# 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

# LHC
BEAMS: 2212
BEAM_ENERGIES: 7000

# HERA
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

Monochromatic

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.

Laser_Backscattering

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 parametrization, see [Zar03]. Note that this parametrization 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.

Simple_Compton

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.

EPA

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

Spectrum_Reader

A user defined spectrum is used to describe the energy spectrum of the assumed new beam particles. The name of the corresponding spectrum file needs to be given through the keywords SPECTRUM_FILES.

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, @emph{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).

### 5.2.1.1. Laser Backscattering¶

The energy distribution of the photon beams is modelled by the CompAZ parametrisation, 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).

### 5.2.1.2. 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.

### 5.2.1.3. EPA¶

The equivalent photon approximation, cf. [AGH+08], [BGMS74], has a few free parameters:

EPA_q2Max

Parameter of the EPA spectra of the two beams, defaults to 2. in units of GeV squared.

EPA_ptMin

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.

EPA_Form_Factor

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.

EPA_AlphaQED

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

EPA_q2Max, EPA_ptMin, EPA_Form_Factor 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.

## 5.2.2. Intrinsic Transverse Momentum¶

The intrinsic transverse momentum of the colliding particles can be set by subsettings of the INTRINSIC_KPERP setting:

INTRINSIC_KPERP:
Parameter_1: <value_1>
Parameter_2: <value_2>
...


The possible parameters and their defaults are

ENABLED (default: true)

Setting this to false disables the intrinsic transverse momentum altogether.

SCHEME (default for protons: 0)

This parameter specifies the scheme to calculate the intrinsic transverse momentum of the beams in case of hadronic beams, such as protons.

MEAN (default: 1.1)

This parameter specifies the mean intrinsic transverse momentum in GeV for the beams in case of hadronic beams, such as protons.

If two values are provided, the intrinsic momenta means of the two beams are set to these two values, respectively.

SIGMA (default: 0.85)

This parameter specifies the width of the Gaussian distribution in GeV of the intrinsic transverse momenta for the beams in case of hadronic beams, such as protons.

If two values are provided, the intrinsic momenta widths of the two beams are set to these two values, respectively.

EXP (default: 0.55)

This parameter specifies the energy extrapolation exponent of the width of the Gaussian distribution of intrinsic transverse momentum for the beams in case of hadronic beams, such as protons.

If two values are provided, the exponents for each of the two beams are set to these two values, respectively.

EREF (default: 7000)

This parameter specifies the reference scale in GeV in the energy extrapolation of the width of the Gaussian distribution of intrinsic transverse momentum for the beams in case of hadronic beams, such as protons.

If two values are provided, the reference scales for each of the two beams are set to these two values, respectively.

If the option BEAM_REMNANTS: false is specified, pure parton-level events are simulated, i.e. no beam remnants are generated. Accordingly, partons entering the hard scattering process do not acquire primordial transverse momentum.