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Monte Carlo2. Matching, MPI’s and Hadronization

Torbjorn Sjostrand

Department of Astronomy and Theoretical PhysicsLund University

Solvegatan 14A, SE-223 62 Lund, Sweden

TRIUMF, Vancouver, Canada, 5 July 2013

Event Generators Reminder

An event consists of many different physics steps,which have to be modelled by event generators:

Torbjorn Sjostrand Monte Carlo 2 slide 2/1

Matrix elements vs. parton showers

ME : Matrix Elements+ systematic expansion in αs (‘exact’)+ powerful for multiparton Born level+ flexible phase space cuts− loop calculations very tough− negative cross section in collinear regions

⇒ unpredictive jet/event structure− no easy match to hadronization

PS : Parton Showers− approximate, to LL (or NLL)− main topology not predetermined

⇒ inefficient for exclusive states+ process-generic ⇒ simple multiparton+ Sudakov form factors/resummation

⇒ sensible jet/event structure+ easy to match to hadronization


PS matching to MEs: realistic hard default


Matrix Elements and Parton Showers

Recall complementary strengths:• ME’s good for well separated jets• PS’s good for structure inside jetsMarriage desirable! But how?Very active field of research; requires a lecture series of its own

Reweight first PS emission by ratio ME/PS (simple POWHEG)

Combine several LO MEs, using showers for Sudakov weights

CKKW: analytic Sudakov – not used any longerCKKW-L: trial showers gives sophisticated SudakovsMLM: match of final partonic jets to original ones

Match to NLO precision of basic process

MC@NLO: additive ⇒ LO normalization at high p⊥POWHEG: multiplicative ⇒ NLO normalization at high p⊥

Combine several orders, as many as possible at NLO

MENLOPSUNLOPS (U = unitarized = preserve normalizations)


Simple POWHEG (a.k.a. merging)

= cover full phase space with smooth transition ME/PS.

Want to reproduce W ME =1

σ(LO)

dσ(LO + g)

d(phasespace)by shower generation + correction procedure

wanted︷︸︸︷W ME =

generated︷︸︸︷W PS

correction︷︸︸︷W ME

W PS

• Exponentiate ME correction by shower Sudakov form factor:

W PSactual(Q

2) = W ME(Q2) exp

(−∫ Q2

max

Q2

W ME(Q ′2) dQ ′2)

• Do not normalize W ME to σ(NLO) (error O(α2s ) either way)


PYTHIA final-state shower merging

PYTHIA performs merging with generic FSR a → bcg ME,in SM: γ∗/Z0/W± → qq, t → bW+, H0 → qq,and MSSM: t → bH+, Z0 → qq, q → q′W+, H0 → qq, q → q′H+,χ → qq, χ → qq, q → qχ, t → tχ, g → qq, q → qg, t → tg

g emission for different Rbl3 (yc): mass effects

colour, spin and parity: in Higgs decay:


Vetoed Parton Showers – 1

Generic method to combine ME’s of several different ordersto NLL accuracy; has become a standard tool for many studiesBasic idea:

consider (differential) cross sections σ0, σ1, σ2, σ3, . . .,corresponding to a lowest-order process (e.g. W production),with more jets added to describe more complicated topologies,in each case to the respective leading order

σi , i ≥ 1, are divergent in soft/collinear limit

absent virtual corrections would have ensured “detailedbalance”, i.e. an emission that adds to σi+1 subtracts from σi

such virtual corrections correspond (approximately) to theSudakov form factors of parton showers

so use shower routines to provide missing virtual corrections⇒ rejection of events (especially) in soft/collinear regions

S. Catani, F. Krauss, R. Kuhn, B.R. Webber, JHEP 0111 (2001) 063; L. Lonnblad, JHEP0205 (2002) 046;

F. Krauss, JHEP 0208 (2002) 015; S. Mrenna, P. Richardson, JHEP0405 (2004) 040;

M.L. Mangano et al., JHEP0701 (2007) 013


Vetoed Parton Showers – 2

Summary of CKKW(-L)/MLM:use ME for real emissionsand PS for virtual corrections(to ∼ restore unitarity).

CKKW-L:

1 generate n-body by MEmixed in proportions

∫dσn

above p⊥min cut

2 reconstruct fictitiousp⊥-ordered PS

p!0 p!1 p!2 p!3 p!min

4 reject from fix αs = αs(p⊥min) to αs(p⊥i )

5 run trial shower between each p⊥i and p⊥i+1

6 reject if shower branching ⇒ Sudakov factor

7 regular shower below p⊥min (or below p⊥n for n = nmax)


Vetoed Parton Showers – 3) [

pb]

jet

N≥) +

- l+ l

→*(γ(Z

/σ

-310

-210

-110

1

10

210

310

410

510

610

= 7 TeV)sData 2011 (ALPGENSHERPAMC@NLO

+ SHERPAATHLACKB

ATLAS )µ)+jets (l=e,-l+ l→*(γZ/-1 L dt = 4.6 fb∫

jets, R = 0.4tanti-k| < 4.4jet > 30 GeV, |yjet

Tp

0≥ 1≥ 2≥ 3≥ 4≥ 5≥ 6≥ 7≥

NLO

/ D

ata

0.60.8

11.21.4 + SHERPAATHLACKB

0≥ 1≥ 2≥ 3≥ 4≥ 5≥ 6≥ 7≥

MC

/ D

ata

0.60.8

11.21.4 ALPGEN

jetN0≥ 1≥ 2≥ 3≥ 4≥ 5≥ 6≥ 7≥

MC

/ D

ata

0.60.8

11.21.4 SHERPA

[1/G

eV]

jet

T/d

pσ

) d- l+ l→* γ

Z/σ

(1/

-710

-610

-510

-410

-310

-210

-110 = 7 TeV)sData 2011 (

ALPGENSHERPAMC@NLO

+ SHERPAATHLACKB

ATLAS )µ 1 jet (l=e,≥)+ -l+ l→*(γZ/-1 L dt = 4.6 fb∫

jets, R = 0.4tanti-k| < 4.4jet > 30 GeV, |yjet

Tp

100 200 300 400 500 600 700

NLO

/ D

ata

0.60.8

11.21.4 + SHERPAATHLACKB

100 200 300 400 500 600 700M

C /

Dat

a0.60.8

11.21.4 ALPGEN

(leading jet) [GeV]jetT

p100 200 300 400 500 600 700

MC

/ D

ata

0.60.8

11.21.4 SHERPA


MC@NLO

Total rate should be accurate to NLO.NLO results are obtained for all observables when (formally)expanded in powers of αs.Hard emissions are treated as in the NLO computations.Soft/collinear emissions are treated as in shower MC.


POWHEG

dσ = B(v)dΦv

[R(v , r)

B(v)exp

(−∫

p⊥

R(v , r ′)

B(v)dΦ′r

)dΦr

],

B(v) = B(v) + V (v) +

∫dΦr [R(v , r)− C (v , r)] .

v ,dΦv Born-level n-body variables and differential phase spacer ,dΦr extra n + 1-body variables and differential phase spaceB(v) Born-level cross sectionV (v) Virtual correctionsR(v , r) Real-emission cross sectionC (v , r) Conterterms for collinear factorization of parton densities.

Note that∫

B(v)dΦv ≡ σNLO and∫

[· · ·dΦr ] ≡ 1.

So pick the real emission with largest p⊥ according to completeME’s + ME-based Sudakov, with NLO normalization, andlet showers do subsequent evolution downwards from this p⊥ scale.


Interpolation between POWHEG and MC@NLO

Master formula for meaningful NLO implementations:

dσ = dσR,hard+(σB + σR,soft + σV )

[dσR,soft

σBexp

(−∫

dσR,soft

σB

)]ordered in “p⊥”, with shower from selected “p⊥” downwardsPOWHEG: σR,hard = 0MC@NLO: σR,soft = σR,MC

“Best” choice process-dependent (guess NLO behaviour of σR)

S.Alioli, P. Nason, C. Oleari, E. Re, JHEP 00904 (2009) 002Torbjorn Sjostrand Monte Carlo 2 slide 13/1

ME–PS Matching: Legs and Loops

Issue: ? multileg does not guarantee∑

n=0 σH+n jet = σH;

? loop only guarantees σH to NLO and σH+1 jet to LO.

Recent progress: σH to NLO, σH+1 jet to NLO, σH+≥2 jet to LO.

Requires careful unitarity considerations, expansion of PDF’s, . . .⇒ lengthy formulae and even lengthier procedures:

this means that once we want to add a one-jet NLO calculation, we have to subtract its

integrated version from zero-jet events. Similarly we need to remove the O!!0

s (µR)"

and

O!!1

s (µR)"

in the UMEPS tree-level weights, not only for the one-jet events but also for

the corresponding subtracted zero-jet events. In this way we ensure that the inclusive

zero-jet cross section is still given by the NLO calculation and we will also improve the

O(!2s )!term of exclusive zero-jet observables.

The UNLOPS prediction for an observable O, when simultaneously merging inclusive

NLO calculations for m=0, . . . ,M jets, and including up to N tree-level calculations, is

given by

"O# =M!1#

m=0

$d"0

$· · ·$

O(S+mj)

%

Bm +&'Bm

(

!m,m+1

!M#

i=m+1

$

sBi"m !

M#

i=m+1

) $

s

'Bi"m

*

!i,i+1

!N#

i=M+1

$

s

'Bi"m

+

+

$d"0

$· · ·$

O(S+Mj)

%

BM +&'BM

(

!M,M+1!

N#

i=M+1

$

s

'Bi"M

+

+N#

n=M+1

$d"0

$· · ·$

O(S+nj)

%'Bn !

N#

i=n+1

$

s

'Bi"n

+

(3.10)

Here we see, in the first line, the addition of the Bm and the removal of the O (!ms (µR))

and O!!m+1

s (µR)"

terms of the original UMEPS 'Bm contribution. On the second line we

see the subtracted integrated Bm+1 term to make the m-parton NLO-calculation exclusive

and the corresponding O (!ms (µR))- and O

!!m+1

s (µR)"-subtracted UMEPS term together

with subtracted terms from higher multiplicities where intermediate states in the clustering

were below the merging scale. The third line is the special case of the highest multiplicity

corrected to NLO, and the last line is the standard UMEPS treatment of higher multiplic-

ities.

The full derivation of this master formula is given in appendix D, where we also discuss

the case of exclusive NLO samples and explain the necessity for subtraction terms from

higher multiplicities. We will limit ourselves to including only zero- and one-jet NLO

calculations in the results section. For the sake of clarity we will thus only discuss this

special case here. For this case, the UNLOPS prediction (when including only up to two

tree-level jets) is

"O# =

$d"0

%

O(S+0j)

,

B0 !$

sB1"0 !

) $

s

'B1"0

*

!1,2

!$

s

'B2"0

-

+

$O(S+1j)

.B1 +

&'B1

(

!1,2!$

s

'B2"1

/

+

$ $O(S+2j)'B2 (3.11)

– 16 –

(UNLOPS, L. Lonnblad, S. Prestel)

Future: further complications or new synthesis?


Event topologies

Expect and observe high multiplicities at the LHC.What are production mechanisms behind this?


What is minimum bias (MB)?

MB ≈ “all events, with no bias from restricted trigger conditions”σtot =σelastic + σsingle−diffractive + σdouble−diffractive + · · ·+ σnon−diffractive

Schematically:

Reality: can only observe events with particles in central detector:no universally accepted, detector-independent definitionσmin−bias ≈ σnon−diffractive + σdouble−diffractive ≈ 2/3 × σtot


What is underlying event (UE)?

In an event containing a jet pair or another hard process, howmuch further activity is there, that does not have its origin in thehard process itself, but in other physics processes?

Pedestal effect: the UE contains more activity than a normal MBevent does (even discarding diffractive events).

Trigger bias: a jet ”trigger” criterion E⊥jet > E⊥min is more easilyfulfilled in events with upwards-fluctuating UE activity, since theUE E⊥ in the jet cone counts towards the E⊥jet. Not enough!


What is pileup?

〈n〉 = Lσ

where L is machine luminosity per bunch crossing, L ∼ n1n2/Aand σ ∼ σtot ≈ 100 mb.Current LHC machine conditions ⇒ 〈n〉 ∼ 10− 20.

Pileup introduces no new physics, and is thus not furtherconsidered here, but can be a nuisance.However, keep in mind concept of bunches of hadronsleading to multiple collisions.


The divergence of the QCD cross section

Cross section for 2 → 2 interactions is dominated by t-channel

gluon exchange, so diverges like dσ/dp2⊥ ≈ 1/p4

⊥ for p⊥ → 0.

Integrate QCD 2 → 2qq′ → qq′

qq → q′q′

qq → ggqg → qggg → gggg → qq(with CTEQ 5L PDF’s)


What is multiple partonic interactions (MPI)?

Note that σint(p⊥min), the number of (2 → 2 QCD) interactionsabove p⊥min, involves integral over PDFs,

σint(p⊥min) =

∫∫∫p⊥min

dx1 dx2 dp2⊥ f1(x1, p

2⊥) f2(x2, p

2⊥)

dσ

dp2⊥

with∫

dx f (x , p2⊥) = ∞, i.e. infinitely many partons.

So half a solution to σint(p⊥min) > σtot is

many interactions per event: MPI (historically MI or MPPI)

σtot =∞∑

n=0

σn

σint =∞∑

n=0

n σn

σint > σtot ⇐⇒ 〈n〉 > 1


Colour screening

Other half of solution is that perturbative QCD is not valid atsmall p⊥ since q, g are not asymptotic states (confinement!).

Naively breakdown at

p⊥min '~rp≈ 0.2 GeV · fm

0.7 fm≈ 0.3 GeV ' ΛQCD

. . . but better replace rp by (unknown) colour screening length d inhadron:


Regularization of low-p⊥ divergence

so need nonperturbative regularization for p⊥ → 0 , e.g.

dσ

dp2⊥∝

α2s (p

2⊥)

p4⊥

→α2

s (p2⊥)

p4⊥

θ (p⊥ − p⊥min) (simpler)

or →α2

s (p2⊥0 + p2

⊥)

(p2⊥0 + p2

⊥)2(more physical)

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

Typically 2 – 3 interactions/event at theTevatron, 4 – 5 at the LHC, but may bemore in “interesting” high-p⊥ ones.


MPI effects

By now several direct tests of back-to-back jet pairs and similar.However, only probes high-p⊥ tail of effects.More direct and dramatic are effects on multiplicity distributions:


MPI and event generators

All modern general-purpose generators are built on MPI concepts

PYTHIA implementation main points:

MPIs are gererated in a falling sequence of p⊥ values;recall Sudakov factor approach to parton showers.

Energy, momentum and flavour are subtracted from protonby all “previous” collisions.

Protons modelled as extended objects, allowing both centraland peripheral collisions, with more or less activity.

(Partons at small x more broadly spread than at large x .)

Colour screening increases with energy, i.e. p⊥0 = p⊥0(Ecm),as more and more partons can interact.

(Rescattering: one parton can scatter several times.)

Colour connections: each interaction hooks up with coloursfrom beam remnants, but also correlations inside remnants.

Colour reconnections: many interaction “on top of” eachother ⇒ tightly packed partons ⇒ colour memory loss?


Interleaved evolution

• Transverse-momentum-ordered parton showers for ISR and FSR• MPI also ordered in p⊥

⇒ Allows interleaved evolution for ISR, FSR and MPI:

dPdp⊥

=

(dPMPI

dp⊥+∑ dPISR

dp⊥+∑ dPFSR

dp⊥

)× exp

(−∫ p⊥max

p⊥

(dPMPI

dp′⊥+∑ dPISR

dp′⊥+∑ dPFSR

dp′⊥

)dp′⊥

)Ordered in decreasing p⊥ using “Sudakov” trick.Corresponds to increasing “resolution”:smaller p⊥ fill in details of basic picture set at larger p⊥.

Start from fixed hard interaction ⇒ underlying event

No separate hard interaction ⇒ minbias events

Possible to choose two hard interactions, e.g. W−W−


Colour correlations and 〈p⊥〉(nch) – 1


Colour correlations and 〈p⊥〉(nch) – 2

Comparison with data, generators before and after LHC data input:

chN 0 50 100

[G

eV]

〉 T p〈

0.6

0.8

1

1.2

1.4

1.6ATLASPythia 8Pythia 8 (no CR)

7000 GeV pp Soft QCD (mb,diff,fwd)

mcp

lots

.cer

n.ch

200

k ev

ents

≥R

ivet

1.8

.2,

Pythia 8.175

ATLAS_2010_S8918562

> 0.5 GeV/c)T

> 1, pch

(Nch vs NT

Average p

0 50 1000.5

1

1.5Ratio to ATLAS

see also A. Buckley et al.,Phys. Rep. 504 (2011) 145

[arXiv:1101.2599[hep-ph]]


Jet pedestal effect – 1

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.

Studied in particular by Rick Field, with CDF/CMS data:



Cosmic QCD 2013 LPTHE Paris, May 15, 2013

Rick Field – Florida/CDF/CMS Page 47

““TevatronTevatron”” to the LHCto the LHC"Transverse" Charged Particle Density: dN/dKdI

0.0

0.4

0.8

1.2

0 5 10 15 20 25 30 35

PTmax (GeV/c)

"Tra

nsve

rse"

Cha

rged

Den

sity

RDF Preliminary Corrected Data

Charged Particles (PT>0.5 GeV/c)

1.96 TeV

300 GeV

900 GeV

PYTHIA Tune Z1

7 TeV



Cosmic QCD 2013 LPTHE Paris, May 15, 2013

Rick Field – Florida/CDF/CMS Page 58

MB versus the UEMB versus the UE

Charged Particle Density

0.0

0.2

0.4

0.6

0.8

1.0

0.1 1.0 10.0

Center-of-Mass Energy (TeV)

Cha

rged

Den

sity


Charged Particles (|K|<0.8, PT>0.5 GeV/c)

CMS squaresCDF dots

OverallAt least 1 charged particle

"Transverse"5 < PTmax < 6 GeV/c

Overall Charged Particle Density

0.20

0.30

0.40

0.50

0.1 1.0 10.0


Cha

rged

Den

sity



CMS red squaresCDF blue dots

At least 1 charged particle

"Transverse" Charged Particle Density: dN/dKdI

0.2

0.4

0.6

0.8

1.0

0.1 1.0 10.0


"Tra

nsve

rse"

Cha

rged

Den

sity



5.0 < PTmax < 6.0 GeV/c


¨ Corrected CDF and CMS data on the

overall density of charged particles with pT

> 0.5 GeV/c and |K| < 0.8 for events with at

least one charged particle with pT > 0.5

GeV/c and |K| < 0.8 and on the charged

particle density, in the “transverse” region

as defined by the leading charged particle

(PTmax) for charged particles with pT > 0.5

GeV/c and |K| < 0.8 with 5 < PTmax < 6

GeV/c. The data are plotted versus the

center-of-mass energy (log scale).

"Transverse" Charged Particle Density: dN/dKdI

0.2

0.4

0.6

0.8

1.0

0.1 1.0 10.0


"Tra

nsve

rse"

Cha

rged

Den

sity


5.0 < PTmax < 6.0 GeV/c


Tune Z1 Generator Level

PYTHIA Tune Z1


Overall Charged Particle Density

0.20

0.30

0.40

0.50

0.60

0.1 1.0 10.0


Cha

rged

Den

sity



At least 1 charged particle



PYTHIA Tune Z1

Charged Particle Density

0.0

0.2

0.4

0.6

0.8

1.0

0.1 1.0 10.0


Cha

rged

Den

sity


CMS squaresCDF dots

OverallAt least 1 charged particle

"Transverse"5 < PTmax < 6 GeV/c



PYTHIA Tune Z1

Amazing!

Conclusion: “transMIN” (MPI+BBR) increases much faster withEcm than “transDIF” (ISR+FSR), proportionately speaking.


Diffraction

Ingelman-Schlein: Pomeron as hadron with partonic contentDiffractive event = (Pomeron flux) × (IPp collision)

DiffractionIngelman-Schlein: Pomeron as hadron with partonic contentDiffractive event = (Pomeron flux) ! (IPp collision)

pp

IP

p

Used e.g. inPOMPYTPOMWIGPHOJET

1) !SD and !DD taken from existing parametrization or set by user.2) Shape of Pomeron distribution inside a proton, fIP/p(xIP, t)gives diffractive mass spectrum and scattering p" of proton.3) At low masses retain old framework, with longitudinal string(s).Above 10 GeV begin smooth transition to IPp handled with full ppmachinery: multiple interactions, parton showers, beam remnants, . . . .4) Choice between 5 Pomeron PDFs.Free parameter !IPp needed to fix #ninteractions$ = !jet/!IPp.5) Framework needs testing and tuning, e.g. of !IPp.

1) σSD and σDD taken from existing parametrization or set by user.

2) fIP/p(xIP, t) ⇒ diffractive mass spectrum, p⊥ of proton out.

3) Smooth transition from simple model at low masses to IPp withfull pp machinery: multiple interactions, parton showers, etc.

4) Choice between 5 Pomeron PDFs.

5) Free parameter σIPp needed to fix 〈ninteractions〉 = σjet/σIPp.


Hadronization

Hadronization/confinement is nonperturbative ⇒ only models.

Begin with e+e− → γ∗/Z0 → qq and e+e− → γ∗/Z0 → qqg:

Y

XZ

Y

XZ


The QCD potential – 1

In QCD, for large charge separation, field lines are believedto be compressed to tubelike region(s) ⇒ string(s)

Gives force/potential between a q and a q:

F (r) ≈ const = κ ⇐⇒ V (r) ≈ κr

κ ≈ 1 GeV/fm ≈ potential energy gain lifting a 16 ton truck.

Flux tube parametrized by center location as a function of time⇒ simple description as a 1+1-dimensional object – a string .



Linear confinement confirmed e.g. by lattice QCD calculationof gluon field between a static colour and anticolour charge pair:

At short distances also Coulomb potential,important for internal structure of hadrons,but not for particle production (?).



Full QCD = gluonic field between charges (“quenched QCD”)plus virtual fluctuations g → qq (→ g)=⇒ nonperturbative string breakings gg . . . → qq


String motion

The Lund Model: starting point

Use only linear potential V (r) ≈ κrto trace string motion, and let stringfragment by repeated qq breaks.

Assume negligibly small quark masses.Then linearity between space–time andenergy–momentum gives∣∣∣∣dE

dz

∣∣∣∣ = ∣∣∣∣dpz

dz

∣∣∣∣ = ∣∣∣∣dE

dt

∣∣∣∣ = ∣∣∣∣dpz

dt

∣∣∣∣ = κ

(c = 1) for a qq pair flying apartalong the ±z axis.But signs relevant: the q moving inthe +z direction has dz/dt = +1but dpz/dt = −κ.

B. Andersson et a!., Patton fragmentation and string dynamics 41

____ ____ <V-L/2 L12 X -p p~

Fig. 2.1. The motion of q and ~ in the CM frame. The hatched areas Fig. 2.2. The motion of q and ~ in a Lorentz frame boosted relative toshow where the field is nonvanishing. the CM frame.

M2. In fig. 2.2 the same motion is shown after a Lorentz boost /3. The maximum relative distance hasbeen contracted to L’ = Ly(1 — /3) L e~and the time period dilated to T’ = TI’y = T cosh(y) where yis the rapidity difference between the two frames.In this model the “field” corresponding to the potential energy carries no momentum, which is a

consequence of the fact that in 1 + 1 dimensions there is no Poynting vector. Thus all the momentum iscarried by the endpoint quarks. This is possible since the turning points, where q and 4 have zeromomentum, are simultaneous only in the CM frame. In fact, for a fast-moving q4 system the q4-pairwill most of the time move forward with a small, constant relative distance (see fig. 2.2).In the following we will use this kind of yo-yo modes as representations both of our original q4 jet

system and of the final state hadrons formed when the system breaks up. It is for the subsequent worknecessary to know the level spectrum of the yo-yo modes. A precise calculation would need aknowledge of the quantization of the massless relativistic string but for our purposes it is sufficient touse semi-classical considerations well-known from the investigations of Schrodinger operator spectra.We consider the Hamiltonian of eq. (2.14) in the CM frame with q = x

1 — x2

H=IpI+KIql (2.18)

and we note that our problem is to find the dependence on n of the nth energy level E~. If thespatial size of the state is given by 5~then the momentum size of such a state with n — 1 nodes is

IpI=nI& (2.19)

and the energy eigenvalue E~corresponds according to variational principles to a minimum of

H(6~)= n/&, + Kô~ (2.20)

i.e.

2Vttn. (2.21)


The Lund Model

Combine yo-yo-style string motion with string breakings!

Motion of quarks and antiquarks with intermediate string pieces:

A q from one string break combines with a q from an adjacent one.

Gives simple but powerful picture of hadron production.


Where does the string break?

Fragmentation starts in the middle and spreads outwards:

Corresponds to roughly same invariant time of all breaks,τ2 = t2 − z2 ∼ constant,with breaks separated by hadronic area m2

⊥ = m2 + p2⊥.

Hadrons at outskirts are more boosted.

Approximately flat rapidity distribution, dn/dy ≈ constant

⇒ total hadron multiplicity in a jet grows like lnEjet.


How does the string break?

String breaking modelled by tunneling:

P ∝ exp

(−

πm2⊥q

κ

)= exp

(−

πp2⊥q

κ

)exp

(−

πm2q

κ

)

• Common Gaussian p⊥ spectrum, 〈p⊥〉 ≈ 0.4 GeV.

• Suppression of heavy quarks,

uu : dd : ss : cc ≈ 1 : 1 : 0.3 : 10−11.

• Diquark ∼ antiquark ⇒ simple model for baryon production.

String model unpredictive in understanding of hadron mass effects⇒ many parameters, 10–20 depending on how you count.


The Lund gluon picture – 1

Gluon = kink on string

Force ratio gluon/ quark = 2,cf. QCD NC/CF = 9/4, → 2 for NC →∞No new parameters introduced for gluon jets!



Energy sharing betweentwo strings makes hadronsin gluon jets softer, moreand broader in angle:

Jetset 7.4Herwig 5.8Ariadne 4.06Cojets 6.23

OPAL

(1/N

even

t ) d

n ch. /

dxE

xE

uds jetgluon jet

k⊥ definition:ycut=0.02

0. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.10

-3

10-2

10-1

1

10

10 2

0.51.

1.5

Cor

rect

ion

fact

ors

0

0.05

0.1

0.15

0 5 10 15 20 25 30 35

gincl. jetsuds jetsJetset 7.4Herwig 5.9Ariadne 4.08AR-2AR-3

nch.

P(n ch

.)

(a) OPAL |y| ) 2

0

0.05

0.1

0.15

0.2

0 5 10 15 20

gincl. jetsuds jetsJetset 7.4Herwig 5.9Ariadne 4.08AR-2AR-3

nch.P(

n ch.)

(b) OPAL |y| ) 1

Jetset 7.4Herwig 5.8Ariadne 4.06Cojets 6.23

0. 10. 20. 30. 40. 50. 60.0.

0.02

0.04

0.06

0.08

OPAL

(1/E

jet ) d

Ejet /dχ

χ (degrees)

uds jetgluon jet

k⊥ definition:ycut=0.02

0.5

1.

1.5

Cor

rect

ion

fact

ors



Particle flow in the qqg event plane depleted in q–q regionowing to boost of string pieces in q–g and g–q regions:


String vs. Cluster

program PYTHIA HERWIGmodel string cluster

energy–momentum picture powerful simplepredictive unpredictive

parameters few many

flavour composition messy simpleunpredictive in-between

parameters many few

“There ain’t no such thing as a parameter-free good description”Torbjorn Sjostrand Monte Carlo 2 slide 43/1

Colour flow in hard processes – 1

One Feynman graph can correspond to several possible colourflows, e.g. for qg → qg:

while other qg → qg graphs only admit one colour flow:


Colour flow in hard processes – 2

so nontrivial mix of kinematics variables (s, t)and colour flow topologies I, II:

|A(s, t)|2 = |AI(s, t) +AII(s, t)|2

= |AI(s, t)|2 + |AII(s, t)|2 + 2Re(AI(s, t)A∗II(s, t)

)with Re

(AI(s, t)A∗II(s, t)

)6= 0

⇒ indeterminate colour flow, while• showers should know it (coherence),• hadronization must know it (hadrons singlets).Normal solution:

interferencetotal

∝ 1

N2C − 1

so split I : II according to proportions in the NC →∞ limit, i.e.

|A(s, t)|2 = |AI(s, t)|2mod + |AII(s, t)|2mod

|AI(II)(s, t)|2mod = |AI(s, t) +AII(s, t)|2(

|AI(II)(s, t)|2

|AI(s, t)|2 + |AII(s, t)|2

)NC→∞


Colour Reconnection Revisited

Colour rearrangement wellestablished e.g. in B decay.

Introduction(V.A. Khoze & TS, PRL72 (1994) 28, ZPC62 (1994) 281,EPJC6 (1999) 271;L. Lonnblad & TS, PLB351 (1995) 293, EPJC2 (1998) 165)

!W,!Z,!t ! 2 GeV!h > 1.5 GeV for mh > 200 GeV!SUSY " GeV (often)

! =1

!!

0.2GeV fm

2GeV= 0.1 fm # rhad ! 1 fm

$ hadronic decay systems overlap,between pairs of resonances$ cannot be considered separate systems!

Three main eras for interconnection:1. Perturbative: suppressed for " > ! by propaga-

tors/timescales$ only soft gluons.2. Nonperturbative, hadronization process:

colour rearrangement.

B0

d

bc

W! c

s

!

"

!

"

B0

d

b

c

W!c

sg

!

"

K0S

!

"

J/!

3. Nonperturbative, hadronic phase:Bose–Einstein.

Above topics among unsolved problems of strong in-teractions: confinement dynamics, 1/N2

C effects, QMinterferences, . . . :

• opportunity to study dynamics of unstable parti-cles,

• opportunity to study QCD in new ways, but• risk to limit/spoil precision mass measurements.

So far mainly studied for mW at LEP2:

1. Perturbative: !!mW" <#5 MeV.2. Colour rearrangement: many models, in general

!!mW" <#40 MeV.

e!

e+

W!

W+

q3

q4

q2

q1

!

"

!

"!+

!+

#

$BE

3. Bose-Einstein: symmetrization of unknown am-plitude, wider spread 0–100 MeV among models,but realistically !!mW" <#40 MeV.

In sum: !!mW"tot < m!, !!mW"tot/mW<#0.1%; a

small number that becomes of interest only becausewe aim for high accuracy.

At LEP 2 search for effects in e+e− → W+W− → qqq2 q3q4:

perturbative 〈δMW〉 . 5 MeV : negligible!

nonperturbative 〈δMW〉 ∼ 40 MeV : signs but inconclusive.

Bose-Einstein 〈δMW〉 . 100 MeV : full effect ruled out.

Hadronic collisions with MPI’s: many overlapping colour sources.Reconnection established by 〈p⊥〉(nch), but details unclear.


The Mass of Unstable Coloured Particles – 1

MC: close to pole mass, in the sense of Breit–Wigner mass peak.t, W, Z: cτ ≈ 0.1 fm < rp .

t

t

W

b

At the Tevatron: mt = 173.20± 0.51± 0.71 GeV = PMAS(6,1)At the LHC: mt = 173.4± 0.4± 0.9 GeV (CMS) = 6:m0 ?

Need better mass definition for coloured particles?


The Mass of Unstable Coloured Particles – 2

Dependence*of*Top*Mass*on*Event*

Kinema2cs*

10*

!  First#top#mass#measurement#binned#in#kinema3c#observables.#!  Addi2onal*valida2on*for*the*top*mass*measurements.**

!  With*the*current*precision,*no*mis^modelling*effect*due*to*

"  color*reconnec2on,*ISR/FSR,**b^quark*kinema2cs,*difference*

between*pole*or*MS~*masses.*

color*recon.*

ISR/FSR*

b^quark*kin.*

Global*χ2/ndf*=*0.9*based*on*

mt1D*and*JES*which*are*

independent*(comparing*data*

and*MadGraph)*neglec2ng*

correla2ons*between*

observables.*

CMS^PAS^TOP^12^029*

NEW*

0 50 100 150 200 250 300>

[G

eV

]2

Dt

- <

m2

Dt

m-4

-2

0

2

4

)-1Data (5.0 fbMG, Pythia Z2MG, Pythia P11MG, Pythia P11noCRMC@NLO, Herwig

= 7 TeV, lepton+jetssCMS preliminary,

[GeV

]

[GeV]T,t,had

p0 50 100 150 200 250 300

da

ta -

MG

Z2

-5

0

5

E. Yazgan(Moriond 2013)


QCD and BSM physics

BNV ⇒ junction topology⇒ special handling ofshowers and hadronization

Hidden valleys:showers potentially interleavedwith normal ones;hadronization in hidden sector;decays back to normal sector

R-hadron formation

Squarkfragmenting tomeson or baryon

Gluinofragmenting tobaryon or glueball

Most hadronization properties by analogy with normalstring fragmentation, butglueball formation new aspect, assumed ⇠ 10% of time (or less).

Torbjorn Sjostrand QCD Aspects of BSM Physics slide 12/18

R-hadrons: long-lived g or q;new: hadronization of massive object “inside” the string


The Road Ahead – 1

What will be the role of the LHC?

• to study a rich set of new particles predominantly decaying toleptons, photons and invisible particles?

• to study a rich set of new particles predominantly decaying topartons, i.e. jets?

• to study a SM Higgs in boring detail, but do little else(cf. top at the Tevatron)?

• to become a QCD machine for lack of better (cf. HERA)?

Either way, generators will always be needed, but to a varying degree.

Many obvious evolutionary steps for generators:

• automated NLO ⇒ POWHEG calculations

• UNLOPS: combining CKKW-L–style matching with NLO

• parton showers with complete NLL accuracy

• improved MPI and hadronization frameworks


The Road Ahead – 2

And some revolutionary ones:

• automated multiloops for complete NnLO calculations,e.g. formalism with inherent Sudakov form factors

• lattice QCD describes hadronization

But what is progress (in the eyes of experimentalists)?

• more complicated models with more tunable parameters,giving better agreement with data?

• more sophisticated/predictive models with fewer tunableparameters, giving worse agreement with data?


Documents

Monte Carlo 2. Matching, MPI's and Hadronizationhome.thep.lu.se/~torbjorn/talks/van2ho.pdfARIEL Construction Reaches Milestone 23 May 2013 - The careful disassembly of the tower crane