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R. Pittau
Torino, May 25th 2007
1
High Energy hadronic collisions at
the LHC
1
http://hands-on-cern.physto.se/ani/acc_lhc_atlas/lhc_atlas.swf
2
The Factorization Theorem
dσ
dX=∑
j,k
∫
X
fj(x1, Qi)fk(x2, Qi)dσj,k(Qi, Qf)
dXF (X → X;Qi, Qf)
dσ X → F → Xf(x,Qi)
︸ ︷︷ ︸
Parton Shower
f ⇒ Sum over all initial state histories leading to pj = xPproton.
F ⇒ Transition from partonic final state to the hadronic observable.
3
dσ
dX=∑
j,k
∫
X
fj(x1, Qi)fk(x2, Qi)dσj,k(Qi, Qf)
dXF (X → X;Qi, Qf)
dσ X → F → Xf(x,Qi)
︸ ︷︷ ︸
Parton Shower
4
The Matrix Element computation (at the tree level)
1) Elicity Methods
2) The Dyson Schwigner approach
Helicity Methods
• One evaluates directly the amplitudes as complex numbers
(instead of squaring them) ⇒explicit representations of the wave functions of the external particles
(εµ, u, v) are needed :
• Massless vector:
ε(λ)µ (k) =1√2
uλ(k)γµuλ(n)
u−λ(n)uλ(k), n2 = 0 , λ = ± .
5
• Massless (Weyl) spinors:
v−(1) = u+(1) = 1A v−(1) = u+(1) = 1A
v+(1) = u−(1) = 1A v+(1) = u−(1) = 1A
(12, 0) + (0, 1
2) SL(2, C) representation of the Lorentz group.
• γ matrices (Weyl representation):
γµ =
0 σµBA
σABµ 0
, γ5 =
σ0 0
0 −σ0
.
see e.g. J.G.M. Kuijf, Ph.D. Thesis, RX-1335, LEIDEN, (1991)
6
• Basic rules and spinorial inner products:
σABµ σµCD = 2 εACεBD , εAB =
0 1
−1 0
= εAB = εAB = εAB ,
εAB ≡ −εBA , 1B = 1AεAB , < 12 >≡ 1A2
A , [12] ≡ 1A2A ,
< 12 > [12] = 2 p1 · p2 .
7
• Example e+e− → µ+µ− in QED (all incoming momenta and massless particles):
2
1
4
3
A(++) ∝ v+(1)γµu−(2) v+(3)γµu−(4) = 1A 2B 3C 4D σµBAσ
µ
DC
= 2 1A 2B 3C 4DεBDεAC = 2 [42] < 31 > .
• Helicity techniques based on spinorial inner products are
successfully used also in one-loop calculations (but care is necessary
when using dimensional regularization).
8
• Although each diagram can be computed efficiently multi-particle
amplitudes involve the evaluation of an exceedingly large numbers of
Feynamn diagrams. e.g.
Process n = 7 n = 8 n = 9 n = 10
g g → n g 559,405 10,525,900 224,449,225 5,348,843,500
qq → n g 231,280 4,016,775 79,603,720 1,773,172,275
Table 1: Number of Feynman diagrams corresponding to amplitudes with different num-
bers of quarks and gluons.
F. Caravaglios, M. L. Mangano, M. Moretti and R. P., NPB 539 (1999) 215
A pure numerical approach to the calculations of transition
amplitudes is welcome. This can be done with the ALPHA
algorithm
F. Caravaglios and M. Moretti, PLB 358 (1995) 332
9
The Idea: The Matrix Element ‘is’ the Legendre Transform Z of the
(effective) Lagrangian Γ (1PI Green Functions generator) → the
problem can be re-casted as a minimum problem, more suitable for a
numerical approach (DS equation).
The Dyson-Schwinger equations
F. A. Berends and W. Giele, NPB 306 (1988) 759
A. Kanaki and C. G. Papadopoulos, hep-ph/0012004
An alternative to the Feynman graph representation is provided by
the Dyson-Schwinger approach.
Dyson-Schwinger equations express recursively the n-point Green’s
functions in terms of the 1−, 2−, . . . , (n− 1)-point functions.
10
• Imagine a 0-dimensional universe with only one point φ. The
Quantum Field Theory describing such a system is comlpetely
specified by all possible p-point (Euclidean) Green Functions:
Gp ≡< φp >= N
∫
dφφp e−S(φ) .
• They can be obtained from a Generating Functional as follows:
Z(J) = N
∫
dφ e−S(φ)+Jφ =∑
p≥0Gp
Jp
p!.
• The DS Equations follow from the standard identity that the
integral of a derivative is zero:
0 = N
∫
dφd
dφ
{
e−S(φ)+Jφ}
= N
∫
dφ {−S ′(φ) + J} e−S(φ)+Jφ
= {−S ′(∂J) + J}Z(J) .
11
• Therefore one obtains the following Dyson-Schwinger equations:
S ′(∂J)Z = JZ(J) .
• For instance in QED these equations can be graphically
represented as follows:
= +
• This gives rise to a recursive algorithm easily implementable in a
Computer Code (ALPGEN).
12
dσ
dX=∑
j,k
∫
X
fj(x1, Qi)fk(x2, Qi)dσj,k(Qi, Qf)
dXF (X → X;Qi, Qf)
dσ X → F → Xf(x,Qi)
︸ ︷︷ ︸
Parton Shower
13
The convolution with the pdf’s
• To complete the calculation, one needs to perform the integration
over the parton distribution functions
• Those distribution functions are extracted from deep inelastic
scattering data
see e.g. S. Willenbrock, BNL-43793 (1990)
• They are available as prepackaged computer programs, that can be
used to perform the integral numerically. The most popular sets are:
- CTEQ
J. Pumplin et al., JHEP 0207, 012 (2002)
- MRST
A. D. Martin, R. G. Roberts, W. J. Stirling and R. S. Thorne, Eur. Phys. J. C 14, 133 (2000)
14
dσ
dX=∑
j,k
∫
X
fj(x1, Qi)fk(x2, Qi)dσj,k(Qi, Qf)
dXF (X → X;Qi, Qf)
dσ X → F → Xf(x,Qi)
︸ ︷︷ ︸
Parton Shower
15
Subprocess selection
•The calculation of the cross section for multi-parton final states
involves typically the sum over a large set of subprocesses and
flavour configurations e.g. for the Wbb final state:
jp subprocess jp subprocess jp subprocess
1 qq′ → WQQ 2 qg → q′WQQ 3 gq → q′WQQ
4 gg → qq′WQQ 5 qq′ → WQQq′′q′′ 6 qq′′ → WQQq′q′′
7 q′′q → WQQq′q′′ 8 qq → WQQq′q′′ 9 qq′ → WQQqq
10 q′q → WQQqq 11 qq → WQQqq′ 12 qq → WQQq′q
13 qq → WQQqq′ 14 qq′ → WQQqq 15 qq′ → WQQq′q′
16 qg → WQQq′q′′q′′ 17 gq → WQQq′q′′q′′ 18 qg → WQQqqq′
19 qg → WQQq′qq 20 gq → WQQqqq′ 21 gq → WQQq′qq
22 gg → WQQqq′q′′q′′ 23 gg → WQQqqqq′
Each of these subprocesses receives contributions from several possible flavour
configurations (e.g. ud→ WQQgg , us→ WQQgg, etc.)
16
• The subdivision in subprocesses can be designed to allow to sum
the contribution of different flavour configurations by simply adding
trivial factors such as parton densities or CKM factors, which
factorize out of a single, flavour independent, matrix element.
• For example the overall contribution from the 1st process in the listis given by
[u1d2 cos
2 θc + u1s2 sin2 θc + c1s2 cos
2 θc + c1d2 sin2 θc
]× |M(qq′ → WQQgg)|2
where qi = f(xi), i = 1, 2, are the parton densities for the quark
flavour q. Contributions from charge-conjugate or isospin-rotated
states can also be summed up, after trivial momentum exchanges.
17
• For example, the same matrix element calculation is used to
describe the four events:
u(p1)d(p2) → b(p3)b(p4)g(p5)g(p6)e+(p5)ν(p6)
u(p1)d(p2) → b(p3)b(p4)g(p5)g(p6)e−(p5)ν(p6)
d(p1)u(p2) → b(p3)b(p4)g(p5)g(p6)ν(p5)e+(p6)
d(p1)u(p2) → b(p3)b(p4)g(p5)g(p6)ν(p5)e−(p6)
• Event by event, the flavour configuration for the assigned
subprocess is then selected with a probability proportional to the
relative size of the individual contributions to the luminosity,
weighted by the Cabibbo angles.
18
dσ
dX=∑
j,k
∫
X
fj(x1, Qi)fk(x2, Qi)dσj,k(Qi, Qf)
dXF (X → X;Qi, Qf)
dσ X → F → Xf(x,Qi)
︸ ︷︷ ︸
Parton Shower
19
The perturbative Parton Shower
• It is important because a lot of final state jets are typically
observed, in hadronic collisions, coming from QCD radiation that,
subsequently, hadronizes. It is still pertubatively calculable by
introducing the so called Sudakov Form Factors.
• In QED (at the LL):
Q
= dσ0
(
1− α
πlog2
Q
Q0
)
, Q > Q0 > 0 ,
where the log2 comes from the overlap of soft and collinear
emissions.
20
• Thanks to factorization theorems one can exponentiate this result
to get
dσrad = dσ0 exp
{
−απlog2
Q
Q0
}
.
• In QCD (at the LL): α→ CFαs, CF = N2c−12Nc
= 43 and
dσrad = dσ0 exp
{
−αsCF
πlog2
Q
Q0
}
.
• The term
exp
{
−αsCF
πlog2
Q
Q0
}
represents the probability for a quark of NOT radiating any gluon
when passing from a scale Q to a scale Q0 < Q.
21
• In reality αs = αs(Q) and one defines
∆q(Q0, Q) ≡ exp
{
−∫ Q
Q0
dq Γq(q,Q)
}
,
where
Γq(q,Q) =2CF
π
αsq
(
logQ
q− 3
4
)
= P (q → qg)
is the q → qg Altarelli-Parisi splitting function.
• When αs is a constant, taking the integral reproduces the previous
expression (at the LL).
22
• Analogously, with
Γg(q,Q) = P (g → gg) and Γf(q) = P (g → qq) ,
one defines a Sudakov Form factor for the gluon
∆q(Q0, Q) ≡ expx
{
−∫ Q
Q0
dq [Γg(q,Q) + Γf(q)]
}
.
• Knowing the ∆q,g(Q0, Q) one can easily construct Monte-Carlo
programs to explicitly generate the perturbative Parton Shower
cascade (in principle including an infinite number of emissions).
• However the results will be only reliable in the soft/collinear
regime. Outside one should calculate the exact Matrix elements
⇒ possible double counting problem
⇒ CKKW and Matching a la MLM (see later)
• In QCD, at each colour flow corresponds a different structure of
Sudakov Form Factors ⇒
23
Reconstruction of colour flows
• The emission of soft gluon radiation in shower MC programs
accounts for quantum coherence, which is implemented via the
prescription of angular ordering in the parton cascade.
• The colour flow is the set of colour connections among the partons
which defines the set of dipoles for a given event.
• In order to reliably evolve a multi-parton state into a multi-jet
configuration, it is necessary to associate a specific colour-flow
pattern to each generated parton-level event.
24
• Consider for example the case of multigluon processes. The
scattering amplitude for n gluons with momenta pµi , helicities εµi and
colours ai (with i = 1, . . . , n), can be written as
F.A. Berends and W. Giele, NPB 294 (1987) 700
M. Mangano, S. Parke and Z. Xu, NPB 298 (1988) 653
M({pi}, {εi}, {ai}) =∑
P (2,3,...,n)
tr(λai1 λai2 . . . λain )A({pi1}, {εi1}; . . . {pin}, {εin}) .
• The functions A({Pi}) (known as dual or colour-ordered
amplitudes) are gauge-invariant, cyclically-symmetric functions of
the gluons’ momenta and helicities.
• Each dual amplitude A({Pi}) corresponds to a set of diagrams
where colour flows from one gluon to the next, according to the
ordering specified by the permutation of indices.
25
• When summing over colours the amplitude squared, different
orderings of dual amplitudes are orthogonal at the leading order in
1/N 2
∑
col′s
|M({pi}, {εi}, {ai})|2 = Nn−2(N 2−1)∑
Pi
[
|A({Pi})|2 +1
N 2(interf.)
]
.
• At the leading order in 1/N 2, therefore, the square of each dual
amplitude is proportional to the relative probability of the
corresponding colour flow
• Each flow defines, in a gauge invariant way, the set of colour
currents which are necessary and sufficient to implement the colour
ordering prescription necessary for the coherent evolution of the
gluon shower.
26
• Because of the incoherence of different colour flows, each event can
be assigned a specific colour configuration by comparing the relative
size of |A({Pi})|2 for all possible flows.
• When working at the physical value of Nc = 3, the interferences
among different flows cannot be neglected in the evaluation of the
square of the matrix element. As a result, the basis of colour flows
does not provide an orthogonal set of colour states:
Our solution for and efficient color flow generation including 1/N
corrections in the Matrix Element evaluation
⇒
27
- Choose a standard SU(3) orthonormal basis (Gell-Mann matrices
for example).
- Randomly select a non-vanishing colour assignment for the
external gluons.
- If the event is accepted choose randomly among the contributing
dual amplitudes a color flow on the basis of their relative weight.
• Two advantages:
1) Dual amplitudes required only for a small number of phase space
points.
2) Contributing dual amplitudes to a given external coulor
assignment ¿ than total number.
28
The CKKW algorithm
• As an example take e+e− → n-jets.
• First recall that, in QCD, two objects i and j are resolved (using
the kT algorithm) if
yij ≡ 2 min{E2i , E
2j }(1− cos θij)/Q
2 > ycut. (1)
• One can reproduce (at the LL accuracy) the e+e−n-jet fractions at
the kT resolution
yini =Q2
0
Q2
using a probabilistic diagrammatic (NOT Feynman diagrams)
approach as follows:
29
Q
Q0
Q0
⇒ R2 = ∆q(Q0, Q)2
Q
Q0
Q0
Q0q
⇒ R3 = 2∆q(Q0, Q)2∫ Q
Q0
dq Γq(q,Q)∆g(Q0, q) .
• If ycut > yini one can improve the above description by replacing Γ
with the appropriate tree-level matrix element squared.
For example, for the 3-jet distribution
Γq(q,Q)→ |Mqqg|2 .
30
In general
• At ycut > yini
1) choose the n-parton configuration with probability proportional to
the tree level matrix elements squared |Mn|2;
2) distribute all momenta according to |Mn|2;
3) reconstruct a probabilistic diagram by using the kT algorithm;
4) reweight |Mn|2 by a product of Sudakov form factors;
5) the argument of the form factors and the running coupling are
computed at the typical scales on the nodal values of the
reconstructed probabilistic diagram.
• At ycut < yini one uses instead a parton shower subjected to a
’veto’ procedure, which cancels the yini dependence
⇒ double counting is avoided
31
The Matching a la MLM
• Simpler procedure
1) parton level events are defined by a minimum ET threshold EminT
for the partons and a minimum separation ∆Rij > Rmin;
2) a tree structure is reconstructed by using the kT algorithm, but
using information of the colour flow of the event ;
3) αs(Qi) is computed at the typical scales Qi on the nodal values of
the reconstructed probabilistic diagram;
4) the event is showered (using PYTHIA or HERWIG) without
applying any ’veto’ procedure;
5) no Sudakow reweighing is applied, rather, after the showering, a
jet cone algorithm (Rmin, EminT ) is applied and
only events where jet and partons match are kept ;
32
Few examples of matching (njets = 3): hard partonparton emitted by the shower
Matched NOT matched: double logdouble counting
NOT matched: single logdouble counting
Matched: keep only if njets = Nmax
33
6) Events obtained by applying this procedure to the parton level
with increasing multiplicity can then be combined to obtain fully
inclusive samples spanning a large multiplicity range.
This algorithm is implemented in ALPGEN.
34
2
The ALPGEN Generator
35
The ALPGEN GeneratorM.L. Mangano, M. Moretti, F. Piccinini, R. P., A.D. Polosa, JHEP07(2003)001
• Collection of MC codes for many processes relevant in
hadron–hadron collisions (TEVATRON and LHC)
• Exact LO matrix element calculations of dσ based on the ALPHA
algorithm
• Parton-level event generation (weighted and unweighted)
• Interface to Herwig/Pythia for the evolution of the partonic final
state through parton shower with matching a la MLM
• ALPGEN can be downloaded from the code home page
http://mlm.home.cern.ch/m/mlm/www/alpgen/
where a detailed documentation is also available
36
Up to now available processes
• W +N jets, Z/γ +N jets, N ≤ 6
• WQQ+N jets, Z/γQQ+N jets (Q = b, t), N ≤ 4
• W + c+N jets, N ≤ 5
• n W +m Z + p Higgs + l photons +N jets,
n+m+ p+ l ≤ 8, N ≤ 3
• QQ+N jets, (Q = b, t), N ≤ 6
• QQQ′Q′ +N jets, (Q,Q′ = b, t) , N ≤ 4
• N jets, N ≤ 6
• QQH +N jets, (Q = b, t), N ≤ 4
• N photons + M jets, N > 0, N +M ≤ 8 and M ≤ 6
37
NEW processes
• single top production: tq, tb, tW , tbW , No extra jets
• H +N jets, N ≤ 3, effective ggH coupling
• W + photons +N jets, up to 2 γ’s
• W + photons +QQ+N jets, up to 2 γ’s
• QQ+N photons +N jets, (Q = b, t), M +N ≤ 6
38
Tutorial (How to use ALPGEN)
• Go to http://mlm.home.cern.ch/m/mlm/www/alpgen/ and
download in an empty directory the file v210.tgz by clicking:
NEW: The source code for version V2.10
• Then give the command:
> tar -xzvf v210.tgz
resulting in the following directory structure:
2Qlib compare Makefile QQhlib vbjetwork wphqqlib zqqwork
2Qphlib compile.mk Njetlib QQhwork wcjetlib wphqqwork
2Qphwork DOCS Njetwork toplib wcjetwork wqqlib
2Qwork ft90V.tar.gz phjetlib topwork wjetlib wqqwork
4Qlib herlib phjetwork v210.tgz wjetwork zjetlib
4Qwork hjetlib prc.list validation wphjetlib zjetwork
alplib hjetwork pylib vbjetlib wphjetwork zqqlib
39
• It is possible to validate the whole package by giving the command:
> make validate
It will compile all processes and will run them with few points,
comparing then the results with a library of results to see if the
installation worked or whether there are differences.
Then change directory:
> cd validation
to see the result of the check:
> more val.summary
40
Let us now show how to run a specific process (e.g. Wbb+ 1 jet).
• Go to the corresponding directory:
> cd wqqwork
that looks like
alpgen.inc cnfg.dat input Makefile pdflnk wqq.inc wqqusr.f
• Then complile the code with the command
> make gen
that will generate the executable file
wqqgen
• Run it by giving the command
> wqqgen < input
(the default input file corresponds to Wbb+ 1 jet)
41
• The result of the run is stored is a series of files
contained in the directory, that now looks like
alpgen.inc Makefile wbbj.grid2 wbbj.stat wqqgen wqqusr.o
cnfg.dat pdflnk wbbj.mon wbbj.top wqq.inc
input wbbj.grid1 wbbj.par wbbj.wgt wqqusr.f
Before discussing the output we show how to prepare
the input file
42
1 ! imode
wbbj ! label for files
0 ! start with: 0=new grid, 1=previous warmup grid, 2=previous generation grid
10000 2 ! Nevents/iteration, N(warm-up iterations)
100000 ! Nevents generated after warm-up
*** The above 5 lines provide mandatory inputs for all processes
*** (Comment lines are introduced by the three asteriscs)
*** The lines below modify existing defaults for the hard process under study
*** For a complete list of accessible parameters and their values,
*** input ’print 1’ (to display on the screen) or ’print 2’ to write to file
ihvy 5
njets 1
ickkw 0
ptjmin 20
ptbmin 20
etajmax 1
etabmax 1
drjmin 0.7
drbmin 0.7
43
• There are hidden parameters, with default values. To see the entire
list type:
> ./wqqgen
• Then it appears on the screen:
Input RUN generation mode:
0: generate weighted events, no evt dumps to file
1: generate wgtd events, write to file for later unweighting
2: read events from file for unweighting or processing
or documentation modes:
3: print parameter options and defaults, then stop
4: write to par.list parameter options and defaults, then stop
5: write to prc.list complete list of processes, parameter
options and defaults, scale choices, PDF, etc., then stop
• Now write
> 4
• to genarate the file par.list, that reads:
44
------
hard process code (not to be changed):
ihrd= 1
------
Select pp (1) or ppbar (-1) collisions:
ih2= -1
------
beam energy in CM frame (e.g. 7000 for LHC):
ebeam= 980.
------
parton density set:
ndns= 5
NDNS Set Lambda_4 Lambda_5_2loop Scheme
1 CTEQ4M .298 .202 MS
2 CTEQ4L .298 .202 MS
3 CTEQ4HJ .298 .202 MS
4 CTEQ5M .326 .226 (as=0.118) MS
5 CTEQ5L * .192 .144 (asLO=0.127) MS
6 CTEQ5HJ .326 .226 (as=0.118) MS
45
7 CTEQ6M .326 .226 (as=0.118) MS
8 CTEQ6L .326 .226 (as=0.118) MS
9 CTEQ6L1 .215 .165 (asLO=0.130) MS
10-50 CTEQ6xx .326 .226 (as=0.118) MS
101 MRST99 COR01 .321 .220 MS
102 MRST2001 .342 .239 (as=0.119 ) MS
103 MRST2001 .310 .214 (as=0.117 ) MS
104 MRST2001 .378 .267 (as=0.121 ) MS
105 MRST2001J .378 .267 (as=0.121) MS
106 MRST2002LO * .22 .167 (asLO=0.13) MS
PDF sets followed by * are obtained from a 1-loop analysis,
and the relative values of Lambda refer to 1-loop.
The MSbar scheme is used by default with 1-loop
structure functions.
In all cases the values of Lambda and loop order are set
automatically by the code, The user only needs to input ndns
------
scale option (process dependent):
46
iqopt= 1
Options for Factorization/renormalization scale Q:
iqopt=0 => Q=qfac
iqopt=1 => Q=qfac*sqrt{m_W^2+ sum_jets(m_tr^2)}
iqopt=2 => Q=qfac*mW
iqopt=3 => Q=qfac*sqrt{m_W^2+ pt_W^2}
iqopt=4 => Q=qfac*sqrt{sum_jets(m_tr^2)}
where:
- m_tr^2=m^2+pt^2, summed over heavy quarks and light jets
To select CKKW scale input ’ickkw 1’
(mandatory for later use of jet matching)
In imode=2 select clustering option ’cluopt’:
cluopt=1: kperp propto pt(cluster) (default)
cluopt=2: kperp propto mt(cluster)
kperp is then rescaled by ktfac
------
Q scale rescaling factor:
qfac= 1.
------
CKKW scale option: set to 1 to enable jet-parton matching:
47
ickkw= 0
------
scale factor for ckkw alphas scale:
ktfac= 1.
------
number of light jets:
njets= 0
------
heavy flavour type for procs like WQQ, ZQQ, 2Q, etc(4=c, 5=b, 6=t):
ihvy= 5
------
charm mass:
mc= 1.5
------
bottom mass:
mb= 4.7
------
top mass:
mt= 174.3
------
48
minimum pt for light jets:
ptjmin= 20.
------
ptmin for bottom quarks (in procs with explicit b):
ptbmin= 20.
------
ptmin for charm quarks (in procs with explicit c):
ptcmin= 20.
------
minimum pt for charged leptons:
ptlmin= 0.
------
minimum missing et:
metmin= 0.
------
max|eta| for light jets:
etajmax= 2.5
------
max|eta| for b quarks (in procs with explicit b):
etabmax= 2.5
49
------
max|eta| for c quarks (in procs with explicit c):
etacmax= 2.5
------
max abs(eta) for charged leptons:
etalmax= 10.
------
min deltaR(j-j), deltaR(Q-j) [j=light jet, Q=c/b]:
drjmin= 0.699999988
------
min deltaR(b-b) (procs with explicit b):
drbmin= 0.699999988
------
min deltaR(c-c) (procs with explicit charm):
drcmin= 0.699999988
------
min deltaR between charged lepton and light jets:
drlmin= 0.
------
first random number seed (5-digit integer):
50
iseed1= 12345
------
second random number seed (5-digit integer):
iseed2= 67890
------
W decay modes, in imode=2:
iwdecmod= 1
------
kt scale option. 1:kt propto pt, 2:kt propto mt:
cluopt= 1
------
first random number seed for unweighting (5-digit integer):
iseed3= 12345
------
second random number seed for unweighting (5-digit integer):
iseed4= 67890
51
• All these default values can be changed by writing in the input file,
in any place, the changed values
• For example, in our input file, the default value etajmax= 2.5 has
been changed by the statement
etajmax 1
We are now ready to discuss
the output files
52
wbbj.stat
W b bbar + 1 jets
W-> ell nu
=======================================
b mass: 4.7
Generation cuts for the partonic event sample:
Light jets:
ptmin= 20. |etamax|= 1. dR(j-j),dR(Q-j)> 0.7
b quarks:
ptmin= 20. |etamax|= 1. dR(QQ)> 0.7
Leptons:
ptmin(lep)= 0. |etamax|= 10. Et(miss)> 0. dR(l-j)> 0.
RUNNING PARAMETERS
-------------------
Electroweak parameters:
iewopt= 3:
input mW, mZ, GF calculate the rest
53
M(W)= 80.419 Gamma(W)= 2.04807653
M(Z)= 91.188 Gamma(Z)= 2.44194427
M(H)= 120. Gamma(H)= 0.
gW= 0.65323291; sin^2(thetaW)= 0.222246533; 1/aem(mZ)= 132.50698
Quark masses:
m(top)= 174.3 m(b)= 4.7
Beams’ parameters:
beam1=proton, beam2=antiproton
Ebeam= 980. PDF set=CTEQ5L
as(MZ)[nloop= 1] = 0.127003172
starting generation of 10000. events
average ph-space eff= 0.342536138
avgwgt(pb)= 0.0152015651+- 0.00187552134 maxwgt= 7.65766369
unwgt eff = 0.00198514399
sub-processes:
54
jproc= 1 total(pb): 0.0108255596+- 0.0017552771
jproc= 2 total(pb): 0.00236215767+- 0.000554153443
jproc= 3 total(pb): 0.00201384775+- 0.000374062198
cumulated cross-section:
avgwgt(pb)= 0.0152015651+- 0.00187552134
starting generation of 10000. events
average ph-space eff= 0.436891083
avgwgt(pb)= 0.019895344+- 0.00268578981 maxwgt= 14.9961835
unwgt eff = 0.00132669383
sub-processes:
jproc= 1 total(pb): 0.0136988128+- 0.00249145625
jproc= 2 total(pb): 0.00288165339+- 0.000481786113
jproc= 3 total(pb): 0.00331487788+- 0.000890439387
cumulated cross-section:
55
avgwgt(pb)= 0.0167401609+- 0.00153770483
starting generation of 100000. events
average ph-space eff= 0.409294254
avgwgt(pb)= 0.017476239+- 0.000574471343 maxwgt= 26.1532933
unwgt eff = 0.000668223264
sub-processes:
jproc= 1 total(pb): 0.0114901936+- 0.000490463401
jproc= 2 total(pb): 0.00322185443+- 0.000225250821
jproc= 3 total(pb): 0.00276419101+- 0.000200695731
cumulated cross-section:
avgwgt(pb)= 0.0173860873+- 0.000538143309
56
wbbj.top
• The pre-defined histograms of any variable, loaded by the user in
wqqusr.f before the run, are stored here, in the Topdrawer format.
For example
57
wbbj.mon
• Stores intermediate information. It is rewritten each 105 points:
processed= 100000.0 events
average ph-space eff= 0.409294254
avgwgt(pb)= 0.017476239+- 0.000574471343 maxwgt= 26.1532933
unwgt eff= 0.000668223264
sub-processes:
jproc= 1 total: 0.0114901936+- 0.000490463401
jproc= 2 total: 0.00322185443+- 0.000225250821
jproc= 3 total: 0.00276419101+- 0.000200695731
58
• The files wbbj.par, wbbj.grid1 and wbbj.grid2 are for internal
use
What shown up to now is enough to produce results at the parton
level. If, instead, one needs to produce actual events (e.g. to perform
detector simulations of more realistic studies), the following is also
needed
59
• The file wbbj.wgt contains the weighted events generated during
the run. To generate unweighted events do the following 4 steps
1) Run again the code:
> ./wqqgen
Output:
Input RUN generation mode:
0: generate weighted events, no evt dumps to file
1: generate wgtd events, write to file for later unweighting
2: read events from file for unweighting or processing
or documentation modes:
3: print parameter options and defaults, then stop
4: write to par.list parameter options and defaults, then stop
5: write to prc.list complete list of processes, parameter
options and defaults, scale choices, PDF, etc., then stop
60
2) Input:
> 2
Output:
Input string labeling output and input files
(e.g. w2j to output files w2j.stat, etc.)
3) Input:
> wbbj
Output:
Parameters and results written to wbbj_unw.par
Topdrawer plots (if any) written to wbbj_unw.top
Wgted events are read from wbbj.wgt
Unwgted events are written to wbbj.unw
read in generation parameters:
ihvy = 5.
njets = 1.
ickkw = 0.
61
ptjmin = 20.
ptbmin = 20.
etajmax = 1.
etabmax = 1.
drjmin = 0.7
drbmin = 0.7
Input decay params to replace defaults: type and value
(input ’print 1’ to display the list of parameter types and their current values)
(input ’ctrl-D’ to terminate the input sequence)
4) Input:
> ctrl-D
Output:
starting scan/unweighting of 5450. events
Crosssection(pb)= 0.0173861+- 0.000538143
Generated 176 unweighted events, lum= 10123.0293pb-1
62
• The generated unweigted events can be found in the file wbbj.unw
and are written in a format that can be easily translated to the
standard Les Houches Accord
E. Boos et al., hep-ph/0109068
• For example the first of the 176 generated unweighted events reads
1 1 7 0.100000E+01 0.118382E+03
2 3 0 118.206
-1 0 1 -147.774
5 2 0 12.285 -33.814 -16.966 4.700
-5 0 1 40.632 -48.437 14.085 4.700
21 3 2 -19.046 42.996 24.373 0.000
12 0 0 3.867 44.875 -0.971 0.000
-11 0 0 -37.738 -5.619 -50.088 0.001
63
Showering and Hadronizing events (with Herwig)
• Compile Herwig by going to the appropriate directory (it takes a
while...):
> cd herlib
> make hwuser
• Return to the working directory and run from the the Herwig
executable file (hwuser). Input:
> cd ../wqqwork
> ../herlib/hwuser
Output:
64
HERWIG 6.510 31st Oct. 2005
Please reference: G. Marchesini, B.R. Webber,
G.Abbiendi, I.G.Knowles, M.H.Seymour & L.Stanco
Computer Physics Communications 67 (1992) 465
and
G.Corcella, I.G.Knowles, G.Marchesini, S.Moretti,
K.Odagiri, P.Richardson, M.H.Seymour & B.R.Webber,
JHEP 0101 (2001) 010
INPUT NAME OF FILE CONTAINING EVENTS
(FOR "file.unw" ENTER "file")
• Input:> wbbj
• The 176 unweihted events are now fully showered and hadronized.
They can be analyzed on line, during the running of Herwig, from
SUBROUTINE HWANAL in hwuser.f (see the Herwig Manual for more
details).
65
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