final state pT

Breaking of binary scaling (2) Shadowing Parton densities for nucleons inside a nucleus are different from those in free nucleons (seen for the first time by EMC collaboration, 1983)

These initial state effects are not related to QGP formation!

Non–perturbative effect, parameterized by fitting simultaneously various sets of data. Still large uncertainties are present

),(),(),( 2

22

QxfQxfQxR p

i

AiA

i

The new frontier: b-jet tagging

63

Jets are tagged by cutting on discriminating variables based on the flight distance of the secondary vertex enrich the sample with b-jets

b-quark contribution extracted using template fits to secondary vertex invariant mass distributions

Factor 100 light-jet rejectionfor 45% b-jet efficiency

Beauty vs light: high vs low pT

64

Low pT: different suppression for beauty and light flavours, but:

Different centrality Decay kinematics

High pT: similar suppression for light flavour and b-tagged jets

Fill the gap!