Supersymmetry signals of supercritical string cosmology at the Large Hadron Collider

Transcription

1 PHYSICAL REVIEW D 79, 55 (9) Supersymmetry signals of supercritical string cosmology at the Large Hadron Collider Bhaskar Dutta, Alfredo Gurrola, eruki Kamon, Abram Krislock, A. B. Lahanas, N. E. Mavromatos, 3 and D. V. Nanopoulos,4,5 Department of Physics, exas A&M University, College Station, exas , USA Physics Department, Nuclear and Particle Physics Section, University of Athens, GR-57 7, Athens, Greece 3 King s College London, Department of Physics, University of London, Strand WCR LS, London, United Kingdom 4 Astroparticle Physics Group, Houston Advanced Research Center (HARC), Mitchell Campus, Woodlands, exas 7738, USA 5 Division of Natural Sciences, Academy of Athens, 8 Panepistimiou Avenue, Athens 679, Greece (Received August 8; published 4 March 9) We investigate the minimal supergravity signals at the Large Hadron Collider in the context of supercritical string cosmology (SSC). In this theory, the presence of a time dependent dilaton provides us with a smoothly evolving dark energy and modifies the dark matter allowed region of the minimal supergravity model with standard cosmology. Such a dilaton dilutes the supersymmetric dark matter density (of neutralinos) by a factor OðÞ and consequently the regions with too much dark matter in the standard scenario are allowed in the SSC. he final states expected at the Large Hadron Collider in this scenario, unlike the standard scenario, consist of Z bosons, Higgs bosons, and/or high energy taus. We show how to characterize these final states and determine the model parameters. Using these parameters, we determine the dark matter content and the neutralino-proton cross section. All these techniques can also be applied to determine model parameters in SSC models with different supersymmetry breaking scenarios. DOI:.3/PhysRevD PACS numbers:.6.jv, e, 98.8.Cq I. INRODUCION he recent WMAP data [] have determined the content of the Universe very precisely. he dark matter and dark energy compose about 3% and 73% of the total energy density of the Universe, respectively. he origin of dark matter can be explained in supersymmetry (SUSY) models, where the lightest SUSY particle, the neutralino (in most SUSY models) [], is the dark matter candidate. SUSY, combined with supergravity grand unification (SUGRA GU) [3], resolves a number of the problems inherent in the standard model (SM). he SUGRA GU model not only solves the gauge hierarchy problem and predicts grand unification at the GU scale M G 6 GeV but also allows for the spontaneous breaking of SUGRA at the M G scale in a hidden sector, leading to an array of soft breaking masses. he renormalization group equations then show that this breaking of SUGRA leads naturally to the breaking of SUðÞUðÞ of the SM at the electroweak scale [4]. SUSY breaking masses around a ev for most of the SUSY parameter space are allowed by other experimental constraints. It is also very interesting to note that achieving the WMAP relic density requires the annihilation cross section of the lightest neutralino ( ~ ) in these SUSY models to be of order pb with M ~ Oð GeVÞ. Such a mass scale is reachable at the CERN LHC. he origin of dark energy is not well understood. he simplest proposal is to add a cosmological constant in Einstein s equation. However, the reason why the dark matter content is comparable to the dark energy content at the present time remains a puzzle. Another proposal is that a quintessence scalar field is responsible for dark energy [5]. However, this requires the field to have a very small mass and is not well motivated in particle physics models. In the context of string theory, the dilaton can play the role of dark energy [6,7]. One also finds proposals which involve, for example, modifications to general relativity, braneworld scenarios, or topological defects, which are invoked to explain this fundamental issue. In this paper, we will investigate experimental signatures of SUSY as consequences of a rolling dilaton in the Q-cosmology scenario [6] which offers an alternative framework that establishes the supercritical (or noncritical) string cosmology (or SSC). In the SSC framework, the dark energy has two components: One component arises from the dilaton,, and the other arises from the Q which is associated with the central charge deficit. Both Q and the dilaton have time dependent pieces. It was shown that the SSC scenario [8] is consistent with the smoothly evolving dark energy at least for the last 9 yr ( <z<:6), in accordance with the very recent observations on supernovae [9]. he presence of this time dependent dilaton affects the relic density calculation since it modifies the Boltzmann dn equation in the following way: dt þ 3Hn þhviðn n e q Þ n _ ¼. he relic density is given by =9=79(5)=55(5) 55- Ó 9 he American Physical Society

2 BHASKAR DUA et al. PHYSICAL REVIEW D 79, 55 (9) h ¼ R ðh Þ () where R exp½ R x f x ð H _ =xþdxš and ðh Þ denotes the relic density that is obtained by ordinary cosmology. It is possible to determine R by solving for from the field equations for this SSC scenario. he value of R is about. in order to satisfy the recent observation of the evolution of dark energy in the range <z<:6. his new factor changes the profile of the dark matter allowed region in SUSY models. o investigate the SUSY signatures we use the minimal SUGRA (msugra) model and calculate the dark matter content in the context of the SSC framework. We note that the low-energy limit of string theory is certainly much more complicated than msugra, and there are many different ective theories, depending on the details of compactification and SUSY breaking []. he relevant dark matter phenomenological analyses are highly model dependent []. In some cases, such as the orbifoldcompactified heterotic models [], there might be situations in which the couplings of matter with stabilized dilatons lead to nonthermal dark matter, thus leading to completely different phenomenology. However, the SSC framework is characterized by a nonstabilized dilaton which runs in cosmic time [8]. In this context, it is possible to have thermalization of weakly interacting dark matter, such as the msugra lightest neutralino (~ ) which couples to the dilaton. In this sense, the msugra framework provides a sufficiently nontrivial and generic pilot study of the novel ects the running dilaton has on the abundance of thermal dark matter relics. he msugra parameters are the universal scalar mass, m, the universal gaugino mass, m =, the universal soft breaking trilinear coupling constant, A, the ratio of Higgs expectation values, tan, and the sign of, the bilinear Higgs coupling constant. In the case of the standard cosmology, if we concentrate on smaller values of m and m =, then the stau-neutralino (~ - ~ ) coannihilation region is the only dark matter allowed region (which is also allowed by the g constraint) []. However, due to the presence of the extra factor R, the parameter space in the SSC scenario requires larger values of m. his is because a smaller annihilation cross section is required in the presence of the dilaton contribution. he magnitude of m is however, still much smaller than the focus point region [3] (in this region, the magnitude of is small and therefore the lightest neutralino has a large Higgsino component). his difference in m will produce new types of signals at the LHC for the SSC model. For example, in the case of the standard cosmology, the allowed region for low m requires the ~ and ~ to have nearly degenerate masses within GeV. his produces low-energy s in the final states [4 6]. In contrast, in the SSC model, Z bosons, Higgs bosons or high energy s appear in the final states. hese final states, which we will discuss for this SSC scenario, actually exist in most regions of the SUSY parameter space. herefore, even without any cosmological motivation, searching for these signals is a worthwhile exercise. Furthermore, even though we have used the SSC as our motivation to probe the signals of the SUGRA model, one can come up with any other cosmological framework where the Boltzmann equation is modified in such a way that the Universe is not really overclosed in this wide region of SUGRA paramater space. his analysis is valid for all these scenarios. One can also use other SUSY breaking scenarios in the context of SSC. Our analysis of signals can still be applicable in those new scenarios. However, additional observables may be required in order to determine the model parameters. he determination of the factor R in Eq. () is important since it will tell us whether we satisfy the cosmological observation for the evolution of dark energy for <z<:6. In order to calculate R we need to calculate the relic density precisely at the collider. In this paper, we first show how to analyze and develop appropriate cuts to extract the signals in the newly allowed parameter space in order to determine model parameters. We also construct new observables necessary for the determination of such parameters. hen, using these parameters, we determine the accuracy of the result for the dark matter content. Finally, when the LHC will be operating, the dark matter direct detection experiments also will be probing the SUSY parameter space. he neutralino-proton scattering cross section is different for this newly allowed parameter space compared to the standard cosmology case. hus we also determine the accuracy of the result for the neutralino-proton scattering cross section based on the LHC measurements. his will be very useful when we combine the data from these direct detection experiments with the LHC data to extract the final model. he remainder of this paper is organized as follows: In Sec. II, we discuss the parameter space of this model and compare with the standard cosmology, followed by characterizing the SUSY signals at the LHC in Sec. III. In Sec. IV, we show the determination of model parameters and the prediction of relic density and neutralino-proton cross section. We conclude in Sec. V, where some comments on the applicability of our main results to other string theory models are also discussed briefly. II. PARAMEER SPACE he msugra model parameters are already significantly constrained by various experimental results. Most important for limiting the parameter space are (i) the light Higgs mass bound of M h > 4 GeV from LEP [7], (ii) the b! s branching ratio bound of :8 4 < BðB! X s Þ < 4:5 4 (we assume here a relatively broad range, since there are theoretical uncertainties in 55-

3 SUPERSYMMERY SIGNALS OF SUPERCRIICAL SRING... PHYSICAL REVIEW D 79, 55 (9) matter (or neutralino) relic density. We can find which regions of the parameter space will agree with the dark matter relic density observed by WMAP. he region allowed by WMAP for the standard big bang cosmology is vastly different from the region for the SSC model [8]. he comparison of these two regions is shown in Fig. for the case of A ¼ and tan ¼ 4. We see a clear separation between the standard big bang cosmology region and the SSC region. he standard big bang cosmology region is the very narrow region ranging from 35 & m = & 9 GeV (85 & M ~g & GeV), and & m & 35 GeV. he SSC region is much broader for m = & 8 GeV, and is higher in m which ranges from 4 to 5 GeV. FIG. (color online). WMAP allowed parameter space for the SSC and standard big bang cosmology shown for A ¼, tan ¼ 4. he very thin gray (green) band is where the neutralino relic density calculated by standard big bang cosmology agrees with the WMAP3 limits :95 < h < :7. he thicker dark purple band shows the same agreement using the SSC calculation of the relic density. Also shown are the Higgs mass boundary (dash-dotted blue line), muon g boundaries (dashed and dotted red lines), a hatched cyan region which is excluded by b! s experimental bounds, and a lower solid red region where the neutralino is not the lightest supersymmetric particle. extracting the branching ratio from the data) [8], (iii) the bound on the dark matter relic density: :95 < CDM h < :7 [], (iv) the bound on the lightest chargino mass of M ~ > 4 GeV from CERN LEP [], and (v) the muon magnetic moment anomaly a, where the present deviation from the SM value is ð9:5 8:Þ [ 5]. Assuming the future data confirm the a anomaly, the combined ects of g and M ~ > 4 GeV then only allow >. Figure shows g curves for :7 9, :9 9, 3:59 9, and 4:43 9 which are within two sigma deviation. Since the msugra parameters determine the masses of our supersymmetric particles, they also determine the dark III. SIGNALS A HE LHC he SSC region of parameter space has some unique characteristics which are distinguishable from the ~ -~ coannihilation region which appears for the lower values of m. For example, let us consider the decay chains of the dominant SUSY production mechanism at the LHC, which will produce the squark and gluino, in pairs (e.g., ~q ~g ). In the coannihilation region, the dominant decay chain for the squark (~q L )is~q L! q ~! q~! q~. Here ~ is the second lightest neutralino. hus, this region produces s, along with jets and missing transverse energy, E6. However, the characteristic decay in the SSC region is ~! h ~. In this case, we would expect h! b b, along with jets and E6. Figure shows the branching ratios for the ~ decay. As we increase m =, the branching ratios shift from Higgs dominant decay chains to dominant decay chains. However, we will easily distinguish this SSC dominated region from the coannihilation region by observing a large mass difference between ~ and ~. For even lower m = values (m = & 35 GeV), the ~! Z~ decay becomes dominant. ypical mass spectra are shown for points in the Higgs boson, Z boson, and two final state dominated regions in ables I, II, and III. A. Signals We have three possible signals in this model. hese signals are the following: (i) Higgs þ jets þ E6 ; (ii) Z þ jets þ E6 ; (iii) þ jets þ E6 : he present experimental world average for b! s is ð3:5 :3 9Þ 4 [9] and the SM contribution has been evaluated to be ð3:5 :3Þ 4 []. he b! s constraint does not have much of an impact in our analysis. he signals, Higgs þ jets þ E6 and tau þ jets þ E6, in our study are available for a large region of parameter space. he Z þ jets þ E6 final states however arise in the parameter space where b! s is large which we mention later. We, however, still discuss this final state since it is easy to evade the b! s constraint without much change in the final state.. Higgs þ jets þ E6 he Higgs þ jets þ E6 signal appears in the lower m = region (4 & m = & 5 GeV) within the SSC band of parameter space in Fig.. he Higgs þ jets þ E6 signal is characterized by the decay chain, ~q L! q ~! qh ~. he ~ does not interact in the detector, and thus leaves a large E6 signal. he h and jet carry information about the SUSY particles in this chain. In particular, the h þ jet invariant mass distribution has an end point which depends 55-3

4 BHASKAR DUA et al. PHYSICAL REVIEW D 79, 55 (9) Branching Ratio (%) Branching Ratio (%) m / m = 6 GeV + Z + h τ + τ m / = 4 GeV + Z + h τ + τ m Branching Ratio (%) Branching Ratio (%) m / m = 7 GeV + Z + h τ + τ m / = 5 GeV + Z + h τ + τ FIG. (color online). he dominant decay branching ratios of decays from the ~ are shown here. Each of the four plots shows how the branching ratios vary with m at constant m =. ogether they survey the SSC band of parameter space in Fig.. m upon their masses: M end h q ¼ v ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q ðm M ~q L M ÞðM þ M M þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðm M M Þ 4M M Þ u ~ þ ~ h ~ ~ h ~ h ~ t : () h M ~ For our analysis, we generate events using PYHIA [6], which is linked with ISASUGRA [7] to generate the msugra mass spectrum. We pass these events to a detector simulator called PGS4 [8]. o measure the end point, we begin by selecting our events with the following cuts [5]: (i) at least two jets with p GeV as well as jj :5, (ii) E6 8 GeV, (iii) p jet þ p jet þ E6 6 GeV, and (iv) at least two b-tagged jets [8] with p GeV and jj :5. hese cuts remove the majority of the SM background, such as tt, W þ jets, and Z þ jets [9], as well as some background from SUSY events which do not contain the decay chain ~q L! q~! qh ~. Unforeseen SM backgrounds at the LHC can be shape analyzed from the data and then subtracted from our desired signal. Next we identify Higgs bosons in the event. We select all pairs of b-tagged jets with p b GeV and :4 < R bb <. he lower R limit is due to a jet clustering cone size in PGS4, while the upper limit is motivated by a study of Higgs decays in msugra events (m ¼ 47 GeV, m = ¼ 4 GeV) at the generator level (see Fig. 3). We then form the b pair invariant mass. Figure 4 shows a peak between and GeV, consistent with the Higgs mass, along with a continuum background. For each b pair, we form b þ jet systems, using the two jets with the greatest transverse momenta of the event. hese 55-4

5 SUPERSYMMERY SIGNALS OF SUPERCRIICAL SRING... e~l e~r ~ ~ ~ ~ ~ Þ (%) ~! h Bð Bð ~! Z ~ Þ (%) 3 ~t ~t b~ b~ e~l e~r ~ ~ ~ ~ ~! h ~ Þ (%) Bð ~! Z ~ Þ (%) Bð ~t ~t b~ b~ e~l e~r ~ ~ ~ ~ Rbb (b p > GeV) ~! h ~ Þ (%) Bð ~! ~ Þ (%) Bð two leading jets will primarily come from three different decay chains: (i) q~! q~ g, ~, (ii) q~r! q ~. ~! qh (iii) q~l! q Each b pair combined with these two leading jets will form two ective masses, Mbbj, and Mbbj. If we combine the ~ with our Higgs, it can have a larger jet from q~r! q ~! Mbbj than the end point expected from the q~l! q ~ qh decay chain. hus, we simply choose the lesser of nd. his selection is Mbbj and Mbbj, denoting it as Mbbj similar to that shown in Ref. [9]. At this stage, we still suffer from bb combinatoric background as seen in Fig. 4. o estimate the combinatoric background in the Higgs mass window, we perform a Rbb b b FIG. 3. Correlation between pmin minðp ; p Þ and Rbb from h! bb at the generator level for msugra events at m ¼ 47 GeV, m= ¼ 4 GeV. Here Rbb is a separation between b and b in - space. he inset histogram is the Rbb distribution for pmin > GeV. his shows that bb pairs from a single Higgs decay will most often have a separation of R < for b-jets with transverse momentum greater than GeV. Any b pairs not from a single Higgs decay will instead have no particular separation. nd distribusideband subtraction method. We form the Mbbj tion using b pairs in the Higgs peak window and using b pairs from two sideband windows (7 9 GeV and 3 5 GeV) in Fig. 4. his second distribution is scaled by the ratio of the background shape evaluated in the Higgs window to the sideband windows (see Fig. 4). hen we nd distribution from the subtract this scaled sideband Mbbj nd Higgs Mbbj distribution. Since the kinematical end point occurs when the Higgs is back to back with the jet, we select events with Rh j > :. Number of Counts / GeV u~l u~r u~l u~r 6 ABLE III. SUSY masses (in GeV) and dominant branching ~ for the point m ¼ 44 GeV, m= ¼ 6 GeV, ratios for tan ¼ 4, A ¼, and >. For this point, ~ h ¼ :6 and p ~ ¼ 7:9 pb. he total production cross section for this point is ¼ :446 pb. g~ 8 ABLE II. SUSY masses (in GeV) and dominant branching ~ for the point m ¼ 47 GeV, m= ¼ 3 GeV, ratios for tan ¼ 4, A ¼, and >. We chose this point to examine despite the fact that it is within the region excluded by b! s. ~ at its maximal We did this to examine the behavior of ~! Z branching ratio. he total production cross section for this point is ¼ 7: pb g~ Number of Counts /.5 b~ b~ 4 g~ ~t ~t u~l u~r 5 p(b or b) ABLE I. SUSY masses (in GeV) and dominant branching ~ for the point m ¼ 47 GeV, m= ¼ 44 GeV, ratios for ~! ~ is tan ¼ 4, A ¼, and >. Notice that the kinematically forbidden. For this point, ~ h ¼ :89 and p ~ ¼ :4 9 pb. he total production cross section for this point is ¼ :6 pb. PHYSICAL REVIEW D 79, 55 (9) Mbb FIG. 4 (color online). he invariant mass distribution of PGS b jet pairs. he central dark gray (blue) bins are the Higgs peak window. We perform a background subtraction by selecting the light gray (green) sideband windows. he background fit is the black curve. 55-5

6 BHASKAR DUA et al. PHYSICAL REVIEW D 79, 55 (9) In order to determine the end point, we fit the mass distribution to a combination of a Landau probability distribution function, P L, and a straight line: kpl ðx; x fðxþ ¼ peak ;Þ if x<x peak ; kp L ðx; x peak ;Þþðx x peak Þ if x>x peak ; (3) where x corresponds to the Higgs plus jet invariant mass, x peak is the most probable value of the Landau distribution, k scales the height of the function, and is the slope of the linear portion. Figure 5 shows the fittings at two msugra points around our reference point described in able I. One can see the change in the shape and the end point as m = increases. he slight change in shape between the two histograms in Fig. 5 is due to the fact that the SUSY background for this signal does not shift as we vary m =, and that it dies off around 8 GeV. hus, the m = ¼ 4 GeV histogram which has an end point around 75 GeV has a slight shoulder after the end point, whereas the m = ¼ 48 GeV histogram has an end point around 9 GeV with no shoulder. Despite such shoulders, the shape of the distribution stays similar as we vary the model parameter m =. hus we can use the same fitting function for such points. Also, since the end point, M end does not depend on any third h q generation sparticles [see Eq. ()], it is independent of the parameters A and tan. However, if we increase m the situation changes. For higher m values the ~q becomes significantly heavier than the ~g. he result of this, for instance in the case of m ¼ 65 GeV and m = ¼ 44 GeV, is that Bð~q L! q~gþ ¼% and Bð~q L! q~gþ ¼ %. he quark jets from such decay chains are much softer than background jets from lower m points. hus, the Number of Counts / 5 GeV nd M bbj FIG. 5 (color online). he Higgs (tagged b jet pair) plus jet invariant mass distribution reconstructed through PGS in two 5 fb msugra samples at ðm ;m = Þ¼ð47; 4 GeVÞ and (47, 48 GeV) for the black histogram with gray (red) fit and gray, filled (blue) histogram with dark gray (dark blue) fit, respectively. We fix tan ¼ 4, A ¼, and >. Number of Counts / 5 GeV nd M bbj FIG. 6 (color online). he Higgs (tagged b jet pair) plus jet invariant mass distribution reconstructed through PGS in a 5 fb msugra sample at m ¼ 65 GeV, m = ¼ 44 GeV, tan ¼ 4, A ¼, and >. nature of the background changes, which changes the shape of the Higgs plus jet invariant mass distribution: he end point becomes very sharp. hus a simple linear fit is sufficient to find the end point. A sample fit of this higher m region is shown in Fig. 6.. Z þ jets þ E6 he final state of Z þ jets þ E6 events becomes a key signal in a lower m = region (m = 3 GeV) where the ~! qh ~ decays are kinematically suppressed. he decay chain and end point equation [Eq. ()] are exactly the same under the replacement of the Higgs boson mass with the Z boson mass. o construct the Z plus jet invariant mass and measure the end point, we follow the very same procedure as the Higgs plus jet analysis, but with Z! ll decays. We select events with the same initial cuts as in the Higgs plus jet analysis and reconstruct the Z! ll decays instead of the Higgs decays. o select our Z bosons we find pairs of isolated leptons with p > GeV in our event. We keep pairs of leptons with invariant mass within the Z mass window, where 85 <M ll < 97 GeV. hen we form l þ jet systems using the two jets with the greatest transverse momenta. We again keep only the lesser of the two l þ jet invariant masses, Mllj nd. o ensure we select mostly Z bosons within this signal we use an opposite-sign sameflavor minus opposite-sign opposite-flavor subtraction. A sample distribution of the result is shown in Fig. 7. his figure shows us a measurable end point very similar to that of the Higgs plus jet invariant mass technique. 3. þ jets þ E6 he þ jets þ E6 signal appears in the higher m = region (m = * 5 GeV) within the SSC band of parame- 55-6

7 SUPERSYMMERY SIGNALS OF SUPERCRIICAL SRING... PHYSICAL REVIEW D 79, 55 (9) Number of Counts / 5 GeV nd M llj Number of Counts / GeV M ττ FIG. 7. he Z plus jet invariant mass distribution reconstructed through PGS in one 5 fb msugra sample at m ¼ 47 GeV, m = ¼ 3 GeV, tan ¼ 4, A ¼, and >. ter space in Fig.. he full decay chain ~q L! q ~! ~! ~ produces a characteristic final state consisting of s, high p jets from the ~q L decay, and E6 from the ~. Again, the two particles and the jet carry information about the supersymmetric particles in the decay chain. he visible ditau invariant mass distribution and the plus jet invariant mass distribution both have end points depending on the supersymmetric particle masses: v ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi M end ¼ M ~ M M u ~ ~ t M ; (4) ~ M end M ~ v ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi M M j ¼ M u ~ ~q L ~ t M : (5) ~q L M ~ We again make use of such kinematical observables by measuring these end points. However, in this case, we are restricted by the background for M end. o avoid this background, we measure the peak instead, since the peak is proportional to the end point. Events were generated using ISAJE [7] and the detector ects were simulated using PGS4 [8]. o measure these observables, we select our events with the following cuts [4]: (i) at least two jets with p GeV as well as jj :5, (ii) E6 8 GeV, and (iii) p jet þ p jet þ E6 6 GeV. (iv) We reject events where either one of the two leading jets is tagged as a b jet [8]. FIG. 8 (color online). he ditau invariant mass distribution reconstructed through PGS in two 5 fb msugra samples at ðm ;m = Þ¼ð44; 65 GeVÞ and (44, 575 GeV) for the black and gray (blue, filled) histograms, respectively. We fix tan ¼ 4, A ¼, and >. hese cuts remove the majority of SM backgrounds (tt, W þ jets, and Z þ jets), as well as background from SUSY events containing stops or sbottoms. Here again, unforeseen SM backgrounds at the LHC can be shape analyzed from the data and then subtracted from our desired signal. We do not discuss the details of the event selections, but instead refer the reader to our previous and ongoing studies [4 6]. Sample M and M j distributions for points similar to that shown in able III are displayed in Figs. 8 and 9. hese figures also show how the peak and end point shift under changes of m =. Since the end point of the þ jet invariant mass distribution, Mj end, does not depend on any third generation superparticles [see Eq. (5)], it will only Number of Counts / 5 GeV M jττ FIG. 9 (color online). he plus jet invariant mass distribution reconstructed through PGS in two 5 fb msugra samples at ðm ;m = Þ¼ð44; 65 GeVÞ and (44, 575 GeV) for the black histogram with gray (red) fit and gray, filled (blue) histogram with dark gray (dark blue) fit, respectively. We fix tan ¼ 4, A ¼, and >. 55-7

8 BHASKAR DUA et al. PHYSICAL REVIEW D 79, 55 (9) shift for variations of the msugra parameters m and m =. However, the peak of the invariant mass distribution, M peak, depends on the stau mass [see Eq. (4)], and will thus depend on all four msugra parameters. IV. DEERMINING MODEL PARAMEERS We have shown in previous works [4 6] that we can obtain mass measurements of the supersymmetric particles in the neutralino-stau coannihilation region by utilizing each final state and parametrizing kinematical observables, such as those described in the previous section, in terms of the SUSY masses. Our goal is to determine the msugra model parameters m, m =, A, and tan since we want to determine the dark matter content and the neutralinoproton cross section. he fifth msugra model parameter, sgnðþ, is assumed to be positive, since this is preferred by measurements of the b! s branching ratio and the muon g [3]. o determine the msugra parameters, we will thus need four kinematical observables which are linearly independent functions of those parameters. he determination of the parameters is then accomplished by inverting four such functional relationships. As discussed above, certain regions of the msugra parameter space might give rise to very different signals. For each region we can combine different observables to determine the four msugra parameters. However, so far, there are not four observables which can be made for each signal described above. hus we introduce the following additional kinematical observables which are valid in any region: M, M ðbþ, and MðbÞ. he ective mass, M, is defined by M ¼ p jet þ p jet þ p jet3 þ p jet4 þ E6 ; (6) where all four leading jets are not b-tagged jets. his combination carries the information of the characteristic SUSY scale. he majority of the p of the jets is characteristic of the gluino and first two generation squark decays, and the majority of the E6 is due to the lightest neutralino escaping the detector. As such, the observable M depends only on the msugra parameters m and m =. his is because the parameters A and tan only affect the third generation superparticles. When we construct the ective mass distribution, we use the following cuts [9]: (i) at least one jet with p GeV and an additional three jets p 5 GeV, where all such jets have jj :5, (ii) no isolated leptons with jj :5, (iii) E6 GeV and E6 : M, (iv) transverse sphericity, S > :. (v) We reject events where any of the four leading jets is tagged as a b jet [8]. We find the peak value with an iterative fitting technique. Number of Counts / 5 GeV First, we fit the distribution iteratively with an asymmetric Gaussian function. he purpose of the iterative fit is simply to find the ideal fitting range. Once that is found, we fit with a cubic polynomial to find the peak position. A sample ective mass distribution showing the result of this procedure is shown in Fig.. his figure also shows that as m = increases, the peak increases. wo very similar observables can also be constructed. he b ective mass, M ðbþ, is defined by M ðbþ ¼ pjetðbþ þ p jet þ p jet3 þ p jet4 þ E6 ; (7) and the b ective mass, M ðbþ, is similarly defined by M ðbþ ¼ p jetðbþ M þ p jetðbþ FIG. (color online). he ective mass distribution reconstructed through PGS in two 5 fb msugra samples at ðm ;m = Þ¼ð47; 4 GeVÞ and (47, 48 GeV) for the black histogram with gray (red) fit and gray, filled (blue) histogram with dark gray (dark blue) fit, respectively. We fix tan ¼ 4, A ¼, and >. þ p jet3 þ p jet4 þ E6 : (8) Here there are no restrictions on the nonleading jets; they can be either b tagged or not. By including the leading b jets, which are primarily decay products of the superpartners to the third generation quarks, we include information about the parameters A and tan. o construct these distributions, we use the very same cuts as we used for M, with some exceptions. For the M ðbþ distribution, the leading p jet must be tagged as a b jet, otherwise we reject the event. For the M ðbþ distribution, the two leading p jets must both be tagged as b jets. Again, the nonleading jets in M ðbþ and MðbÞ can be either b tagged or not. We also use the same fitting algorithm for these distributions as we have used for M. Sample M ðbþ and M ðbþ ective mass distributions are shown in Figs. and. 55-8

9 SUPERSYMMERY SIGNALS OF SUPERCRIICAL SRING... PHYSICAL REVIEW D 79, 55 (9) Number of Counts / 5 GeV (b) M FIG. (color online). Same as Fig., except that this is the b ective mass distribution and that the peak fits are not shown. Number of Counts / 5 GeV (b) M FIG. (color online). Same as Fig., except that this is the b ective mass distribution. Now that we have all the observables we need, we can determine the four msugra parameters in any region. We will now describe examples of this method for a Higgs boson dominated region, a ~ dominated region, and a Z boson dominated region. Higgs þ jets þ E6 : For the Higgs dominant region, we use the following four observables to determine our msugra parameters: (i) ective mass: M peak ¼ f ðm ;m = Þ, (ii) b ective mass: M ðbþpeak ¼ f ðm ;m = ;A ; tanþ, (iii) b ective mass: M ðbþpeak ¼ f 3 ðm ;m = ; A ; tanþ, (iv) Higgs plus jet invariant mass: M nd;end bbj f 4 ðm ;m = Þ. hese functional forms are determined by examining how each kinematical observable changes while varying one of the msugra parameters. Examples of this are shown in Figs. 3 and 4. o determine our msugra parameters, we invert these functional forms into functions of the msugra parameters in terms of the kinematical observables. hen we can simply plug in the values of the observables into the inverted functions to solve for the msugra parameters. o get the uncertainties of the msugra determinations, we propagate the uncertainties of the measured observables through the inverted functions using a Monte Carlo method. We perform a sample analysis for the Higgs region with the following result: m ¼ 47 5 GeV, m = ¼ 44 5 GeV, A ¼ 95 GeV, and tan ¼ hese uncertainties were achieved at fb. he relation between the uncertainties and the luminosity is shown for these parameters in Figs. 5 and 6. Using these results, we can also calculate the neutralino relic density [3] and ¼ 4 5 end m jbb 8 m end jbb m m / FIG. 3 (color online). he left plot shows the change in M nd;end bbj under variations of m (m = ¼ 44 GeV) within the Higgs dominant region of parameter space. he right plot shows the same for variations in m = (m ¼ 47 GeV). Combining the functions plotted results in the functional form M nd;end bbj ¼ f 4 ðm ;m = Þ. he uncertainty bands (dashed lines) represent 5 fb of data. 55-9

10 BHASKAR DUA et al. PHYSICAL REVIEW D 79, 55 (9) (b) Peak M A (b) Peak M tanβ FIG. 4 (color online). he left plot shows the change in M ðbþpeak under variations of A within the Higgs dominant region of parameter space (m ¼ 47 GeV, m = ¼ 44 GeV). he right plot shows the same for variations in tan. Combining the functions plotted along with variations in m and m = results in the functional form M ðbþpeak ¼ f ðm ;m = ;A ; tanþ. he uncertainty bands (dashed lines) represent fb of data. 9 6 ) δ(m ) / δ(m FIG. 5. he left plot shows the change in the measurement uncertainty of m in the Higgs dominant region of parameter space (m ¼ 47 GeV, m = ¼ 44 GeV) for different luminosities. he right plot shows the same for the uncertainty in m =. ) δ(a δ(tanβ) FIG. 6. Same as Fig. 5 but for A and tan. 55-

11 SUPERSYMMERY SIGNALS OF SUPERCRIICAL SRING... PHYSICAL REVIEW D 79, 55 (9) Ωh pb) -9 ( σ - p tanβ tanβ FIG. 7. he left plot shows the uncertainty ellipse on the ~ h - tan plane in the Higgs dominant region of parameter space (m ¼ 47 GeV, m = ¼ 44 GeV). he right plot shows the same for the p ~ - tan plane. he uncertainty in tan is the main source of both the uncertainty of ~ h as well as the uncertainty of p ~. hese results are for fb of data. proton-neutralino cross section. he results for fb are ~ h ¼ : :5 and p ~ ¼ð:9 3:7Þ 9 pb. he uncertainty ellipses on the ~ h - tan and p ~ - tan planes are shown in Fig. 7. Since the uncertainties in each of these values are larger than %, the uncertainty ellipses get pushed into negative (unphysical) values of ~ h and p ~. As such, we have cut these ellipses off at the x-axes in Fig. 7. Z þ jets þ E6 : he analysis technique in the Z dominant region is just the same as the Higgs region if we replace the Higgs plus jet invariant mass with the Z plus jet invariant mass. he end point of the latter can be measured with better precision. his is due to both an Branching Ratio (%) h Excluded by b s γ Z m / m =47 GeV FIG. 8 (color online). he branching ratios for ~! h ~ and ~! Z~ as a function of m = for m ¼ 47 GeV, A ¼, and tan ¼ 4. Also shown is the b! s exclusion region (cyan filled region) from Fig.. increase in production cross section and the ease of reconstructing Z bosons from lepton pairs. his results in a more precise determination of ~ h and p ~ comparable to that of the ~ dominant region shown below. However, we suffer from small BðZ! llþ values. For a useful measurement, we need Bð~! Z~ Þ * 5%. However, such a region does not exist outside of the b! s bound, as shown in Fig. 8. For lower tan, the same conclusion holds since we get constraints on the smaller values of m = due to Higgs mass. herefore, we do not go into detailed analysis of the determination of model parameters in the Z þ jets þ E6 region. However, one can use the observables of the Higgs þ jets þ E6 region, e.g., M, M ðbþ, and M ðbþ, to reconstruct the model parameters. þ jets þ E6 : For the ~ dominant region, we use the following four observables to determine our msugra parameters: (i) ective mass: M peak ¼ f ðm ;m = Þ, (ii) b ective mass: M ðbþpeak ¼ f ðm ;m = ;A ; tanþ, (iii) ditau invariant mass: M peak ¼ f 3 ðm ;m = ; A ; tanþ, (iv) ditau plus jet invariant mass: M peak j ¼ f 4ðm ;m = Þ. We again perform an inversion to determine our msugra parameters, as well as propagate the uncertainties in the same way as in the Higgs region. Our sample analysis for this region yields m ¼ 44 3 GeV, m = ¼ 6 6 GeV, A ¼ 45 GeV, tan ¼ 4: :7, ~ h ¼ :3 :9, and p ~ ¼ð7:6 :6Þ pb. hese uncertainties were achieved at 5 fb. he parameter tan is determined with much higher accuracy since we can use observables involving staus; the staus are very sensitive to tan. Again we show the relation 55-

12 BHASKAR DUA et al. PHYSICAL REVIEW D 79, 55 (9) ) δ(m ) / δ(m FIG. 9. Same as Fig. 5 except within the ~ dominant region of parameter space (m ¼ 44 GeV, m = ¼ 6 GeV). ) δ(a δ(tanβ) FIG.. Same as Fig. 5 except for A and tan within the ~ dominant region of parameter space (m ¼ 44 GeV, m = ¼ 6 GeV)...9 Ωh...9 pb) -9 ( σ - p tanβ tanβ FIG.. Same as Fig. 7 except within the ~ dominant region of parameter space (m ¼ 44 GeV, m = ¼ 6 GeV). hese results are for 5 fb of data. 55-

13 SUPERSYMMERY SIGNALS OF SUPERCRIICAL SRING... PHYSICAL REVIEW D 79, 55 (9) between the uncertainties and the luminosity for this result in Figs. 9 and. We also again show the uncertainty ellipses on the ~ h - tan and p ~ - tan planes in Fig.. Since tan is determined with better accuracy compared to the Higgs dominant region, the relic density and proton-neutralino cross section are also determined with a better accuracy. V. CONCLUSIONS AND DISCUSSION In this paper, we have studied the msugra final states at the LHC which are motivated by SSC. In the SSC case, the time dependent dilaton not only contributes to the dark energy but also to the Boltzmann equation which determines the dark matter content of the Universe. Consequently the dark matter profile in this model is different compared to the standard cosmology. We found that the dark matter allowed region has larger values of m compared to the standard cosmology case. hus, the final states in the SSC scenario are different from those of the standard cosmology. For example, in the case of standard cosmology for smaller values of m (also allowed by the g constraint), we have low-energy taus in the final state due to the proximity of the stau to the neutralino mass in the stau-neutralino coannihilation region. On the other hand, in the SSC case the final states contain Z bosons, Higgs bosons, or high energy taus. In fact these final states dominate in most of the allowed SUGRA parameter space. herefore, by analyzing the parameter space of the SSC model we actually investigate most regions of the SUGRA parameter space at the LHC. We analyzed the signals involving Higgs þ jets þ E6, Z þ jets þ E6, and þ jets þ E6 and constructed observables such as the end points of invariant mass distributions M bbj, M Zj, and M j and the peak position of M. In order to determine all parameters of the msugra model we needed additional observables such as the peak positions of the ective masses M ðbþ and M ðbþ. hese observables are used for determining tan. We found that m, m =, and tan can be determined with %, 3%, and 44% accuracies, respectively, in the Higgs boson dominated final states region for fb of data [3]. he Z boson dominated final state region is mostly ruled out by other experimental data. However, the technique used to analyze the Z boson dominated region is nearly identical to that of the Higgs boson dominated region. In the stau dominated region, m, m =, and tan can be determined with 5%, %, and 7% accuracies, respectively, for 5 fb of data [3]. he accuracy of determining tan is improved in the tau dominated final state region since we use observables involving the staus which are very sensitive to the variation of tan. Once all the parameters are known, the dark matter content can be determined in all these cases. In the Higgs dominant case, the accuracy of determining the dark matter content is 5% for fb of data. In contrast, the accuracy of relic density in the stau dominated region is 8% for 5 fb of data, which is much better due to a higher accuracy of tan determination. hese techniques can be applied in the case of nonuniversal models as well, where we will need more observables to determine the model parameters. When the LHC will be operating, we will also have results from the dark matter direct detection experiment. We found that the cross section for these experiments can be predicted from the LHC measurements with an accuracy of 95% for fb of data in the Higgs boson dominated region and % for 5 fb of data in the stau dominated region. his cross section however includes uncertainty due to the form factors. As a remark, our phenomenological study assumed several key detector performances of the present ALAS and CMS detectors, such as b-tagging and tau identification iciencies. We find that one needs 5 fb of data. he regime of such high luminosity can be realized with the LHC s luminosity upgrade as well as the upgrade of both ALAS and CMS detectors. hus, our results are just a guideline for the physics case if the performance of both upgraded detectors is the same even at such high luminosity operation of the luminosity-upgraded LHC. In this analysis we examined the overdense region of the msugra model since the underlying cosmological theory converts the overdense region into a region with correct relic abundance. his analysis holds for any cosmological model with similar features. Before closing we repeat some cautionary remarks regarding the microscopic model dependence of such studies []. As already mentioned in the Introduction, the lowenergy limit of string theory is incredibly nonunique, as it depends on the complicated details of compactification and SUSY breaking procedures. Various models lead to different predictions, and some of them may lead to completely different phenomenology as far as dark matter studies are concerned. For instance, there are heterotic string models entailing nonthermal dark matter [], whose detection requires totally different techniques from the ones employed here. Nevertheless, there are string models which can be analyzed rather generically within the methods outlined in this work, in the sense that the observables discussed in this analysis can also be used to extract information on dark matter in such string-inspired models as well. For instance, the moduli-dominated sector of the heterotic (orbifold-compactified) class of models examined in Ref. [] has five parameters: the gravitino mass m 3=, the vacuum expectation value of the real part of the (uniform) Kahler modulus ht þ ti, the modular weights of the Pauli-Villars regulators parametrized by p, the value of the Green-Schwarz coicient GS, and tan. he parameters of this model can be determined in the same spirit as shown in the paper and thereby the dark matter density can also be 55-3

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