Input data cards

The input data in grape.cards are explained in this section. All of the items are optional and are set to default values if not specified. Default values are written in the brackets starting with D=. The items are not explicitly displayed in case that they are the only one for their cards.

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KFLBEAM
KF code of the lepton beam ( INTEGER,D=-11); 11:electron, -11:positron.

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EPOL $~~~P~~~\theta~~~\phi$
Polarization of the lepton beam ( REAL);
$P$ = degree of the polarization in the range $[-1,1]$ ( D=0.),
$\theta$ = polar angle of the polarization vector in degree ( D=0.),
$\phi$ = azimuthal angle of the polarization vector in degree ( D=0.).
The positive direction of the z-axis on the polarization vector is in the direction of the lepton beam.

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EBEAM
Lepton beam momentum in MeV/c ( REAL,D=27520.).

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PBEAM
Proton beam momentum in MeV/c ( REAL,D=820000.).

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PROCESS
Process type of the proton vertex ( INTEGER,D=1);
1:elastic, 2:quasi-elastic, 3:DIS.

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LPAIR
Dilepton channel ( INTEGER,D=2); 1:di-$e$, 2:di-$\mu$, 3:di-$\tau$.

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ISR
Initial state radiation flag for the beam lepton ( INTEGER,D=1); 0:off, 1:on.

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QFLV
Scattered quark in the DIS process ( INTEGER,D=1);
1:$u$, 2:$\bar{u}$, 3:$d$, 4:$\bar{d}$, 5:$s$, 6:$\bar{s}$, 7:$c$, 8:$\bar{c}$, 9:$b$, 10:$\bar{b}$, 11:$t$, 12:$\bar{t}$.

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MERGE
Merging mode in the DIS process ( INTEGER,D=0); 0:off.
In some cases, contributions from different quarks can be included in the cross-section calculation adding the parton densities if the mass difference is negligible. The possible combinations of QFLV and MERGE are written in Table1. The mass of the quark specified with QFLV is used in the amplitude and the kinematics calculations.

Table 1: Possible combinations of QFLV and MERGE

QFLV	MERGE	Quarks	BH	QED/EW/CO/Z$^0$
1	1234	$u+\bar{u}+d+\bar{d}$	Yes	No
1	123456	$u+\bar{u}+d+\bar{d}$ $\,+\,s+\bar{s}$	Yes	No
1	12345678	$u+\bar{u}+d+\bar{d}$ $\,+\,s+\bar{s}$ $\,+\,c+\bar{c}$	Yes	No
1	1234567890	$u+\bar{u}+d+\bar{d}$ $\,+\,s+\bar{s}$ $\,+\,c+\bar{c}$ $\,+\,b+\bar{b}$	Yes	No
1	17	$u+c$	Yes	Yes
2	28	$\bar{u}+\bar{c}$	Yes	Yes
3	35	$d+s$	Yes	Yes
4	46	$\bar{d}+\bar{s}$	Yes	Yes
3	359	$d+s+b$	Yes	Yes
4	460	$\bar{d}+\bar{s}+\bar{b}$	Yes	Yes

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NGROUP
Author group described in the PDFLIB manual ( INTEGER,D=5).

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NSET
PDF set described in the PDFLIB manual ( INTEGER,D=5).
The default is GRV94(LO).

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GRASEL
Feynman diagram selection ( INTEGER,D=3);
1:2-$\gamma$ Bethe-Heitler (without $e^{\pm}e^{\pm}$ interference in case of di-$e$),
2:2-$\gamma$ Bethe-Heitler (including $e^{\pm}e^{\pm}$ interference in case of di-$e$),
3:QED diagrams( i.e. all the diagrams except for the Z$^0$ contribution),
4:EW diagrams( i.e. all the diagrams),
13:QED-Compton type diagrams only,
14:Z$^0$ production diagrams only.
In case of di-$\mu,\tau$, the first and the second selections give the same result.

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ITMX1
Number of iterations in the grid optimization step of BASES. ( INTEGER,D=4).
This should be larger than 2.

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ITMX2
Number of iterations in the integration step of BASES ( INTEGER,D=10).
This should be larger than 5.

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NCALL
Number of sampling points in each iteration of BASES ( INTEGER,D=1000000).
This should be large so that any accuracy of each iteration in the integration step of BASES is better than 0.5%.

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NGEN
Number of events to be generated by spring ( INTEGER,D=100).

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NMOD$~~~N_{mod}$
Printing a message per $N_{mod}$ events in the event generation ( INTEGER,D=1000).

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PSISR
Switch for the initial state parton shower by PYTHIA ( INTEGER,D=1); 0:off, 1:on.
This has an effect only on event generations of the DIS process. No effect on elastic and quasi-elastic events. This item is copied to MSTP(61) in the PYTHIA common block /PYPARS/.

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PSFSR
Switch for the final state parton shower by PYTHIA ( INTEGER,D=1); 0:off, 1:on.
This item is copied to MSTP(71) in the PYTHIA common block /PYPARS/.

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PSBRA
Parton shower branchings in PYTHIA ( INTEGER,D=2);
1:QCD, 2:QCD+QED.
This item is copied to MSTJ(41) in the PYTHIA common block /PYDAT1/.

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PSSUP
Suppression of the PYTHIA parton shower ( INTEGER,D=0); 0:off, $>$$=$1:on.
This item is copied to MSTJ(40) in the PYTHIA common block /PYDAT1/.

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PYDECAY
Switch for fragmentation and decay in PYTHIA ( INTEGER,D=1); 0:off, 1:on.
No effect on elastic and quasi-elastic events.
This item is copied to MSTP(111) in the PYTHIA common block /PYPARS/.

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PRIPT
Primordial $k_t$ distribution in the proton ( INTEGER,D=1);
0:off, 1:gaussian, 2:exponential.
No effect on elastic and quasi-elastic events. This item is copied to MSTP(91) in the PYTHIA common block /PYPARS/.

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PYLIST
Printing the contents of /PYJETS/ ( LOGICAL,D=TRUE).

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NLIST
Number of events whose /PYJETS/ is printed out ( INTEGER,D=10).

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NTPYT
Output of generated events into a Ntuple file: grp.rz
from the PYTHIA common block /PYJETS/ ( LOGICAL,D=FALSE).
The meanings of the Ntuple variables are in the following.
npy : Number of particles ( integer)
px(1:npy),py(1:npy),pz(1:npy) : x,y,z-component of momentum
in GeV/c ( real*4)
pe(1:npy) : Energy in GeV ( real*4)
pm(1:npy) : Mass in GeV ( real*4)
kf(1:npy) : KF code ( integer)
sta(1:npy) : Status code ( integer)
mot(1:npy) : Line number of the mother particle ( integer)

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Q2RNGME$~~~Min~~~Max$
Range for the negative momentum transfer squared at the electron vertex $Q^2_e$ without ISR ( REAL), i.e. $Q^2_e = - \bigl\{ p_{_{e^{\pm}(in)}} - p_{_{e^{\pm}}}\bigr\}^2$ where $p_{_{e^{\pm}(in)}}$ is a 4-momentum of the incoming lepton after ISR.
$Min$ = the minimum in GeV$^2$ ( D=0.),
$Max$ = the maximum in GeV$^2$ ( D=1.E20).
In case of di-$e$ with $e^{\pm}e^{\pm}$ interference, smaller one of the two $Q^2_e$ values is used.

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Q2RNGOB$~~~Min~~~Max$
Range for the negative momentum transfer squared at the electron vertex $Q^2_e$ including ISR ( REAL), i.e. $Q^2_e = - \bigl\{ p_{_{e^{\pm}(in)}} - p_{_{e^{\pm}}}\bigr\}^2$ where $p_{_{e^{\pm}(in)}}$ is a 4-momentum of the incoming lepton before ISR.
$Min$ = the minimum in GeV$^2$ ( D=0.),
$Max$ = the maximum in GeV$^2$ ( D=1.E20).
In case of di-$e$ with $e^{\pm}e^{\pm}$ interference, smaller one of the two $Q^2_e$ values is used.

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MHAD$~~~Min~~~Max$
Range for the mass of the hadronic system $M_{had}$ ( REAL);
$Min$ = the minimum in GeV ( D=1.08),
$Max$ = the maximum in GeV ( D=1.E20).
No effect on elastic events.

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Q2P$~~~Min~~~Max$
Range for the negative momentum transfer squared at the proton vertex $Q_p^2$ ( REAL);
$Min$ = the minimum in GeV$^2$ ( D=0.),
$Max$ = the maximum in GeV$^2$ ( D=1.E20).
In case of the DIS process, $Q_p^2$ is used as a QCD scale for PDF.

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THMIN $~~~\theta_{min}^{(1)} ~~~\theta_{min}^{(2)} ~~~\theta_{min}^{(3)} ~~~\theta_{min}^{(4)}$

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THMAX $~~~\theta_{max}^{(1)} ~~~\theta_{max}^{(2)} ~~~\theta_{max}^{(3)} ~~~\theta_{max}^{(4)}$

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EMIN $~~~E_{min}^{(1)} ~~~E_{min}^{(2)} ~~~E_{min}^{(3)} ~~~E_{min}^{(4)}$

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EMAX $~~~E_{max}^{(1)} ~~~E_{max}^{(2)} ~~~E_{max}^{(3)} ~~~E_{max}^{(4)}$

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PMIN $~~~P_{min}^{(1)} ~~~P_{min}^{(2)} ~~~P_{min}^{(3)} ~~~P_{min}^{(4)}$

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PMAX $~~~P_{max}^{(1)} ~~~P_{max}^{(2)} ~~~P_{max}^{(3)} ~~~P_{max}^{(4)}$

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PTMIN $~~~Pt_{min}^{(1)} ~~~Pt_{min}^{(2)} ~~~Pt_{min}^{(3)} ~~~Pt_{min}^{(4)}$

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PTMAX $~~~Pt_{max}^{(1)} ~~~Pt_{max}^{(2)} ~~~Pt_{max}^{(3)} ~~~Pt_{max}^{(4)}$
$(1)$ : for scattered proton or quark,
$(2)$ : for scattered $e^{\pm}$,
$(3)$ : for produced $l^{\mp}$,
$(4)$ : for produced $l^{\pm}$.
The above 8 data cards are used for describing the detector cut in the laboratory frame ( REAL). Each final state particle is required to satisfy the following,

$\theta_{min}^{(i)} < \theta < \theta_{max}^{(i)}$   AND  $E_{min}^{(i)} < E < E_{max}^{(i)}$

AND  $P_{min}^{(i)} < P < P_{max}^{(i)}$   AND  $Pt_{min}^{(i)} < Pt < Pt_{max}^{(i)}$

where $\theta$(degree), $E$(GeV), $P$(GeV/c) and $Pt$(GeV/c) indicate polar angle, energy, momentum and transverse momentum, respectively. The default values correspond to not applying this cut.

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THPTMCT $~~~\theta_{min}~~~\theta_{max}$

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PTMXCT $~~~~Pt_{min}~~~Pt_{max}$
Using the above 2 data cards, final state leptons are required to satisfy the following ( REAL),

$\theta_{min} < \theta^M < \theta_{max}$   AND  $Pt_{min} < Pt^M < Pt_{max}$

where $Pt^M$(GeV/c) indicates the maximum transverse momentum among the 3 final state leptons( $e^{\pm},l^{\mp},l^{\pm}$), and $\theta$(degree) is the polar angle of the lepton with $Pt^M$. The default values correspond to not applying this cut.

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MASSLL $~~~~Min1~~~Max1~~~~~Min2~~~Max2$
Range for the mass of the produced dilepton system ( REAL);
$Min1$ = the minimum in GeV ( D=0.),
$Max1$ = the maximum in GeV ( D=1.E20).
In case of di-$\mu$,$\tau$, $Min2$ and $Max2$ are not used.
In case of di-$e$ with $e^{\pm}e^{\pm}$ interference, there are two masses; $M_{e^+e^-}^{(1)}$, $M_{e^+e^-}^{(2)}$
( $M_{e^+e^-}^{(1)} < M_{e^+e^-}^{(2)}$), and they are required to satisfy the following,

$Min1 < M_{ee}^{(1)} < Max1$   AND  $Min2 < M_{ee}^{(2)} < Max2$.

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MASSELL$~~~Min~~~Max$
Range for the mass of the final state lepton system of $e^{\pm},l^{\mp},l^{\pm}$ ( REAL);
$Min$ = the minimum in GeV ( D=1.),
$Max$ = the maximum in GeV ( D=1.E20).

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MASSQLL$~~~Min~~~Max$
Range for the mass of the scattered quark and produced dilepton system of $q\,\,l^+ l^-$ ( REAL);
$Min$ = the minimum in GeV ( D=5.),
$Max$ = the maximum in GeV ( D=1.E20).
This cut has an effect only on the DIS process.
In case of di-$e$ with $e^{\pm}e^{\pm}$ interference, smaller one of the 2 values is used.

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IVISI $N_{visi}$

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THEVMIN $~~~\theta_{min}^{(1)} ~~~\theta_{min}^{(2)} ~~~\theta_{min}^{(3)} ~~~\theta_{min}^{(4)}$

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THEVMAX $~~~\theta_{max}^{(1)} ~~~\theta_{max}^{(2)} ~~~\theta_{max}^{(3)} ~~~\theta_{max}^{(4)}$

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EVMIN $~~~E_{min}^{(1)} ~~~E_{min}^{(2)} ~~~E_{min}^{(3)} ~~~E_{min}^{(4)}$

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EVMAX $~~~E_{max}^{(1)} ~~~E_{max}^{(2)} ~~~E_{max}^{(3)} ~~~E_{max}^{(4)}$

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PTVMIN $~~~Pt_{min}^{(1)} ~~~Pt_{min}^{(2)} ~~~Pt_{min}^{(3)} ~~~Pt_{min}^{(4)}$

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PTVMAX $~~~Pt_{max}^{(1)} ~~~Pt_{max}^{(2)} ~~~Pt_{max}^{(3)} ~~~Pt_{max}^{(4)}$
$(1)$ : for scattered proton or quark,
$(2)$ : for scattered $e^{\pm}$,
$(3)$ : for produced $l^{\mp}$,
$(4)$ : for produced $l^{\pm}$.
The above 6 data cards are used for describing the detector cut in the laboratory frame ( REAL except for $N_{visi}$: INTEGER). $N_{visi}$ particle(s) are(is) required to satisfy the following,

$\theta_{min}^{(i)} < \theta < \theta_{max}^{(i)}$   AND  $E_{min}^{(i)} < E < E_{max}^{(i)}$   AND  $Pt_{min}^{(i)} < Pt < Pt_{max}^{(i)}$

where $\theta$(degree), $E$(GeV) and $Pt$(GeV/c) indicate polar angle, energy and transverse momentum, respectively. As for $N_{visi}$, D=-1, which corresponds to not applying this cut. The test run at the end of this paper is instructive for understanding this cut.