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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
Torbjorn Sjostrand Monte Carlo 2 slide 3/1
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)
Torbjorn Sjostrand Monte Carlo 2 slide 5/1
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)
Torbjorn Sjostrand Monte Carlo 2 slide 6/1
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:
Torbjorn Sjostrand Monte Carlo 2 slide 7/1
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
Torbjorn Sjostrand Monte Carlo 2 slide 8/1
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)
Torbjorn Sjostrand Monte Carlo 2 slide 9/1
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
Torbjorn Sjostrand Monte Carlo 2 slide 10/1
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.
Torbjorn Sjostrand Monte Carlo 2 slide 11/1
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.
Torbjorn Sjostrand Monte Carlo 2 slide 12/1
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?
Torbjorn Sjostrand Monte Carlo 2 slide 14/1
Event topologies
Expect and observe high multiplicities at the LHC.What are production mechanisms behind this?
Torbjorn Sjostrand Monte Carlo 2 slide 15/1
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
Torbjorn Sjostrand Monte Carlo 2 slide 16/1
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!
Torbjorn Sjostrand Monte Carlo 2 slide 17/1
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.
Torbjorn Sjostrand Monte Carlo 2 slide 18/1
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)
Torbjorn Sjostrand Monte Carlo 2 slide 19/1
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
Torbjorn Sjostrand Monte Carlo 2 slide 20/1
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:
Torbjorn Sjostrand Monte Carlo 2 slide 21/1
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.
Torbjorn Sjostrand Monte Carlo 2 slide 22/1
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:
Torbjorn Sjostrand Monte Carlo 2 slide 23/1
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?
Torbjorn Sjostrand Monte Carlo 2 slide 24/1
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−
Torbjorn Sjostrand Monte Carlo 2 slide 25/1
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]]
Torbjorn Sjostrand Monte Carlo 2 slide 27/1
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:
Torbjorn Sjostrand Monte Carlo 2 slide 28/1
Jet pedestal effect – 2
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
Torbjorn Sjostrand Monte Carlo 2 slide 29/1
Jet pedestal effect – 3
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
RDF Preliminary Corrected Data
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
Center-of-Mass Energy (TeV)
Cha
rged
Den
sity
RDF Preliminary Corrected Data
Charged Particles (|K|<0.8, PT>0.5 GeV/c)
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
Center-of-Mass Energy (TeV)
"Tra
nsve
rse"
Cha
rged
Den
sity
RDF Preliminary Corrected Data
Charged Particles (|K|<0.8, PT>0.5 GeV/c)
5.0 < PTmax < 6.0 GeV/c
CMS red squaresCDF blue dots
¨ 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
Center-of-Mass Energy (TeV)
"Tra
nsve
rse"
Cha
rged
Den
sity
Charged Particles (|K|<0.8, PT>0.5 GeV/c)
5.0 < PTmax < 6.0 GeV/c
RDF Preliminary Corrected Data
Tune Z1 Generator Level
PYTHIA Tune Z1
CMS red squaresCDF blue dots
Overall Charged Particle Density
0.20
0.30
0.40
0.50
0.60
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 red squaresCDF blue dots
At least 1 charged particle
RDF Preliminary Corrected Data
Tune Z1 Generator Level
PYTHIA Tune Z1
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
RDF Preliminary Corrected Data
Tune Z1 Generator Level
PYTHIA Tune Z1
Amazing!
Conclusion: “transMIN” (MPI+BBR) increases much faster withEcm than “transDIF” (ISR+FSR), proportionately speaking.
Torbjorn Sjostrand Monte Carlo 2 slide 30/1
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.
Torbjorn Sjostrand Monte Carlo 2 slide 31/1
Hadronization
Hadronization/confinement is nonperturbative ⇒ only models.
Begin with e+e− → γ∗/Z0 → qq and e+e− → γ∗/Z0 → qqg:
Y
XZ
Y
XZ
Torbjorn Sjostrand Monte Carlo 2 slide 32/1
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 .
Torbjorn Sjostrand Monte Carlo 2 slide 33/1
The QCD potential – 2
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 (?).
Torbjorn Sjostrand Monte Carlo 2 slide 34/1
The QCD potential – 3
Full QCD = gluonic field between charges (“quenched QCD”)plus virtual fluctuations g → qq (→ g)=⇒ nonperturbative string breakings gg . . . → qq
Torbjorn Sjostrand Monte Carlo 2 slide 35/1
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)
Torbjorn Sjostrand Monte Carlo 2 slide 36/1
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.
Torbjorn Sjostrand Monte Carlo 2 slide 37/1
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.
Torbjorn Sjostrand Monte Carlo 2 slide 38/1
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.
Torbjorn Sjostrand Monte Carlo 2 slide 39/1
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!
Torbjorn Sjostrand Monte Carlo 2 slide 40/1
The Lund gluon picture – 2
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
Torbjorn Sjostrand Monte Carlo 2 slide 41/1
The Lund gluon picture – 3
Particle flow in the qqg event plane depleted in q–q regionowing to boost of string pieces in q–g and g–q regions:
Torbjorn Sjostrand Monte Carlo 2 slide 42/1
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:
Torbjorn Sjostrand Monte Carlo 2 slide 44/1
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→∞
Torbjorn Sjostrand Monte Carlo 2 slide 45/1
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.
Torbjorn Sjostrand Monte Carlo 2 slide 46/1
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?
Torbjorn Sjostrand Monte Carlo 2 slide 47/1
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)
Torbjorn Sjostrand Monte Carlo 2 slide 48/1
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
Torbjorn Sjostrand Monte Carlo 2 slide 49/1
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
Torbjorn Sjostrand Monte Carlo 2 slide 50/1
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?
Torbjorn Sjostrand Monte Carlo 2 slide 51/1