sigma (mb)

2008 CTEQ – MCnet Summer School on QCD Phenomenology and Monte Carlo Event Generators 8–16 August 2008 Debrecen, Hungary

Minimum-Bias and

Underlying-Event Physics

Torbj ¨ orn Sj ¨ ostrand

Department of Theoretical Physics, Lund University

What is minimum bias?

≈ “all events, with no bias from restricted trigger conditions”

σ_tot = σ_elastic+σsingle−diffractive+σdouble−diffractive+. . .+σnon−diffractive

y dn/dy

reality: σ_min−bias ≈ σnon−diffractive+σdouble−diffractive ≈ 2/3 × σ_tot

What is underlying event?

y dn/dy

underlying event jet

pedestal height

What is multiple interactions?

Cross section for 2 → 2 interactions is dominated by t-channel gluon exchange, so diverges like dˆσ/dp²_⊥ ≈ 1/p⁴_⊥ for p_⊥ → 0.

integrate QCD 2 → 2 qq^′ → qq^′

qq → q^′q^′ qq → gg qg → qg gg → gg gg → qq

with CTEQ 5L PDF’s

0.01 0.1 1 10 100 1000 10000

0 5 10 15 20 25 30 35 40 45 50

sigma (mb)

pTmin (GeV)

Integrated cross section above pTmin for pp at 14 TeV jet cross section total cross section

σ_int(p_⊥min) =

ZZZ

p_⊥min dx₁ dx₂ dp²_⊥ f₁(x₁, p²_⊥) f₂(x₂, p²_⊥) dˆσ dp²_⊥ Half a solution to σ_int(p_⊥min) > σ_tot: many interactions per event

σ_tot =

∞ X

n=0

σ_n σ_int =

∞ X

n=0

n σ_n

σ_int > σ_tot ⇐⇒ hni > 1

n P_n

hni = 2

0 1 2 3 4 5 6 7

If interactions occur independently then Poissonian statistics

P_n = hniⁿ

n! e^−hni

but energy–momentum conservation

⇒ large n suppressed

Other half of solution:

perturbative QCD not valid at small p_⊥ since q, g not asymptotic states (confinement!).

Naively breakdown at p_⊥min ≃ ¯h

rp ≈ 0.2 GeV · fm

0.7 fm ≈ 0.3 GeV ≃ Λ_QCD

. . . but better replace rp by (unknown) colour screening length d in hadron

r r

d resolved

r r

d

screened λ ∼ 1/p_⊥

so modify dˆσ

dp²_⊥ ∝ α²_s(p²_⊥)

p⁴_⊥ → α²_s(p²_⊥)

p⁴_⊥ θ (p_⊥ − p_⊥min) (simpler) or → α²_s(p²_⊥0 + p²_⊥)

(p²_⊥0 + p²_⊥)² (more physical)

p²_⊥ dˆσ/dp²_⊥

0

where p_⊥min or p_⊥0 are free parameters, empirically of order 2 GeV

Typically 2 – 3 interactions/event at the Tevatron, 4 – 5 at the LHC, but may be more

in “interesting” high-p_⊥ ones.

Basic generation of multiple interactions

• For now exclude diffractive (and elastic) topologies,

i.e. only model nondiffractive events, with σ_nd ≃ 0.6 × σ_tot

• Differential probability for interaction at p_⊥ is dP

dp_⊥ = 1 σ_nd

dσ dp_⊥

• Average number of interactions naively hni = 1

σ_nd

Z _Ecm/2 0

dσ

dp_⊥ dp_⊥

• Require ≥ 1 interaction in an event

or else pass through without anything happening

P_≥1 = 1 − P₀ = 1 − exp(−hni) (Alternatively: allow soft nonperturbative interactions even if no perturbative ones.)

Can pick n from Poissonian and then generate n independent interactions according to dσ/dp_⊥ (so long as energy left), or better. . .

. . . generate interactions in ordered sequence p_⊥1 > p_⊥2 > p_⊥3 > . . .

• recall “Sudakov” trick used e.g. for parton showers:

if probability for something to happen at “time” t is P (t)

and happenings are uncorrelated in time (Poissonian statistics) then the probability for a first happening after 0 at t₁ is

P(t₁) = P (t₁) exp



−

Z _t1

0 P (t) dt



and for an i’th at t_i is

P(t_i) = P (t_i) exp −

Z _ti

t_i−1 P (t) dt

!

• Apply to ordered sequence of decreasing p_⊥, starting from Ecm/2 P(p_⊥ = p_⊥i) = 1

σ_nd dσ

dp_⊥ exp

"

−

Z _p

⊥(i−1)

p_⊥

1 σ_nd

dσ

dp^′_⊥dp^′_⊥

#

• Use rescaled PDF’s taking into account already used momentum

=⇒ n_int narrower than Poissonian

Impact parameter dependence

So far assumed that all collisions have equivalent initial conditions, but hadrons are extended,

e.g. empirical double Gaussian:

ρ_matter(r) = N₁ exp −r² r²₁

!

+ N₂ exp −r² r²₂

!

where r₂ 6= r₁ represents “hot spots”, and overlap of hadrons during collision is

O(b) =

Z

d³x dt ρ^boosted_1,matter(x, t)ρ^boosted_2,matter(x, t) or electromagnetic form factor:

Sp(b) =

Z d²k 2π

exp(ik · b) (1 + k²/µ²)² where µ = 0.71 GeV → free parameter, which gives

O(b) = µ²

96π (µb)³ K₃(µb)

1e-05 0.0001 0.001 0.01 0.1 1

0 1 2 3 4 5 6 7 8

O(b)

b

Tune A double Gaussian old double Gaussian Gaussian ExpOfPow(d=1.35) exponential EM form factor

p p

b

b hni

1 all

n ≥ 1

• Events are distributed in impact parameter b

• Average activity at b proportional to O(b)

⋆ central collisions more active ⇒ P_n broader than Poissonian

⋆ peripheral passages normally give no collisions at all ⇒ finite σ_tot

• Also crucial for pedestal effect (more later)

PYTHIA implementation

(1) Simple scenario (1985):

first model for event properties based on perturbative multiple interactions no longer used (no impact-parameter dependence)

(2) Impact-parameter-dependence (1987):

still in frequent use (Tune A, Tune DWT, ATLAS tune, . . . )

• double Gaussian matter distribution,

• interactions ordered in decreasing p_⊥,

• PDF’s rescaled for momentum conservation,

• but no showers for subsequent interactions and simplified flavours (3) Improved handling of PDFs and beam remnants (2004)

• Trace flavour content of remnant, including baryon number (junction)

u u

d

• Study colour (re)arrangement

among outgoing partons (ongoing!)

• Allow radiation for all interactions

(4) Evolution interleaved with ISR (2004)

• Transverse-momentum-ordered showers dP

dp_⊥ = dP_MI

dp_⊥ + ^X dP_ISR dp_⊥

!

exp −

Z _p⊥i−1 p_⊥

dP_MI

dp^′_⊥ + ^X dP_ISR dp^′_⊥

!

dp^′_⊥

!

with ISR sum over all previous MI

interaction number

p_⊥

p_⊥max

p_⊥min

hard int.

1 p_⊥1

mult. int.

2

mult. int.

3 p_⊥2

p_⊥3

ISR

ISR

ISR p^′_⊥1

(5) Rescattering (in progress)

is 3 → 3 instead of 4 → 4:

HERWIG implementation

(1) Soft Underlying Event (1988), based on UA5 Monte Carlo

´ H µ C¶ ·N <= < U º Ö QN K FIWV ? KN < F= B R Q IJ S I ;< W Q AM= K

ZX ç ` ì _ ] _ ê a` Yjk i ^` mn flop t Z[ s

[ Z\ w v^] ] q

y

Ü = O ; FI

P = S IJ A Q I ;K M I< F

B IS

N FI AJ < ; Q >K

= M @ AB _ `a

xK

N < F= B < O

= J= B ; F= M N J FIK >B= <= K= ? F= M _ ` a I< B= ; ?: = M

• Distribute a (∼ negative binomial) number of clusters independently in rapidity and transverse momentum according to parametrization/extrapolation of data

• modify for overall energy/momentum/flavour conservation

• no minijets; correlations only by cluster decays

(2) Jimmy (1995; HERWIG add-on; part of HERWIG++)

• only model of underlying event, not of minimum bias

• similar to PYTHIA (2) above; but details different

• matter profile by electromagnetic form factor (with tuned size)

• no p_⊥-ordering of emissions, no rescaling of PDF:

abrupt stop when (if) run out of energy (3) Ivan (2002, code not public; in progress)

• also handles minimum bias

• soft and hard multiple interactions together fill whole p_⊥ range

SHERPA implementation

(1) Conventional approach (2005)

• Based on formalism of PYTHIA (2) but

• Full showers for all interactions, with CKKW matching (2) k_⊥-factorization-based approach (2007)

• unintegrated PDFs and off-shell matrix elements

• consistent with BFKL evolution (small x)

• combination with multiple interactions in progress

PhoJet (& relatives) implementation

(1) Cut Pomeron (1982)

• Pomeron predates QCD; nowadays ∼ glueball tower

• Optical theorem relates σ_total and σ_elastic

∝

2

⇒

• Unified framework of nondiffractive and diffractive interactions

• Purely low-p_⊥: only primordial k_⊥ fluctuations

• Usually simple Gaussian matter distribution (2) Extension to large p_⊥ (1990)

• distinguish soft and hard Pomerons (cf. Ivan):

soft = nonperturbative, low-p_⊥, as above hard = perturbative, “high”-p_⊥

• hard based on PYTHIA code, with lower cutoff in p_⊥

without multiple interactions

with multiple interactions

Direct observation of multiple interactions

Four studies: AFS (1987), UA2 (1991), CDF (1993, 1997) Order 4 jets p_⊥1 > p_⊥2 > p_⊥3 > p_⊥4 and define ϕ

as angle between p_⊥1 ∓ p_⊥2 and p_⊥3 ∓ p_⊥4 for AFS/CDF Double Parton Scattering

1 2

3

4

|p_⊥1 + p_⊥2| ≈ 0

|p_⊥3 + p_⊥4| ≈ 0 dσ/dϕ flat

Double BremsStrahlung

1 2

3 4

|p_⊥1 + p_⊥2| ≫ 0

|p_⊥3 + p_⊥4| ≫ 0

dσ/dϕ peaked at ϕ ≈ 0/π for AFS/CDF

AFS 4-jet analysis (pp at 63 GeV): observe 6 times Poissonian prediction, with impact parameter expect 3.7 times Poissonian,

but big errors ⇒ low acceptance, also UA2

Figure 1:
S distribution for 1VTX data (points). The DP component to the data, determined by the two-dataset method to be 52.6% of the sample, is shown as the shaded region (the shape is taken from MIXDP). Also shown is the admixture 52.6% MIXDP + 47.4% PYTHIA, normalized to the data (line).

16

CDF 3-jet + prompt photon analysis Yellow region = double parton scattering (DPS) The rest =

PYTHIA showers

σ_DPS = σ_Aσ_B

σ_eff for A 6= B =⇒ σ_eff = 14.5 ± 1.7^+1.7_−2.3 mb Strong enhancement relative to naive expectations!

Same study also planned for LHC Selection for DPS delicate balance:

showers dominate at large p_⊥

⇒ too large background

multiple interactions dominate at small p_⊥, but there jet

identification difficult .

(jet 3) (GeV/c) p

10 20 30 40 50

(nb / GeV/c)

/dp σ d

10

10

1

MI off

Pythia 8.108

+ X @ 14 TeV γ

→ pp

(R = 0.4), CDF selections kT

Jet pedestal effect

Events with hard scale (jet, W/Z, . . . ) have more underlying activity!

Events with n interactions have n chances that one of them is hard, so “trigger bias”: hard scale ⇒ central collision

⇒ more interactions ⇒ larger underlying activity.

Centrality effect saturates at p_⊥hard ∼ 10 GeV.

Studied in detail by Rick Field, comparing with CDF data:

“MAX/MIN Transverse” Densities

x Define the MAX and MIN “transverse” regions on an event-by-event basis with MAX (MIN) having the largest (smallest) density.

x The “transMIN” region is very sensitive to the “beam-beam remnant” and x

Jet #1 Direction 'I

“Toward”

“TransMAX” “TransMIN”

“Away”

Jet #1 Direction

'I

“TransMAX” “TransMIN”

“Toward”

“Away”

“Toward-Side” Jet

“Away-Side” Jet Jet #3

“TransMIN” very sensitive to the “beam-beam remnants”!

MC Tools for the LHC CERN July 31, 2003

Rick Field - Florida/CDF Page 28

Tuned PYTHIA 6.206 Tuned PYTHIA 6.206

“Transverse” P

“Transverse” P _{T T} Distribution Distribution

"Transverse" Charged Particle Density: dN/dKdI

0.00 0.25 0.50 0.75 1.00

0 5 10 15 20 25 30 35 40 45 50

PT(charged jet#1) (GeV/c)

"Transverse" Charged Density

1.8 TeV |K|<1.0 PT>0.5 GeV CDF Preliminary

data uncorrected theory corrected

CTEQ5L

PYTHIA 6.206 (Set A) PARP(67)=4

PYTHIA 6.206 (Set B) PARP(67)=1

PARP(67)=4.0 (old default) is favored over PARP(67)=1.0 (new default)!

P_T(charged jet#1) > 30 GeV/c

"Transverse" Charged Particle Density

1.0E-06 1.0E-05 1.0E-04 1.0E-03 1.0E-02 1.0E-01 1.0E+00

0 2 4 6 8 10 12 14

PT(charged) (GeV/c) Charged Density dN/dKdIdPT (1/GeV/c)

CDF Data

data uncorrected theory corrected

1.8 TeV |K|<1 PT>0.5 GeV/c PT(chgjet#1) > 5 GeV/c

PT(chgjet#1) > 30 GeV/c

PYTHIA 6.206 Set A PARP(67)=4

PYTHIA 6.206 Set B PARP(67)=1

¨ Compares the average “transverse” charge particle density (|K|<1, P_T>0.5 GeV) versus P_T(charged jet#1) and the P_T distribution of the “transverse” density, dN_chg/dKdIdP_T with the QCD Monte-Carlo predictions of two tuned versions of PYTHIA 6.206 (P_T(hard) > 0, CTEQ5L, Set B (PARP(67)=1) and Set A (PARP(67)=4)).

Rick Field December 1, 2004

Leading Jet: “MAX & MIN Transverse” Densities

PYTHIA Tune A HERWIG

"MAX/MIN Transverse" Charge Density: dN/dKdI

0.0 0.4 0.8 1.2 1.6

0 50 100 150 200 250

ET(jet#1) (GeV)

"Transverse" Charge Density CDF Preliminary

data uncorrected theory + CDFSIM

PYTHIA Tune A 1.96 TeV

Charged Particles (|K|<1.0, PT>0.5 GeV/c)

"MAX"

"MIN"

"AVE"

Leading Jet

"MAX/MIN Transverse" Charge Density: dN/dKdI

0.0 0.4 0.8 1.2 1.6

0 50 100 150 200 250

ET(jet#1) (GeV)

"Transverse" Charge Density CDF Preliminary

data uncorrected theory + CDFSIM

HERWIG 1.96 TeV

Charged Particles (|K|<1.0, PT>0.5 GeV/c)

"MAX"

"MIN"

"AVE"

Leading Jet

"MAX/MIN Transverse" PTsum Density: dPT/dKdI

0.0 0.5 1.0 1.5 2.0 2.5

0 50 100 150 200 250

ET(jet#1) (GeV)

"Transverse" PTsum Density (GeV/c)

CDF Preliminary

data uncorrected theory + CDFSIM

PYTHIA Tune A 1.96 TeV

Charged Particles (|K|<1.0, PT>0.5 GeV/c)

"MAX"

"MIN"

"AVE"

Leading Jet

"MAX/MIN Transverse" PTsum Density: dPT/dKdI

0.0 0.5 1.0 1.5 2.0 2.5

0 50 100 150 200 250

ET(jet#1) (GeV)

"Transverse" PTsum Density (GeV/c)

CDF Preliminary

data uncorrected theory + CDFSIM

HERWIG 1.96 TeV

Charged Particles (|K|<1.0, PT>0.5 GeV/c)

"MAX"

"MIN"

"AVE"

Leading Jet

Charged particle density and PTsum density for “leading jet” events versus ET(jet#1) for PYTHIA Tune A and HERWIG.

KITP Collider Workshop February 17, 2004

Rick Field - Florida/CDF Page 75

“ “ Transverse 1” Region Transverse 1” Region vs vs

“Transverse 2” Region

“Transverse 2” Region

"Transverse 1" vs "Transverse 2"

0.5 1.0 1.5 2.0 2.5 3.0 3.5

0 2 4 6 8 10 12 14

"Transverse 1" Nchg

"Transverse 2" Nchg

CDF Run 2 Preliminary

data uncorrected theory + CDFSIM

Charged Particles (|K|<1.0, PT>0.5 GeV/c) 1.96 TeV

Leading Jet 30 < ET(jet#1) < 70 GeV

HW PY Tune A

"Transverse 1" vs "Transverse 2"

0.8 1.0 1.2 1.4 1.6 1.8

0 2 4 6 8 10 12 14

"Transverse 1" Nchg

"Transverse 2" <PT> (GeV/c)

Charged Particles (|K|<1.0, PT>0.5 GeV/c)

CDF Run 2 Preliminary

data uncorrected theory + CDFSIM

Leading Jet 30 < ET(jet#1) < 70 GeV

1.96 TeV ^{PY Tune A}

HW

"Transverse 1" vs "Transverse 2"

0.5 1.0 1.5 2.0 2.5 3.0

0 2 4 6 8 10 12

"Transverse 1" Nchg

"Transverse 2" Nchg

CDF Run 2 Preliminary

data uncorrected theory + CDFSIM

Charged Particles (|K|<1.0, PT>0.5 GeV/c) Back-to-Back

30 < ET(jet#1) < 70 GeV PY Tune A

HW

"Transverse 1" vs "Transverse 2"

0.50 0.75 1.00 1.25 1.50

0 2 4 6 8 10 12

"Transverse 1" Nchg

"Transverse 2" <PT> (GeV/c)

Charged Particles (|K|<1.0, PT>0.5 GeV/c)

CDF Run 2 Preliminary

data uncorrected theory + CDFSIM

Back-to-Back 30 < ET(jet#1) < 70 GeV

PY Tune A

HW

Rick Field December 1, 2004

PYTHIA Tune A vs JIMMY: “Transverse Region”

"MAX/MIN Transverse" PTsum Density: dPT/dKdI

0.0 0.5 1.0 1.5 2.0 2.5

0 50 100 150 200 250

ET(jet#1) (GeV)

"Transverse" PTsum Density (GeV/c)

CDF Preliminary

data uncorrected theory + CDFSIM

PYTHIA Tune A 1.96 TeV

Charged Particles (|K|<1.0, PT>0.5 GeV/c)

"MAX"

"MIN"

"AVE"

Leading Jet

"Transverse" PTsum Density: dPT/dKdI

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0 50 100 150 200 250 300 350 400 450 500

PT(jet#1) (GeV/c)

"Transverse" PTsum Density

RDF Preliminary

generator level

Charged Particles (|K|<1.0, PT>0.5 GeV/c) Max Transverse

Min Transverse

Average Transverse 1.96 TeV

PYA = dashed JM = solid

x (left) Run 2 data for charged scalar PTsum density (|K|<1, pT>0.5 GeV/c) in the MAX/MIN/AVE “transverse” region versus P_T(jet#1) compared with PYTHIA Tune A (after CDFSIM).

x (right) Shows the generator level predictions of PYTHIA Tune A (dashed) and JIMMY (P_Tmin=1.8 GeV/c) for charged scalar PTsum density (|K|<1, p_T>0.5 GeV/c) in the MAX/MIN/AVE “transverse” region versus P_T(jet#1).

x The tuned JIMMY now agrees with PYTHIA for PT(jet#1) < 100 GeV but produces much more activity than PYTHIA Tune A (and the data?) in the

“transverse” region for P_T(jet#1) > 100 GeV!

KITP Collider Workshop February 17, 2004

Rick Field - Florida/CDF Page 58

Back Back - - to to - - Back Back “Associated” “Associated”

Charged Particle Densities Charged Particle Densities

'I

Jet#1 Region

PTmaxT Direction

Jet#2 Region

¨ Shows the 'I dependence of the “associated” charged particle density, dN^chg/dKdI, p_T > 0.5 GeV/c, |K| < 1, PTmaxT > 2.0 GeV/c (not including PTmaxT) relative to PTmaxT (rotated to 180^o) and the charged particle density, dNchg/dKdI, p_T > 0.5 GeV/c, |K| < 1, relative to jet#1 (rotated to 270^o) for “back-to-back events” with 30 < E_T(jet#1) < 70 GeV.

Jet #1 Direction 'I

“Toward”

“Transverse” “Transverse”

“Away”

Jet #2 Direction

Charged Particle Density: dN/dKdI

2

6 10 14

18 22

26 30

34 38

42 46

50 54

58

62

66

70

74

78

82

86

90

94

98

102

106

110

114

118

122

126 130

134 138 142 146 150 154 158 162 166 174 170 178 182 190 186 194 198 202 206 210 214 218 222 226 230 234 238 242 246 250 254 258 262 266 270 274 278 282 286

290 294

298 302

306 310

314 318

322 326

330 334

338 342

346 350 354 358

CDF Preliminary

data uncorrected

30 < ET(jet#1) < 70 GeV Back-to-Back

Charged Particles (|K|<1.0, PT>0.5 GeV/c)

"Transverse"

Region "Transverse"

Region Jet#1

Associated Density PTmaxT > 2 GeV/c

(not included) PTmaxT

Polar Plot

“Back-to-Back”

“associated” density

“Back-to-Back”

charge density

0.5

1.0

1.5

2.0

KITP Collider Workshop February 17, 2004

Rick Field - Florida/CDF Page 71

“ “ Associated” Charge Density Associated” Charge Density PYTHIA Tune A

PYTHIA Tune A vs vs HERWIG HERWIG

Associated Particle Density: dN/dKdI

0.1 1.0 10.0

0 30 60 90 120 150 180 210 240 270 300 330 360

'I (degrees)

Associated Particle Density

PTmaxT > 2.0 GeV/c PY Tune A

Back-to-Back 30 < ET(jet#1) < 70 GeV Charged Particles

(|K|<1.0, PT>0.5 GeV/c)

PTmaxT

CDF Preliminary

data uncorrected

theory + CDFSIM PTmaxT not included

"Jet#1"

Region

Associated Particle Density: dN/dKdI

0.1 1.0 10.0

0 30 60 90 120 150 180 210 240 270 300 330 360

'I (degrees)

Associated Particle Density

PTmaxT > 2.0 GeV/c HERWIG

Back-to-Back 30 < ET(jet#1) < 70 GeV Charged Particles

(|K|<1.0, PT>0.5 GeV/c)

PTmaxT

CDF Preliminary

data uncorrected

theory + CDFSIM PTmaxT not included

"Jet#1"

Region

Data - Theory: Associated Particle Density dN/dKdI

-1.6 -0.8 0.0 0.8 1.6

0 30 60 90 120 150 180 210 240 270 300 330 360

'I (degrees)

Data - Theory

CDF Preliminary

data uncorrected theory + CDFSIM

Charged Particles (|K|<1.0, PT>0.5 GeV/c)

Back-to-Back 30 < ET(jet#1) < 70 GeV PYTHIA Tune A

PTmaxT "Jet#1"

Region PTmaxT > 2.0 GeV/c (not included)

Data - Theory: Associated Particle Density dN/dKdI

-1.0 -0.5 0.0 0.5 1.0

0 30 60 90 120 150 180 210 240 270 300 330 360

'I (degrees)

Data - Theory

CDF Preliminary

data uncorrected theory + CDFSIM

Charged Particles (|K|<1.0, PT>0.5 GeV/c)

Back-to-Back 30 < ET(jet#1) < 70 GeV HERWIG

PTmaxT "Jet#1"

Region PTmaxT > 2.0 GeV/c (not included)

For PTmaxT > 2.0 GeV both PYTHIA and HERWIG produce

slightly too many “associated”

particles in the direction of PTmaxT!

But HERWIG (without multiple parton interactions) produces

too few particles in the direction opposite of PTmaxT!

PTmaxT > 2 GeV/c

Multiple interactions also preferred by HERA photoproduction data:

underlying activity in photoproduction vs. DIS

0 0.2 0.4 0.6 0.8 1 1.2 1.4

0 0.2 0.4 0.6 0.8 1

x_γ^jets

<ET>/(∆η∆φ) [GeV/rad]

(anti)correlations in energy flow around jet

-1 0 1 2 3 4

-3 -2 -1 0 1

η*

Ω(η*) [10-3 ]

Colour correlations

hp_⊥i(n_ch) is very sensitive to colour flow

p p

long strings to remnants ⇒ much n_ch/interaction ⇒ hp_⊥i(n_ch) ∼ flat

p p

short strings (more central) ⇒ less n_ch/interaction ⇒ hp_⊥i(n_ch) rising

KITP Collider Workshop February 17, 2004

Rick Field - Florida/CDF Page 35

“ “ Transverse” < Transverse” < p p _{T T} > versus > versus

“Transverse”

“Transverse” N N chg chg

Jet #1 Direction 'I

“Toward”

“Transverse” “Transverse”

“Away”

Jet #1 Direction 'I

“Toward”

“Transverse” “Transverse”

“Away”

Jet #2 Direction

¨ Shows <p_T> versus N^chg in the “transverse” region (p_T > 0.5 GeV/c, |K| < 1) for

“Leading Jet” and “Back-to-Back” events with 30 < E_T(jet#1) < 70 GeV compared with

“min-bias” collisions.

“Leading Jet”

“Back-to-Back”

¨ Look at the <p_T> of particles in the “transverse” region (p_T > 0.5 GeV/c, |K| < 1) versus the number of particles in the “transverse” region: <p_T> vs N^chg.

Min-Bias

"Transverse" Average PT versus Nchg

0.5 1.0 1.5 2.0

0 2 4 6 8 10 12 14 16 18 20 22

Number of Charged Particles

Average PT (GeV/c)

CDF Run 2 Preliminary

data uncorrected theory + CDFSIM

Charged Particles (|K|<1.0, PT>0.5 GeV/c) PYTHIA Tune A 1.96 TeV

Min-Bias

Leading Jet 30 < ET(jet#1) < 70 GeV

Back-to-Back 30 < ET(jet#1) < 70 GeV

Extrapolation to LHC

Energy dependence of p_⊥min and p_⊥0:

Larger collision energy

⇒ probe parton (≈ gluon) density at smaller x

⇒ smaller colour screening length d

⇒ larger p_⊥min or p_⊥0 Post-HERA PDF fits steeper at small x

⇒ stronger energy dependence

Current PYTHIA 8 default, tied to CTEQ 5L, is p_⊥0(s) = 2.15 GeV s

(1.8 TeV)²

!_0.08

5^thNovember 2004 Minimum-bias and the Underlying Event at the LHC

A. M. Moraes

LHC predictions: pp collisions at ¥s = 14 TeV

0 2 4 6 8 10

10² 10³ 10⁴ 10⁵

PYTHIA6.214 - tuned PYTHIA6.214 - default PHOJET1.12

pp interactions-

UA5 and CDF data

dN chg/dȘatȘ=0

¥s (GeV)

•PYTHIAmodels favour ln²(s);

•PHOJET suggests a ln(s)dependence.

LHC

2 4 6 8 10 12

0 10 20 30 40 50

CDF data

PYTHIA6.214 - tuned

PHOJET1.12 LHC

Tevatron

x1.5 x 3

dN_chg/dȘ ~ 30

dN_chg/dȘ ~ 15

Central Region

(min-bias dN_chg/dȘ ~ 7)

Transverse < Nchg>

P_t(leading jet in GeV)

5^thNovember 2004 Minimum-bias and the Underlying Event at the LHC

A. M. Moraes

LHC predictions: JIMMY4.1 Tunings A and B vs.

PYTHIA6.214 – ATLAS Tuning (DC2)

5 10 15 20

0 10 20 30 40 50

CDF data

JIMMY4.1 - Tuning A JIMMY4.1 - Tuning B

PYTHIA6.214 - ATLAS Tuning

Transverse < N chg>

P_t (leading jet in GeV) Tevatron LHC

x 4

x 5

x 3

18 PTJIM=4.9

PTJIM=4.9

= 2.8

= 2.8 x (14 / 1.8)x (14 / 1.8)^0.270.27

x3

x2.7 LHC

Tevatron

•energy dependent PTJIM •energy dependent PTJIM generates UE predictions generates UE predictions similar to the ones

similar to the ones generated by PYTHIA6.2 generated by PYTHIA6.2 –– ATLAS.

ATLAS.

UE tunings: Pythia vs. Jimmy

Multiple Interactions Outlook

Issues requiring further thought and study:

• Multi-parton PDF’s f_a1a2a3···(x₁, Q²₁, x₂, Q²₂, x₃, Q²₃, . . .)

• Close-packing in initial state, especially small x

• Impact-parameter picture and (x, b) correlations

e.g. large-x partons more central!, valence quarks more central?

• Details of colour-screening mechanism

• Rescattering: one parton scattering several times

• Intertwining: one parton splits in two that scatter separately

• Colour sharing: two FS–IS dipoles become one FS–FS one

• Colour reconnection: required for hp_⊥i(n_charged)

• Collective effects (e.g. QGP, cf. Hadronization above)

• Relation to diffraction: eikonalization, multi-gap topologies, . . .

Action items:

• Vigorous experimental program at LHC

• Study energy dependence: RHIC (pp) → Tevatron → LHC

• Develop new frameworks and refine existing ones Much work ahead!

MPI@LHC'08 - Perugia, Italy, October 27-31 2008 http://www.pg.infn.it/mpi08/index.htm

Home Programme Registration Registered Partecipants Organizing Committee

Accomodation Guidelines & Travelling Contacts Bullettin & Poster Instructions for Authors

Perugia, Italy, 27- 31 October, 2008

Courtesy of David Roberts for

"ElementalParticles"

News & Announce

22/03/08 - Firts Bulletin available

Welcome to the first International Workshop on Multiple Partonic Interactions at the LHC "1st MPI@LHC".

The objective of this first workshop on Multiple Partonic Interactions (MPI) at the LHC is to raise the profile of MPI studies, summarizing the legacy from the older phenomenology at hadronic colliders and favouring further specific

contacts between the theory and experimental communities. The MPI are experiencing a growing popularity and are currently widely invoked to account for observations that would not be explained otherwise: the activity

of the Underlying Event, the cross sections for multiple heavy flavour production, the survival probability of large rapidity gaps in hard diffraction,

etc. At the same time, the implementation of the MPI effects in the Monte Carlo models is quickly proceeding through an increasing level of sophistication and complexity that in perspective achieves deep general implications for the LHC physics. The ultimate ambition of this workshop is to

promote the MPI as unification concept between seemingly heterogeneous research lines and to profit of the complete experimental picture in order to constrain their implementation in the models, evaluating the spin offs on the

LHC physics program.

.