Input & Output

We use yaml runcards for piping input and output files.

Input

The input is split into two runcards: a theory runcard and an operator runcard. Note that we are not assuming any default values for the keywords, but instead the user has to provide the full definition. However, for the benchmarking environment we do provide some default settings.

Theory Runcard

The theory runcard (compatible with the NNPDF theory database) defines the physical setup and environment. The benchmark settings are available at banana.data.theories.default_card.

theory input runcard

Name	Type	Description
PTO	int	QCD perturbation theory order: 0 = LO, 1 = NLO, 2 = NNLO, 3 = N3LO.
ModEv	str	Evolution method. Possible options are: iterate-exact abbreviated with EXA, decompose-exact, perturbative-exact, iterate-expanded abbreviated with EXP, decompose-expanded, perturbative-expanded, truncated abbreviated with TRN, ordered-truncated.
XIF	float	Factorization to renormalization scale ratio. 1 means no scale variation.
ModSV	str	Scale variation method, used only if XIF!=1. Possible options are: expanded or exponentiated.
Q0	float	Initial PDF evolution scale (in GeV).
nf0	int or None	Number of flavors active ant the Q0 scale. If not provided it is inferred from the heavy quark threshold scales.
MaxNfPdf	int	Maximum number of flavors in the PDF evolution.
alphas	float	Reference value of the strong coupling \(\alpha_s\) (Note that we have to use \(\alpha_s\) here, instead of \(a_s\) for legacy reasons).
Qref	float	Reference scale at which the alphas value is given (in GeV).
nfref	int or None	Number of flavors active at the Qref scale. If not provided it is inferred from the heavy quark threshold scales.
MaxNfAs	int	Maximum number of flavors in the strong coupling evolution.
QED	int	If 1 include QED evolution.
alphaqed	float	Reference value of the electromagnetic coupling \(\alpha_{em}\).
Qedref	float	Reference scale at which the alphaqed value is given (in GeV).
HQ	str	Heavy quark scheme: if POLE use heavy quark pole masses, if MSBAR use heavy quark \(\overline{MS}\) masses.
mc	float	Charm quark mass (in GeV).
Qmc	float	Reference scale at which the charm quark mass is given (in GeV). Used only with HQ='MSBAR'.
kcThr	float	Ratio between the charm mass scale and the nf=4 threshold scale.
mb	float	Bottom quark mass (in GeV).
Qmb	float	Reference scale at which the bottom quark mass is given (in GeV). Used only with HQ='MSBAR'.
kbThr	float	Ratio between the bottom mass scale and the nf=5 threshold scale.
mt	float	Top quark mass (in GeV).
Qmt	float	Reference scale at which the top quark mass is given (in GeV). Used only with HQ='MSBAR'.
ktThr	float	Ratio between the top mass scale and the nf=6 threshold scale.
IC	bool	If 1 allow for intrinsic charm evolution.
IB	bool	If 1 allow for intrinsic bottom evolution.

Operator Runcard

The operator runcard defines the numerical setup and the requested operators. The benchmark settings are available at ekomark.data.operators.

operator input runcard

Name	Type	description
interpolation_xgrid	list(float)	x-grid at which the EKO is computed.
mugrid	list(float)	target grid at which the EKO is computed (in GeV).
interpolation_is_log	bool	If True use logarithmic interpolation.
interpolation_polynomial_degree	int	Polynomial degree of the interpolating function.
debug_skip_non_singlet	bool	If True skip the non singlet sector, useful for debug purposes.
debug_skip_singlet	bool	If True skip the singlet sector, useful for debug purposes.
ev_op_max_order	int	Perturbative expansion order of unitary evolution matrix. Needed only for perturbative evolution methods.
ev_op_iterations	int	Number of evolution steps.
backward_inversion	str	Backward matching inversion method, relevant only for backward evolution in VFNS.
n_integration_cores	int	Number of cores used during the integration. 0 means use all; -1 all minus 1.

Output

The eko output is represented by the class Output. An instance of this class is a dict and contains the following keys:

output runcard

Name	Type	Description
Q2grid	dict	All operators at the requested values of \(Q^2\) represented by the key
eko_version	float	The EKO version
inputgrid	list(float)	The input x-grid
inputpids	list(int)	The input list of participating partons listed by their PID.
interpolation_is_log	bool	If True use logarithmic interpolation.
interpolation_polynomial_degree	int	Polynomial degree of the interpolating function.
targetgrid	list(float)	The target x-grid
targetpids	list(int)	The target list of participating partons listed by their PID

Since the final EKO is a rank 4-tensor we store in the output all the different grids for each dimension:targetpids,targetgrid,inputpids,inputgrid. The Q2grid values are the actual tensor for the requested \(Q^2\). Each of them contains two keys:

• operators a dict with all evolution kernel operators where the key indicates which distribution is generated by which other one and the value represents the eko in matrix representation - this can either be the plain list representation or the binary representation (as provided by numpy.ndarray.tobytes())

• errors a dict with the integration errors associated to the respective operators following the same conventions as the operator dictionary

Each element (EKO) is a rank-4 tensor with the indices ordered in the following way: EKO[pid_out][x_out][pid_in][x_in] where pid_out and x_out refer to the outgoing PDF and pid_in and x_in to the incoming PDF. The ordering of pid_out/pid_in is determined by the targetpids/inputpids parameter of the output and the order of x_out/x_in by targetgrid/inputgrid.

To further explore how an Output object looks like you can follow this tutorial.