Initial determination of the spins of the gluino and squarks at LHC Jing Shao University of Michigan Based on work in collaboration with Gordon Kane, Alexey Petrov and Liantao Wang Madison, Apr. 29, 2008
Motivation • Solving the hierachy problem usually requires some SM partners to cancel the quadratic divergence in SM. • A leading example is SUSY. Experimentally to confirm it, one has to determine the spin of the new particle. • There has been a lot of work; use angular correlation A. J. Barr; J.M. Smillie & B.R. Webber, L.T. Wang & I. Yavin; P. Meade & M. Reece; C. Csaki, J. Heinonen & M. Perelstein; S.Thomas …… -- May work for light sleptons, or large statistics.
Basic Idea • What we are emphasizing is that a proper use of the rate information is extremely helpful in the early determination of the spin • The basic observation is that the cross sections of particles with different spin will differ significantly in many cases • Experimentally one will estimate the cross section and mass of the new particle. In most situations, this would immediately imply the spin • Method works best when one production mechanism dominants, e.g. color octets at LHC
Our Strategy • Initially test most reasonable hypotheses -- color octet if M~ 1TeV, σ ~ pb -- no fine-tuned mass degeneracies that could confuse results. • Then later repeat with more alternatives -- color triplet, or a mixture of several productions -- special mass splittings (return to this later)
A Simple Example: Top at Tevatron • The production of top quark is dominated by s-channel q qbar g t tbar • For spin-0 or spin-1, there is a chirality suppression. But not spin-1/2. • Large difference in the cross sections spin of top was measured by σ + M μR= μF= s
Gluino pair production • The production cross section of color octet is completely determined by the spin and its mass (assume color triplets are decoupled). • Very different for different spin -- g’ is a spin-1 massive gauge boson (KK gluon) -- gs is a spin-0 color octet -- scale: μR= μF= mass
Squark pair production • Cross section of squark pair production again depends on the spin and mass. (Assume color octets are decoupled) • Include first and second generation quark partners μR= μF= m q’ is the quark partner in the Same-spin scenario
Caveats • The cross sections are calculated at tree-level. NLO calculation will increase the cross section. However the K-factors for cases with different spin are not very different. – should not change the hierarchy of the cross sections • Measuring the production cross section may not be easy in practice – efficiency, branching ratios • To determine the spin, need to measure the mass of the new color particle. – not trivial • Assume all these can be done when LHC data are available.
Degeneracy? • Typical transverse variables (Ht, Pt) are mainly sensitive to the mass differences between initial and subsequent particles in the decay chain mass measurement is hard, and there are “degeneracies” • For example, consider gluino in SUSY and gluon partner in another scenario. If kinematical observables only depend on the mass difference, say M-MLSP, then adjusting the mass difference in the alternative scenario will fit the distribution as well. • If other information is available about the mass, then no degeneracy. But this typically will not occur with early LHC data. (but could from other experimental data) • When there are multiple production channels, there is probably no degeneracy (come back to this later).
Simulation • Same-spin scenario is implemented using MadGraph user model. -- spin-1 gluon partner g’ -- spin-1/2 partner of SM quarks q’ (u’,d’,c’,s’) • Parton-level events generated by MG/ME; use CTEQ 6L • Particles are decayed using BRIDGE and then showered and reconstructed using pythia + PGS4 • Use Level I trigger; mssing ET > 90GeV, Jet Pt > 50 GeV, η< 2.5
Squark example • Squark mass = 550 GeV, same-spin partner q’ mass = 900 GeV • Decay: q + Bino ; q’ q + B’ Same ΔM adjusted ΔM
Gluino Examples • gluino mass = 800 GeV, same-spin partner g’ mass = 1060 GeV • Decay: q qbar + Bino ; g’ q qbar + B’ Same ΔM adjusted ΔM
More production channels • There are generically other production channels. For example in SUSY, pp / / are usually all important. • The relative difference of these channels are different for different spin scenarios. – they cannot be matched at the same time • This provides a way to determine the spin if the cross sections of each channels can be measured.
Cross sections of multiple channels • Compare SUSY with Same-spin scenario. • Match g’ pair production rate with that of gluino fix g’ mass
Cross sections of multiple channels • Compare SUSY with Same-spin scenario. • Match g’ pair production rate with that of gluino fix g’ mass • Take msquark = 550 GeV andvary q’ mass to match gluino-squark production mq’=780 GeV • σ (squark)=8pb; σ(q’)=19pb -- cannot be matched!
More realistic study • In the real situation, it’s hard to measure cross section of each channel separately. • However, the differences could be seen in the jet multiplicity, if each channel leads to different number of jets (or other kinematical quantities). • This difference in jet multiplicity may be smeared by varying the masses if isolation cuts are imposed. However, even this happens, there could be other kinematical distributions which are different. • We will fit total cross section and jet multiplicity and check whether there is difference in HT distribution. remove the degeneracy
Example (Mgluino < Msquark ) • SUSY: gluino mass 608GeV, squark mass 550GeV. gluino q + squark, squark q + Bino • match total cross section and jet-multiplicity (not perfect) mg’=900GeV, mq’=800GeV,mB’=550GeV • Ht distributions are different (notice the difference in width).
Another example (Mgluino < Msquark ) • SUSY: gluino mass 630GeV, squark mass 800GeV. gluino q qbar + squark, squark gluino + Bino • Ht distribution cannot be matched (notice the difference in width).
Conclusion • The cross section information can be used to determine the spin in the early stage. The result can be checked later by examing the spin correlation. • It works well in simple situations, but may need more work for complicated situations. • There could be no degeneracy if LSP mass is constrained by other experiments, e.g. dark matter relic density.