Virtual Effects of Split SUSY in Higgs Productions at Linear Colliders

Home , Split supersymmetry

arXiv:hep-ph/0612273v2 21 Feb 2007 e ne h oua assumption about popular than the lighter under be TeV light- must 1 the chargino, i.e., and eigenstates, neutralino (except est mass higgsinos lightest and dark gauginos whose cosmic of gluinos), masses the con- However, the stronger on much 4]. straints imposes may [3, WMAP TeV by they measured 10 and matter as that scale heavy TeV out as below be gauginos turns necessarily require It not higgsinos does or unification the matter. con- coupling and gauge dark the couplings the cosmic by gauge of required of unification is explanation light- the higgsinos The of and sideration gauginos requirements. direct of and various ness considering constraints by indirect pos- masses the and their examine of to range important is sible it split-SUSY, in gsinos the SUSY story, on higgsinos. true studies and the gauginos theoretical is be and will split-SUSY experimental if of the So, like focus colliders ILC. foreseeable and at pos- LHC accessible are and higgsinos supersym- and light gauginos sibly scalar only bosons) all and Higgs superheavy which additional are in and (sfermions be [2], particles to split-SUSY metric out of turn may kind SUSY fine-tuning a constant, the like cosmological in just the fine-tuning nature, for the map in and if works test However, physics precision particle and structure. its fingerprints on detailed in its its zero of out will some to [1] ILC reveal fine- expects the least the LHC then at solving the or physics, by it If particle discover required in experiments. as problem collider TeV-scale, tuning future at of is focus exploration SUSY central its a theory, be string will and cosmology physics, cle ofcltt h oldrsace o agnsadhig- and gauginos for searches collider the facilitate To parti- in appealing so is (SUSY) supersymmetry Since ita ffcso pi UYi ig rdcin tLna C Linear at Productions Higgs in SUSY Split of Effects Virtual through hsc ffcs nti okw suesltsprymtya productio supersymmetry Higgs split in assume le higgsinos we percent and work of gauginos this effects WMAP-allowed In virtual the the proc effects. render some physics ILC in the effects cou of virtual dar luminosity and and/or cosmic constrained productions the stringently direct for are their account higgsinos to and order gauginos In Had (ILC). Large CERN Collider the Linear like colliders foreseeable at accessible lee yafwpreti oepr fteWA-loe para WMAP-allowed the of part some in the percent to few a by altered ASnmes 48.y 95.35.+d 14.80.Ly, numbers: PACS colliders. the at supersymmetry rs etoso hriopi rdcin n a ffrcom offer can and productions pair chargino of sections cross nsltsprymtyteguio n igio r h on the are higgsinos and gauginos the supersymmetry split In .INTRODUCTION I. e Wang Fei W W 1 W W 4 etrfrHg nryPyis snhaUiest,Beiji University, Tsinghua Physics, Energy High for Center 2 eateto hsc,HnnNra nvriy ixag4 Xinxiang University, Normal Henan Physics, of Department uinprocess fusion nttt fTertclPyis cdmaSnc,Beijin Sinica, Academia Physics, Theoretical of Institute 3 uina h L.W n httepouto rs eto of section cross production the that find We ILC. the at fusion CS WrdLbrtr) ..o 70 ejn 000 Ch 100080, Beijing 8730, P.O.Box Laboratory), (World CCAST 1 ey Wang Wenyu , e M + e 1 − = → 2 Dtd oebr1,2018) 14, November (Dated: uin Xu Fuqiang , M ν e 2 ν ¯ / e with 2 h sblw1.Sc ita ffcsaecreae ihthe with correlated are effects virtual Such 1%. below is 2 i i Yang Min Jin , h ig oo.Sc ita ffcso ekyinteract- weakly of effects virtual of Such interactions boson. of gauge Higgs effects the the virtual on the concentrate reveal we sfermions to split-SUSY, involve small So, always superheavy. be are loops Higgs- which to vertex and relevant expected interactions the are quark since interactions top split-SUSY, Yukawa For in fermion physics. effects new virtual to particles sensitive heaviest its and the SM are the they in top since and have [10] [9] may processes processes SUSY boson quark Higgs that in shown effects is virtual can sizable It disen- which measured. processes through precisely some is in be pro- particles effects to virtual these the way their of tangling space other existence The parameter the small. the reveal unobservably of are but rates part in space, duction remained large parameter quite WMAP-allowed the are the in ILC of and pair part LHC chargino some the the at that rates showed looking production [5] productions. directly pair analysis is chargino previous way as Our One such productions, ways. their two the for in at ILC explored be and can LHC matter dark cosmic the by strained examine There- to ILC. important and charginos. is LHC and it the neutralinos heavy split-SUSY, of the quite explore reach be to the may of fore, it out [8], gluon- thus LHC the and the in of produced the environment copiously and is rich be higgsinos gluino to and the expected gauginos usually among although particle So, colored the neu- only Theoretically, charginos. than heavier much and [3]. TeV be tralinos to 18 con- speculated as usually matter high is uni- gluino dark as coupling gauge be the by can to constrained fication mass subject its directly and straints not is gluino 7]. 6, [5, respectively M 1 h etaio n hrio nsltSS con- split-SUSY in charginos and neutralinos The the charginos, and neutralinos the unlike that Note and o oldr(H)adteInternational the and (LHC) Collider ron se.Tecenevrnetadhigh and environment clean The esses. db xlrda h oldr through colliders the at explored be ld lmnayifraini rbn split probing in information plementary M e ennfli naeigtenew the unraveling in meaningful vel atrmaue yWA,these WMAP, by measured matter k ysprymti atce possibly particles supersymmetric ly 2 ns dcluaetevruleet of effects virtual the calculate nd en h ()adS()guiomasses, gaugino SU(2) and U(1) the being ee pc,wietecorrection the while space, meter e + 3 e , 2 − unu Zhang Huanjun , 000 China 100080, g g108,China 100084, ng → 30,China 53007, Zh e and + e ina − e + → e − Zh 2 → olliders , 4 a be can ν e ν ¯ hep-ph/0612273 e h 2 ing neutralinos and charginos are usually at percent level The chargino mass matrix is given by and only the high-luminosity e+e− collider like the ILC M2 √2mW sin β can possibly have such percent-level sensitivity. As the , (2) √ discovery machine, the LHC, however, is not expected „ 2mW cos β µ « to be able to disentangle such percent-level quantum ef- and the neutralino mass matrix is given by fects due to its messy hadron backgrounds. So in this M1 0 mZ sW cβ mZ sW sβ work we investigate the virtual effects of the WMAP- − + − 0 0 M2 mZcW cβ mZ cW sβ 1 allowed split-SUSY in Higgs productions e e Zh − , (3) + − → mZ sW cβ mZ cW cβ 0 µ and e e νeν¯eh through W W fusion at the ILC. Note B − − C → B mZ sW sβ mZ cW sβ µ 0 C that although the SUSY corrections to these processes @ − − A were calculated in the literature [11, 12], our studies in where sW = sin θW and cW = cos θW with θW being this work are still necessary since those calculations were the weak mixing angle, and sβ = sin β and cβ = cos β performed in the framework of the general minimal su- with β defined by tan β = v2/v1, the ratio of the vac- persymmetric model and did not consider the dark mat- uum expectation values of the two Higgs doublets. M1 ter constraints. and M2 are respectively the U(1) and SU(2) gaugino This work is organized in the follows. In Sec. II we mass parameters, and µ is the mass parameter in the i j calculate the split-SUSY loop contributions to Higgs pro- mixing term µǫij HuH in the superpotential. The di- + − + − d duction e e Zh and e e νeν¯eh through W W − + agonalization of (2) gives two charginosχ ˜1,2 with the fusion at the ILC.→ In Sec. III we→ present some numerical convention Mχ˜+ < Mχ˜+ ; while the diagonalization of results for the parameter space under WMAP dark mat- 1 2 (3) gives four neutralinosχ ˜0 with the convention ter constraints. The conclusion is given in Sec. IV. Note 1,2,3,4 Mχ˜0 < Mχ˜0 < Mχ˜0 < Mχ˜0 . So the masses and mix- that for the SUSY parameters we adopt the notations in 1 2 3 4 ings of charginos and neutralinos are determined by four [13]. We assume the lightest supersymmetric particle is parameters: M1, M2, µ and tan β. the lightest neutralino, which solely makes up the cosmic Note that the low energy lagrangian in Eq.(1) should dark matter. be understood as an effective theory after squarks, sleptons, and heavier Higgs bosons are integrated out. Then, as is discussed in [2], the Higgs-higgsino-gaugino cou- II. CALCULATIONS plings in Eq.(1) should deviate from the SUSY results shown in the off-diagonal elements of the mass matrices A. About split-SUSY in Eqs.(2) and (3), although such deviation is negligible for numerical results. In split-SUSY the Higgs sector at low energy is fine- In split SUSY the possible channels of Higgs (h) pro- tuned to have only one Higgs doublet [2] and the effective ductions at the ILC are the Higgs-strahlung process spectrum of superparticles contains the higgsinos H˜ , e+e− Z∗ Zh and W W -fusion process e+e− u,d → → → winos W˜ i, bino B˜ and gluinog ˜. The most genenral renor- νeν¯eh. Both processes will be precisely measured at malizable Lagrangian at low energy (say TeV scale) con- the ILC if the light Higgs boson h is indeed found at tains the interactions the LHC. Since these processes may be sensitive to new physics, they may serve as a good probe for TeV-scale λ 2 = m2H†H H†H new physics. Other channels, such as the production L − 2 of h associated with a CP-odd Higgs boson A and the u ∗ d e ¯ hij q¯j uiǫH + hij q¯j diH + hij ℓj eiH charged Higgs pair production, cannot occur due to the − superheavy A and the superheavy charged Higgs bosons. M 3 M2 M1 + gÃgÃ + W˜ aW˜ a + B˜B˜ 2 2 2 † ˜ T ˜ H a ˜ a ′ ˜ ˜ B. Split-SUSY loop effects in Higgs productions at +µHu ǫHd + g˜uσ W +˜guB Hu √2 the ILC T H ǫ a ˜ a ′ ˜ ˜ + g˜dσ W +˜gdB Hd + h.c. , (1) + − √2 − The tree-level e e Zh process is shown in Fig. 1. For the one-loop effects→ of split SUSY, we need to where ǫ = iσ2. Thus the Higgs sector in split-SUSY calculate the diagrams containing the effective Z-boson is same as in the SM except for the additional Higgs propagator and several effective vertices shown in Fig. 2. couplings to gauginos and higgsinos. Other four Higgs Note that the box diagrams always involve sfermions in bosons in the MSSM are superheavy and decouple. As the loops and thus drop out since all sfermions are super- is well known, an upper bound of about 135 GeV exists heavy in split SUSY. In our calculations we use the on- for the lightest Higgs boson in the MSSM [14], which is shell renormalization scheme [15]. For each effective ver- relaxed to about 150 GeV in split-SUSY [2]. tex or Z-boson propagator, we need to calculate several The gauginos (winos and bino) and higgsinos mix into loops plus the corresponding counterterms. For the new the mass eigenstates called charginos and neutralinos. rare vertices induced at loop level, such as γZh, there are 3 no corresponding counterterms. Since in split-SUSY all fective vertices shown in Fig. 5. Just like the diagrams scalar superparticles are superheavy and decouple from shown in Fig. 3, each effective vertex or W -boson propa- this process, the loops only involve charginos and neu- gator contains several loops plus the corresponding coun-

tralinos, as shown in Fig. 3. terterms, as shown in Fig. 6.

− FIG. 1: Feynman diagrams for e+e Zh at tree-level. − → FIG. 4: Feynman diagrams for WW -fusion process e+e → hνeν¯e at tree-level. e+ Z e+ Z

e+ ν¯ e+ ν¯ e+ ν¯ Z Z Z W W W W h e− h e− h (a) (b) W h h + + W e Z e Z − W − W − e ν e ν e ν (a) (b) (c) − FIG. 5: Feynman diagrams for WW -fusion process e+e Z γ → νeν¯eh with one-loop corrected propogators and eﬀective ver- e− e− h tices. (c) h (d) FIG. 2: Feynman diagrams for e+e− Zh with one-loop χ0 corrected propagators and eﬀective vertices→ in split-SUSY. ˜i W W W W W W = + 0 + χ˜i , χ˜j χ˜+ Z Z Z Z Z Z j = + h h h + 0 = χ˜ + χ˜i h h h W W Wj W W W = + 0 + Z Z Z Z Z Z χ˜i χ˜j

0 + χ˜i , χ˜j h + h h W W = γ Z γ Z FIG. 6: Feynman diagrams for each one-loop corrected propagator and effective vertex in Fig. 5. + χ˜j + − Z Z Z Note that for e e νeν¯eh, in addition to the W W - fusion contribution shown→ in Fig. 4, another contribution + + = χ˜j + comes from Higgs-strahlung process e e− Zh followed e e eγ e e e + − → by Z νeν¯e. The cross section of e e Zh νeν¯eh → → → peaks at the threshold of √s = MZ + Mh and then falls FIG. 3: Feynman diagrams for each one-loop corrected prop- rapidly as √s increases, where √s is the center-of-mass agator and effective vertex in Fig. 2. (c.m.) energy of e+e− collision. By contrast, the cross section of W W -fusion process grows monotonously as √s + − + − For the W W -fusion process e e νeν¯eh our cal- increases and is far dominant over e e Zh νeν¯eh + − → → → culations are similar as for e e Zh. The tree-level for √s Mh. In our calculation we assume √s = 1 TeV → ≫ Feynman diagram is shown in Fig. 4 and for one-loop ( Mh) and thus we only consider W W -fusion process. split-SUSY effects we need to calculate the diagrams con- ≫Note that in the literature [12] the supersymmetric taining the effective W -boson propagator and several ef- corrections to this W W -fusion process have been com- 4 puted, but those calculations focus on the loops involving + - sfermions (squarks and sleptons). In our calculations in -0.5 e e → Z h the scenario of split-SUSY, we consider the loops involv- -1 ing charginos and neutralinos, ignoring the loops involving sfermions since all sfermions are superheavy in split- -1.5 SUSY. So far in the literature such chargino/neutralino loop corrections have not been reported. -2 (%)

Each loop diagram is composed of scalar loop functions 0 -2.5 σ [16] which are calculated by using LoopTools [17]. The / ∆σ calculations of the loop diagrams are tedious and the an- -3 alytical expressions are lengthy, which are not presented here. -3.5

-4

III. NUMERICAL RESULTS -4.5

-5 In split-SUSY the masses of squarks and the CP-odd 300 400 500 600 700 800 900 1000 Higgs boson A are assumed to be arbitrarily superheavy. √ s | (GeV) FIG. 7: The relative one-loop correction of split-SUSY to the As our previous study showed [5], their effects in low en- + − ergy processes will decouple as long as they are heavier cross section of e e Zh versus the c.m. energy. 2 → than about 10 TeV. The Higgs mass Mh can be calculated from Feynhiggs [18] and in our calculations we as- e+e- → Z h 1.5 sume the masses of squarks and Higgs boson A are 200 √ s | = 1 TeV TeV. Among the low-energy parameters of split-SUSY, 1 i.e., tan β, M2, M1 and µ, Mh is sensitive to tan β and a large tan β leads to a large Mh. In our calculations we fix tan β = 40 since a large value of tan β is favored 0.5 by current experiments. Our results are not sensitive to (%) 0 σ tan β in the region of large tan β value and our results / 0 are approximately valid for tan β & 10. With the input ∆σ values of tan β and squark masses, we get M = 120 GeV h -0.5 from Feynhiggs [18]. With the fixed value of tan β, there remained three -1 split-SUSY parameters: M2, M1 and µ. We further use 2 the unification relation M1 = 5M2 tan θW /3 0.5M2, which is predicted in the minimal supergravity≃ model. -1.5 Thus finally we have two free SUSY parameters. The 200 400 600 800 1000 M ~χ + (GeV) SM parameters used in our results are taken from [19]. 1 FIG. 8: Same as Fig.7, but versus the chargino mass for the c.m. energy of 1 TeV. A. Numerical results without WMAP constraints

+ − of e e Zh versus the lightest chargino mass Mχ˜+ In order to show the features of our results, we first → 1 (in this case the chargino mass M ˜+ is almost equal to present some results without considering the WMAP χ1 dark matter constraints. In Fig. 7 we show the relative M2 due to the superheavy higgsinos). The peak hap- pens at M + = √s/2 due to threshold effects. When the one-loop correction of split-SUSY to the cross section of χ˜1 e+e− Zh versus the c.m. energy of e+e− collision for chargino mass gets heavier than 1 TeV, the corrections → M2 = 400 GeV and µ = 600 GeV. In this case the light- becomes very small, showing the decoupling property. est chargino mass M + = 387 GeV. We see from Fig. χ˜1 7 that the corrections are negative and have a peak at √s =2M + due to the threshold effects. The magnitude B. Numerical results with WMAP constraints χ˜1 of the corrections for √s = 1 TeV, which will be taken for our following studies, is relatively small. Now we require the lightest neutralinos make up the In Fig. 8 we fix √s = 1 TeV and µ = 100 TeV (note cosmic dark matter relic density measured by WMAP, 2 that the scenario with a very large µ is proposed and ar- which is given by 0.085 < ΩCDM h < 0.119 at 2σ [21] gued in [20]), and by varying M2 we show the relative with h =0.73 being the Hubble constant. Of course, the one-loop correction of split-SUSY to the cross section direct bounds from LEP experiments [22] need to be also 5 considered, which are: (i) the lightest chargino heavier ier, the chargino pair production rate at the ILC drops than about 103 GeV; (ii) the lightest neutralino heavier rapidly. Of course, when the chargino is heavier than 500 than about 47 GeV; (iii) tan β larger than 2. Note that GeV, beyond the threshold of the ILC (with c.m. energy the LEP bound tan β > 2 is obtained from the search of 1 TeV), the charginos cannot be pair produced. Then limit of the lightest Higgs boson for squarks below 1 TeV. it is interesting to observe that for a chargino between 500 Such a bound may be relaxed in split-SUSY because of and 600 GeV, although the ILC cannot produce chargino superheavy squarks. pairs, the virtual effects in e+e− Zh can still reach a We then perform a scan over the parameter space of couple of percent in magnitude and→ thus may be observ- M2 and µ. The 2σ allowed region is shown in Fig. 2 of able at the ILC with a high integrated luminosity. Fi- Ref. [5]. (Note that in [5] we used the one-year WMAP nally, when the chargino is heavier than about 600 GeV, 2 data 0.094 < ΩCDM h < 0.129. The allowed region with it will probably remain unaccessible because both the one-year WMAP data is approximately same as that with chargino pair production rates and the virtual effects are three-year WMAP data). very small due to the decoupling property of SUSY. Note that for e+e− Zh we numerically compared our results with the full→ one-loop corrections given in 4 10 + - → χ~+ ~χ- [11] (we thank the authors of [11] for giving us their e e 1 1

| fortran code). In our calculations we only considered √s = 1 TeV LHC the chargino and neutralino loops, while in their calculations the sfermion loops are also considered besides 3 WMAP 2σ 10 the chargino and neutralino loops. In principle, their results in the limit of superheavy sfermions should ap-

(fb) proach to our results. We found that although their for- σ ILC tran code does not work well for superheavy sfermions 10 2 (say above 10 TeV) due to the limitation of numerical calculation, for a given point in the parameter space our results agree well with those by using their fortran code with all sfermions above 1 TeV.

200 400 600 800 1000 1200 3 + - e e → Z h − 0.2 e+ ν 2 √s | = 1 TeV W h W WMAP 2σ - 1 0 e ν (%) 0 σ /

0 (%) ∆σ 0 -0.2 σ /

-1 ∆σ -0.4

-2

200 400 600 800 1000 1200 -0.6 M ~χ + (GeV) 1 FIG. 9: The shaded areas are the 2σ region of split-SUSY parameter space allowed by the WMAP dark matter measure- -0.8 ment in the planes of the chargino pair production rate (upper 3 panel) and the one-loop correction of split-SUSY to the cross 10 − section of e+e Zh (lower panel) versus the chargino mass. M ~χ + (GeV) → 1 FIG. 10: Same as the lower panel of Fig.9, but for the WW - + − fusion process e e νeν¯eh. In Fig. 9 we show the one-loop correction of split- → SUSY to the cross section of e+e− Zh (lower panel) with comparison to the chargino pair→ production rate The one-loop correction of split-SUSY to the cross sec- + − (upper panel). The chargino pair production rate is cal- tion of W W -fusion process e e νeν¯eh is very small culated at tree-level, as in our previous work [5]. in magnitude, below one percent,→ as shown in Fig. 10. From Fig. 9 we see that when the chargino is lighter Even with a high luminosity the ILC can hardly reveal than about 300 GeV, the chargino pair production rate at such a small deviation from the measurement of this pro- the ILC is large and the corresponding virtual eﬀects in cess. The reason why the virtual eﬀects in the s-channel e+e− Zh are positive. When the chargino gets heav- process e+e− Zh is much larger in magnitude than in → → 6

+ − + − + − the t-channel process e e νeν¯eh may be that for the ductions e e Zh and e e νeν¯eh through W W s-channel process the virtual→ sparticles (charginos and fusion at the ILC.→ We found that→ the production cross neutralinos) in the loops could be more energetic and section of e+e− Zh can be altered by a few percent in cause larger quantum effects. some part of the→ WMAP-allowed parameter space, while + − Anyway, such virtual effects of split-SUSY, no matter the correction to the W W fusion process e e νeν¯eh large or small in magnitude, could be informative and is below 1%. → complementary to the real sparticle productions in probing split-SUSY at colliders. For example, if split-SUSY Such virtual effects are correlated with the cross sec- turns out to be the true story and the chargino pair pro- tions of chargino pair productions and thus can offer com- duction is observed with the chargino mass around 150 plementary information in probing split supersymmetry GeV at the ILC, then we know from Figs. 9 and 10 at the colliders. Our results indicate that if the light- that the virtual effects of SUSY must be about 2.5% for est chargino is in the light region allowed by the WMAP process e+e− Zh and 0.1% for W W -fusion process dark matter (say below 200 GeV), then at the ILC and + − → − e e νeν¯eh. LHC the chargino pair production rates are large and → the virtual effects of charginos/neutralinos in the process e+e− Zh at the ILC can reach a few percent, both IV. CONCLUSION of which→ may be measurable and cross-checked. An interesting observation is that for a chargino between 500 In split supersymmetry, gauginos and higgsinos are the and 600 GeV, although the ILC (with c.m. energy of 1 only supersymmetric particles possibly accessible at fore- TeV) cannot produce chargino pairs, the virtual effects in e+e− Zh can still reach a couple of percent in magni- seeable colliders like the LHC and the ILC. In order to → account for the cosmic dark matter measuerd by WMAP, tude and thus may be observable at the ILC with a high the parameter space of the gauginos and higgsinos in integrated luminosity. The WMAP-allowed region with split supersymmetry are stringently constrained, which the chargino heavier than about 600 GeV will most likely can be explored at the LHC and the ILC through di- remain unaccessible because both the chargino produc- rect productions and the virtual effects of these gaugi- tion rates and the virtual effects are very small due to nos and higgsinos. The clean environment of the ILC the decoupling property of SUSY. may render the virtual effects of percent level meaningful in probing the new physics. In this work we assumed split supersymmetry and calculated the virtual effects of This work is supported in part by National Natural the WMAP-allowed gauginos and higgsinos in Higgs pro- Science Foundation of China.

[1] K. Abe et al., hep-ph/0109166; T. Abe et al., (2001); M. J. Herrero, S. Peñaranda and D. Temes, Phys. hep-ex/0106056; J. A. Aguilar-Saavedra, et al., Rev. D 64, 115003 (2001); A. Dobado, M. J. Herrero, hep-ph/0106315. Phys. Rev. D 65, 075023(2002); M. Carena, et al., Phys. [2] N. Arkani-Hamed, S. Dimopoulos, hep-th/0405159; G.F. Rev. D 60, 075010 (1999); Phys. Rev. D 62, 055008 Giudice, A. Romanino, Nucl. Phys. B 699, 65 (2004); (2000). N. Arkani-Hamed, S. Dimopoulos, G. F. Giudice, A. Ro- [10] For SUSY-QCD effects in tt¯ productions, see, e. g., C. S. manino, Nucl. Phys. B 709, 3 (2005). Li, et al., Phys. Rev. D 52, 5014 (1995); Phys. Lett. B [3] L. Senatore, Phys. Rev. D 71, 103510 (2005). 379, 135 (1996); S. Alam, K. Hagiwara, S. Matsumoto, [4] F. Wang, W. Y. Wang, J. M. Yang, Phys. Rev. D 72, Phys. Rev. D 55, 1307 (1997); Z. Sullivan, Phys. Rev. 077701 (2005). D 56, 451 (1997); For SUSY-QCD effects in FCNC top [5] F. Wang, W. Y. Wang, J. M. Yang, Eur. Phys. Jour. C interactions, see, e. g., C. S. Li, R. J. Oakes, J. M. Yang, 46, 521 (2006). Phys. Rev. D 49, 293 (1994); G. Couture, C. Hamzaoui [6] A. Pierce, Phys. Rev. D 70, 075006 (2004); A. Arvani- and H. Konig, Phys. Rev. D 52, 1713 (1995); J. L. Lopez, taki, P. W. Graham, hep-ph/0411376. D. V. Nanopoulos and R. Rangarajan, Phys. Rev. D 56, [7] A. Masiero, S. Profumo, P. Ullio, Nucl. Phys. B 712, 86 3100 (1997); G. M. de Divitiis, R. Petronzio and L. Sil- (2005). vestrini, Nucl. Phys. B 504, 45 (1997); C. S. Li, et al., [8] For the studies of split-SUSY gluino at LHC, see, e.g., K. Phys. Lett. B 599, 92 (2004); J. Cao, et al., Nucl. Phys. Cheung, W.-Y. Keung, Phys. Rev. D 71, 015015 (2005); B 651, 87 (2003); Phys. Rev. D 74, 031701 (2006). M. J. G. Gonzalez, S. Reucroft, J. Swain, Phys. Rev. D 74, Frank, I. Turan, Phys. Rev. D 74, 073014 (2006). 027701 (2006). [11] P.Chankowski, S.Pokorski, J.Rosiek, Nucl. Phys. B 423, [9] SUSY-QCD may have large residue effects in Higgs pro- 437 (1994). cesses, see, e.g., G. Gao, R. J. Oakes, J. M. Yang, Phys. [12] T. Hahn et al., Nucl. Phys. B 652, 229 (2003); H. Eberl Rev. D 71, 095005 (2005); J. Cao, et al., Phys. Rev. D 68, et al., Nucl. Phys. B 657,378 (2003). 075012 (2003); G. Gao, et al., Phys. Rev. D 66, 015007 [13] H. E. Haber and G. L. Kane, Phys. Rep. 117, 75 (1985); (2002). H. E. Haber, et al., Phys. Rev. D 63, 055004 J. F. Gunion and H. E. Haber, Nucl. Phys. B 272, 1 7

(1986). mun. 118, 153 (1999); T. Hahn, Nucl. Phys. Proc. Suppl. [14] H.E. Haber, R. Hempﬂing, Phys. Rev. Lett. 66, 1815 135, 333 (2004). (1991); Y. Okada, M. Yamaguchi, T. Yanagida, Prog. [18] S.Heinemeyer, hep-ph/0407244 Theor. Phys. 85, 1 (1991); Phys. Lett. B 262,54(1991); [19] W. M. Yao et al., J. Phys. G33, 1 (2006). J. Ellis, G. Ridolﬁ, F. Zwirner, Phys. Lett. B 257, 83 [20] K. Cheung, C.-W. Chiang, Phys. Rev. D 71, 095003 (1991); Phys. Lett. B 262, 477 (1991); J. R. Espinosa (2005). and R. J. Zhang, JHEP 0003 (2000) 026. [21] D. N. Spergel, et al., astro-ph/0603449. [15] A. Denner, Fortschr. Phys. 41 (1993)4 [22] LEP2 SUSY Working Group homepage, http://lepsusy. [16] G. ’t Hooft and M. J. G. Veltman, Nucl. Phys. B 153, web.cern.ch/lepsusy/ 365 (1979). [17] T. Hahn and M. Perez-Victoria, Comput. Phys. Com-