5.2. Beam parameters

Mandatory settings to set up the colliding particle beams are

  • The initial beam particles specified through BEAMS, given by their PDG particle number. For (anti)protons and (positrons) electrons, for example, these are given by \((-)2212\) or \((-)11\), respectively. The code for photons is 22. If you provide a single particle number, both beams will consist of that particle type. If the beams consist of different particles, a list of two values have to be provided.

  • The energies of both incoming beams are defined through BEAM_ENERGIES, given in units of GeV. Again, single values apply to both beams, whereas a list of two values have to be given when the two beams do not have the same energy.

Examples would be

BEAMS: 2212

BEAMS: [-11, 2212]
BEAM_ENERGIES: [27.5, 820]

More options related to beamstrahlung and intrinsic transverse momentum can be found in the following subsections.

5.2.1. Beam Spectra

If desired, you can also specify spectra for beamstrahlung through BEAM_SPECTRA. The possible values are


The beam energy is unaltered and the beam particles remain unchanged. That is the default and corresponds to ordinary hadron-hadron or lepton-lepton collisions.


This can be used to describe the backscattering of a laser beam off initial leptons. The energy distribution of the emerging photon beams is modelled by the CompAZ parameterisation, see [Zar03]. Note that this parameterisation is valid only for the proposed TESLA photon collider, as various assumptions about the laser parameters and the initial lepton beam energy have been made. See details below.


This corresponds to a simple light backscattering off the initial lepton beam and produces initial-state photons with a corresponding energy spectrum. See details below.


This enables the equivalent photon approximation for colliding protons, see [AGH+08]. The resulting beam particles are photons that follow a dipole form factor parameterisation, cf. [BGMS74]. The authors would like to thank T. Pierzchala for his help in implementing and testing the corresponding code. See details below.


This enables the Proton–Pomeron flux for diffractive jet production, see details below.


This enables the Proton–Reggeon flux, see details below.

The BEAM_SMIN and BEAM_SMAX parameters may be used to specify the minimum/maximum fraction of cms energy squared after Beamstrahlung. The reference value is the total centre of mass energy squared of the collision, not the centre of mass energy after eventual Beamstrahlung.

The parameter can be specified using the internal interpreter, see Interpreter, e.g. as BEAM_SMIN: sqr(20/E_CMS). Laser Backscattering

The energy distribution of the photon beams is modelled by the CompAZ parameterisation, see [Zar03], with various assumptions valid only for the proposed TESLA photon collider. The laser energies can be set by E_LASER. P_LASER sets their polarisations, defaulting to 0.. Both settings can either be set to a single value, applying to both beams, or to a list of two values, one for each beam. The LASER_MODE takes the values -1, 0, and 1, defaulting to 0. LASER_ANGLES and LASER_NONLINEARITY can be set to true or to false (default). Simple Compton

This corresponds to a simple light backscattering off the initial lepton beam and produces initial-state photons with a corresponding energy spectrum. It is a special case of the above Laser Backscattering with LASER_MODE: -1. EPA

The equivalent photon approximation, cf. [AGH+08], [BGMS74], has a few free parameters, listed below. Each of these parameters has to be set in the subsetting EPA, like so

  Q2Max: 4.5

The usual rules for yaml structure apply, c.f. Input structure.


Parameter of the EPA spectra of the two beams, defaults to 3. in units of GeV squared. For the electron, the maximum virtuality is taken to be the minimum of this value and the kinematical limit, given by

\[Q^2_{max,kin} = \frac{(m_e x)^2}{1-x} + E_e^2 (1-x) \theta^2_{max}\]

with \(m_e\) the electron mass, \(E_e\) the electron energy, \(x\) the energy fraction that the photon carries and \(\theta_{max}\) the maximum electron deflection angle, see below.


Parameter of the EPA spectrum of an electron beam, cf. [FMNR93]. Describes the maximum angle of the electron deflection, which translates to the maximum virtuality in the photon spectrum. It defaults to 0.3.


In Sherpa version 3, a more accurate Weizsäcker-Williams weight for electron beams is used, as described in [Sch96] and [FMNR93]. By default, Sherpa uses this improved version of the formula, if you would like to use the previous version, set this switch to true.


Infrared regulator to the EPA beam spectra. Given in GeV, the value must be between 0. and 1. for EPA approximation to hold. Defaults to 0., i.e. the spectrum has to be regulated by cuts on the observable, cf Selectors.


Form factor model to be used on the beams. The options are 0 (pointlike), 1 (homogeneously charged sphere, 2 (gaussian shaped nucleus), and 3 (homogeneously charged sphere, smoothed at low and high x). Applicable only to heavy ion beams. Defaults to 0.


Value of alphaQED to be used in the EPA. Defaults to 0.0072992701.

Q2Max, PTMin, Form_Factor, XMin can either be set to single values that are then applied to both beams, or to a list of two values, for the respective beams. Pomeron

The Pomeron flux is implemented as used in :cite`H1:2006zyl` [GKG18] [A+06a] and, integrating out the momentum transfer, is given by

\[f_{\mathbb{P}}(x) = \int^0_{-t_\mathrm{max}} A_\mathbb{P} \frac{e^{B_\mathbb{P} t}}{{x}_\mathbb{P}^{2 \alpha_\mathbb{P}\left(t\right) -1}} = A_\mathbb{P} x^{1 - 2 \alpha\left(0\right)} \frac{1-\mathrm{e}^{-B_\mathbb{P} t_\mathrm{max}} x^{2 \alpha^\prime t_\mathrm{max}}} {B_\mathbb{P} - 2 \alpha^\prime \mathrm{log}(x)}\]

where \(t\) is the squared transferred four-momentum and \(\alpha\) is assumed to be linear, \(\alpha_\mathbb{P}\left(t\right) = \alpha\left(0\right) + \alpha^\prime t\). The default values are set to the ones obtained in Fit A in [A+06b] and can each be changed like so:

  tMax: 1.
  xMax: 1.
  xMin: 0.
  B: 5.5
  Alpha_intercept: 1.111
  Alpha_slope: 0.06

where Alpha_intercept and Alpha_slope are \(\alpha\left(0\right)\) and \(\alpha^\prime\), respectively. Please note that tMax is the absolute value, i.e. a positive number. xMax denotes the fraction of the proton momentum taken by the Pomeron.

Other fluxes can be implemented upon request. Reggeon

The Reggeon flux, defined in complete analogy to the Pomeron flux above. Default values taken from [A+06b], set to:

  tMax: 1.
  xMax: 1.
  xMin: 0.
  B: 1.6
  Alpha_intercept: 0.5
  Alpha_slope: 0.3
  n: 1.4e-3

The parameter n is the relative normalization of the Reggeon flux with respect to the Pomeron flux.

5.2.2. Beam Polarization

Sherpa can also provide cross-sections for polarized beams. These calculations can only be provided using the AMEGIC ME generator. The value for the beam polarization can be given as a percentage e.g. 80 or in decimal form e.g. 0.8 . The flavour of BEAM_1/BEAM_2 follows the definition given to BEAMS.

  BEAM_1: 0.8
  BEAM_2: -0.3