R. Pittau Torino, May 25th 2007 -...

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




︸︷︷︸

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




︸︷︷︸

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




︸︷︷︸

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




︸︷︷︸

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

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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:

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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



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


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avgwgt(pb)= 0.0167401609+- 0.00153770483



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


avgwgt(pb)= 0.0173860873+- 0.000538143309

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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

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wbbj.mon

• Stores intermediate information. It is rewritten each 105 points:

processed= 100000.0 events


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

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• 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

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• 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

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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.

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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

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• 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

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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:

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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).

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