The -model of Bose-Einsten Correlationswes/talks/wildbad-kreuth15.pdf · 2015-10-03 ·...

TauModel L3-Atlas anticor conclusion BACKUP

The τ -model of Bose-Einsten CorrelationsSome Recent Results

W.J. Metzger

Radboud University Nijmegen

XLV Symposium on Multiparticle DynamicsWildbad Kreuth

4–9 October 2015

ISMD XLV p. 1


BEC – ‘Classic’ Parametrizations

R2 = ρ(p1,p2)ρ0(p1,p2) = γ · [1 + λG] · (1 + εQ)

• GaussianG = exp

(−(rQ)2

)• Edgeworth expansion

G = exp(−(rQ)2

)·[1 + κ

3! H3(rQ)]

Gaussian if κ = 0 κ = 0.71± 0.06• symmetric Lévy

G = exp (−|rQ|α) , 0 < α ≤ 2α is index of stabilityGaussian if α = 2 α = 1.34± 0.04

Cannot accomodate the the dip of R2 inthe region 0.6 < Q < 1.5 GeV

L3, EPJC 71 (2011) 1648

Gauss Edgew LévyCL: 10−15 10−5 10−8

ISMD XLV p. 2


The τ -model

T.Csörgo, W.Kittel, W.J.Metzger, T.Novák, Phys.Lett.B663(2008)214T.Csörgo, J.Zimányi, Nucl.Phys.A517(1990)588

• Assume avg. production point is related to momentum:xµ(pµ) = a τpµ

where for 2-jet events, a = 1/mt

τ =

√t2 − r 2

z is the “longitudinal” proper timeand mt =

√E2 − p2

z is the “transverse” mass

• Let δ∆(xµ − xµ) be dist. of production points about their mean,and H(τ) the dist. of τ . Then the emission function is

S(x ,p) =∫∞

0 dτH(τ)δ∆(x − a τp)ρ1(p)

• In the plane-wave approx. F.B.Yano, S.E.Koonin, Phys.Lett.B78(1978)556.

ρ2(p1,p2) =∫

d4x1d4x2S(x1,p1)S(x2,p2)(1 + cos

([p1 − p2] [x1 − x2]

) )• Assume δ∆(xµ − xµ) is very narrow — a δ-function. Then

R2(p1,p2) = 1 + λReH(

a1Q2

2

)H(

a2Q2

2

), H(ω) =

∫dτH(τ) exp(iωτ)

ISMD XLV p. 3


BEC in the τ -model

• Assume a Lévy distribution for H(τ)Since no particle production before the interaction, H(τ) is one-sided.Characteristic function is

H(ω) = exp[− 1

2

(∆τ |ω|

)α (1− i sign(ω) tan(απ2

) )+ i ωτ0

], α 6= 1

where• α is the index of stability, 0 < α ≤ 2;• τ0 is the proper time of the onset of particle production;• ∆τ is a measure of the width of the distribution.

• Then, R2 depends on Q,a1,a2

R2(Q, a1, a2) = γ

{1 + λ cos

[τ0Q2(a1 + a2)

2+ tan

(απ2

)(∆τQ2

2

)αaα

1 + aα2

2

]· exp

[−(

∆τQ2

2

)αaα

1 + aα2

2

]}· (1 + εQ)

ISMD XLV p. 4


BEC in the τ -model

R2(Q, a1, a2) = γ{

1 + λ cos[τ0Q2(a1+a2)

2 + tan(απ2

) (∆τQ2

2

)α aα1 +aα22

]· exp

[−(

∆τQ2

2

)α aα1 +aα22

]}· (1 + εQ)

Simplification:

• effective radius, R, defined by R2α =(

∆τ2

)α aα1 +aα22

• Particle production begins immediately, τ0 = 0• Then

R2(Q) = γ[1 + λ cos

((RaQ)2α

)exp

(− (RQ)2α

)]· (1 + εQ)

where R2αa = tan

(απ2

)R2α

Compare to sym. Lévy parametrization:R2(Q) = γ

[1 + λ exp

(−|rQ| α

)](1 + εQ)

• R describes the BEC peak• Ra describes the anticorrelation dip• τ -model: both anticorrelation and BEC are related to ‘width’ ∆τ of H(τ)

ISMD XLV p. 5


2-jet Results on Simplified τ -model from L3 Z decayR2α

a = tan(απ2

)R2α

χ2/dof = 95/95Ra free

χ2/dof = 91/94

R2αa = tan

(απ2

)R2α agrees well with data L3, EPJC 71 (2011) 1648

ISMD XLV p. 6


3-jet Results on Simplified τ -model from L3 Z decayR2α

a = tan(απ2

)R2α

χ2/dof = 113/95CL = 10%

Ra freeχ2/dof = 84/94

R2αa = tan

(απ2

)R2α agrees less well with data L3, EPJC 71 (2011) 1648

ISMD XLV p. 7


BEC in e+e− and ppUse (mostly) simplified τ -modelwith τ0 = 0• L3: e+e− at

√s = MZ

• 0.8 · 106 events• Durham ycut = 0.006:

0.5 · 106 2-jet events0.3 · 106 > 2 jets, “3-jet”

• mixed event ref. sample

• ATLAS: pp at√

s = 7 TeVAstaloš thesis http://hdl.handle.net/2066/143448

• 107 min. bias events• |η| < 2.5• opposite hemisphere

ref. sample

Results are preliminary (unpublished)and not approved by the collaborations

BOSE-EINSTEIN CORRELATIONS

IN 7 TEV PROTON-PROTON COLLISIONS

IN THE ATLAS EXPERIMENT

Doctoral thesis

to obtain the degree of doctor

from Radboud University Nijmegen

on the authority of the Rector Magnificus prof. dr. Th.L.M. Engelen,

according to the decision of the Council of Deans

and

from Comenius University Bratislava

on the authority of the Rector Magnificus prof. RNDr. Karol Micieta, PhD.

to be defended in public on Wednesday, September 30, 2015

at 10:30 hrs

by

Róbert Astaloš

born on December 28, 1985

in Banská Bystrica, Slovakia

ISMD XLV p. 8


2-jet e+e− – All pp min. biasL3 2-jet

R2αa = tan

(απ2

)R2α

χ2/dof = 95/95

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

(Q)

2R

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7 = 7 TeVsData 2010

2≥ ch

20 MeV, n≥ 100 MeV, Q ≥ T

p(a)

dataWF Gaussian fitWF Exponential fit

vy fiteWF LQO Gaussian fit

QO Exponential fitTau model fit

freea

Tau model fit, R

Q [GeV]

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

∈

30

20

10

0

10

Q [GeV]

0 0.05 0.1 0.15

(Q)

2R

1.1

1.2

1.3

1.4

1.5

1.6

1.7

(b)

Q [GeV]

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

(Q)

2R

0.98

0.985

0.99

0.995

1

1.005

1.01

(c)

anticorrelation region also in pp – only τ -model with Ra free describes itBEC peak best described by τ -model with Ra free and sym. LévyBEC peak next best described by a quantum optical exponential parametrizationand by τ -model χ2(Q ≤ 0.36) = 115, 116, 157, 186Only τ -model with Ra free describes entire range of Q

ISMD XLV p. 9


Multiplicity dependencee+e− simplified τ -model pp, various parametrizations

sym. Lévy

>ch

< n

0 20 40 60 80 100 120 140

R [fm

]

1

1.5

2

2.5

3

3.5

4

4.5

5 20 MeV≥ 100 MeV, Q ≥

Tp

quantum optical exp

>ch

< n

0 20 40 60 80 100 120 140

R [fm

]

0.5

1

1.5

2

2.5

20 MeV≥ 100 MeV, Q ≥ T

p

pp: shape of R vs. Nch nearly independent ofparametrizationpp: value of R is different – different meaning inparametrizationsshape in e+e− similar to ppdifferent ref. samples give similar shapesexcept ULS flattens at high Nch

exponential

>ch

< n

0 20 40 60 80 100

R [fm

]

1

1.5

2

2.5

3 20 MeV≥ 100 MeV, Q ≥

Tp

2ULS R

2ROT R

2OHP R

2MIX R

ISMD XLV p. 10


Dependence on kt = pt pair/2 = | ~pt1 + ~pt2|/2pp – conventional parametrizationsUn-Like Sign ref. sample

exponential

466 Page 10 of 25 Eur. Phys. J. C (2015) 75:466

[GeV]Tk

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

λ

0

0.2

0.4

0.6

0.8

1

1.2

ATLAS pp 900 GeV

ATLAS pp 7 TeV

ATLAS pp 7 TeV HM

Exponential fit

Exponential fit

Exponential fit

ATLAS 5.2<|η 100 MeV, |≥T

p

[GeV]Tk

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

R [fm

]

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

ATLAS pp 900 GeV

ATLAS pp 7 TeV

ATLAS pp 7 TeV HM

Exponential fit

Exponential fit

Exponential fit

STAR pp 200 GeV

1.8 TeVpE735 p

ATLAS 5.2<|η 100 MeV, |≥T

p

(a) (b)

Fig. 5 The kT dependence of the fitted parameters: a λ and b

R obtained from the exponential fit to two-particle double-ratio at√s =0.9, 7 and 7 TeV high-multiplicity events. The average transverse

momentum kT of the particle pairs is defined as kT = |pT,1 + pT,2|/2.

The solid, dashed and dash-dotted curves are results of the exponen-

tial fits for 0.9, 7 and 7 TeV high-multiplicity data, respectively. The

results are compared to the corresponding measurements by the E735

experiment at the Tevatron [80], and by the STAR experiment at RHIC

[81]. The error bars represent the quadratic sum of the statistical and

systematic uncertainties

[GeV]Tk

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

λ

0.2

0.4

0.6

0.8

1

1.2

= 2 - 9ch n

= 10 - 24ch n

= 25 - 80ch n

= 81 - 125ch n

ATLAS = 7 TeVs

| < 2.5η 100 MeV, |≥T

p

[GeV]Tk

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

R [fm

]

0

0.5

1

1.5

2

2.5

3

3.5

= 2 - 9ch n

= 10 - 24ch n

= 25 - 80ch n

= 81 - 125ch n

ATLAS = 7 TeVs

| < 2.5η 100 MeV, |≥T

p

(a) (b)

Fig. 6 The kT dependence of the fitted parameters: a λ and b R

obtained from the exponential fit to the two-particle double-ratio cor-

relation function R2(Q) at√

s = 7 TeV for the different multiplic-

ity regions: 2 ≤ nch ≤ 9 (circles), 10 ≤ nch ≤ 24 (squares),

25 ≤ nch ≤ 80 (triangles) and 81 ≤ nch ≤ 125 (inverted triangles).

The average transverse momentum kT of the particle pairs is defined as

kT = |pT,1 + pT,2|/2. The error bars represent the quadratic sum of

the statistical and systematic uncertainties

estimates the production and decay of the ω-meson in the Q

region of 0.3–0.44 GeV. This region is thus excluded from

the fit range for kT > 500 MeV bin results.

In the region most important for the BEC parameters, the

quality of the exponential fit is found to deteriorate as kT

increases. This is due to the fact that at large kT values, the

characteristic BEC peak becomes steeper than the exponen-

tial function can accommodate. Despite the deteriorating fit

quality, the behaviour of the fitted parameters is presented

for comparison with previous experiments.

The fit values of the λ and R parameters are shown in Fig. 5

as a function of kT. The values of both λ and R decrease with

increasing kT.

The decrease of λ with kT is well described by an expo-

nential function, λ(kT) = µ e−νkT . The kT dependence of the

R parameter is also found to follow an exponential decrease,

R(kT) = ξ e−κkT . The shapes of the kT dependence are sim-

ilar for the 7 TeV and the 7 TeV high-multiplicity data. The

results of the fits are presented in Table 2.

In Fig. 5b, the kT dependence of the R parameter is

compared to the measurements performed by the E735 [80]

and the STAR [81] experiments with mixed-event reference

samples. These earlier results were obtained from Gaus-

sian fits to the single-ratio correlation functions and there-

fore the values of the measured radius parameters are mul-

tiplied by√

π as discussed in Sect. 2.4. The values of the

123

ATLAS, Eur.Phys.J.C(2015)75:466

OHP ref. samplesym. Lévy

[MeV]Tk

0 200 400 600 800 1000

R [fm

]

2.5

3

3.5

4

4.5 2≥ ch

20 MeV, n≥ 100 MeV, Q ≥ T

p

optical exponential

[MeV]Tk

0 200 400 600 800 1000

R [fm

]

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8 2≥ ch

20 MeV, n≥ 100 MeV, Q ≥ T

p

Astaloš thesis

• exponential parametrization:ULS ref. sample: R decreases with kt (all Nch)with other ref. samples, R is first constant, thenincreasing with kt

• other ‘classic parametrizations’: R increaseswith kt

exponential

[MeV]Tk

100 200 300 400 500 600 700 800 900R

[fm

]

1

1.5

2

2.5

3

3.5

4 2≥ ch

20 MeV, n≥ 100 MeV, Q ≥ T

p

2ULS R

2ROT R

2OHP R

2MIX R

ISMD XLV p. 11


kt = | ~pt1 + ~pt2|/2 dependence

simplified τ -model

e+e−, w.r.t. thrust axisRa constrained e+e−, Ra free

pp, w.r.t. beam directionRa free

[MeV]Tk

0 200 400 600 800 1000

R [fm

]

20

0

20

40

60

80

100 2≥ ch

20 MeV, n≥ 100 MeV, Q ≥ T

p

in e+e− dependence of R on kt depends on ‘jettiness’in e+e− 3-jet R decreases with kt.in e+e− 2-jet and in pp R first increases slightly and then falls with kt.kt dependence of R is dependent on parametrization and on ref. sample

ISMD XLV p. 12


Dependence on the Rapidity of the pair

e+e−, + thrust axis = hemisphere of jet with highest E qqg

• Rall y and Ry<−1increase with y23

• but Ry>1 constantwith y23

• 2-jet: Ry>1 = Ry<−1

Conclusion: Increase inR is mainly due to gluonR−1<y<1 > Ry>|1| for 2-jetgluon mini-jet in ‘2-jet sam-ple’?

ISMD XLV p. 13


Simplified τ -model in LCMS

In τ -model: R2Q2 =⇒ R2LQ2

L + R2sideQ

2side + R2

outQ2out

• RL constant with y23 Rside increases with y23

Conclusion: Increase in R is mainly due to increase in transverse planeAgrees with conclusion that increase is mainly due to harder gluon:Gluon makes event ‘fatter’

ISMD XLV p. 14


Effect of fit range

Besides ref. sample, another large systematic effect is the choice of fit range

0 1 2 3 4 5

(Q)

2R

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

= 7 TeVsData 2010

2≥ ch

20 MeV, n≥ 100 MeV, Q ≥ T

p(a)

data

2 GeV≤fit for Q

3 GeV≤fit for Q

4 GeV≤fit for Q

5 GeV≤fit for Q

Q [GeV]

0 1 2 3 4 5

∈

10

5

0

5

10

15

Using the opposite hemisphere ref. sample,and Exponential parametrization:

QU (GeV) Q excl. R (fm) λ2 - 2.02± 0.01 0.70± 0.013 - 2.28± 0.01 0.78± 0.014 0.5–3.0 2.30± 0.02 0.77± 0.015 0.5–4.0 2.29± 0.02 0.76± 0.01

Q [GeV]

0 0.05 0.1 0.15 0.2

(Q)

2R

1.1

1.2

1.3

1.4

1.5

1.6

1.7

(b)

Q [GeV]

0 1 2 3 4 5

(Q)

2R

0.98

0.985

0.99

0.995

1

1.005

1.01

(c)

QU = 2, 3: baseline tries to describeanticorrelationQU larger, with excluded regions canlead to stable results,but this is simply bricolageand it is a long extrapolationParametrization is just wrong

ISMD XLV p. 15


Effect of fit rangeBetter to use a parametrization that fits (better): τ -model with Ra freeand QU sufficiently beyond the anticorrelation regionUsing the opposite hemisphere ref. sample,

0 1 2 3 4 5

(Q)

2R

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

= 7 TeVsData 2010

2≥ ch

20 MeV, n≥ 100 MeV, Q ≥ T

p(a)

data

2 GeV≤fit for Q

3 GeV≤fit for Q

4 GeV≤fit for Q

5 GeV≤fit for Q

Q [GeV]

0 1 2 3 4 5

∈

6

4

2

0

2

4

6

8

Q [GeV]

0 0.05 0.1 0.15 0.2

(Q)

2R

1.1

1.2

1.3

1.4

1.5

1.6

1.7

(b)

Q [GeV]

0 1 2 3 4 5

(Q)

2R

0.98

0.985

0.99

0.995

1

1.005

1.01

(c)

QU 2 GeV 3 GeV 4 GeV 5 GeVα 0.108± 0.001 0.186± 0.005 0.235± 0.003 0.261± 0.003

R (fm) 17.8± 0.7 6.7± 0.5 4.1± 0.2 3.3± 0.1Ra (fm) 43.4± 1.2 3.0± 0.2 1.80± 0.04 1.52± 0.02λ 3.08± 0.05 1.91± 0.10 1.36± 0.05 1.15± 0.03

• much less dependent on fit range than other parametrizations• α quite different from e+e− 2-jet value of 0.41± 0.02+0.04

−0.06ISMD XLV p. 16


Anti-Correlation Region

In addition to L3 observation of anticorrelation in e+e− (Ecms = MZ),CMS has observed it in pp min. bias at 7 TeV JHEP 05 (2011) 29

Now it is also seen in ATLAS data (Astaloš thesis)

In addition to / Instead of the space-momentum correlation of the τ -model,anti-correlation can also be caused by the finite size of pions Białas, Zalewski

Detailed investigation of the anti-correlation may resolve this.

Use simplified τ -model, τ0 = 0 to investigate anticorrelation regionin e+e−: L3 data, 0.8 · 106 events,in pp: ATLAS data (Astaloš thesis) 107 events, |η| < 2.5

We compare fit results with Ra free, since they provide the best description ofthe anti-correlation dip.

ISMD XLV p. 17


Anti-Correlation Regione+e− jet dependence:

Going from narrow 2-jet to wide 3-jet,anticorrelation region becomes deeper and moves slightly lower in Q

ISMD XLV p. 18


Anti-Correlation Region – Multiplicity dependencee+e−2-jet (y J

23 < 0.023) pp min. bias

anticorrelation region is deeper and at higher Q in e+e− than in ppwith increasing N minimum moves to lower Q (effect is larger in pp than in e+e−)

and becomes less deep (also seen by CMS)ISMD XLV p. 19


Anti-Correlation Region – kt dependencee+e−2-jet (y J

23 < 0.023) pp min. bias

in e+e− anticorrelation region shows little or no dependence on ktin pp the depth decreases with ktbut the position of the minimum is approx. constant

ISMD XLV p. 20


Conclusions/Comments/Lessons1. τ -model

• τ -model is closely related to a string picture• strong x-p correlation• fractal - Lévy distribution

• BEC in pp (CMS, Astaloš ATLAS thesis) are described by simplified τ -model formulaOf all parametrizations tried, only τ -model with Ra free describes the data.

• suggests that BEC in pp is (mostly) from string fragmentation2. Ref. sample is important

• Comparison of results using different ref. samples is very problematic• Agreement among LHC expts. would facilitate comparisons, e.g.,

• central rapidity vs. forward rapidity• pp, pA, AA

3. Anticorrelation region is important• To study it

• Look beyond Q = 2 GeV – at least to 3, preferably to 4 or 5 GeV• Do not use Unlike-Sign ref. sample

• It depends on Nch, kt, jets. What else ?• Is space-momentum correlation, as in the τ -model, the correct explanation?

4. R depends on• in e+e−: Njets, Nch, kt, rapidity• in pp: Nch, kt.

Also on (mini)jets, rapidity, color reconnection, Nstrings, color ropes?ISMD XLV p. 21


ADDITIONAL MATERIAL

ISMD XLV p. 22


Quantum Optics parametrizations

In addition to ‘classic’ and τ -model parametrizations,Róbert Astaloš’s thesis includes fits of parametrizations based on a quantumoptical approach Weiner, Phys. Rep. 327 (2000) 249

• Gaussian

R2(Q) ∝ 1 + 2p(1− p) exp(−R2Q2) + p2 exp(−2R2Q2)

• Lorentzian in R, exponential in Q

R2(Q) ∝ 1 + 2p(1− p) exp(−RQ) + p2 exp(−2RQ)

p is the degree of chaoticity of the pion emissionNote that for p = λ = 1 these reduce to the ‘classical’ Gaussian and exponentialparametrizationsLike the ‘classical’ parametriazations, these parametrizations cannotaccomodate anticorrelation

ISMD XLV p. 23


Dependence on kt = pt pair/2 = | ~pt1 + ~pt2|/2pp – conventional parametrizationsUn-Like Sign ref. sample

exponential

The ATLAS Collaboration: Two-particle Bose–Einstein correlations 11

[GeV]Tk

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

λ

0

0.2

0.4

0.6

0.8

1

1.2

ATLAS pp 900 GeV

ATLAS pp 7 TeVATLAS pp 7 TeV HM

Exponential fit

Exponential fit Exponential fit

ATLAS | < 2.5η 100 MeV, |≥T

p

(a)

[GeV]Tk

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

R [f

m]

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

ATLAS pp 900 GeVATLAS pp 7 TeVATLAS pp 7 TeV HM

Exponential fit Exponential fit Exponential fit

STAR pp 200 GeV

1.8 TeVpE735 p

ATLAS | < 2.5η 100 MeV, |≥T

p

(b)

Fig. 5. The kT dependence of the fitted parameters (a) λ and (b) R obtained from the exponential fit to two-particle double-ratio at

√s =0.9 TeV, 7 TeV and 7 TeV high-multiplicity events. The average transverse momentum kT of the particle pairs is

defined as kT = |pT,1 +pT,2|/2. The solid, dashed and dash-dotted curves are results of the exponential fits at 0.9 TeV, 7 TeVand 7 TeV HMT, respectively. The results are compared to the corresponding measurements by the E735 experiment at theTevatron [69], and by the STAR experiment at RHIC [70]. The error bars represent the quadratic sum of the statistical andsystematic uncertainties.

[GeV]Tk

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

λ

0.2

0.4

0.6

0.8

1

1.2

= 2 - 9ch n = 10 - 24ch n = 25 - 80ch n = 81 - 125ch n

ATLAS = 7 TeVs

| < 2.5η 100 MeV, |≥T

p

(a)

[GeV]Tk

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

R [f

m]

0

0.5

1

1.5

2

2.5

3

3.5

= 2 - 9ch n = 10 - 24ch n = 25 - 80ch n = 81 - 125ch n

ATLAS = 7 TeVs

| < 2.5η 100 MeV, |≥T

p

(b)

Fig. 6. The kT dependence of the fitted parameters (a) λ and (b) R obtained from the exponential fit to the two-particledouble-ratio correlation function R2(Q) at

√s = 7 TeV for the different multiplicity regions: 2 ≤ nch ≤ 9 (circles), 10 ≤ nch ≤ 24

(squares), 25 ≤ nch ≤ 80 (triangles) and 81 ≤ nch ≤ 125 (inverted triangles). The average transverse momentum kT of theparticle pairs is defined as kT = |pT,1 + pT,2|/2. The error bars represent the quadratic sum of the statistical and systematicuncertainties.

ATLAS, Arxiv.1502.07947v1

OHP ref. samplesym. Lévy

[MeV]Tk

0 200 400 600 800 1000

R [fm

]

2.5

3

3.5

4

4.5 2≥ ch

20 MeV, n≥ 100 MeV, Q ≥ T

p

optical exponential

[MeV]Tk

0 200 400 600 800 1000

R [fm

]

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8 2≥ ch

20 MeV, n≥ 100 MeV, Q ≥ T

p

Astaloš thesis

Mix S. Padula, WPCF2014, ArXiv:1502.05757

(GeV)inv

Q0 0.5 1 1.5 2

Sin

gle

Rat

io

0.8

1

1.2

1.4

1.6

1.8

2

datamc

η∆Ref: Same Track Density in

CMS Preliminarypp@ 2.76 TeV

(GeV)inv

Q0 0.5 1 1.5 2

Dou

ble

Rat

io

0.8

1

1.2

1.4

1.6

1.8

2

Fit: Exponential

η∆Ref: Same Track Density in pp@ 2.76 TeV

CMS Preliminary

Figure 1: 1-D single ratios as a function of Qinv for data and Monte Carlo(Pythia 6-Z2 tune) from to pp collisions at 2.76 TeV are shown (left), as well asthe corresponding double ratio superimposed by the exponential fit (right).

(GeV)⟩T

k⟨0.2 0.3 0.4 0.5 0.6 0.7

λ

0

0.5

1

1.5

9≤Nch≤224≤Nch≤1079≤Nch≤25

CMS Preliminary [email protected] TeV

Fit:Exponential

7 TeV

(GeV)⟩T

k⟨0.2 0.3 0.4 0.5 0.6 0.7

(fm

)in

vR

0

1

2

3 9≤Nch≤224≤Nch≤1079≤Nch≤25

CMS Preliminary [email protected] TeV

Fit:Exponential

7 TeV

Figure 2: The fit parameters λ (left) and Rinv (right) from exponential fits tothe double ratios are shown in different Nch and kT bins, from pp collisionsat 2.76 and 7 TeV (full sample). The statistical uncertainties are indicated byerror bars (in some cases, smaller than the marker’s size), the systematic onesby empty (2.76 TeV data) or shaded boxes (7 TeV data).

⟩ch

N⟨0 5 10 15 20 25 30 35 40 45

(fm

)in

vR

0

0.5

1

1.5

2

2.5

CMS Preliminary

= 0.9 TeVsData -

= 0.9 TeVsFit -

= 7 TeVsData -

= 7 TeVsFit -

= 2.76 TeVsData -

= 2.76 TeVsFit -

= 7 TeVsData -

= 7 TeVsFit -

JHEP05(2011)029

⟩ch

N⟨5 10 15 20 25 30 35 40 45

∆

0

0.01

0.02

0.03

0.04

= 0.9 TeVs

= 7 TeVs

= 2.76 TeVs

= 7 TeVs

CMS Preliminary JHEP05(2011)029

Figure 3: Comparative plots with results in Ref. [4]. Left: Rinv versus < Nch >(acceptance and efficiency corrected), for pp collisions at 2.76 and 7 TeV (fit

curves are proportional to N1/3ch ). The inner error bars represent statistical

uncertainties and the outer ones, statistical and systematic uncertainties addedin quadrature. Right: The anticorrelation’s depth, ∆, versus < Nch >.

7

with ULS ref. sample, Rdecreases with kt (all Nch)with other ref. samples, Rincreases with kt

exponential

[MeV]Tk

100 200 300 400 500 600 700 800 900

R [fm

]1

1.5

2

2.5

3

3.5

4 2≥ ch

20 MeV, n≥ 100 MeV, Q ≥ T

p

2ULS R

2ROT R

2OHP R

2MIX R

ISMD XLV p. 24


Jets and Rapidityorder jets by energy: E1 > E2 > E3Note: thrust only defines axis |~nT|, not its direction.Choose positive thrust direction such that jet 1 is in positive thrust hemisphererapidity, yE, of particles fromjet 1, jet 2, jet 3: q

q

g

yD23 < 0.002 0.002 < yD

23 < 0.006 0.006 < yD23 < 0.018 0.018 < yD

23ID 10216

mkhists2_d00-02_data94.hst

yE

jet 1 3%gjet 2 8%gjet 3 89%g

0

2000

4000

6000

8000

10000

x 10

-6 -4 -2 0 2 4 6

ID 10216


yE


0

2000

4000

6000

8000

10000

x 10

-6 -4 -2 0 2 4 6

ID 10216


yE


0

2000

4000

6000

8000

10000

x 10

-6 -4 -2 0 2 4 6

ID 10216

mkhists_d18_data94.hst

yE


0

2000

4000

6000

8000

10000

x 10

-6 -4 -2 0 2 4 6

• yE > 1 almost all jet 1 almost all quark• yE < −1 mostly jet 2, some jet 3 mostly quark• −1 < yE < 1 jet-3 enriched largely gluonISMD XLV p. 25


Simplified τ -model in LCMS

In τ -model: R2Q2 =⇒ R2LQ2

L + R2sideQ

2side + R2

outQ2out

• Durham, JADE agree• RL constant with y23 Rside increases with y23

Conclusion: Increase in R is mainly due to increase in transverse planeAgrees with conclusion that increase is mainly due to harder gluon:Gluon makes event ‘fatter’

ISMD XLV p. 26


Jets

Jets — JADE and Durham algorithms• force event to have 3 jets:

• normally stop combining when all ‘distances’between jets are > ycut

• instead, stop combining when there are only 3jets left

• y23 is the smallest ‘distance’ between any 2 ofthe 3 jets

• y23 is value of ycut where number of jetschanges from 2 to 3

log10(y23) Durham

IDEntries

6011 804574

mkhists_d06_data94.hst

0.00

2

0.00

6

0.01

8

0

5000

10000

15000

20000

25000

-4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5

define regions of yD23 (Durham):

yD23 < 0.002 narrow two-jet or

0.002 < yD23 < 0.006 less narrow two-jet yD

23 < 0.006 two-jet0.006 < yD

23 < 0.018 narrow three-jet 0.006 < yD23 three-jet

0.018 < yD23 wide three-jet

and similarly for y J23 (JADE): 0.009, 0.023, 0.056

ISMD XLV p. 27


Results from R2,√

s = MZ (Gaussian parametrization)

– correction for π purity increases λ– mixed ref. gives smaller λ, r than + – ref. – Average means little

ISMD XLV p. 28

The -model of Bose-Einsten Correlationswes/talks/wildbad-kreuth15.pdf · 2015-10-03 ·...

Documents

Transcript of The -model of Bose-Einsten Correlationswes/talks/wildbad-kreuth15.pdf · 2015-10-03 ·...