ATLAS detector and physics performance : Technical Design Report, 1

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Summary

ATLAS detector and physics performance

• The requirements of gauge invariance and renormalisability are sufficient to guarantee that the Standard Model Lagrangian conserves baryon and lepton number.
• Events were selected with two b-jets near the Higgs mass, two hard jets, and no other jets with pT > 100 GeV to reduce the combinatorial background.
• The statistical uncertainty on the slepton mass was estimated and 252 GeV (bottom plot).
• The combination of a large production cross section and distinctive signatures makes it easy to separate SUSY from the Standard Model background.

)cos2P 20-3 -m,(A,-wotb)

• The resulting left-right mixing is mainly important for the third generation; the eigenstates are _ called r1,2, b1,2, and Z, 2.
• There can also be mixings among generations of sfermions -including new sources of CP violation.
• It does not seem possible to construct a phenomenologically acceptable model with spontaneous supersymmetry breaking using only the MSSM fields.
• In supergravity models gravity is the sole messenger [20-111.
• These masses are split when they are run down to the weak scale with the RGE's [20-121.

20.2 Supergravity models

• The parameters of the five LHCC points are listed in Table 20 -3; the particle masses are listed in Table 20 -4.
• Point 3 is the 'comparison point', selected so that other existing or proposed accelerators could find something.
• The gluino mass is 350 GeV, and it has a high probability to decay via S + 616 + j$'bb ; the Points 1 and 2 both have gluino and squark masses near 1 TeV, about the upper limit expected from fine tuning arguments.
• Point 4 was chosen to be near the boundary for electroweak symmetry breaking, implying that p is small so that there is quite strong mixing between gauginos and Higgsinos in Equations 20-l and 20-2.
• (One weakness of the GMSB and R-parity violating models considered in Section 20.3 and Section 20.4 is that they do not provide cold dark matter.

20.2.2 Exclusive SUGRA measurements for moderate tan p

• For very large tanp the splitting among the slepton masses becomes larger, and the only twobody decay available may be X$' + Zjz' + X$+r-.
• If this is the only two-body mode, its branching ratio will be nearly unity.
• In general the longer the chain that can be identified and reconstructed, the stronger the constraints will be.
• Sections20.2.3-20.2.7 describe such analyses for the five LHCC SUGRA points based on this general approach.
• The statistics on the Standard Model backgrounds often correspond to much less than one year.

20.2.3 PI-SUGRA signatures

• Given these decay modes, events were selected by requiring [20-22,20-241: mainly from two independent if decays; it is responsible for the tail of events beyond this endpoint.
• The Standard Model background, which is tiny, comes mainly from ti events.
• If the branching ratios were less favourable, one could plot instead the flavour-subtracted combination e+e-+ u+u--e'ur and cancel the background up to statistical fluctuations.
• Given the high statistics and small background, the endpoint can be determined with an accuracy limited only by systematics, estimated to be 0.1% or 50 MeV.
• A small n implies not only that the heavier charginos and neutralinos are relatively light but also that there is strong mixing between the gauginos and Higgsinos, so they have gauge-like rather than Higgs-like couplings to light flavours.

ATLAS detector and physice performance

• Error on the endpoint for three years at low luminosity was estimated [20-251 using a Kolmogorov test to be (68.13_,, _ . +OS + 0 07 ) GeV, where the first error is statistical and the second is systematic, coming mainly from the 0.1% uncertainty in the electromagnetic energy scale.
• A full analysis would require generating many samples of events varying all the parameters of the minimal SUGRA or other SUSY model.
• Therefore, the dilepton endpoint would be sensitive to any difference in the right-handed slepton masses at about the 0.1% level, assuming of course the same event rates as at this point.
• If this resolution could be achieved, the uncertainty on the edge measurement would be probably dominated by the statistical error, and by the uncertainties in the modelling of the background.

20.2.4 More complex leptonic SUGRA signatures

• The energies and momenta of the tagged b -jets were corrected to the true energy (see Section 12.5.1.3), to account for losses from neutrinos and from energy leaking out of the R = 0.4 cone.
• This correction was actually derived for the h + 65 analysis and will be discussed in Section 20.2.5 below.
• Since the mass difference is small, the resolution on the difference is better than that on the individual masses; the kinematics is analogous to that familiar from D' _j Drc.
• Because there is a lot of background, the error on the iL mass is conservatively estimated to be &20 GeV [20-241; the purely statistical error would be much less than this.

20.2.6 Thresholds and model-independent SUGRA masses

• For Point 5, although the l+l-edge, Pq edge, 1+1-q 4-body endpoint, and hq edge described earlier give four constraints on the GL, ji!j ,7 R , and Xy masses, it turns out that there exists a solution for any value of the Xp mass.
• Including the 1+1-q threshold described here makes it possible to determine all the masses involved from kinematics alone.
• The measured quantities were then Clearly the allowed masses are highly correlated.
• If this constraint were not included, the gp mass would be essentially undetermined.

20.2.7 Other signatures for SUGRA Points 1 -5

• This subsection contains a number of examples for the five LHCC points listed in Table 20 -3.
• In some cases masses have been extracted by using the shapes of distributions and not just kinematic endpoints.

Volume II

• With these cuts there are a total of 600 signal events with backgrounds of 140 WW events and 140 ti events for an integrated luminosity of 300 RI-' .
• While the signatures for sleptons are obviously difficult, it would be possible to detect the 1, at this point with ATLAS using the full luminosity of the LHC.
• Since the Drell-Yan cross section can be calculated with reasonable accuracy, it is possible to estimate the mass using the observed rate, but the accu- racy will be limited by the knowledge of the efficiency of the cuts and by the uncertainty on the branching ratio and on the luminosity measurement (See Chapter 13).
• In principle the endpoint of the trilepton mass can be used to determine the slepton mass, although the rates are marginal.

ATLAS detector and physics petformance

• Volume II Technical Design Report 25 May 7999 SUGRA.
• Because the masses are low, the cross section is large; this sample corresponds to an integrated luminosity of about 6 W-l.
• It accepts 41% of the r hadronic decays while giving a rejection of about 15 against light quark jets, which is adequate for the purpose.
• These results from full simulation provided the basis for z identification and reconstruction in the SUSY and the Standard Model background samples.
• The jets found from the particle-level simulation were compared with the r's from the event generator.

ATLAS defector and physics performance

• Finally, tan p is determined by the Higgs mass, which also fixes the sign of CL.
• The errors on m. are larger and only improve slowly with increasing luminosity because the determination of the squark mass is limited by systematics.

20.2.10 Non-universal SUGRA models

• A completely general SUGRA model has as many weak-scale parameters as the MSSM, so a general exploration is not possible without some experimental guidance.
• Since low-energy tests severely constrain flavour mixing and CP -violating phases, these are assumed to be absent, although there is no good justification for this assumption.
• This still leaves nineteen real parameters plus sgnu, corresponding to the parameters of ISAJET.
• Three possible deviations from universality at the GUT scale have been considered: non-universal Higgs masses, non-universal 5 and 10 sfermion masses, and non-universal third generation masses.
• Each case can be characterised by one additional parameter.

20.3 Gauge mediated SUSY breaking models

• It appears that the backgrounds are dominated by irreducible physics processes, so that the detector performance is not critical.
• Detailed GEANT-based studies have been performed for non-pointing photons at Point Gla and for qrasi-stable sleptons at Point G2b.

20.3.2 GMSB Point Gl b

• The SUSY cross section at Point Glb is 7.6 pb, the same as at Point Gla.
• The NLSP, the XF, is neutral and long-lived; most of them escape the detector, giving signatures that are qualitatively like those in SUGRA models.
• A qualitatively new feature is that the Xf can occasionally decay in the tracking volume, giving rise to a photon that does not point to the interaction vertex.
• Since the ATLAS electromagnetic calorimeter provides directional information, it can measure such photons, giving information on the ip lifetime and hence on Cgrav .
• It will be discussed in Section 20.3.2.4 after the other signatures.

ATLAS detector and physics performance Volume II Technical Design Report 25 May 1999

• There is also a small peak visible in the figure from Z decays which could be measured with more luminosity.
• This measurement would help to confirm the two body nature of the decay and potentially would provide information on the Higgsino content of the light neutralinos.

ATLAS detector and physics pehrmance Volume II Technical Design Report 25 May 7999

• For this analysis [20-371 it is assumed that the lifetime cz is large compared to the length L(n) inside of the tracker, so that the decay probability is given by L(n)/( pycz) and the decays occur uniformly along the path length.
• The mean energy of these photons is 84.4 GeV.
• While the distribution peaks at zero, the angles are generally large compared to the resolution.
• Converting this rate to a measurement of a lifetime requires that the mass and momentum distribution of the ip be determined from other measurements.
• The rate for prompt photons in SUSY events has not been calculated but is expected to be of order (X/II:, so the background should be much less than one event.

A$ (ns>

• The mean delay, 2.67 ns, is long compared to the time resolution of about 100 ps for the ATLAS electromagnetic calorimeter.
• This provides an independent way to detect non-prompt photons and a cross-check on the whole analysis.

20.3.4 GMSB Point G2b

• Since the decay in + 2,rL is not kinematically allowed, the Z, and fiR also are long-lived, decaying to gravitinos with about the same lifetime.
• Each event therefore contains two quasi-stable heavy particles which pass through the calorimeter and look essentially like muons in the detector except that they have Q < 1, as shown in Figure 20 -72.
• The slepton masses can be measured using the ATLAS muon system as a time-of-flight system, and the SUSY events can then be fully reconstructed [20-361.
• It should be possible to see such decays in the central tracker, but this is a difficult pattern recognition problem which has not yet been addressed.

20.3.5 Fitting GMSB parameters

• Results of the fits [20-361 for these four parameters are given for the same Low-L, High-L, and Ultimate scenarios as in Section 20.2.9 except that for the first two the theoretical error on the light Higgs mass is taken to be -+3 GeV , somewhat more conservative than the value assumed in the SUGRA fits.
• The parameter Cgrav is independent from the other parameters, and is determined in each case from the NLSP lifetime as already discussed.
• No study of the determination of non-minimal GMSB parameters has yet been made.

20.351 Point Gla

• It may be possible to obtain a better determination of the parameters at this point, but doing so would require generating many samples of events and comparing the predicted distributions with the data.
• Thus, this point serves as a caution about drawing overly optimistic conclusions about the generality of the methods discussed in this chapter.

20.4 R-Parity breaking models

• All the studies were performed within the minimal SUGRA model, with the Xp forced to decay to the appropriate quark/lepton combination.
• The first step in the study was to verify that SUSY events can still be sorted out from the Standard Model background, even in the absence of the classic EFiss signature.
• This is straightforward for the L-violating couplings, which in most of the cases produce a high number of leptons in the final state, and requires a more careful analysis for the B-violating case.
• The next step was to study, for the five sample points in the SUGRA parameter space, the same exclusive decay chains that were studied for the R-conserving case.
• On the other hand, in many cases it will be possible to reconstruct the jiy from its decay products, opening the possibility of the full reconstruction of the masses of the particles taking part in the identified decay chains.

20.5 Conclusion

• If SUSY exists at the weak scale, then its discovery at the LHC should be straightforward.
• The SUSY cross section is dominated by gluinos and squarks, which are strongly produced with cross sections comparable to the Standard Model backgrounds at the same Q2.
• Gluinos and squarks then decay via a series of steps into the LSP (which may itself decay if R -parity is vio-.

Figures

Figure 20-71’ Trilepton mass distribution for chargino signal at Point G2a. The shaded histogram is the Standard Model background.

Figure 20-43 shows the distribution of visible masses resulting from scaling the generated masses by f7.5% from the nominal values in order to test the sensitivity. These curves could be distinguished statistically, but understanding the background under the edge might be a problem since it is still quite large.

Table 20-14 Results of a fit of the measurements in Table 20-13 to the minimal SUGRA model. There are solutions for both signs of p .

Figure 20-105 Invariant mass of 2: with a hard jet in Figure 20-106 Invariant mass of 2: with a hard jet in Point 1 (h,,, f 0) for an integrated luminosity of 30 fb-’ . The expected positions of the mass of the Point 5 (hlZ2 # 0) for an integrated luminosity of 30 fb-’ . The expected positions of the masses of the right handed squark is shown. right handed squark is shown.

Figure 20-6: Efficiency vs significance for a photon from iy + Gy to be non-pointing at Point Gl b.

Figure 20-114 Invariant mass of a candidate jig with

Figure 20-80, shows a peak about 3% below the average iL mass of 674 GeV. The figure also shows the distribution for the subset of events tagged as b ‘s. (No correction to the b-jet energy scale was made.) In contrast to the Xy j case, there is a clear peak close to the average b mass - 647 GeV with a splitting of only 9 GeV -which is significantly below the GL mass. While the de-

Figure 20-29 Distribution of the larger bbq mass at Point 5. No sideband subtraction or b -jet energy cor-

Figure 20-32 Distribution of the fractional difference Figure 20-33 Distribution of the fractional difference between the reconstructed and the true squark mass from model-independent analysis for Point 5. between the reconstructed and the true iQ mass from model-independent analysis for Point 5.

Figure 20-47 Lego plot of the reconstructed Ms vs Mg -Mb, at Point 6.

Figure 20-75 Reconstructed slepton masses at Point G2b for a Ins time resolution and A? > 1Ons.

Figure 20-92 Distribution of the invariant mass of the Figure 20-93 Distributions of the invariant mass off softer jip with the two leptons in the event. The distribution is peaked around the nominal i! mass of the softer ip with the two leptons in the event for two different values of the jiz mass: 212 GeV (top plot) 233 GeV. and 252 GeV (bottom plot).

Figure 20-115. From a gaussian fit to the observed peak the br mass is measured to be m- = (276.6 f 3) GeV , where the error is dominated by the uncertainty in the b-jet energy scale. Fc% the events within f10 GeV of the i1 peak, the invariant mass of the 61 candidate with the soft b-jet can be calculated, as shown in Figure 20-116, yielding a measurement of the gluino mass: mg = (301+ 3) GeV.

Figure 26-I 17 The dependence of the masses of bl and i from the assumed value of the ii,” mass for Point 3 (A,,, f 0).

Figure 20-51 Higgs mass and jig + ji:Z branching ratios as functions of tanp and sgnp scanned over the allowed values of the other parameters.

Figure 20-61 has an endpoint at 105.1 GeV, which of course is the same as for Point Gla. There is more Standard Model background than before because there are no photons in the signal events, but the background is still small; the spikes in the background curve in the figure are fluctuations that reflect the limited Monte Carlo statistics. Hence, the error on this endpoint should again be about O.l%, limited by the absolute lepton energy scale. The sharp endpoint is characteristic of a sequential decay through a slepton.

Figure 29-110 invariant mass of the jet-ii combination as described in the text at Point 5 (I,,, # 0 ) for an integrated luminosity of 30 fb-’ . The arrows shows the expected position of the iL mass.

Figure 20-16 M(g) - M(bl) projection of Figure 20- 14. The dashed_curve shows the projection with a cut 230 GeV -C M(bl) < 330 GeV .

Figure 20-83 Same as Figure 20-76 with the addi- Figure 20-84 Combination of ‘il from Figure 20-83 in tional requirement Meff < 100 GeV. the mass range 110-120 GeV with an additional lepton.

Figure 20-87 mT, cent distribution for SUSY signal (shaded histogram), and for signal+background (full line histogram), after requiring at least eight jets with pT > 50 GeV . The different components of the background are also shown separately.

Figure 20’70 lj mass distribution for the same sample as in Figure 20-69. The dashed lines are linear fits over 150-280 GeV and 30.5400 GeV.

Full text

BROOKHAVEN NATIONAL LABORATORY
18 June 1999
BNL - 52570
ATLAS DETECTOR AND PHYSICS PERFORMANCE
TECHNICAL DESIGN REPORT
Chapter 20: Supersymmetry
The ATLAS Collaboration*
* See http: //atlasinfo. tern. ch/Atlas/Welcome. html for a list of the ATLAS Col-
laboration membership.
This manuscript has been authored under contract number DE-AC02-98CH10886 with the U.S. Depart-
ment of Energy. Accordingly, the U.S. Government retains a non-exclusive, royalty-free license to publish or
reproduce the published form of this contribution, or allow others to do so, for U.S. Government ournoses.

ATLAS DETECTOR AND
PHYSICS PERFORMANCE
TECHNICAL DESIGN REPORT
Chapter 20: Supersymmetry
The ATLAS Collaboration1
This chapter summarizes the ability of the ATLAS Detector at the CERN LHC to
search for SUSY and to make precision measurements of SUSY if it is discovered. The
primary emphasis is on detailed studies of selected points in the minimal supergravity
model, the minimal gauge mediated SUSY breaking model, and R-parity violating
models.
Thic cl
nrllmont wac written with Fra.meMaker. A Postscript file of this chapter can
I lllU U”~UIII~II” ,..A” . . LAW..“-* . . -J-_ - _-_ ____. ____d_
be obtained from http://www.cern.ch/Atlas/GROUPSjPHYSICS/TDR/physics_tdr/
printout/Volume_II/Supersymmetry.ps.
'See http://atlasinfo.cern.ch/Atlas/Welcome.html for a list of the ATLAS Collaboration
membership.

.
V
.
(blank page)

ATLAS detector and physics performance
Technical Design Report
Volume II
25 May 1999
20 Supersymmetry
20.1 Introduction
Supersymmetry -
or SUSY - is one of the best motivated extensions of the Standard Model, so
the study of SUSY is a primary goal of the LHC. If SUSY exists at the weak scale, M - 1 TeV ,
then discovering evidence for SUSY particles at the LHC seems to be straightforward. There-
fore, ATLAS has concentrated on the problems of making precision measurements of SUSY
masses (or combinations thereof) and of using these to infer properties of the underlying SUSY
model.
While the Standard Model has been tested to an accuracy of order 0.1% [20-l], the I-Eggs sector
responsible for generating the masses of the W and Z bosons and of the quarks and leptons has
not been tested yet. The Higgs boson is the only scalar field in the Standard Model. Scalar fields
are special in that loop corrections to their squared masses are quadratically divergent: they are
proportional to the cutoff A2, while all other divergences are proportional only to log h2. Some
new mass scale be ,;nd the St%dard Model must exist, if only the reduced Planck scale
MP = (8nCNewton)
Y
= 2.4 x 10 GeV associated with gravity, and the loop corrections to the
Higgs mass are naturally of order this scale. This is known as the hierarchy problem 120-21. The
only known solutions - other than accepting an incredible fine tuning - are to embed the Higgs
bosons in a supersymmetric theory or to replace the elementary Higgs boson with a dynamical
condensate as in technicolor models.
SUSY [20-3,20-41 is the maximal possible extension of the Lorentz group. It has fermionic gener-
ators Q, Q which satisfy
tQ,iZ, = -2~7
[Qt Ppl = tQ, Q> = tik e> = 0
where Pb is the momentum operator and y, are the Dirac matrices. SUSY therefore relates par-
ticles with the same mass and other quantum numbers differing by + l/2 unit of spin,
Qlboson) = Ifermion),
Qlfermion) = Jboson) .
In the Minimal Supersymmetric extension of the Standard Model (MSSM) each cl-&al fermion
fL, R has a scalar sfermion partner f~, R , and each massless gauge boson A,, with two helicity
states fl has a massless spin- l/2 gaugino partner with helicities f1/2. There must also be two
complex Higgs doublets and their associated Higgsinos to avoid triangle anomalies. The com-
plete list of particles is shown in Tables 20-l and 20-2. The.interacti0n.s of SUSY particles are ba-
sically obtained from the Standard Model ones by replacing any two lines in a vertex by their
SUSY partners; for example, the gluon-quark-quark and gluino-quark-squark couplings are the
same. See [20-41 for the construction of the complete Lagrangian.
SUSY provides a solution to the hierarchy problem because it implies an equal number of bos-
ens and fermions, which give opposite signs in loops and so cancel the quadratic divergences.
This cancellation works to all orders: since the masses of fermions are only logarithmic diver-
gent, this must also be true for boson masses in a supersymmetric theory. When SUSY is broken,
20 Supersymmetry 813