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despite the great success of the standard model ( sm ) , the mechanism for electroweak symmetry breaking remains to be tested in experiments . there are many reasons to believe there is physics beyond the sm . in particular , the minimal supersymmetric standard model ( mssm ) is one of the best motived theories where it is possible to describe the cold dark matter in the universe and where the unification of the gauge couplings is achieved . in low energy supersymmetry it is assumed that the susy breaking scale is at tev following the naturalness criterion . recently , arkani - hamed and dimopoulos @xcite , have noticed that gauge coupling unification can be achieved in a supersymmetric model where all scalars , except for one higgs doublet , are very heavy . most of the unpleasant aspects of low energy supersymmetry , such as excessive flavour and cp violation , very fast dimension 5 proton decay , and tight constraints on the higgs mass , are eliminated . at the same time , there is a candidate to describe the cold dark matter in the universe . several phenomenological studies in this scenario , now called split supersymmetry , have been performed @xcite . it is expected that the higgs boson will be discovered in the next generation of collider experiments . therefore , one of the main issues in higgs boson physics is the identification of observable useful to distinguish between the sm higgs @xmath1 and the lightest higgs in possible extensions of the sm . there are several studies devoted to this very important issue in the context of the mssm @xcite .    as we mention before we hope at future collider experiments we will discover at least a neutral particle with spin zero , the higgs boson , and the lightest supersymmetric particles , the neutralinos and charginos . since in split supersymmetry the interactions of the lightest higgs boson with the sm fermions are the same as the interactions of the sm higgs , through the decays into two sm fermions it is not possible to make the identification of the higgs . therefore we have to use the decays at one loop , where the effect of virtual particles present in split susy is relevant . in this letter we investigate this issue and we argue that the way to address it is studying the decays of the higgs boson into two photons . we show several numerical examples where it is possible to appreciate large differences between the decay rates in the sm and in split supersymmetry . in order to identify the higgs boson at future colliders the predictions of all its decay rates have to match with their measurements . this is the case of sm higgs boson @xmath1 or the lightest higgs boson @xmath2 of the supersymmetric extension of the standard model . it is particularly difficult to distinguish between the sm higgs boson and the mssm lightest higgs boson in the decoupling limit @xcite . this is precisely what happens in split supersymmetry , where all scalars are very heavy except for one higgs doublet and for the neutralinos and charginos which are all light . therefore , in split supersymmetry we expect that at future colliders the lightest higgs boson will be discovered together with charginos and neutralinos . however , their discovery is not enough to claim that the observed higgs corresponds to the split susy light higgs , since we have to measure its couplings with a good precision .    in the context of the mssm there are studies about the possibility to distinguish between different higgses through the couplings @xmath3 @xcite , @xmath4 @xcite and @xmath5 @xcite . also the quantity @xmath6 has been studied extensively @xcite .    in this letter we study the possibility to identify the light higgs in split supersymmetry @xcite . since in this case all sfermions and higgs bosons , except for the lightest one , are very heavy it is not possible to use the quantity @xmath7 nor the coupling @xmath3 . the @xmath8 and @xmath9 couplings are equal at tree level in the sm and in split susy . there are not differences at one - loop , since all squarks or sleptons in the loops are very heavy . in the case of @xmath3 coupling , this is a one - loop induced coupling with quark contributions being common to both the sm and split - susy , and with the difference being the squark contributions , which are negligible . the two other possibilities are to use the couplings @xmath4 and @xmath5 . however , it is not possible to use the first one since we know that the @xmath10 is very small and it will be very difficult to determine it with a very good precision @xcite . therefore we concentrate on the possibility to use the coupling @xmath5 for our study . the decay @xmath11 can be observed at the lhc but with an error larger than @xmath12 @xcite . at electron - positron colliders there is the additional possibility of photon - photon collisions , where the rate @xmath13 can be measured with a @xmath14 precision @xcite . this combined with a measurement of @xmath15 with a @xmath16 @xcite , gives a determination of @xmath17 with a @xmath18 error . the decay rate @xmath19 is given by @xcite : @xmath20 where @xmath21 is the fine structure constant , @xmath22 is the @xmath23 gauge coupling constant , @xmath24 is the @xmath25 boson mass , and @xmath26 is the higgs boson mass . there is an amplitude @xmath27 for each charged particle inside the loop , and depends on a loop function @xmath28 whose form varies according to the spin of the particle in the loop .    in split supersymmetry the relevant contributions are : @xmath29 where @xmath30 , @xmath31 , @xmath32 are the amplitudes for the contributions with @xmath25 bosons , fermions , and charginos inside the loop , respectively . the parameter @xmath33 , where @xmath34 is the mass of the particle inside the loop , and @xmath26 is the higgs mass . @xmath35 for quarks and squarks , while @xmath36 for leptons and sleptons , and @xmath37 is the electric charge of the fermion @xmath38 . the couplings of the lightest higgs to the internal particles are given by : @xmath39 @xmath40 with @xmath41 and @xmath42 . the matrices @xmath43 and @xmath44 are the matrices which diagonalize the chargino mass matrix . the loop functions @xmath45 , @xmath46 and @xmath47 can be found in @xcite .    in split supersymmetry , the higgs couplings to fermions and @xmath25 bosons are sm - like , giving contributions which are equal in both models . therefore , the chargino contribution will determinate the difference between the decays into two photons in the sm and split susy . in order to quantify the difference between the decay rate of the sm higgs and the lightest higgs into two photons in split supersymmetry we define the following quantity :    @xmath48    we calculate this quantity using the above formulas for different values of the relevant parameters , which are the higgs mass , the higgsino mass parameter @xmath49 , the @xmath23 gaugino mass @xmath50 , and @xmath51 . we take @xmath52 gev and consider it as an independent parameter . notice that in the case of split supersymmetry , since we accept the fine - tuning and we integrate out all superheavy scalars , the higgs mass basically does not change when we vary the rest of the parameters . the loops corrections with charginos and neutralinos are not very important , see for example @xcite .    in figure [ dmu ] we see how this quantity changes as a function of the parameter @xmath49 , for given values of @xmath50 and @xmath53 . note that it is possible to achieve differences up to @xmath54 when the chargino contribution is large . as this difference is achieved , the branching ratio of the decay into two photons is of the order of @xmath55 . we impose the experimental bound @xmath56 gev , which limits the curves at low values of @xmath49 . as the magnitude of the parameter @xmath49 increases the chargino masses increase also , the heavier faster than the lightest . in general , larger chargino masses produce smaller contributions to @xmath11 and thus the parameter @xmath57 decreases . for a similar reason , curves defined by larger values of the gaugino mass @xmath50 have smaller @xmath57 . these curves are defined by @xmath58 gev ( red crosses ) , @xmath59 gev ( blue x s ) , and @xmath60 gev ( green circles ) . two different values of @xmath51 are considered in this figure , @xmath61 and 50 with the smaller value giving larger @xmath57 . another interesting point to notice in this figure is the correlation between the sign of @xmath49 ( actually , the sign of @xmath62 since we work with @xmath63 ) and the sign of @xmath57 .    in fig . [ dm2 ] we show the variation of @xmath57 as a function of @xmath50 for @xmath61 and @xmath64 , 250 , and 350 gev . it is clear that when @xmath50 is increased our quantity decreases since the chargino contributions are less important , due to their larger mass . the three curves are limited at low @xmath50 by the experimental lower bound on the chargino mass described before . at the other extreme ( @xmath65 gev ) the light chargino mass is given by 133 , 213 , and 262 gev for @xmath64 , 250 , and 350 gev , respectively . despite these large chargino masses , @xmath57 remains above 1% in the whole parameter space shown in the figure .    in fig . [ dtb ] we have the dependence of @xmath57 on @xmath51 , and plot three curves with increasing values of @xmath49 and @xmath50 , as indicated in the figure . in all cases @xmath57 decreases with @xmath51 from several percent at low values to less than 1 - 2% at large values . the decay rate for @xmath11 in the mssm with the higgs sector in the decoupling limit was studied in @xcite . it was found that contributions from the stop sector are larger when the left - right mixing is large , and that contributions from charginos decrease with @xmath51 . at small @xmath51 chargino and stop contributions have opposite signs and a cancellation could occurs . of course , this cancellation does not happens in split supersymmetry , obtaining larger decay rates @xmath0 . in general , smaller decay rates are obtained at large values of @xmath51 : chargino contributions are small in both the mssm and split susy , with the stop contribution adding to the @xmath25 contribution in the mssm . larger decay rates are found in the mssm at high @xmath51 when the sbottom loops are also important . we hope that the results presented in this section will be useful to understand the possibility to distinguish between the sm higgs boson and the lightest higgs boson in split susy . in split supersymmetry the light higgs boson couplings to sm particles are identical to the couplings of the sm higgs boson . we point out that a way to distinguish between them is through the decay into two photons . we show several numerical examples where we appreciate large differences of several percent between the predictions for @xmath0 in the two models , making possible the discrimination at future photon - photon colliders . once the higgs boson and the charginos are discovered at the next generation of collider experiments , the well defined predictions for the higgs decay into two photons will constitute an important cross check to identify the light higgs boson in split susy . h.  e.  haber , nucl . * 116 * ( 2003 ) 291 [ arxiv : hep - ph/0212010 ] . m.  dubinin , h.  j.  schreiber and a.  vologdin , eur . j.  c * 30 * ( 2003 ) 337 [ arxiv : hep - ph/0302250 ] . m.  carena and h.  e.  haber , prog . * 50 * ( 2003 ) 63 [ arxiv : hep - ph/0208209 ] . z.  bern , l.  j.  dixon and c.  schmidt , phys . d * 66 * ( 2002 ) 074018 [ arxiv : hep - ph/0206194 ] . l.  s.  group _ et al . _ , arxiv : hep - ph/0410364 . d.  asner , b.  grzadkowski , j.  f.  gunion , h.  e.  logan , v.  martin , m.  schmitt and m.  m.  velasco , arxiv : hep - ph/0208219 . d.  asner _ et al . _ , j.  c * 28 * ( 2003 ) 27 [ arxiv : hep - ex/0111056 ] . s.  soldner - rembold and g.  jikia , nucl . instrum . meth .  a * 472 * ( 2001 ) 133 [ arxiv : hep - ex/0101056 ] . j.  f.  gunion , h.  e.  haber and r.  van kooten , arxiv : hep - ph/0301023 . j. f. gunion et al , higgs hunter s guide .
we investigate the possibility to distinguish between the standard model higgs boson and the lightest higgs boson in split supersymmetry . 
 we point out that the best way to distinguish between these two higgs bosons is through the decay into two photons . 
 it is shown that there are large differences of several percent between the predictions for @xmath0 in the two models , making possible the discrimination at future photon - photon colliders . 
 once the charginos are discovered at the next generation of collider experiments , the well defined predictions for the higgs decay into two photons will become a cross check to identify the light higgs boson in split supersymmetry .