Particael
EN

A new workspace for particle physics

Developed with academic guidance.

Recorded LO and NLO cross sectionsFive recorded mass points from 300 to 2500 GeV at 14 TeV. Cross section in pb on a logarithmic scale. Shading is NLO seven-point scale variation. Depth separates calculation series, not a physical observable.10⁻⁸10⁻⁶10⁻⁴10⁻²10⁻¹30010002500Particle mass m [GeV]Cross section σ [pb]
  • LO (Born)
  • NLO
Pair production · 14 TeV · NLO scale variation
Five recorded mass points · Data

Calculations

Explore cross sections and distributions from recorded calculations.

Calculation method

LO

Tree-level prediction

Leading-order cross section

pp · 14 TeV
Leading-order production ratesLO cross sections and their scale envelope. The vertical axis is logarithmic. 30060010001500250010⁻⁷10⁻⁵10⁻³10⁻¹Cross section σ [pb]Particle mass m [GeV]Leading-order production ratesLO cross sections and their scale envelope. The vertical axis is logarithmic. 3001000250010⁻⁷10⁻⁵10⁻³10⁻¹Cross section σ [pb]Particle mass m [GeV]
LOScale variation
Scale variation around the central cross section.
Data and calculation details

This recorded calculation has not yet been validated for publication. Here, LO means the Born contribution evaluated with the same PDF set as NLO.

The tree-level cross section across the particle mass scan.

The production cross section falls across the particle mass scan. A tree-level calculation supplies the baseline against which radiative corrections are compared.

The shaded region follows the seven-point scale variation at each calculated mass. Both the absolute rate and its scale dependence belong to the specified process and setup.

Collision
pp · 14 TeV
Mass scan
300–2500 GeV
PDF
CT18NNLO
Scales
μR = μF = Mpair

This example uses the shared fixed-order setup. Scale and PDF uncertainty are distinct; no PDF or Monte Carlo integration uncertainty is included in these bands. Connecting segments guide the eye.

Particael calculation

Download data · CSVDownload figure · SVGMethods and sources
Plotted numeric values
Mass [GeV]LO [pb]LO scale min [pb]LO scale max [pb]NLO [pb]NLO scale min [pb]NLO scale max [pb]
3000.02234110.021744040.022939110.0265466330.0261879240.026949086
6000.00115779860.00109229190.00123040960.00142178420.00138870540.0014538487
10007.7774148e-057.1637334e-058.4826843e-059.8257854e-059.50051e-050.00010129836
15005.1161499e-064.6120172e-065.7104542e-066.6995559e-066.4080702e-066.9706241e-06
25004.0191048e-083.500969e-084.6524205e-085.6636245e-085.3094488e-085.9989013e-08

Scale dependence at leading order

pp · 14 TeV
Relative scale dependence at LO100 × (σvariation / σcentral − 1), using the same seven-point prescription at every mass. 300600100015002500-15-1001015Scale variation [%]Particle mass m [GeV]Relative scale dependence at LO100 × (σvariation / σcentral − 1), using the same seven-point prescription at every mass. 30010002500-15015Scale variation [%]Particle mass m [GeV]
LO scale envelope
Seven-point scale variation relative to the central value.
Data and calculation details

This recorded calculation has not yet been validated for publication. Here, LO means the Born contribution evaluated with the same PDF set as NLO.

Varying the renormalisation and factorisation scales probes the dependence on unphysical scale choices at a fixed perturbative order.

The envelope is expressed relative to the central cross section at each mass, so the change in sensitivity can be compared along the scan.

Collision
pp · 14 TeV
Mass scan
300–2500 GeV
PDF
CT18NNLO
Scales
μR = μF = Mpair

This example uses the shared fixed-order setup. Scale and PDF uncertainty are distinct; no PDF or Monte Carlo integration uncertainty is included in these bands. Connecting segments guide the eye.

Particael calculation

Download data · CSVDownload figure · SVGMethods and sources
Plotted numeric values
Mass [GeV]LO min [%]LO max [%]NLO min [%]NLO max [%]
300-2.67247362.6767259-1.3512411.5160228
600-5.65786666.2714707-2.32656972.2552297
1000-7.89055779.0681739-3.31042653.0944152
1500-9.853751511.616241-4.35082124.0460622
2500-12.89182115.757631-6.25351665.9198275

Calculation method

NLO

Virtual and real-emission QCD

NLO / LO ratio

pp · 14 TeV
NLO corrections relative to LOK = σNLO / σLO,central. The band varies the NLO numerator and keeps the LO denominator fixed. 3006001000150025001.11.21.31.41.5K = σNLO / σLOParticle mass m [GeV]NLO corrections relative to LOK = σNLO / σLO,central. The band varies the NLO numerator and keeps the LO denominator fixed. 300100025001.11.21.31.41.5K = σNLO / σLOParticle mass m [GeV]
NLO / central LONLO scale variation
NLO scale variation, normalised to a fixed central LO value.
Data and calculation details

This recorded calculation has not yet been validated for publication. Here, LO means the Born contribution evaluated with the same PDF set as NLO.

The K-factor expresses the NLO cross section as a ratio to the central LO result. Across this scan, it rises from 1.188 at 300 GeV to 1.409 at 2500 GeV.

The denominator is fixed when constructing the band. This isolates NLO scale variation and avoids treating two independently varied predictions as one uncertainty.

Collision
pp · 14 TeV
Mass scan
300–2500 GeV
PDF
CT18NNLO
Scales
μR = μF = Mpair

This example uses the shared fixed-order setup. Scale and PDF uncertainty are distinct; no PDF or Monte Carlo integration uncertainty is included in these bands. Connecting segments guide the eye.

Particael calculation

Download data · CSVDownload figure · SVGMethods and sources
Plotted numeric values
Mass [GeV]KNLO scale min / LONLO scale max / LO
3001.1882421.1721861.206256
6001.22800651.19943611.2557009
10001.26337421.22155121.3024683
15001.30949171.25251811.3624746
25001.40917561.32105261.4925964

NLO cross section

pp · 14 TeV
Cross sections at NLO QCDCentral LO and NLO rates across five recorded masses. The band is the NLO seven-point scale envelope. 30060010001500250010⁻⁷10⁻⁵10⁻³10⁻¹Cross section σ [pb]Particle mass m [GeV]Cross sections at NLO QCDCentral LO and NLO rates across five recorded masses. The band is the NLO seven-point scale envelope. 3001000250010⁻⁷10⁻⁵10⁻³10⁻¹Cross section σ [pb]Particle mass m [GeV]
NLO QCDLO referenceNLO scale variation
NLO scale variation, with the central LO reference.
Data and calculation details

This recorded calculation has not yet been validated for publication. Here, LO means the Born contribution evaluated with the same PDF set as NLO.

NLO and Born predictions from the same calculation setup.

Virtual and real-emission QCD contributions modify the leading-order prediction. Here the NLO rate is compared with the Born contribution from the same calculation setup.

The solid curve carries the NLO scale envelope; the dashed curve is the LO reference. A narrower scale band is one diagnostic of perturbative stability, not a complete uncertainty estimate.

Collision
pp · 14 TeV
Mass scan
300–2500 GeV
PDF
CT18NNLO
Scales
μR = μF = Mpair

This example uses the shared fixed-order setup. Scale and PDF uncertainty are distinct; no PDF or Monte Carlo integration uncertainty is included in these bands. Connecting segments guide the eye.

Particael calculation

Download data · CSVDownload figure · SVGMethods and sources
Plotted numeric values
Mass [GeV]LO [pb]LO scale min [pb]LO scale max [pb]NLO [pb]NLO scale min [pb]NLO scale max [pb]
3000.02234110.021744040.022939110.0265466330.0261879240.026949086
6000.00115779860.00109229190.00123040960.00142178420.00138870540.0014538487
10007.7774148e-057.1637334e-058.4826843e-059.8257854e-059.50051e-050.00010129836
15005.1161499e-064.6120172e-065.7104542e-066.6995559e-066.4080702e-066.9706241e-06
25004.0191048e-083.500969e-084.6524205e-085.6636245e-085.3094488e-085.9989013e-08

LO and NLO scale dependence

pp · 14 TeV
Scale dependence at LO and NLOScale variation relative to the corresponding LO or NLO central prediction. Zero denotes each central value. 300600100015002500-15-1001015Scale variation [%]Particle mass m [GeV]Scale dependence at LO and NLOScale variation relative to the corresponding LO or NLO central prediction. Zero denotes each central value. 30010002500-15015Scale variation [%]Particle mass m [GeV]
LO envelopeNLO envelope
Scale variation relative to each central prediction.
Data and calculation details

This recorded calculation has not yet been validated for publication. Here, LO means the Born contribution evaluated with the same PDF set as NLO.

The two envelopes use the same mass points and scale-variation prescription. Each is normalised to its own central cross section.

In this scan, the NLO scale envelope is narrower at every mass point. This comparison shows the remaining scale dependence; PDF and numerical integration uncertainties must be considered separately.

Collision
pp · 14 TeV
Mass scan
300–2500 GeV
PDF
CT18NNLO
Scales
μR = μF = Mpair

This example uses the shared fixed-order setup. Scale and PDF uncertainty are distinct; no PDF or Monte Carlo integration uncertainty is included in these bands. Connecting segments guide the eye.

Particael calculation

Download data · CSVDownload figure · SVGMethods and sources
Plotted numeric values
Mass [GeV]LO min [%]LO max [%]NLO min [%]NLO max [%]
300-2.67247362.6767259-1.3512411.5160228
600-5.65786666.2714707-2.32656972.2552297
1000-7.89055779.0681739-3.31042653.0944152
1500-9.853751511.616241-4.35082124.0460622
2500-12.89182115.757631-6.25351665.9198275

Calculation method

NLO+PS

Matched parton shower

Pair transverse momentum

pp · 100 TeV · m = 1800 GeV84 bins · 60 GeV per bin
MG5 heavy pair transverse momentum: central histogram, relative uncertainty and CUT to NOCUT ratio84 bins from 0 to 5040 GeV. Bin cross sections in pb, Monte Carlo errors and the recorded CUT/NOCUT ratio. Reconstructed from the HwU data and gnuplot recipe, with Tahoma typography. Zero-valued bins are gaps in the logarithmic panel.heavy pair ptMG5_aMC@NLO + Pythia8σ per bin [pb]10⁻⁷10⁻⁶10⁻⁵10⁻⁴Relative MC uncertainty-101CUT / NOCUT-2-101010002000300040005040Pair transverse momentum pT [GeV]NOCUTCUT
Cross section per bin; bars show Monte Carlo errors.
Data and calculation details

The 3D view shows the main histogram. Switch to 2D to see the relative MC uncertainty and the AUX diagnostic panel as well.

The original simulation bins, with two selections and Monte Carlo errors.

Collision
pp · 100 TeV
Particle mass
1800 GeV
Bin width
60 GeV
Uncertainty
Monte Carlo integration error

The histogram preserves the individual bins produced by the event simulation. Inspect the tail, compare the two selections, or switch to the flat figure for the original three-panel arrangement.

This figure was redrawn from the recorded MG5 HwU output and its gnuplot instructions. The 2D view preserves the histogram steps, axis ranges, per-bin units, MC errors and CUT/NOCUT ratio, with typography adapted to the site. It is a rendering of the calculation data, rather than an image exported by MG5.

The 3D view displays the main cross-section panel. Depth separates the two selections; it is not an additional physical observable. The 2D figure also shows relative MC uncertainties and the ratio stored in the AUX histogram. Zero bins are retained in this table and appear as gaps on the logarithmic axis. Error bars are clipped at the plot limits.

Download all bins · CSVDownload 2D figure · SVGMethods and sources
All 84 original bins, including zero-valued bins
Bin min [GeV]Bin max [GeV]NOCUT [pb/bin]NOCUT MC error [pb/bin]CUT [pb/bin]CUT MC error [pb/bin]CUT/NOCUTCUT/NOCUT error
0600.0002527213.585215e-060.00019390893.130864e-060.767284480.016491273
601200.00015105672.83877e-060.00011728242.491054e-060.77641310.022019164
1201809.644199e-052.253579e-067.467421e-051.980132e-060.774291470.027366295
1802406.828054e-051.90846e-065.26136e-051.675143e-060.770550440.032645468
2403005.080775e-051.631195e-063.855727e-051.426291e-060.75888560.03717081
3003604.114403e-051.474737e-063.118747e-051.284831e-060.758007180.041392576
3604203.201718e-051.283903e-062.474498e-051.13101e-060.772865690.046993429
4204802.684367e-051.177445e-061.966909e-051.00854e-060.732727310.04944216
4805402.381766e-051.097879e-061.776563e-059.489102e-070.745901570.052625354
5406001.737518e-059.6138e-071.31778e-058.397018e-070.758426680.064004377
6006601.53253e-058.812275e-071.103031e-057.497824e-070.719745130.064081513
6607201.53741e-058.771634e-071.107912e-057.481922e-070.720635350.063709075
7207801.132315e-057.465986e-078.492361e-066.474937e-070.749999870.075600165
7808401.107912e-057.450016e-078.297135e-066.474937e-070.748898380.077146301
8409009.810142e-067.022058e-077.321001e-066.056749e-070.746268610.081640832
9009609.224462e-066.709808e-076.881741e-065.795472e-070.746031690.083018292
96010208.394748e-066.438043e-076.442481e-065.649781e-070.767441860.089406483
102010808.004295e-066.250304e-076.003221e-065.412922e-070.749999970.089459754
108011407.125775e-065.937588e-075.417541e-065.188221e-070.760273940.096511301
114012005.807994e-065.32418e-074.099761e-064.473206e-070.705882440.10059289
120012605.271121e-065.072138e-073.514081e-064.141384e-070.666666730.10143011
126013203.806921e-064.310489e-072.733174e-063.652357e-070.71794870.12574898
132013804.929474e-065.001196e-073.806921e-064.419632e-070.772277330.11906873
138014404.050954e-064.4465e-073.123627e-063.904534e-070.771084290.1282719
144015003.904534e-064.365402e-073.026014e-063.843041e-070.775000040.1311309
150015603.318854e-064.024702e-072.48914e-063.485494e-070.749999850.13892973
156016203.026014e-063.843041e-072.586754e-063.55318e-070.854838740.15991872
162016802.830787e-063.717006e-072.391527e-063.416467e-070.84482760.16392605
168017402.1963e-063.346017e-071.659427e-062.9284e-070.755555710.17614617
174018002.245107e-063.31023e-071.854654e-063.008646e-070.826087130.18109014
180018601.75704e-062.9284e-071.17136e-062.391029e-070.666666670.17568211
186019201.805847e-062.968794e-071.561814e-062.760922e-070.864865070.20878387
192019801.366587e-062.582606e-071.02494e-062.236603e-070.749999820.2165063
198020401.854654e-063.008646e-071.708234e-062.887442e-070.921052660.21578439
204021001.366587e-062.582606e-071.268974e-062.488662e-070.928571690.25289865
210021601.02494e-062.236603e-071.02494e-062.236603e-0710.30860678
216022201.659427e-062.845894e-071.561814e-062.760922e-070.941176680.23180809
222022808.297135e-072.012351e-075.856801e-071.690713e-070.705882330.26614375
228023401.122554e-062.340686e-079.273268e-072.127434e-070.826086580.25609993
234024009.761335e-072.182701e-078.785201e-072.070692e-070.899999950.29240384
240024607.321001e-071.890274e-077.321001e-071.890274e-0710.36514831
246025209.273268e-072.127434e-078.297135e-072.012351e-070.894736890.298707
252025802.440334e-071.09135e-072.440334e-071.09135e-0710.63245522
258026404.392601e-071.4642e-074.392601e-071.4642e-0710.47140441
264027008.785201e-072.070692e-078.785201e-072.070692e-0710.33333338
270027602.9284e-071.195514e-072.9284e-071.195514e-0710.57735013
276028207.321001e-071.890274e-076.832934e-071.826179e-070.93333330.34683758
282028804.392601e-071.4642e-074.392601e-071.4642e-0710.47140441
288029403.904534e-071.380461e-073.904534e-071.380461e-0710.49999992
294030003.904534e-071.380461e-073.904534e-071.380461e-0710.49999992
300030604.392601e-071.4642e-073.416467e-071.291303e-070.777777680.39196304
306031202.440334e-071.09135e-071.952267e-079.761335e-080.799999920.53665614
312031802.440334e-071.09135e-071.952267e-079.761335e-080.799999920.53665614
318032402.9284e-071.195514e-072.9284e-071.195514e-0710.57735013
324033002.440334e-071.09135e-072.440334e-071.09135e-0710.63245522
330033604.392601e-071.4642e-074.392601e-071.4642e-0710.47140441
33603420000000
342034802.9284e-071.195514e-072.9284e-071.195514e-0710.57735013
348035409.761335e-086.902306e-089.761335e-086.902306e-0810.99999998
354036002.9284e-071.195514e-072.9284e-071.195514e-0710.57735013
360036604.880667e-084.880667e-084.880667e-084.880667e-0811.4142136
366037201.4642e-078.453564e-089.761335e-086.902306e-080.666666780.60858075
372037809.761335e-086.902306e-089.761335e-086.902306e-0810.99999998
378038409.761335e-086.902306e-089.761335e-086.902306e-0810.99999998
38403900000000
390039602.440334e-071.09135e-072.440334e-071.09135e-0710.63245522
396040209.761335e-086.902306e-089.761335e-086.902306e-0810.99999998
402040804.880667e-084.880667e-084.880667e-084.880667e-0811.4142136
408041401.952267e-079.761335e-081.4642e-078.453564e-080.749999870.57282192
414042009.761335e-086.902306e-089.761335e-086.902306e-0810.99999998
420042601.4642e-078.453564e-081.4642e-078.453564e-0810.81649671
426043209.761335e-086.902306e-089.761335e-086.902306e-0810.99999998
432043804.880667e-084.880667e-080000
438044404.880667e-084.880667e-084.880667e-084.880667e-0811.4142136
444045001.4642e-078.453564e-081.4642e-078.453564e-0810.81649671
450045601.4642e-078.453564e-081.4642e-078.453564e-0810.81649671
45604620000000
46204680000000
46804740000000
474048001.4642e-078.453564e-081.4642e-078.453564e-0810.81649671
480048609.761335e-086.902306e-089.761335e-086.902306e-0810.99999998
48604920000000
492049804.880667e-084.880667e-084.880667e-084.880667e-0811.4142136
498050404.880667e-084.880667e-084.880667e-084.880667e-0811.4142136

Pair transverse momentum

Particle pair · m = 1800 GeVpp · 100 TeV
Distributions after the parton showerBin-centre values of dσ/dpT, shown up to 3000 GeV. Central distributions are shown; no uncertainty band is implied. 010002000300010⁻¹⁰10⁻⁹10⁻⁸10⁻⁷10⁻⁶10⁻⁵dσ/dpT [pb/GeV]Pair pT [GeV]Distributions after the parton showerBin-centre values of dσ/dpT, shown up to 3000 GeV. Central distributions are shown; no uncertainty band is implied. 01500300010⁻¹⁰10⁻⁸10⁻⁶10⁻⁵dσ/dpT [pb/GeV]Pair pT [GeV]
NLO + showerLO + shower
Central distributions; no uncertainty band is shown.
Data and calculation details

The pair transverse momentum after matching to a parton shower.

Matching a fixed-order calculation to a parton shower produces event-level predictions for radiation-sensitive observables. This example shows the transverse momentum of a particle pair.

The two curves compare LO and NLO calculations matched to Pythia 8, with the same collision energy and particle mass.

Collision
pp · 100 TeV
Mass
1800 GeV
PDF
CT18NNLO
Shower
Pythia 8

The bin edges and central differential cross sections are retained in the data table. The scale prescription is the pair invariant mass. Non-positive bins are not connected on the logarithmic axis. No scale or PDF band is drawn in this view.

Particael calculation

Download data · CSVDownload figure · SVGMethods and sources
Plotted numeric values
pT centre [GeV]Bin min [GeV]Bin max [GeV]LO+PS [pb/GeV]NLO+PS [pb/GeV]
300603.97163e-064.2120167e-06
90601202.4114183e-062.5176117e-06
1501201801.5274983e-061.6073665e-06
2101802401.0915472e-061.138009e-06
2702403007.6508433e-078.4679583e-07
3303003605.494455e-076.8573383e-07
3903604204.699995e-075.3361967e-07
4504204803.8187467e-074.473945e-07
5104805403.251275e-073.96961e-07
5705406002.4100833e-072.8958633e-07
6306006602.1497133e-072.5542167e-07
6906607201.649004e-072.56235e-07
7507207801.5221575e-071.8871917e-07
8107808401.3151975e-071.84652e-07
8708409001.2551123e-071.6350237e-07
9309009601.0548285e-071.5374103e-07
99096010201.0214478e-071.3991247e-07
1050102010807.3437417e-081.3340492e-07
1110108011406.0752783e-081.1876292e-07
1170114012006.3423233e-089.67999e-08
1230120012604.940335e-088.7852017e-08
1290126013204.940335e-086.3448683e-08
1350132013805.14062e-088.21579e-08
1410138014404.0724383e-086.75159e-08
1470144015002.4034067e-086.5075567e-08
1530150015603.5383483e-085.5314233e-08
1590156016202.4034067e-085.0433567e-08
1650162016802.5369283e-084.7179783e-08
1710168017402.6704517e-083.6605e-08
1770174018001.4019872e-083.741845e-08
1830180018601.2017033e-082.9284e-08
1890186019201.134942e-083.009745e-08
1950192019801.0681807e-082.277645e-08
2010198020409.3465817e-093.09109e-08
2070204021007.3437417e-092.277645e-08
2130210021601.0014193e-081.7082333e-08
2190216022202.0028383e-092.7657117e-08
2250222022802.0028383e-091.3828558e-08
2310228023402.6704517e-091.8709233e-08
2370234024001.3352258e-091.6268892e-08
2430240024602.6704517e-091.2201668e-08
2490246025201.3352258e-091.5455447e-08
25502520258004.0672233e-09
26102580264007.3210017e-09
2670264027001.3352258e-091.4642002e-08
2730270027606.67613e-104.8806667e-09
2790276028206.67613e-101.2201668e-08
28502820288007.3210017e-09
2910288029401.3352258e-096.5075567e-09
2970294030006.67613e-106.5075567e-09

Calculation method

aNNLO+NNLL

Threshold resummation

Invariant-mass spectrum

Heavy charged-fermion pair · m = 1000 GeVpp · 13 TeV
Resummation relative to NLOCentral dσ/dM values normalised to NLO. Connecting segments guide the eye; no uncertainty band is drawn. 2100250030000.80.911.1(dσ/dM) / (dσ/dM)NLOPair invariant mass M [GeV]Resummation relative to NLOCentral dσ/dM values normalised to NLO. Connecting segments guide the eye; no uncertainty band is drawn. 2100250030000.80.911.1(dσ/dM) / (dσ/dM)NLOPair invariant mass M [GeV]
aNNLO+NNLL / NLOLO / NLONLO = 1
Three recorded points per series, relative to NLO.
Data and calculation details

The invariant mass of the pair fixes the observable and central scale in this recorded Resummino calculation. Dividing by the NLO result makes the relative correction visible.

The aNNLO+NNLL central prediction is 5.2% above NLO at M = 2100 GeV and 6.5% above it at M = 3000 GeV. The three markers are the recorded calculation points.

Collision
pp · 13 TeV
Mass
1000 GeV
PDF
PDF4LHC21_40
Scales
μR = μF = M

Recorded invariant-mass calculations at M = 2100, 2500 and 3000 GeV. The table contains the original differential cross sections in pb/GeV before normalisation. The central scale is the pair invariant mass M. These values are distinct from the published total-rate benchmark.

Recorded Resummino calculation

Download data · CSVDownload figure · SVGMethods and sources
Plotted numeric values
M [GeV]LO [pb/GeV]NLO [pb/GeV]aNNLO+NNLL [pb/GeV]
21007.2370748e-079.0836255e-079.5543134e-07
25003.88813e-074.9517922e-075.2344687e-07
30001.1288432e-071.4623819e-071.556987e-07

Published cross sections

Charged electroweak fermion pairpp · 13 TeV
Published threshold-resummed production ratesPublished charged-pair benchmark from the cited benchmark. Shading shows scale variation; PDF uncertainties are tabulated separately. Redrawn from Fiaschi et al., EPJC 83 (2023) 707, Table 6. CC BY 4.0. Central values and scale variations are transcribed from the printed table; layout and typography are adapted. Source: https://link.springer.com/article/10.1140/epjc/s10052-023-11888-y Licence: https://creativecommons.org/licenses/by/4.0/2005001000150010⁻⁵10⁻⁴10⁻³10⁻²10⁻¹1Cross section σ [pb]Particle mass m [GeV]Published threshold-resummed production ratesPublished charged-pair benchmark from the cited benchmark. Shading shows scale variation; PDF uncertainties are tabulated separately. Redrawn from Fiaschi et al., EPJC 83 (2023) 707, Table 6. CC BY 4.0. Central values and scale variations are transcribed from the printed table; layout and typography are adapted. Source: https://link.springer.com/article/10.1140/epjc/s10052-023-11888-y Licence: https://creativecommons.org/licenses/by/4.0/200800150010⁻⁴10⁻²1Cross section σ [pb]Particle mass m [GeV]
aNNLO+NNLLScale variation
Published reference; shading shows scale variation.
Data and calculation details

This published electroweak pair-production benchmark combines approximate NNLO QCD with next-to-next-to-leading logarithmic threshold resummation.

The shaded region follows the printed scale variations. PDF uncertainties are listed separately in the data table and are not included in this band.

Origin
Published reference
Mass range
200–1500 GeV
PDF
PDF4LHC21_40
Scales
μR = μF = m

The data come from the charged-pair column in the upper, 13 TeV block of Table 6: 14 rows covering masses from 200 to 1500 GeV. Central values are converted from fb to pb, and the quoted percentages determine the scale-band limits. PDF percentages are kept separately.

Redrawn from Fiaschi et al., EPJC 83 (2023) 707, Table 6. CC BY 4.0. Central values and scale variations are transcribed from the printed table; layout and typography are adapted.

Download data · CSVDownload figure · SVGMethods and sources
Plotted numeric values
Mass [GeV]aNNLO+NNLL [pb]Scale min [pb]Scale max [pb]PDF down [%]PDF up [%]
2000.94190.93059720.951319-3.33.3
3000.19820.19681260.1995874-4.14.1
4000.060870.060565650.06117435-4.94.9
5000.022890.022798440.02298156-5.85.8
6000.0097690.0097396930.009808076-6.96.9
7000.0045430.0045339140.004556629-8.18.1
8000.0022480.0022435040.002256992-9.59.5
9000.0011660.0011636680.001169498-11.411.4
10000.00062720.00062657280.0006290816-13.813.8
11000.00034740.00034705260.0003484422-16.916.9
12000.00019710.00019690290.0001976913-20.920.9
13000.00011410.00011398590.0001144423-25.825.8
14006.724e-056.717276e-056.744172e-05-31.931.9
15004.025e-054.020975e-054.03305e-05-39.439.4
Shared setup for the LO and NLO mass scans

Particle pair production at 14 TeV, using CT18NNLO for both displayed orders. The central renormalisation and factorisation scales are the pair invariant mass. Seven-point scale variation uses factors of 0.5, 1 and 2, excluding the two opposite extremes.

These examples use different setups. They should not be read as successive orders of the same calculation. Methods and sources →

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Methods and sources
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Calculated quantities

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Questions and answers

A closer look at the calculations, the figures and access to Particael.

What does Particael calculate?

Particael brings cross sections, differential distributions and parameter studies into a macOS application. LO, NLO QCD, parton-shower matching and threshold resummation apply to compatible processes.

What are the steps in a calculation?

The version under development lets you begin with a process, a model or a setup from the literature. From there, you can edit the MG5 script and follow the calculation in the integrated terminal. You can also reopen or export your project, with the inputs and settings for each process still available.

What does a shaded band represent?

Each figure explains how its uncertainties are defined. Scale variation, PDF uncertainty and Monte Carlo integration error describe different effects. A scale envelope is not a statistical confidence interval.

Can I see how a result was calculated?

Open “Data and calculation details” below a figure for its values, settings, source and downloadable CSV and SVG files. Changing between 3D and 2D preserves the recorded main-panel values. The native histogram also includes diagnostics in 2D.

Which research areas does Particael cover?

The model library covers leptons, neutrinos, gauge interactions, dark matter, effective field theories and quarks. The calculation methods available depend on the process you choose.

Which computers can run Particael?

Particael is being developed for Mac computers with Apple silicon. Each invited build comes with its own requirements and access instructions.

How can I hear about availability?

Particael is still in development. Release emails let you know about availability and new versions; they do not grant access to an invited build.

Is Particael affiliated with the software it uses?

Particael is independent of MadGraph5_aMC@NLO, Pythia 8, LHAPDF, Resummino and the other projects used in its workflows. Their software and publications remain the work of their authors.

Acknowledgements

We thank the researchers behind the physics models and publications, and the developers of MadGraph5_aMC@NLO, Pythia 8, LHAPDF, Resummino and the other open-source tools used in these workflows. You can find the full references in the application under Settings › About. This acknowledgement does not imply endorsement or affiliation.