We provide a comparison of the results of four SUSY mass spectrum
calculations in mSUGRA: Isajet, SuSpect, SoftSusy, and SPheno. In particular,
we focus on the high tan(beta) and focus point regions, where the differences
in the results are known to be large.Comment: Contribution to SUSY02, 17-23 Jun 2002, DESY Hamburg, 7 page

Allanach, B.

Kraml, S.

Porod, W.

English

arXiv

We provide a comparison of the results of four SUSY mass spectrum calculations in mSUGRA: Isajet, SuSpect, SoftSusy, and SPheno. In particular, we focus on the high tan(beta) and focus point regions, where the differences in the results are known to be large

Allanach, Benjamin C

Kraml, Sabine

Porod, Werner

CERN Document Server

Comparison of SUSY mass spectrum calculationsB. Allanach, S. Kraml,1 W. PorodAbstractWe provide a comparison of the results of four SUSY mass spectrum calculationsin mSUGRA: Isajet, SuSpect, SoftSusy, and SPheno. In particular, we focus on thehigh tan β and focus point regions, where the differences in the results are knownto be large.Contribution to SUSY02, 10th International Conference on Supersymmetry and Unificationof Fundamental Interactions, 17–23 June 2002, DESY Hamburg, Germany.1 IntroductionMany SUSY studies rely on computer codes that calculate the mass spectrum of theminimal supersymmetric standard model (MSSM), the couplings, branching ratios, etc.,from given sets of model parameters. For the LHC, for instance, many simulations aredone for particular benchmark scenarios or by mapping the (m0, m1/2) parameter plane.For such studies it is certainly important wheather a particular decay channel is openor not and what branching ratio it has. Also, theoretically or experimentally excludedregions depend on the details of the spectrum. Studies for an e+e− Linear Collider deal, inaddition, with high precision measurements of (s)particle properties, with the determina-tion of the underlying SUSY breaking parameters, their extrapolation to the GUT scale,model destinction, etc. Experimental accuracies of the per-cent or even per-mille level areexpected. It is thus clear that we need theoretical predictions of a precision comparableto the experimental accuracy. However, it has been noticed [1, 2] that dierent programscan give quite dierent results for the same set of input parameters.In this article, we compare the mass spectrum calculations of four public codes:Isajet 7.63 [3], SuSpect 2.005 [4], SoftSusy 1.4 [5], and SPheno 1.0 [6], in the minimal su-pergravity (mSUGRA) framework. We discuss the renormalization group (RG) runningand the implementation of radiative corrections, concentrating on the parameter regionswhere the largest dierences are encountered: large tanβ and large m0. An overview ofwhich corrections are implemented in each of the four programs is given in Table 1.2 Large tanβLarge tanβ has always been recognized as a dicult case since it requires a thoroughtreatement of the bottom Yukawa coupling hb. It is well known [12] that hb gets largetanβ enhanced corrections from SUSY loops, the dominant contributions coming from~b~g and ~t~χ+ exchanges. These generate a H02bb coupling, which is forbidden at tree-level,L  hb H01bb + hb H02bb. This modies the tree-level relation between the bottom mass1Speaker1Isajet 7.63 SuSpect 2.005 SoftSusy 1.4 SPheno 1.0RGEsgauge + Yuk. 2–loop 2–loop 2–loop 2–loopgaugino par. 2–loop 2–loop 2–loop 2–loopscalar par. 2–loop 1–loop 1–loop 2–loopSUSY massesχ˜±, χ˜0 some corr. for χ˜±1 1–loop approx. for ∆M1, ∆M2, ∆µ full 1–loopt˜ — t˜g + tg˜ + Yuk. full 1–loop full 1–loopb˜ — b˜g + bg˜ full 1–loop full 1–loopg˜ gg˜ + qq˜ loops resummedYukawa cpl.ht full 1–loop resum. tg + t˜g˜ full 1–loop full 1–loophb full 1–loop resum. bg + b˜g˜ + t˜χ˜± corr. resummed full 1–loop resum.Higgs sectortadpoles 3rd gen. (s)fermions complete 1–loop corrections [7]h0, H0 1–loop [8] 1–loop [9] 2–loop [10] 2–loop [11]Table 1: RGEs and radiative corrections implemented in Isajet, SuSpect, SoftSusy, andSPheno.and Yukawa coupling, mb = hbv1 ! mb = hbv1(1 + b) with b = (hb/hb) tanβ. In theprograms under discussion this is taken into account ashb(MZ) = m^MSSMb (MZ)/v1(MZ) , m^MSSMb (MZ) =m^SMb (MZ)1 + mb/mb. (1)Here m^SMb is the DR bottom mass in the Standard Model and mb = (mb)b˜g˜+t˜χ˜++...contains the SUSY-loop corrections. The complete 1-loop expression for mb is given in[7].2 Compared to the naive 1-loop expansion m^MSSMb = m^SMb (1−mb/mb), eq. (1) makesa numerical dierence of about 10% in hb and about 10{30% in mA for large tanβ. The re-summation of SUSY threshold corrections [13] will be discussed elsewhere [14]. Althoughall four programs now apply eq. (1), some numerical dierences in hb remain. These arepartly due to dierences in αs: Suspect, SoftSusy and SPheno calculate αs in the DRscheme, Isajet uses the MS value. Another reason is that Isajet uses mb = mb(MSUSY )for the expression mb/mb in eq. (1), while the other programs use mb(MZ) or the bottompole mass; also the gluino masses dier by about 5%. Moreover, the vacuum expectationvalues v1,2 are not running in Isajet.The bottom Yukawa coupling has its largest eect in the Higgs sector. Figure 1 showsthe running of m2H1,2 for m0 = 400 GeV, m1/2 = 300 GeV, A0 = 0, µ > 0, and the twocases tan β = 10 and tanβ = 50. As one can see, there is good agreement for not toolarge tanβ. However, for tanβ = 50, quite dierent results are obtained for m2H1 , whoseevolution is driven by hb:dm2H1dt 38pi2hb Xb + . . . , Xb = (m2Q˜+ m2D˜+ m2H1 + A2b) . (2)2Here note that [3, 4, 5, 6] and [7] partly have different conventions, e.g., for the ordering of the squarkmass eigenstates and the sign of µ.2Note in particular the dotted line which shows the result obtained with Isajet 7.58. Inthis version, the SUSY corrections to hb were not yet resummed.2 4 6 8 10 12 14 16-20-10010202 4 6 8 10 12 14 16-20-1001020m2Hi [104 GeV2] m2Hi [104 GeV2]Log(Q/1 GeV) Log(Q/1 GeV)m2H1 m2H1m2H2 m2H2tanβ = 10 tanβ = 50Figure 1: Running of m2H1,2 as a function of the scale Q, for m0 = 400 GeV, m1/2 =300 GeV, A0 = 0, µ > 0, tanβ = f10, 50g, Mt = 175 GeV. The full (dotted) lines arefor Isajet 7.63 (7.58), the dashed lines are for SuSpect 2.005, the dash-dotted ones forSoftSusy 1.4, and the dash-dot-dotted ones for SPheno 1.0.The dierences in m2H1 directly translate into m2A and thus into the physical Higgsboson masses, sincem2A =1c2β(m2H2 −m2H1+s2β t1v1+c2β t2v2−M2Z . (3)Here m2Hi = m2Hi− ti/vi, i = 1, 2, and t1,2 are the tadpole contributions. The self energiesof Z and A have been neglected in eq. (3). We note that including only the tadpolesfrom the third generation is in general a good approximation. The remaining 1-loopcontributions account for a O(1%) correction.Figure 2 shows the Higgs boson masses obtained by the four programs as a functionof tan β. The new Isajet version 7.63 has led to a majer improvement compared tothe situation discussed in [2, 15] (the results obtained by Isajet 7.58 are again shown asdotted lines in Fig. 2). For mA and mH± there is now agreement within  10% up totanβ  45. Sources for the remaining dierences are pointed out above. Moreover, itmakes a dierence whether one uses running couplings and/or masses for the tadpolest1,2. Here each program has a dierent approach. For the neutral scalars, however, thesituation is not so good. Especially for mh0 , a discrepancy of  4 GeV is too largecompared to the expected experimental accuracy. This discrepancy is mainly due tothe dierent radiative corrections taken into account for the (h0, H0) system. They varybetween 1- and 2-loop, eective potential and diagramatic calculations, see Table 1. Giventhe expected experimental accuracy for mh0 it is clear that the best available calculationshould be used.310 20 30 40 5030040050060010 20 30 40 5030040050060010 20 30 40 5011211311411511611710 20 30 40 50300400500600m[GeV]m[GeV]m[GeV]m[GeV]tanβ tan βtanβ tan βh0H0A0 H±Figure 2: Higgs boson masses as a function of tanβ, for m0 = 400 Gev, m1/2 = 300 GeV,A0 = 0, µ > 0, Mt = 175 GeV; full (dotted) lines: Isajet 7.63 (7.58), dashed: SuS-pect 2.005, dash-dotted: SoftSusy 1.4, dash-dot-dotted: SPheno 1.0.3 Large m0For large m0, the running of m2H2becomes very steep and very sensitive to the top Yukawacoupling ht = m^t/v2 :dm2H2dt 38pi2ht Xt + . . . , Xt = (m2Q˜+ m2U˜+ m2H2 + A2t ) . (4)As a result, the µ parameter given byµ2 =mH1 −m2H2 tan2 βtan2 β − 1 −12M2Z (5)becomes extremely sensitive to ht. This is visualized in Fig. 3 where we show in (a)the running of m2H1,2 for m0 = 1450 GeV, and in (b) µ as a function of m0. The other42 4 6 8 10 12 14 16-50050100150200m2 Hi[104GeV2]Log(Q/1 GeV)m2H1m2H2a)200 600 1000 1400 18000100200300400500µ[GeV]m0 [GeV]b)Figure 3: a) Running of m2H1,2 for m0 = 1450 GeV; b) µ as a function of m0; for m1/2 =300 GeV, A0 = 0, µ > 0, tanβ = 10, and Mt = 175 GeV; full (dotted) lines: Isajet 7.63(7.58), dashed: SuSpect 2.005, dash-dotted: SoftSusy 1.4, dash-dot-dotted: SPheno 1.0.parameters are m1/2 = 300 GeV, A0 = 0, µ > 0, and tanβ = 10. The large discrepancyin µ for m0 > 800 GeV lead to completely dierent chargino/neutralino properties andlikewise to very dierent excluded regions in Isajet compared to the other programs. Forinstance, radiative EWSB breaks down in Isajet for m0 > 1.5 TeV. In SuSpect, SoftSusy,and SPheno, this happens only for m0 > 2.5{2.8 TeV.3In order to understand the behaviour in Fig. 3b it is useful to write eq. (5) in the formµ2 ’ c1 m20 + c2 m21/2 − 0.5M2Z . (6)Approximate analytical expressions for c1 and c2 can be found e.g., in [16, 17]. For A0 = 0and tanβ = 10 we get [17]c1 m^t156.5 GeV2− 1 , c2 m^t102.5 GeV2− 0.52 . (7)Since the Higgs potential is minimized at MSUSY =pmt˜1mt˜2 , we take m^t in eq. (7) asm^t = m^t(MSUSY ). The m0 dependence seen in Isajet is reproduced for m^t  151 GeV.The one of SuSpect, SoftSusy and SPheno is reproduced for m^t  155 GeV. Figure 4shows a contour plot of µ in the (m0, m^t) plane. Notice the fast increasing dependenceon m^t for increasing m0. Notice also that for m^t  156{157 GeV, µ becomes almostindependent of m0, which is the actual focus point condition.There are some obvious dierences in the calculations. For instance, MSUSY , the scalewhere the SUSY parameters are frozen out and the Higgs potential is minimized, variesby about 100 GeV due to dierent radiative corrections to the stop masses, c.f. Table 1.In the loop corrections to mt, analogous dierences occur as discussed above for mb/mb.3After the conference, a sign error was corrected in SPheno. As a consequence, its results for largem0 now nicely agree with those of SoftSusy and SuSpect (contrary to what was presented in the talk).51000 1500 2000 2500 3000150152154156158160m^t[GeV]m0 [GeV]0200300400500 600Figure 4: The parameter µ as given by eq. (6) in the (m0, m^t) plane, for m1/2 = 300 GeV,A0 = 0, and tanβ = 10.Also the evolution of ht between MZ and Mt and the inclusion of threshold eects aredelicate points. However, this is not yet sucient to explain the observed discrepancies.More work is needed to clarify the situation.4 ConclusionsFor the calculation of the SUSY mass spectrum from GUT scale boundary conditions,there are two particular dicult parameter regions where large numerical dierences havebeen noticed: large tan β and large m0. These regions are very sensitive to the bottomand top Yukawa couplings, respectively.The inclusion of the SUSY 1-loop corrections to hb has led to a considerable improve-ment in the large tan β case. In particular, the four programs now agree on mA within< 10% for tan β < 45. Further improvements are of course desirable.For large m0, there are still very large numerical discrepancies due to the correctionsto ht. As a matter of fact, ht is much smaller in Isajet than in the other programs. Somedierences in the calculation of ht have been pointed out, but these do not satisnglyexplain the observed discrepancies. Work is in progress to clarify the situation [14].AcknowledgementsWe thank H. Baer, A. Djouadi, and J.-L. Kneur for useful discussions.6References[1] B. C. Allanach, in Proc. of the APS/DPF/DPB Summer Study on the Future of Par-ticle Physics (Snowmass 2001) ed. R. Davidson and C. Quigg, arXiv:hep-ph/0110227.[2] N. Ghodbane and H. U. Martyn, in Proc. of the APS/DPF/DPB Summer Studyon the Future of Particle Physics (Snowmass 2001) ed. R. Davidson and C. Quigg,arXiv:hep-ph/0201233.[3] H. Baer, F. E. Paige, S. D. Protopopescu and X. Tata, arXiv:hep-ph/0001086;http://paige.home.cern.ch/paige/[4] A. Djouadi, J.-L. Kneur and G. Moultaka,http://www.lpm.univ-montp2.fr:6714/kneur/suspect.html[5] B. C. Allanach, Comput. Phys. Commun. 143 (2002) 305 [arXiv:hep-ph/0104145];http://allanach.home.cern.ch/allanach/softsusy.html[6] W. Porod, in preparation.[7] D. M. Pierce, J. A. Bagger, K. T. Matchev and R. J. Zhang, Nucl. Phys. B 491(1997) 3 [arXiv:hep-ph/9606211].[8] M. A. Bisset, Ph.D. thesis, Univ. Hawaii, UMI-95-32579, 1995.[9] M. Carena, M. Quiros and C. E. Wagner, Nucl. Phys. B 461 (1996) 407 [arXiv:hep-ph/9508343].[10] S. Heinemeyer, W. Hollik and G. Weiglein, Comput. Phys. Commun. 124 (2000) 76[arXiv:hep-ph/9812320].[11] G. Degrassi, P. Slavich and F. Zwirner, Nucl. Phys. B 611 (2001) 403 [arXiv:hep-ph/0105096]; A. Brignole, G. Degrassi, P. Slavich and F. Zwirner, Nucl. Phys. B 631(2002) 195 [arXiv:hep-ph/0112177], arXiv:hep-ph/0206101.[12] R. Hempfling, Phys. Rev. D 49 (1994) 6168; L. J. Hall, R. Rattazzi and U. Sarid,Phys. Rev. D 50 (1994) 7048 [arXiv:hep-ph/9306309].[13] M. Carena, D. Garcia, U. Nierste and C. E. Wagner, Nucl. Phys. B 577 (2000) 88[arXiv:hep-ph/9912516].[14] B. Allanach, S. Kraml and W. Porod, in preparation.[15] S. Kraml, talk at the 2nd workshop of the extended ECFA/DESY study ”Physics andDetectors for a 90 to 800 GeV Linear Collider”, 12{15 Apr 2002, St. Malo, France.[16] M. Carena, M. Olechowski, S. Pokorski and C. E. Wagner, Nucl. Phys. B 426 (1994)269 [arXiv:hep-ph/9402253].[17] M. Drees and S. P. Martin, arXiv:hep-ph/9504324.7

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