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Published for SISSA by Springer

Received: May 31, 2013

Revised: July 16, 2013 Accepted: August 14, 2013 Published: September 13, 2013

Reliability of Monte Carlo event generators for gamma-ray dark matter searches

J.A.R. Cembranos,a A. de la Cruz-Dombriz,b,c V. Gammaldi,a R.A. Linerosd and A.L. Marotoa

aDepartamento de Fsica Terica I, Universidad Complutense de Madrid, E-28040 Madrid, Spain

bInstituto de Ciencias del Espacio (ICE/CSIC) and Institut dEstudis Espacials de Catalunya (IEEC), Campus UAB, Facultat de Cincies,Torre C5-Par-2a, 08193 Bellaterra (Barcelona) Spain

cAstrophysics, Cosmology and Gravity Centre (ACGC) and Department of Mathematics and Applied Mathematics, University of Cape Town,Rondebosch 7701, Cape Town, South Africa

dInstituto de Fsica Corpuscular (CSIC-Universitat de Valncia), Apdo. 22085, E-46071 Valencia, Spain

E-mail: mailto:[email protected]

Web End [email protected] , mailto:[email protected]

Web End [email protected]

Abstract: We study the di erences in the gamma-ray spectra simulated by four Monte Carlo event generator packages developed in particle physics. Two di erent versions of PYTHIA and two of HERWIG are analyzed, namely PYTHIA 6.418 and HERWIG 6.5.10 in Fortran and PYTHIA 8.165 and HERWIG 2.6.1 in C++. For all the studied channels, the intrinsic di erences between them are shown to be signicative and may play an important role in misunderstanding dark matter signals.

Keywords: Monte Carlo Simulations

ArXiv ePrint: 1305.2124

JHEP09(2013)077

[circlecopyrt] SISSA 2013 doi:http://dx.doi.org/10.1007/JHEP09(2013)077

Web End =10.1007/JHEP09(2013)077

Contents

1 Introduction 1

2 Monte Carlo parton shower 22.1 QCD nal-state radiation 22.2 Hadronization 32.3 QED nal-state radiation 4

3 Gamma-ray spectra from dark matter annihilation/decay 43.1 Gamma-ray spectra from DM annihilation: W +W channel 53.2 Gamma-ray spectra from DM annihilation: bb channel 53.3 Gamma-ray spectra from DM annihilation: + channel 53.4 Gamma-ray spectra from DM annihilation: tt channel 8

4 Implications to WIMPs phenomenology 10

5 Conclusions 15

1 Introduction

In the last years, numerous evidences about the existence of a new kind of invisible matter have appeared. Most of them rely on gravitational e ects on galactic and extragalactic scales, such as the rotation curves of spiral galaxies, spatial distribution of gravitational lensing signals and constraints from cosmic microwave background, among others. In spite of them, a conclusive identication of this dark component of matter has not yet been found. Although there are many plausible origins for this component [18], dark matter (DM) is usually assumed to be in the form of thermal relics that naturally freeze-out with the right abundance in many extensions of the Standard Model (SM) of particles [920]. In order to conrm its nature, DM searches have followed di erent directions. On the one hand, DM particles can be produced in laboratory experiments such as high-energy particle colliders [2127]. On the other hand, local DM can be detected in a direct or indirect way [2839].

Direct detection experiments typically operate in deep underground laboratories, while the indirect ones focus on astronomical and cosmological signal detection, with both ground based Cerenkov detectors (such as CTA, HESS and MAGIC amongst others) and satellite experiments (e.g. FERMI, PAMELA, PLANCK and WMAP). If DM particles annihilate or decay into SM particles, the signature of the nal products of such processes may be detected up to some uncertainty in the astrophysical background component. In order to set constraints on the diverse DM models and get a better understanding of the astrophysical

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factor associated with the distribution of this kind of matter, numerous signals detected in gamma-rays, neutrinos, positrons, antiprotons and other particles have been studied in the available literature [4062]. Most of these analysis make use of Monte Carlo event generator packages, that allow to predict the spectra of nal-state particles generated by DM annihilation and decays into SM particles. The most used Monte Carlo generator packages are PYTHIA and HERWIG, both with available versions written either in Fortran or C++.

In this paper we shall focus on the gamma-ray spectra generated by four softwares, showing how the choice of the Monte Carlo code may a ect the DM search. Thus, section 2 is devoted to illustrate the main di erences between PYTHIA 6.418 (Fortran version), PYTHIA8.165 (C++ version), HERWIG Fortran version 6.5.10 and HERWIG C++ version 2.6.1. In section 3 we determine the di erences between the four Monte Carlo codes when four illustrative annihilation channels are studied. In section 4 we then analyze the implications that these di erences may have in the WIMPs phenomenology and DM indirect searches. Finally section 5 shall cover the main conclusions of this communication.

2 Monte Carlo parton shower

The di erential photon ux produced by Monte Carlo event generators software may be understood as the outcome obtained from a particle shower schematization in three fundamentals parts: the QCD Final-State Radiation, the hadronization model and the QED Final-State Radiation. Di erences between available generators in the aforementioned parts, may help understanding the origin of such di erences. Therefore, let us study separately the technicalities of each part as follows (read [63] for further details):

2.1 QCD nal-state radiation

The QCD Final-State Radiation is described by the elementary probability to radiate either quarks or gluons (partons). This probability is universal in the soft (low energy) and collinear (high energy) approximation. In these two limits the branching probability is proportional to [64]:

s(kT )

2 s(Q2max, Q2)Pi,jk(z)

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dQ2

Q2 dz

2 , (2.1)

where s is the coupling constant of the strong interaction, Q2 is the evolution variable, Q2max is its maximum allowed value, z and (1- z) are the energy fraction of the two generated partons, and is the azimuthal angle (z and are dened in the center of mass frame, but other denitions only di er beyond the leading logarithmic order approximation). Pi,jk(z)

is the Altarelli-Parisi [65] splitting function describing the distribution of the fraction z of the emitted parton energy with respect to its parents, where the su xes i and jk stand for the incoming and nal parton species. s(Q21, Q22) holds for the Sudakov form factor accounting for all the non-resolvable e ects of the perturbative theory (quantum loop and resonance among others) acting on the probability of transition between Q1 and Q2 states.

Q2max is set by the hard-scattering, i.e., the head (initial) process of the parton shower, and Q20 is the last process when the parton shower ends and the hadronization begins.

The evolution variable Q2 represents the rst di erence between the Monte Carlo simulations: In HERWIG and HERWIG++ Q2 [similarequal] E2(1 cos ), where E is the energy of the

parent parton and is the emission angle. It was originally implemented in [66, 67]. However, in PYTHIA 6.4 the evolution variable Q2 corresponds to the virtuality of the emitted parton, i.e., its virtual mass, whereas in PYTHIA 8 is given by kT , the transverse momentum of the emitted parton with respect to the emitting one. The latter formulation allows to order the nal-state showers with regard to kT through a sequence of falling transverse-momentum values [68]. In most cases, the two variables used in the two versions of PYTHIA are compatible, but HERWIG turns out to reproduce more accurately the color coherence dependent data in the soft limit.

Finally, the Sudakov form factor for one parton is given by [30]:

S(Q2max, Q2) = exp"

[integraldisplay]

Q2max

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dk2 k2

[integraldisplay]

zmax

zmin

dz s(z, k2)

2 Pi,jk(z)

[bracketrightBigg]

. (2.2)

In multiparton processes, the previous equation needs to be integrated; the integration method di ers for each package. For instance, in PYTHIA zmin = Q20/Q2, whereas in HERWIG zmin = Q0/Q. With regard to zmax, it satises zmax = 1zmin for all the codes. This deni

tion leads to conclude that, for a given value for Q2, the evolution range in the z variable is larger in PYTHIA than in HERWIG. When comparing the two simulations with LEP data, the strong coupling constant s takes also di erent values, being s(MZ) [similarequal] 0.127 in PYTHIA

and s(MZ) [similarequal] 0.116 in HERWIG. This fact depends on the implemented approximation. In

the QCD shower, the soft gluons interference e ects lead to an ordering of subsequent emissions in terms of decreasing angles. This approximation of coherence e ects also depends on the Q2 denition. For the rst mass-ordering version of PYTHIA, in which Q2 m2 with

m2 = E2 k2 0, it had to be implemented as additional requirement. In the case of the

kT -ordering version, with Q2 k2T = z(1 z)m2, it leads directly to the proper behavior.

Finally, due to theoretical analysis, the scale choice s = s(k2T ) = s(z(1 z)m2) is the default one in PYTHIA. On the other hand, HERWIG takes into account this e ect via the angular ordering of emissions in the parton shower by redening the running constant. In this case, s = s z2(1 z2)~q2

, where ~q corresponds to the scale of the decaying parton.

Moreover, a two-loop approximation is reproduced in HERWIG by means of the Monte Carlo scheme with MCs =

MSs (1 + K

MSs /2), where

MSs is dened in the usual modied

minimal subtraction (

MS) scheme in QCD (read [69] for further details). In any case, we conclude that photon emission is not a ected by angular ordering [70].

2.2 Hadronization

When the evolution variable Q2 reaches the value Q20, the parton shower ends and the hadronization begins. Two di erent models to describe hadronization are thus developed in the two aforementioned packages. PYTHIA relies on the String Model Hadronization [70 72] whereas HERWIG does on the Cluster Model Hadronization [7376]. In any case, both models take into account the experimental data collected by the LEP for tuning their parameters. In particular, the standard tunes use data at 100 GeV of center of energy.

In the future, new tunes could also consider the LHC data. In any case, the hadronization model does not seem to a ect the gamma-ray spectra in an appreciable way, except if the 0 production changes signicantly. Finally, let us remember that most of the hadrons formed during the hadronization process are unstable and will eventually decay. The resultant nal states, which are mainly leptons, lead the photon production involving QED processes.

2.3 QED nal-state radiation

The radiation emitted by quarks, W [notdef] bosons, and charged leptons (i.e. Bremsstrahlung radiation), as well as the possibility of pair production, can be added to equation (2.1) introduced above. The Bremsstrahlung component of the Final-State Radiation (FSR) represents the main contribution in the case of gamma-rays produced by DM annihilating/decaying into e+e and + channels. The high energy leptons come directly from the hard process in the rst case and both from hard processes and [notdef] decay in the second one. In any case, associated -photons are produced by Bremsstrahlung e ects in both cases. Bremsstrahlung FSR from hard processes is currently not implemented in HERWIG++ version 2.6.1, being unable to produce gamma-ray spectra in the case of e+e and +

channels, while it is included in both HERWIG and PYTHIA (6.4 and 8). This component clearly a ects all the logarithmic part of gamma-ray spectra at high energy generated with HERWIG++, as shall be shown in the following sections.

With regards to the electroweak (EW) 2 ! 2 processes of the FSR, where photons

are produced or annihilated, PYTHIA 8 accounts for all these processes, except the !

W +W . As for HERWIG, it contains the q ! q processes, but not the process ! f

These two last processes are indeed contained in HERWIG++. However, we veried that di erent sets of such processes did not a ect the gamma-ray spectra in an appreciable way after modifying the codes.

3 Gamma-ray spectra from dark matter annihilation/decay

In this section we study the spectra of four relevant channels by using the four Monte Carlo generators mentioned above. Namely, we have studied the on-shell channels: W +W , bb,

+ and tt since they are representative channels of the phenomenology of annihiliating/decaying DM. The tt channel was studied separately since it presents a particular phenomenology with respect to the other quark channels.

The photon spectra is better described in terms of the dimensionless variable:

x 2

ECM , (3.1)

where E and ECM correspond to the photon and center of mass (CM) energies, respectively. This variable is simply reduced to x E /MDM in the case of annihilating DM and

therefore lies in the range between 0 to 1. Large di erences between spectra are usually present at extremes of x. For this reason, we present the spectra in both linear and logarithmic scales for x. In the rst (second) case the behavior at high (low) x is more clearly shown. For each channel, we focused on two values of DM particle mass: 100 GeV and 1 TeV. In the case of the tt channel the masses under study were 500 GeV and 1 TeV.

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3.1 Gamma-ray spectra from DM annihilation: W +W channel

The simulated gamma-ray spectra for DM particles annihilating into W +W channel appear very similar for x > 105 both for a DM mass of 100 GeV and 1 TeV. This behavior can be seen in gures 1 and 2 respectively. It is clear from the gure the considerably lower uxes generated by HERWIG++ at high energies as compared to the rest of packages, probably because of the absence of Bremsstrahlung from hard processes in the e+e and +

cases commented before. On the other hand, a slight di erence is observed for energies between x = 0.30.7 with HERWIG providing in both cases the highest values. Nonetheless,

the main di erences appear at lower energies as can be seen in gures 1 and 2. In PYTHIA 8, we have generated each photon spectrum by using the resonant process e+e ! , where is a resonance with mass of ECM and a user-dened decay mode. This procedure is very similar to the one we used for PYTHIA 6.4, except that channels were created by using the subroutine PY2ENT. In HERWIG++, we used the scattering of photons as the initial process. The photon spectra are then independent of the initial beams (e+e or ) and solely depend on the energy of the event, i.e. ECM = 2MDM. In PYTHIA 8, the cut-o at low energy strongly depends upon this parameter pTminChgL (dubbed here pT ) and exactly corresponds to its set value, with allowed range of 0.0012.0 and a default value of 0.005. (gure 3 (Right-panel)) In HERWIG++, QEDRadiationHandler is set o by default, so that the cut-o appears to higher energy with respect to the other Monte Carlo generators. In the opposite case, when QEDRadiationHandler is enable and the relevant parameter IFDipole:MinimumEnergyRest varies in values, the spectrum at low energy changes drastically. Smaller values of such parameter enlarge the production of photons at low energies (See gure 3, left-panel).

3.2 Gamma-ray spectra from DM annihilation: bb channel

In the case of DM annihilation into bb channel, the HERWIG++ spectrum appears lower for high energy (x > 0.6) with respect to the other simulations, due to the lack of the Bremsstrahlung photons generated by high energy leptons. Thus, both PYTHIA codes and HERWIG simulations look very similar qualitatively for the two studied values of DM mass as seen in gures 4 and 5. On the other hand, at very small energies x < 104

[parenrightbig]

HERWIG

simulation returns higher values of the ux with respect to the other packages. This fact can be seen in gures 4 and 5. The other codes for these small energies agree very well in their predictions.

3.3 Gamma-ray spectra from DM annihilation: + channel

Di erences in the gamma-spectra appear in the case of DM particles annihilating into leptonic channels. Here we show the + annihilation channel as an illustrative example.

In this channel and for the two studied DM masses, both HERWIG codes present an important suppression of the spectrum for energies in the interval 0.8 < x < 1, while both versions of PYTHIA extend the photon spectra up to x = 1 with higher spectra. This fact can be observed in gures 6 and 7 and may be explained by the absence of Bremsstrahlung gamma-rays generated by high energy leptons when HERWIG codes are used. As can be

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Pythia 8

Herwig Pythia 6.4

Herwig ++

Pythia 8

Herwig Pythia 6.4 Herwig ++

x1.5 dN/dx

x=E/MDM

10 1e-12 1e-10 1e-08 1e-06 0.0001 0.01 1

10 0 0.2 0.4 0.6 0.8 1

Figure 1. (Left-panel) DM particles annihilating into W +W channel with MDM = 100 GeV in logarithmic scale. The simulations are consistent down to x [similarequal] 104. At x [similarequal] 105 Fortran

simulations are bigger than the C++ ones by a factor ten. At x [similarequal] 106 no more photons are

produced in HERWIG++ provided that the QEDRadiationHandler is set o as default. In our simulation, QEDRadiationHandler is switched on with a clear cut-o at energy of 1010. Analogous cut-o appear at x [similarequal] 108 in PYTHIA 8, x [similarequal] 1011 in HERWIG and x [similarequal] 1012 in PYTHIA 6.4 . The

simulations are very di erent at these energy values and physical validity has to be checked. Due to the t of the Monte Carlo software with high energy colliders (such as LEP and LHC) that are poor of data at low energy, simulations at low energies might be unreliable. If this is the case, it is expected that this e ect a ects all the simulated channels. (Right-panel) DM particles annihilating into W +W channel with MDM = 100 GeV in linear scale. Notice the lower ux for HERWIG++ at high energies when compared to the rest of packages

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Pythia 8

Herwig Pythia 6.4 Herwig ++

Pythia 8

Herwig Pythia 6.4 Herwig ++

x1.5 dN/dx

x=E/MDM

10 1e-16 1e-14 1e-12 1e-10 1e-08 1e-06 0.0001 0.01 1

10 0 0.2 0.4 0.6 0.8 1

Figure 2. (Left-panel) W +W annihilation channel with MDM = 1 TeV in logarithmic scale. As in gure 1, the simulations are consistent down to a value of x, that is 106 in the case of MDM = 1 TeV (a factor ten lower in x with respect to the case with MDM = 100 GeV). Similar behaviors of the lower energy cuts-o are also observed, with a general shift of x cut-o value of order 102. (Right-panel) W +W annihilation channel with MDM = 1 TeV in linear scale. All the simulations except for HERWIG++ exhibit the same behavior as in gure 1, but within x [similarequal] 0.3 and

x [similarequal] 0.7 and a maximum discrepancy at x [similarequal] 0.5. The shift with respect to gure 1 can be simply

explained by the increment of the WIMP mass.

10 1e-12 1e-10 1e-08 1e-06 0.0001 0.01 1

kT min=1e-4 kT min=1e-8 kT min=1

kT max kT med kT min

x1.5 dN/dx

10 1e-16 1e-14 1e-12 1e-10 1e-08 1e-06 0.0001 0.01 1

x=E/MDM

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Figure 3. Cut-o at low energy photons in C++ codes. High energy linear scale are not a ected. (Left-panel) W +W annihilation channel with HERWIG++ at MDM = 1 TeV in logarithmic scale.

Di erent cut-o at low energy in logarithmic scale correspond to cuts in the QEDRadiationHandler of kT = 108 , 104 , 1. (Right-panel) bb annihilation channel with PYTHIA 8 at MDM = 1 TeV in logarithmic scale. Here the cut-o are set as the minimum, medium and maximum value of the allowed range of value.

10 1e-12 1e-10 1e-08 1e-06 0.0001 0.01 1

Phytia 8

Herwig Pythia 6.4 Herwig ++

Pythia 8

Herwig Pythia 6.4 Herwig ++

x1.5 dN/dx

x=E/MDM

10 0 0.2 0.4 0.6 0.8 1

Figure 4. (Left-panel) bb annihilation channel with MDM = 100 GeV in logarithmic scale. Three of the four simulations perfectly match down to x [similarequal] 106, where no more photons are produced.

HERWIG Fortran also match down to [similarequal] 105. Here, its simulated ux appears much bigger, with

no photons counted at energies smaller than x [similarequal] 1011. (Right-panel) b

b annihilation channel with MDM = 100 GeV in linear scale. Three of the four simulations are in agreement within the statistical error bars on the full x range, while HERWIG++ gives lower ux above x [similarequal] 0.5.

seen in the leptonic and muonic channel, HERWIG Fortran accounts for an extrapolation with respect to the Bremsstrahlung photons related with hard processes, but it does not provide an exact implementation of this EW process. This is the reason why the gamma-ray spectra simulated with HERWIG Fortran for channels where the Bremsstrahlung radiation contribution is subdominant are in agreement with PYTHIA 6.4 and 8 results, up to the statistical errors. Moreover, a di erence of one order of magnitude appears for energies x 0.8 among PYTHIA codes and HERWIG codes. At intermediate energies, x 103 0.2, all codes agree. For small energies, PYTHIA packages agree in their spectra up to x = 107

Figure 5. (Left-panel) bb annihilation channel with MDM = 1 TeV in logarithmic scale. PYTHIA6.4 agrees with both HERWIG++ and PYTHIA 8 down to x [similarequal] 107, where the spectra of the latter two

packages stop. PYTHIA 6.4 stops providing gamma-rays at x [similarequal] 109. Once again, HERWIG generates

larger gamma-ray uxes at low energy. The di erence at high energy discussed in gure 2 is also apparent on the right panel. (Right-panel) bb annihilation channel with MDM = 1 TeV in linear

scale. As in gure 4, HERWIG++ gives much lower ux above x [similarequal] 0.5. Although HERWIG agrees both

with Pithia 6.4 and PYTHIA 8 within statistical errors, PYTHIA 8 ux (with better statistics) appears two or three times bigger than PYTHIA 6.4 at x [similarequal] 0.6, 0.8.

but not for lower energies where both PYTHIA 8 seems to be strongly suppressed for energies smaller than x = 107.

HERWIG++ produces less photons for small energies x 103, although the

QEDRadiationHandler was enable. Concerning HERWIG, the spectrum can be extended down to x = 1011 and it lies in between the PYTHIA 6.4 and HERWIG++ simulations, for the two studied masses and for small energies. With regard to high energies close to x = 1, HERWIG spectrum is the most suppressed for this channel.

3.4 Gamma-ray spectra from DM annihilation: tt channel

The most remarkable di erences between the four simulations packages appear in the tt channel. To enable top decays in PYTHIA 6.4, the subroutine PYINIT() has to be executed. Alternatively, this process can be implemented by its dominant SM decay, i.e. t ! W +b (or equivalently t ! W

b) [3438]. In order to maintain any non-perturbative e ect, the initial state was made of a four-particle state composed by W +b coming from the t quark and W b from t anti-quark. These choices conserve all kinematics and color properties from the original pair and show the same results as the PYINIT() case. Starting from this conguration, the authors forced decays and hadronization processes to evolve as PYTHIA does. Therefore, the gamma-rays spectra corresponding to this channel have also been included for PYTHIA 6.4 in our analysis using this procedure. For this channel we have studied two DM masses 500 GeV and 1 TeV. The simulated spectra appear very similar in the range 105 < x < 0.1. Nonetheless, at lower and higher energies the four are quite di erent. At large energies, PYTHIA 8 gives the highest ux being able to acquire non-null ux for x 1. The smallest ux is again for HERWIG++ whereas PYTHIA 6.4 and HERWIG lie

in between the other two. These facts can be seen in gures 8 and 9. The four spectra also

Pythia 8

Herwig

Pythia 6.4 Herwig ++

Pythia 8

Herwig

Pythia 6.4 Herwig ++

x1.5 dN/dx

x=E/MDM

10 1e-12 1e-10 1e-08 1e-06 0.0001 0.01 1

x=E/MDM

10 0 0.2 0.4 0.6 0.8 1

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Pythia 8

Herwig Pythia 6.4 Herwig ++

10 1e-12 1e-10 1e-08 1e-06 0.0001 0.01 1

Pythia 8

Herwig Pythia 6.4 Herwig ++

x1.5 dN/dx

0 0.2 0.4 0.6 0.8 1

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x=E/MDM

Figure 6. (Left-panel) + annihilation channel with MDM = 100 GeV in logarithmic scale. The simulations are inconsistent below x [similarequal] 102. PYTHIA codes are more consistent, generating the

same spectral form down to x [similarequal] 107, where PYTHIA 8 has its cut-o . PYTHIA 6.4 spectra attains

smaller energies to almost 1010. HERWIG cut-o reaches almost x [similarequal] 1011, but its ux is lower

than the PYTHIA ones below x = 103 and reaching the maximum inconsistence of almost a factor ten at x = 105. HERWIG++ appears totally inconsistent with the other three packages, with a much lower ux that gets a maximum divergence of 5 orders of magnitude at x [similarequal] 106 where its photons

production stops. (Right-panel) + annihilation channel with MDM = 100 GeV in linear scale. For this leptonic channel, the spectral forms of the four codes di er on the whole energy range. We can see that the spectral cut-o at high energy is similar for both HERWIG codes and PYTHIA ones by pairs. In the interval x [similarequal] 0.6 0.8, simulated gamma-ray ux from PYTHIA 6.4 and HERWIG++

match. At x [similarequal] 0.7, PYTHIA 8 lies a factor 2-3 above HERWIG++ and PYTHIA whereas HERWIG lies the

same factor below. Therefore there exists a non negligible di erence (almost a factor ten), between PYTHIA 8 and HERWIG simulated spectra at this value of x.

10 1e-12 1e-10 1e-08 1e-06 0.0001 0.01 1

Pythia 8

Herwig Pythia 6.4 Herwig ++

Pythia 8 Hwerwig Pythia 6.4 Herwig ++

x1.5 dN/dx

x=E/MDM

10 0 0.2 0.4 0.6 0.8 1

Figure 7. (Left-panel) + annihilation channel with MDM = 1 TeV in logarithmic scale. Compared to gure 6, all the lower cut-o s are shifted by a factor of ten to lower xs, with the exception of PYTHIA 6.4 that is shifted by a factor of a hundred, so that it never crossed HERWIG data as happened with MDM = 100GeV. (Right-panel) + annihilation channel with MDM = 1 TeV in linear scale. The behavior is analogous to the one discussed in gure 6.

di er at high energy due to the (absence of) implementation of Bremsstrahlung e ects. All the possibilities were summarized in table 1. At low energy the di erences may be

10 1e-14 1e-12 1e-10 1e-08 1e-06 0.0001 0.01 1

Pythia 8

Herwig Pythia 6.4 Herwig ++

Pythia 8

Herwig Pythia 6.4 Herwig ++

x1.5 dN/dx

JHEP09(2013)077

10 0 0.2 0.4 0.6 0.8 1

x=E/MDM

Figure 8. (Left-panel) tt annihilation channel with MDM = 500 GeV in logarithmic scale. At low energy the simulations are consistent down to x [similarequal] 105. HERWIG++ drops down at x [similarequal] 107 and

PYTHIA 8 does at 109, producing a higher number of photons 100 times bigger than HERWIG++ at x 107, and almost 10 times lower of PYTHIA 6.4 at the same value of x. PYTHIA 6.4 cuts-o

at x [similarequal] 1013 and HERWIG does at x [similarequal] 1012, where the two spectra match. For higher energies,

HERWIG gamma-ray ux is higher than PYTHIA 6.4, with a maximum factor of ten at x [similarequal] 109.

(Right-panel) tt annihilation channel with MDM = 500 GeV linear scale. The four simulations are manifestly inconsistent between them at high energy. HERWIG++ ux became lower from x [similarequal] 0.2

onwards and cuts o at x < 0.8. At x [similarequal] 0.4 PYTHIA 6.4 and HERWIG are similar between the

statistical errors up to x 0.8, where spectra and cuts-o become di erent. PYTHIA 8 starting from

x [similarequal] 0.6 produces the highest ux with cut-o at x [similarequal] 1.

Package Bremsstrahlung PYTHIA 6.4 Implemented

PYTHIA 8 Implemented

HERWIG Partially implemented HERWIG++ Not implemented

Table 1. Simulations are strongly a ected by the inclusion of Bremsstrahlung radiation and consequently the spectra turn out to look very di erent at high energy.

associated as in the + both to the cut-o in the lowest energy allowed for photons and to the presence or not of the QEDRadiationHandler in the simulation.

4 Implications to WIMPs phenomenology

Monte Carlo generators are essential tools for indirect searches of dark matter. The simulated spectra generated by PYTHIA 6.4, PYTHIA 8, HERWIG and HERWIG++ allow to get predictions about the signal coming from DM annihilation and/or decay. The choice of the Monte Carlo generator software may a ect the predictions on both constraints and upper/lower limits to be imposed on DM annihilation cross section, relic density, astrophysical factor and other relevant quantities. As we discussed in the previous sections, the gamma-ray spectra appear more similar at the energy corresponding to the peak of emission, but important di erences appear at lower and higher energies. Lower energies are less

Figure 9. (Left-panel) tt annihilation channel with MDM = 1 TeV in logarithmic scale. At low energy the simulations are consistent down to x [similarequal] 106. HERWIG++ drops down at x [similarequal] 107

and PYTHIA 8 does at x [similarequal] 1010, producing a higher number of photons that is 100 times higher

than HERWIG++ at x [similarequal] 107, and almost 10 times lower than PYTHIA 6.4 at the same value of x.

PYTHIA 6.4 cuts-o at x [similarequal] 1013 whereas HERWIG does at x [similarequal] 1012 where the two spectra match.

For higher energies, HERWIG provides a higher ux with a maximum factor of ten at x [similarequal] 108.

(Right-panel) tt annihilation channel with MDM = 1 TeV in linear scale. The four simulations are all manifestly inconsistent between them at very high energy. HERWIG++ ux becomes lower from x [similarequal] 0.2 onwards and cuts-o at x < 0.8. At x [similarequal] 0.4, PYTHIA 6.4 splits from HERWIG and PYTHIA

8 that remain with higher ux. PYTHIA 6.4 cuts-o before reaching x = 1, such as HERWIG does, although with very di erent spectral form and a separation of a factor ten at x [similarequal] 0.8. Finally,

HERWIG also splits from PYTHIA 8 at x [similarequal] 0.6, producing the highest ux with cut-o at x = 1.

important in the context of indirect searches, because of the dominance of astrophysical background components. However, the spectra at high energies could be of some interest. As an illustrative example, the next Cherenkov Telescope Array (CTA) is expected to extend the accessible energy range from well below 100 GeV to above 100 TeV [5052] and therefore may cover a wide range of high gamma-ray energies and signatures of DM annihilation in a wider range of masses than for instance FERMI-LAT satellite.

Since PYTHIA 8 includes both a good description of the t quark behavior and the QED radiation, we use it to compare with the other generators. We present the Monte Carlo relative deviation ( MCi) with respect to PYTHIA 8 in gure 10, dened as

MCi = MCi PYTHIA 8

PYTHIA 8 , (4.1) where MCi stands for PYTHIA 6.4, HERWIG and HERWIG++. For a DM mass of 1 TeV, the relative deviations are always less than 20% up to x = 0.2. For the whole high energy range, PYTHIA 6.4 produces typically less photons with a maximum relative error of 50% with respect to PYTHIA 8, apart from the tt channel for which the strong approximation leads to di erences up to 100%. HERWIG exhibits deviations lower than 50% for the W +W

channel up to x [similarequal] 0.6, similar deviations are found for b

b up to x [similarequal] 0.5 and for almost

all the high energy range (up to x = 0.8) for +. In the case of tt channel, deviations

below 50% are found just below x [similarequal] 0.3. HERWIG++ shows di erences up to 100% for all

the annihilation channels when the energy increases beyond those values.

Pythia 8

Herwig

Pythia 6.4

Herwig++

Pythia 8

Herwig

Pythia 6.4 Herwig ++

x1.5 dN/dx

1e-14 1e-12 1e-10 1e-08 1e-06 0.0001 0.01 1

x=E/MDM

10 0 0.2 0.4 0.6 0.8 1

x=E/MDM

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6MC i

x=E/MDM

(a) W +W channel

6MC i

x=E/MDM

(b) bb channel

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6MC i

x=E/MDM

(d) tt channel

Figure 10. Relative deviations versus x at MDM = 1 TeV. The full horizontal line at zero represents PYTHIA 8. The dashed blue line holds for PYTHIA 6.4 vs. PYTHIA 8, the dotted one is HERWIG Fortran vs. PYTHIA 8 and the two-dotted one is HERWIG++ vs. PYTHIA 8.

On the other hand, the total number of photons produced by each event or multiplicity, also a ects the constraints both in the sense of annihilations cross section and astrophysical factor. In indirect searches a typical signicance of the signal between 2 and 5 with respect to the background is demanded. Apart from the specic characteristics of the detector, the ux of photons depends upon the DM density and the distance and distribution of the sources. All these dependences are taken into account by the astrophysical factor

hJ[angbracketright] and the boost factor b. Thus, two simulations should give di erent number of photons

for the same number of events, this situation will a ect the parameters [angbracketleft]J[angbracketright] and b.

As we can see in gure 11, the multiplicity depends not only on the Monte Carlo event generator, but also on the energy of the event and the annihilation channel. In this study, we set a lower photon energy cut-o of xC = 105. It means that the energy cut-o increases with the DM mass. This kind of DM mass depending cut-o allows to reject photons of lower energies, where the simulations present important di erences. However, the excluded range of the spectrum is not relevant for gamma-ray observations. This cut-o is also compatible with typical gamma-ray detectors energy thresholds. As an example, for a DM mass of 10 TeV, the corresponding energy cut lies at 100 MeV. Detector energy thresholds

x=E/MDM

N \/ N ->SM

MDM (GeV)

(a) W +W channel.

N \/ N ->SM

MDM (GeV)

(b) bb channel

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N \/ N ->SM

MDM (GeV)

(d) tt channel

Figure 11. Multiplicity of the four Monte Carlo generators for each annihilation channel. W +W

annihilation channel (upper left panel): Regardless the DM mass value, PYTHIA 6.4 provides the upper limit to the number of generated photons, while HERWIG Fortran provides the lower limit with 23% di erence between them; bb annihilation channel (upper right panel): At MDM 200 GeV, the

multiplicity of the two versions of PYTHIA is the same, as for the multiplicity of the HERWIG versions, but di erent between them. For that value of the mass, the relative deviation on multiplicity between PYTHIA and HERWIG codes almost attains 100%; + annihilation channel (lower left panel): The maximum di erence between the four simulations multiplicities ranges between 20% at low energy up to 72% at higher energy; tt annihilation channel (lower right panel): Relative deviations run from 20% up to 30% depending on the energy of the event.

are typically around 1 10 GeV depending on the particular experimental device [33]. In

any case, we have checked that our results and conclusions about the di erent multiplicities do not depend on the particular choice of this cut-o . Thus we have tested the robustness of our analysis with xC = 103 and MC = 1 GeV. In most of the cases PYTHIA 6.4 gives the multiplicity upper limit, except for the tt annihilation channel maybe due to the approximation of such process [3438] and bb channel at the range MDM > 200 GeV.

On the other hand, the lower limit is given by HERWIG++ in most of the cases, except for W +W and bb (the last one, up to MDM > 200 GeV) annihilation channel.

The multiplicity behavior is well approximated by the following power law relation

MDM (GeV)

Software/PYTHIA 8 W +W bb + tt

PYTHIA 6.4 A = 1.04 A = 1.18 A = 0.96 A = 1.49

B = 0 B = 0.033 B = 0.020 B = 0.077

HERWIG A = 0.84 A = 1.13 A = 1.00 A = 1.02

B = 0 B = 0.068 B = 0.029 B = 0.038

HERWIG++ A = 0.90 A = 0.93 A = 0.96 A = 0.93

B = 0 B = 0.025 B = 0.039 B = 0.031

PYTHIA 8 a = 28.9 a = 7.62 a = 2.29 a = 14.1

b = 0.001 b = 0.331 b = 0.042 b = 0.276

Table 2. Relative behaviors in the total number of photons produced by PYTHIA 6.4, HERWIG and HERWIG++ with respect to PYTHIA 8 in the range 15 GeV - 10 TeV. Here A = aMCi/aPYTHIA 8 and

B = bMCi b

PYTHIA 8. PYTHIA 8 multiplicity parameters are listed at the end of the table.

b, (4.2)

where the a and b coe cients depend on both the Monte Carlo simulator and the annihilation channel. When the SM particle is xed, cosmological constraints obtained by means of the total number of generated gamma photons might depend on the Monte Carlo simulation. As in the previous analysis, in table 2 we give the relations between the total number of photons generated by PYTHIA 6.4, HERWIG and HERWIG++ with respect to PYTHIA 8.

Let us summarize the situation as follows:

W +W annihilation channel: Roughly speaking PYTHIA 6.4 generates one more

photon than PYTHIA 8 for each event, while HERWIG++ and HERWIG Fortran produce 3 and 5 photons less, respectively. Above [similarequal] 200 GeV, this fact introduces a deviation

on the multiplicity of 4% between PYTHIA 6.4 and PYTHIA 8, of 16% between

HERWIG and PYTHIA 8 and of 10% between HERWIG++ and PYTHIA 8. Between

PYTHIA 6.4 and HERWIG in Fortan and HERWIG++ the deviation is 23% and 15%

, respectively. Finally, the deviation between HERWIG and HERWIG++ is 6%. For

kinematic reasons, no photons are produced at energies lower than the mass of the W boson, that is the reason of the cut around [similarequal] 80 GeV.

b annihilation channel: At MDM [similarequal] 200 GeV, the deviation between the multi

plicity of the two versions of PYTHIA is the less than 1%, as for at 100 GeV and HERWIG versions, but di erent between them. At 150 GeV, the number of photons produced by the Fortran versions of PYTHIA code is a 22% bigger than the HERWIG one. For masses below 200 GeV the upper limit is given by PYTHIA 6.4 whereas the lower

one is provided by HERWIG++. At 10 TeV the deviation reach the maximum value of

13%, 40% and 26% between PYTHIA 6.4, HERWIG, HERWIG++ and PYTHIA 8,

respectively. On the other hand, at M > 200 GeV PYTHIA 8 gives the upper limit and HERWIG Fortran the lower one.

JHEP09(2013)077

with the DM mass:

N~~!SM [similarequal]

a [notdef]

[parenleftbigg]

M1 GeV

+ annihilation channel: The number of photons per event produced by the

four Monte Carlo generators is very similar for this channel, but very low. This fact introduce a very important di erence in percent, that reach the maximum of 42%

at 10 TeV between PYTHIA 6.4 and HERWIG++. PYTHIA 6.4 gives here the upper limit, followed by PYTHIA 8, HERWIG Fortran and HERWIG++. At lower energies the di erence between upper and lower limit is less than 20%, and increase up to 72% at higher DM mass.

tt annihilation channel: As in the case of W +W channel, no photons are pro

duced at energies lower than the mass of the top quark because of kinematic reason. Always PYTHIA 8 gives here the upper limit, followed by PYTHIA 6.4, HERWIG Fortran and HERWIG++. All the multiplicities depend on the DM mass in a exponential way, but with di erent exponents. At lower energies the deviation between upper and lower limits is about 20%, and around 30% for events at higher energies.

5 Conclusions

We have analyzed the gamma-ray spectra produced by four Monte Carlo event generator software, namely PYTHIA 6.4, PYTHIA 8, HERWIG Fortran and HERWIG++. These spectra have been largely used in the framework of dark matter indirect searches and the di erences between them may a ect the results for those investigations. Although gamma-ray spectra have been generated for dark matter annihilating in all possible quark-antiquark, leptonic and bosons channels, we chose to show a representative sample of them (bb for the quark-antiquark case, + for the leptonic one and W +W boson annihilation channels). We also included the particular case of the tt and studied it separately.

At the energy of maximum ux, where the simulations are well tted to LEP or LHC data, the di erences between packages are less than 20%. This statement is always true in the range 0.01 < x < 0.2 with possible extension of the range depending on the annihilation channel and the energy of the event (see the bulk of this communication for further details). On the one hand, at lower energy the spectra appear very di erent between them, depending strongly on the cut-o set for the minimal allowed energy in the parton shower. On the other hand, di erences also appear at higher energy. For all the studied channels, the implementation absence of Bremsstrahlung radiation generated by high energy leptons in HERWIG++ leads to a smaller number of high-energy photons when compared to the other softwares. Moreover, in the case of the tt annihilation channel, there is an additional e ect due to the fact that the top quark behavior phenomenology has been improved in the codes released in the last years. Thus, whereas for PYTHIA 6.4 this channel was approximated through the decay into W and b, higher order e ects have been included in the newest software generations. Due to the combination of these two factors, we conclude that the most reliable Monte Carlo event generator software for gamma-ray spectra is PYTHIA 8. For this reason we got estimations for the relative deviations for PYTHIA 6.4, HERWIG Fortran and HERWIG++ with respect to PYTHIA 8.

We conclude that further implementation is needed in HERWIG++ in order to improve its competitiveness in the gamma-ray sector. For the other three Monte Carlo event

JHEP09(2013)077

generators under study in this work, the gamma-ray spectra simulated show also important di erences. Without taking into account very low energies, the relative deviations can only be bounded by 50% for the hadronic (bb) and electro-weak channels (W +W ). The

situation for the tt channel and the leptonic ones (+) is even worse. At high energies, the discrepancies can reach 100%. In fact, the photon uxes predicted by the di erent generators can di er in several orders of magnitude. On the other hand, the situation for the total number of produced photons improves a little, and the maximum di erence is a factor 2 within the studied mass region.

These signicative di erences can play an important role in misunderstanding dark matter signatures. For example, in a dark matter study, once the astrophysical factor is obtained by tting the dark matter gamma-ray spectra, these discrepancies may introduce a deviation on the boost factor proportional to the di erence on the multiplicity. This e ect can be easily estimated with the help of eq. (4.2) and table 2. However, we have shown that the simulated spectral shapes can be very di erent and this fact may have a large impact in the analysis.

Acknowledgments

This work was supported by UCM FPI grants G/640/400/8000 (2011 Program), the Spanish MINECO projects numbers FIS2011-23000, FPA2011-27853-C02-01, FPA2011-22975 and MULTIDARK CSD2009-00064 (Consolider-Ingenio 2010 Programme). AdlCD also acknowledges nancial support from Marie Curie - Beatriu de Pins contract BPB00195, Generalitat de Catalunya and ACGC, University of Cape Town. RL also acknowledges Prometeo/2009/091 (Generalitat Valenciana) and EU ITN UNILHC PITN-GA-2009-237920 nancial support. AdlCD thanks the hospitality of Kavli Institute for Theoretical Physics China (KITPC), Chinese Academy of Sciences, Beijing China for support during the preparation of this manuscript.

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JHEP09(2013)077

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SISSA, Trieste, Italy 2013

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We study the differences in the gamma-ray spectra simulated by four Monte Carlo event generator packages developed in particle physics. Two different versions of PYTHIA and two of HERWIG are analyzed, namely PYTHIA 6.418 and HERWIG 6.5.10 in Fortran and PYTHIA 8.165 and HERWIG 2.6.1 in C++. For all the studied channels, the intrinsic differences between them are shown to be significative and may play an important role in misunderstanding dark matter signals.

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Title

Reliability of Monte Carlo event generators for gamma-ray dark matter searches

Author

Cembranos, J A; R; de la Cruz-Dombriz, A; Gammaldi, V; Lineros, R A; Maroto, A L

Pages

1-21

Publication year

2013

Publication date

Sep 2013

Publisher

Springer Nature B.V.

e-ISSN

10298479

Source type

Scholarly Journal

Language of publication

English

DOI

https://doi.org/10.1007/JHEP09(2013)077

ProQuest document ID

1652879776

SISSA, Trieste, Italy 2013

Reliability of Monte Carlo event generators for gamma-ray dark matter searches

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