### Initialize Histograms for Jet Analysis (Fortran)

Source: https://context7.com/powheg-box/v2/llms.txt

Initializes histogram bookings for jet analysis. Requires ANALYSIS=default and FastJet installation. Histograms are booked for various jet properties and kinematic cuts.

```fortran
! File: pwhg_analysis.f
! Requires: ANALYSIS=default in Makefile; FastJet installed and in PATH.
!
! Jet algorithm parameters (hardcoded):
!   palg = -1    (anti-kT)
!   R    = 0.5   (first clustering pass, variable ptmin)
!   R    = 0.4   (second pass, ptmin=60 GeV, |y|<2.8)
!
! Histograms booked for each of 6 pT_min thresholds (0,20,40,60,80,100 GeV):
!   sigtot, Njet
!   j1..j4: rapidity (y), pseudorapidity (eta), pT, invariant mass
!   j1j2..j3j4: dijet y, eta, pT, mass, Δy, Δeta, Δφ, ΔR
!
! Fixed-cut distributions (leading 3 jets, pT1>80 GeV, |y|<2.8):
!   'J pt 1st/2nd/3rd', 'y 1st/2nd/3rd', 'eta 1st/2nd/3rd'

      subroutine init_hist
      ! Books all histograms via bookupeqbins / bookup
      end

      subroutine analysis(dsig0)
      implicit none
      real * 8 dsig0     ! event weight (or negative weight)
      ! 1. Loop over HEPEVT stable particles → ptrack array
      ! 2. Call fastjetppgenkt(ptrack, ntracks, R, palg, ptmin,
      !                        pj, numjets, jetvec)
      ! 3. Apply pT / rapidity cuts per threshold level
      ! 4. Fill all histograms via filld(name, value, dsig)
      end
```

--------------------------------

### POWHEG BOX Dijet Run Configuration (`powheg.input`)

Source: https://context7.com/powheg-box/v2/llms.txt

Configure collider setup, generation cuts, PDF sets, scale factors, integration grids, and optional flags for event generation.

```fortran
! ── Collider setup ───────────────────────────────────────────────
numevts 50000        ! number of POWHEG events to generate
ih1  1               ! beam 1: 1=proton, -1=antiproton
ih2  1               ! beam 2: 1=proton, -1=antiproton
ebeam1 3500d0        ! beam 1 energy [GeV]  (7 TeV LHC: 3500 each)
ebeam2 3500d0        ! beam 2 energy [GeV]

! ── Generation cut (REQUIRED for IR-safe dijets) ─────────────────
bornktmin 10d0       ! min pT of underlying Born 2→2 config [GeV]
                     ! Observables must be insensitive below this cut.
                     ! Recommended: bornktmin < (leading jet pT cut)/2

! ── PDF sets ─────────────────────────────────────────────────────
! Using built-in MLM PDFs (CTEQ6m = set 131):
ndns1 131
ndns2 131
! Using LHAPDF (CTEQ6m LHA = 10050) — requires PDF=lhapdf in Makefile:
! lhans1 10050
! lhans2 10050

! ── Scale factors ────────────────────────────────────────────────
#renscfact  1d0      ! renormalization scale = muref * renscfact
#facscfact  1d0      ! factorization scale   = muref * facscfact
                     ! muref = pT of underlying Born by default

! ── Integration grid ─────────────────────────────────────────────
use-old-grid    1    ! reuse pwggrids.dat if present
use-old-ubound  1    ! reuse pwgubound.dat if present
ncall1 20000         ! calls for importance-sampling grid construction
itmx1  5             ! grid iterations  (total: 100k calls, ~70 s)
ncall2 20000         ! calls for upper-bounding envelope
itmx2  5             ! upper-bound iterations

! ── Phase-space folding (reduces negative-weight fraction) ───────
foldcsi 5            ! folds in xi (collinear) variable
foldy   5            ! folds in rapidity
foldphi 2            ! folds in azimuth
                     ! total calls = ncall2*itmx2*foldcsi*foldy*foldphi = 5M

nubound 500000       ! calls for radiation upper-bound setup (Born only, fast)

! ── Optional flags ───────────────────────────────────────────────
withnegweights 1     ! allow negative-weight events (recommended)
doublefsr 1          ! suppress FSR emissions harder than emitter
                     ! strongly reduces spikes in showered output
#bornonly 1          ! LO-only underlying Born (no NLO corrections)
#testplots 1         ! produce NLO topdrawer histograms on-the-fly
                     ! (requires ANALYSIS=default)
#iseed 5421          ! fixed random seed
#manyseeds 1         ! parallel multi-seed runs; reads pwgseeds.dat
```

--------------------------------

### Configure HERWIG Shower Parameters (Fortran)

Source: https://context7.com/powheg-box/v2/llms.txt

Configures HERWIG shower parameters before hadron-level event generation from an LHEF file. Requires building with 'make main-HERWIG-lhef' and running the executable.

```fortran
! ── HERWIG interface (setup-HERWIG-lhef.f) ───────────────────────
! Build: make main-HERWIG-lhef
! Run (from the directory containing foo-powheg.input and bar.lhe):
!   ../main-HERWIG-lhef
!   Enter prefix: foo
!   Enter LHE file: bar.lhe
! Output: foo-POWHEG+HERWIG-output.top (topdrawer histograms)

      subroutine setup_HERWIG_parameters
      include 'HERWIG65.INC'
      ptrms  = 2.5d0    ! intrinsic pT spread [GeV]
      maxpr  = 2        ! max events printed
      PRSOF  = 0d0      ! disable soft underlying event
      SOFTME = .FALSE.  ! disable soft matrix-element correction
      end
```

--------------------------------

### Configure PYTHIA Shower Parameters (Fortran)

Source: https://context7.com/powheg-box/v2/llms.txt

Configures PYTHIA shower parameters, including tune selection and optional disabling of showering components for debugging. Build and run identically to the HERWIG interface.

```fortran
! ── PYTHIA interface (setup-PYTHIA-lhef.f) ───────────────────────
! Build: make main-PYTHIA-lhef
! Run identically to HERWIG above.
! Output: foo-POWHEG+PYTHIA-output.top

      subroutine setup_PYTHIA_tune
      call PYTUNE(320)  ! Perugia 0 tune (Feb 2009)
      end

      subroutine setup_PYTHIA_parameters
      ! mstp(86) = 1: limit MPI pT to be less than primary interaction pT
      !               (recommended for jet production; see arXiv:1012.3380)
      ! To disable showering components for speed (debugging):
      !   mstp(61)=0  ! no initial-state shower
      !   mstp(71)=0  ! no final-state shower
      !   mstp(81)=0  ! no multiple interactions
      !   mstp(111)=0 ! no hadronization
      end
```

--------------------------------

### QCD Coupling and Quark Mass Initialisation

Source: https://context7.com/powheg-box/v2/llms.txt

Initializes quark pole masses for the Les Houches interface and prints the strong coupling constant alpha_S at M_Z for verification. Default quark masses follow PYTHIA conventions.

```fortran
      subroutine init_couplings
      implicit none
      include 'pwhg_st.h'
      include 'pwhg_physpar.h'
      end
```

--------------------------------

### Building POWHEG BOX Dijet Executables

Source: https://context7.com/powheg-box/v2/llms.txt

Compile the main event generator and associated analysis or shower interface programs using 'make'.

```bash
# Build the main event generator
cd POWHEG-BOX/Dijet
make

# Build the offline LHE analysis program
make lhef_analysis

# Build the HERWIG shower interface
make main-HERWIG-lhef

# Build the PYTHIA shower interface
make main-PYTHIA-lhef
```

--------------------------------

### Subprocess Flavour List Initialisation

Source: https://context7.com/powheg-box/v2/llms.txt

Enumerates contributing 2->2 QCD subprocesses for dijet production and initializes POWHEG BOX flavour list arrays. Sets Born-level kinematic suppression exponents.

```fortran
      subroutine init_processes
      implicit none
      include 'nlegborn.h'
      integer nflav
      parameter (nflav=5)
      ! Sanity check: nlegborn must equal 4 for 2→2 dijet process
      ! Error if nlegborn.ne.4 → STOP
      end
```

--------------------------------

### NLO Fixed-Order Analysis (No Event Generation)

Source: https://context7.com/powheg-box/v2/llms.txt

Generate fixed-order NLO distributions without producing event files. This is achieved by setting `testplots = 1` and `numevts = 0` in the `powheg.input` file and running `pwhg_main`.

```bash
# ─── Step 4: NLO fixed-order analysis (no event generation) ─────
# In powheg.input, uncomment:
#   testplots 1
#   numevts 0
../pwhg_main
# Produces topdrawer output of fixed-order NLO distributions only.
```

--------------------------------

### Generate Born Phase-Space Kinematics (`born_phsp`)

Source: https://context7.com/powheg-box/v2/llms.txt

Generates underlying 2→2 Born kinematics (τ, y_cm, cos θ) using importance-sampled Monte Carlo. Sets momenta in `kn_cmpborn` and `kn_pborn` common blocks and computes the phase-space Jacobian `kn_jacborn`. Inputs are on a unit hypercube.

```Fortran
! File: Born_phsp.f
! Called by: POWHEG BOX integration driver (sigborn.f in POWHEG-BOX/)
!
! Inputs (unit hypercube):
!   xborn(1) → tau   (parton momentum fraction squared)
!   xborn(2) → y_cm  (partonic centre-of-mass rapidity)
!   xborn(3) → cos(theta1)  (scattering angle)
!
! Outputs (via common blocks):
!   kn_jacborn   – phase-space Jacobian
!   kn_sborn     – partonic centre-of-mass energy squared
!   kn_xb1/xb2  – Bjorken-x values
!   kn_cmpborn   – 4-momenta in the partonic CM frame
!   kn_pborn     – 4-momenta boosted to the lab frame

      subroutine born_phsp(xborn)
      implicit none
      include 'nlegborn.h'
      include 'pwhg_kn.h'
      real * 8 xborn(ndiminteg-3)

!     Phase-space boundaries:
!       4*kn_ktmin^2/S  < tau < 1
!       log(tau)/2      < y   < -log(tau)/2
!       -sqrt(1 - 4*kn_ktmin^2/(S*tau)) < cos(theta) < +sqrt(...)

!     Sampling mode (psgen=3, hardcoded): flat in log(tau) and
!     log((1-cos)/(1+cos)) — optimal for QCD t-channel poles.

!     After the call:
!       kn_born_pt2 = (1 - cos^2(theta)) * kn_sborn / 4
!       kn_cmpborn(0:3, 1:4) set (initial state: legs 1,2; final: 3,4)
!       kn_pborn(0:3, 1:4)   boosted to lab frame via mboost()
      end

```

--------------------------------

### Makefile Configuration for POWHEG BOX Dijet

Source: https://context7.com/powheg-box/v2/llms.txt

Configure compiler, PDF library, and analysis module by editing the top of the Makefile before running 'make'.

```makefile
# Makefile key switches (edit top of Makefile before running make)

# Choose compiler: gfortran or ifort
COMPILER=gfortran

# Choose PDF library: native (built-in MLM) or lhapdf
PDF=lhapdf

# Choose analysis module: none (stub) or default (FastJet-dependent)
ANALYSIS=default
```

--------------------------------

### Born Colour Assignment for Les Houches Output

Source: https://context7.com/powheg-box/v2/llms.txt

Assigns a probabilistic colour-flow configuration to the generated Born event for Les Houches output. It samples planar colour topologies weighted by colour amplitudes.

```fortran
      subroutine borncolour_lh
      implicit none
      include 'LesHouches.h'
      include 'nlegborn.h'
      ! icolup(1:2, 1:4) filled on return
      end
```

--------------------------------

### Build POWHEG-BOX for Dijet Generation

Source: https://context7.com/powheg-box/v2/llms.txt

Compile the POWHEG-BOX code for dijet processes. Ensure the Makefile is configured with the desired compiler (e.g., gfortran) and PDF library (e.g., lhapdf). This step produces the main executable.

```bash
# ─── Step 1: Build ───────────────────────────────────────────────
cd POWHEG-BOX/Dijet
# Edit Makefile: COMPILER=gfortran, PDF=lhapdf, ANALYSIS=default
make                     # produces pwhg_main
```

--------------------------------

### Parallel Multi-Seed Runs for Clusters

Source: https://context7.com/powheg-box/v2/llms.txt

Configure POWHEG-BOX for parallel execution using multiple seeds, suitable for cluster environments. Enable `manyseeds = 1` in `powheg.input` and provide a list of seeds in `pwgseeds.dat`. Run `pwhg_main` multiple times, each with a different seed, and then merge the resulting LHE files for analysis.

```bash
# ─── Step 5: Parallel multi-seed runs (cluster) ──────────────────
# In powheg.input, uncomment:
#   manyseeds 1
# Create pwgseeds.dat with one integer seed per line.
# Run pwhg_main N times (one per seed); each writes pwgevents-N.lhe.
# Merge and analyse with lhef_analysis across all event files.
```

--------------------------------

### Compute Born Matrix Elements and Colour Correlators (`setborn`)

Source: https://context7.com/powheg-box/v2/llms.txt

Computes the Born cross section and the full colour-correlated matrix element matrix for a given 4-momentum configuration and flavour structure using the Kunszt–Soper classification. Outputs include spin-correlated tensors for gluon legs.

```Fortran
! File: Born.f
! Inputs:
!   p(0:3, nlegborn) – 4-momenta of all legs
!   bflav(nlegborn)  – PDG flavour codes (0=gluon, ±1..5=quarks)
! Outputs:
!   born             – spin/colour-averaged |M|^2 at Born level
!   bornjk(j,k)      – colour-correlated Born: <M| T_j·T_k |M>
!   bmunu(0:3,0:3,i) – spin-correlated tensor for gluon legs

!   Process class mapping (Kunszt-Soper Phys.Rev.D46:192):
!     A: q Q → q Q  (different quark flavours, and crossings)
!     B: q q → q q  (identical quarks)
!     C: q q̄ → g g  (quark-antiquark annihilation to gluons)
!     D: g g → g g  (pure gluon scattering)

!   Example: gluon-gluon scattering (D-type)
!   bflav = [0, 0, 0, 0]
!   →  spin_col_avg = 4*(N_c^2-1)^2
!   →  bornjk uses HDsFn, HDtFn, HDuFn for s/t/u channels

!   Helicity amplitudes (from Kunszt-Soper eq. A8/A11):
!     HAtFn(p1,p2,p3,p4) = 2*(s^2 + u^2)/t^2    [A-type, t-channel]
!     HAuFn = HAtFn with p3↔p4                   [A-type, u-channel]
!     HBFn  = 2*s^2/(t*u)                        [B-type]
!     HCtFn = 2*(t^2+u^2)/s^2 * t/u              [C-type, t-channel]
!     HCsFn = 2*(t^2+u^2)/(t*u)                  [C-type, s-channel]
!     HDsFn = 2*(t^2+u^2)*(s^4+t^4+u^4)/(stu)^2 [D-type, s-channel]

      subroutine setborn(p, bflav, born, bornjk, bmunu)
      implicit none
      include 'nlegborn.h'
      real * 8 p(0:3, nlegborn)
      integer  bflav(nlegborn)
      real * 8 born
      real * 8 bornjk(nlegborn, nlegborn)   ! colour correlator matrix
      real * 8 bmunu(0:3, 0:3, nlegborn)    ! spin correlator (gluons only)
      ! ... see Born.f for full implementation
      end

```

--------------------------------

### Shower Events with PYTHIA

Source: https://context7.com/powheg-box/v2/llms.txt

Apply parton showering to the generated POWHEG events using PYTHIA. This step requires compiling the PYTHIA integration tool and running it with the LHEF event file as input.

```bash
# ─── Step 3b: Shower with PYTHIA ────────────────────────────────
cd POWHEG-BOX/Dijet
make main-PYTHIA-lhef
cd testrun-lhc
../main-PYTHIA-lhef
# Prompts: prefix and LHE filename
# Output: testrun-lhc-POWHEG+PYTHIA-output.top
```

--------------------------------

### Tevatron Configuration for POWHEG.input

Source: https://context7.com/powheg-box/v2/llms.txt

This configuration is for the Tevatron collider (√s = 1.96 TeV) using antiprotons. It specifies the number of events, beam types, energies, and PDF sets.

```fortran
! Key differences from the LHC configuration:
numevts 50000
ih1  1               ! proton
ih2 -1               ! antiproton   ← difference from LHC
ebeam1 980d0         ! √s = 1.96 TeV Tevatron  ← difference
ebeam2 980d0
bornktmin 10d0
ndns1 131            ! CTEQ6m (MLM)
ndns2 131
! withnegweights commented out → positive weights only (default)
```

--------------------------------

### Generate POWHEG Events for LHC Dijet

Source: https://context7.com/powheg-box/v2/llms.txt

Run the compiled POWHEG executable to generate dijet events at the LHC. Configure key parameters in `powheg.input`, such as the number of events, beam energies, and generation cuts. This process produces LHEF event files and analysis histograms.

```bash
# ─── Step 2: Generate POWHEG events at the LHC ──────────────────
cd testrun-lhc
# powheg.input (key parameters):
#   numevts  50000
#   ih1/ih2  1 1       (pp collisions)
#   ebeam1/2 3500d0    (√s = 7 TeV)
#   bornktmin 10d0     (generation cut)
#   withnegweights 1
#   doublefsr 1
../pwhg_main
# Output files:
#   pwgevents.lhe          – 50000 POWHEG events in Les Houches format
#   pwgpwhgalone-output.top – topdrawer histograms (if ANALYSIS=default)
#   pwggrids.dat           – importance-sampling grid (cached)
#   pwgubound.dat          – upper-bound normalisations (cached)
# Performance: ~1 hour initialisation + ~5 events/second
```

--------------------------------

### Fortran Momentum-Space Kinematic Helpers

Source: https://context7.com/powheg-box/v2/llms.txt

These Fortran subroutines calculate common kinematic observables for particle momenta, such as transverse momentum, invariant mass, rapidity, pseudorapidity, and angular separations. They are used in the analysis and Born modules of POWHEG-BOX.

```fortran
      subroutine pwhg_getpt(p, pt)
      real * 8 p(4), pt
      pt = sqrt(p(1)**2 + p(2)**2)
      end
```

```fortran
      subroutine pwhg_getinvmass(p, m)
      real * 8 p(4), m
      real * 8 arg
      arg = p(4)**2 - p(1)**2 - p(2)**2 - p(3)**2
      m = sign(1.d0, arg) * sqrt(abs(arg))
      end
```

```fortran
      subroutine pwhg_getrapidity(p, y)
      real * 8 p(4), y
      ! y = 0.5 * log((E + pz)/(E - pz))
      ! Returns ±1e8 if E ≤ 0 or |pz/E| ≥ 1 (collinear protection)
      end
```

```fortran
      subroutine pwhg_getpseudorapidity(p, eta)
      real * 8 p(4), eta
      ! eta = 0.5 * log((1 + cos θ)/(1 - cos θ)) = -ln(tan(θ/2))
      end
```

```fortran
      subroutine pwhg_getdelta_azi(p1, p2, delphi)
      real * 8 p1(4), p2(4), delphi
      ! delphi = |phi1 - phi2|, folded into [0, pi]
      end
```

```fortran
      subroutine pwhg_getR_phieta(p1, p2, R)
      real * 8 p1(4), p2(4), R
      ! R = sqrt((eta1-eta2)^2 + delphi^2)   [anti-kT cone metric]
      end
```

```fortran
      subroutine pwhg_getR_phiy(p1, p2, R)
      real * 8 p1(4), p2(4), R
      ! R = sqrt((y1-y2)^2 + delphi^2)   [rapidity-based cone metric]
      end
```

```fortran
      function pwhg_ptrel(pin, pjet)
      real * 8 pwhg_ptrel, pin(0:3), pjet(0:3)
      ! ptrel = |pin| * sin(angle between pin and pjet)
      end
```

```fortran
      subroutine getyetaptmass(p, y, eta, pt, mass)
      real * 8 p(4), y, eta, pt, mass
      ! Single call returning all four common jet observables
      end
```

```fortran
      subroutine getdydetadphidr(p1, p2, dy, deta, dphi, dr)
      real * 8 p1(*), p2(*), dy, deta, dphi, dr
      ! Returns: Δy, Δη, Δφ ∈ [0,π], ΔR = sqrt(Δη^2 + Δφ^2)
      end
```

--------------------------------

### Shower Events with HERWIG

Source: https://context7.com/powheg-box/v2/llms.txt

Apply parton showering to the generated POWHEG events using HERWIG. Similar to PYTHIA, this involves compiling the HERWIG integration tool and running it with the LHEF event file.

```bash
# ─── Step 3c: Shower with HERWIG ────────────────────────────────
cd POWHEG-BOX/Dijet
make main-HERWIG-lhef
cd testrun-lhc
../main-HERWIG-lhef
# Output: testrun-lhc-POWHEG+HERWIG-output.top
```

--------------------------------

### Set Factorization and Renormalization Scales (`set_fac_ren_scales`)

Source: https://context7.com/powheg-box/v2/llms.txt

Sets the factorization scale `muf` and renormalization scale `mur` for NLO calculations and the POWHEG Sudakov form factor. The default is the transverse momentum of the underlying Born configuration. Scale variation for uncertainty bands is supported via `powheg.input`.

```Fortran
! File: Born_phsp.f
! Called every time a Born configuration is generated.
!
! Default:  mur = muf = muref = pT(underlying Born)
!           = sqrt(kn_cmpborn(1,3)^2 + kn_cmpborn(2,3)^2)
!
! Fixed scale override via powheg.input:
!   fixedscale <value>   → mur = muf = <value> GeV  (constant)
!
! Scale variation (NLO uncertainty bands) via powheg.input:
!   renscfact 0.5d0      → mur = muref * 0.5  (half scale)
!   facscfact 2d0        → muf = muref * 2.0  (double scale)

      subroutine set_fac_ren_scales(muf, mur)
      implicit none
      include 'nlegborn.h'
      include 'pwhg_kn.h'
      real * 8 muf, mur
      ! muref = pT of outgoing parton leg 3 in partonic CM frame
      ! (kn_cmpborn(1,3) = px,  kn_cmpborn(2,3) = py)
      end

```

--------------------------------

### Born Suppression Factor Calculation

Source: https://context7.com/powheg-box/v2/llms.txt

Applies a smooth suppression factor to Born configurations at low pT. Controlled by `bornsuppfact` in `powheg.input`. A negative value disables suppression.

```fortran
      subroutine born_suppression(fact)
      implicit none
      real * 8 fact   ! output: suppression weight in [0, 1]
      ! fact = (pt2 / (pt2 + pt2supp))^3
      ! where pt2 = kn_cmpborn(1,3)^2 + kn_cmpborn(2,3)^2
      end
```

--------------------------------

### Offline LHE Event Analysis

Source: https://context7.com/powheg-box/v2/llms.txt

Perform an offline analysis of the generated LHEF events using the `lhef_analysis` tool. This tool generates topdrawer histograms from the LHE file, providing a direct comparison to the online analysis output.

```bash
# ─── Step 3a: Offline LHE analysis ──────────────────────────────
cd POWHEG-BOX/Dijet
make lhef_analysis
cd testrun-lhc
../lhef_analysis
# Prompts: enter prefix "testrun-lhc" and event file "pwgevents.lhe"
# Output: LHEF_analysis.top   (identical to pwgpwhgalone-output.top)
```

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