Razor Phenomenology ALL. Life is not just cut and count! By the Razor Guys

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1 + 1 Razor Phenomenology ALL Life is not just cut and count! By the Razor Guys

2 + The Razor Variables arxiv: Two variables, based on two different ways of calculating masses: M R is sensitive to the scale of new physics processes M R = ( p j1 + p j ) (p j 1 z + p j z ) R reflects to the transverse shape of the event and is sensitive to the ratio of missing and visible momenta M R T = E miss T (p j 1 T + p j T ) E miss T (p j 1 T + p j T ) R = M R T M R

3 + What is the scale of new physics? 3 Let s consider the canonical SUSY topology we are looking for - Di-suark production, with each suark decaying to a uark and LSP: ( 0 1)( 0 1) suark rest frame 0 1 Each suark undergoes a two-body decay, meaning that, in the suark s rest frame, the uark and LSP will each have the same characteristic momentum: P jet = M /= M M M This is the scale of new physics processes we want to be sensitive to

4 + How do we measure the scale? 4 β T lab frame x z ( 0 1)( 0 1) di-suark (CM) rest frame suark rest frame β CM β CM 0 1 Through a series of physics-motivated approximations we try to go from the lab frame to an approximation of the suarks rest frames, where we can measure the characteristic scale the variable M R is the estimation of this scale, event-by-event

5 + M R and new physics scale = 900 GeV 0.05 m ~ m ~ = 750 GeV = 1100 GeV, m = 500 GeV a.u m ~ = 1150 GeV, m = 50 GeV ( 0 1)( 0 1) M R For di-suark pair-production (SMS T), the M R distribution peaks at the characteristic scale: M = M M M

6 + M R and new physics scale What happens to M R for topologies that differ from the one where it was derived? 6 a.u g = 900 GeV 0.08 g = 750 GeV 0.07 g = 1100 GeV, m = 500 GeV m g ~ = 50 GeV M R Here, gluinos are pair-produced and undergo 3-body decays to two jets and an LSP g g ( 0 1 )( 0 1 ) For di-gluino pair-production (SMS T1), the M R distribution peaks at the characteristic scale: M = M M M

7 + M R and new physics scale How much background is there for a given signal? ( 0 1)( 0 1) 7 ] [GeV/c m Average M R over all signal regions > < M R ELE Box 4.4 fb 1 M m g ~ [GeV/c ] 0 To zero-th order, the background is decided by the signal s scale the relevant background is that with M R around the scale But there is one more relevant variable in understanding sensitivity to new physics: R

8 + R and new physics ELE Box 4.4 fb 1 R is sensitive to the balance between visible and missing momentum in the event The variable R is also used to suppress background g g ( 0 1 )( 0 1 ) Almost identical but slightly diferent -body decays (like suark-suark) have higher values of R on average than 3-body decay (like gluino-gluino) because the ratio of invisible to visible momenta is larger ] [GeV/c ] m [GeV/c m Average R over all signal regions [GeV/c ] m g ~ ( 0 1)( 0 1) Average R over all signal regions [GeV/c ] m ~ > > < R < R

9 + R and new physics a.u m ~ m ~ m ~ m ~ = 900 GeV = 750 GeV = 1100 GeV, m = 500 GeV = 50 GeV ( 0 1)( 0 1) R For a given signal topology, R is nearly identically distributed over a wide range of characteristic scales R is sensitive to the scale invariant shape of the event, M R is sensitive to the characteristic scale

10 + R and new physics M 1/ CMSSM tanβ=10 suark-suark Average R over all signal regions M 0 gluino-gluino The transition over the CMSSM plane from suark-suark to gluino-gluino dominated production can be seen in the R distribution > < R 10

11 CMSSM tanβ=10 Average M R over all signal regions 11 M 1/ > < M R M 0 Generally, models with larger scale (higher M R ) have less background è greater sensitivity On the other hand, physics tells us that higher scale implies lower x-section - R largely decides which effect wins

12 10 4 ttbar+jets simulated events 1 Events / 3.5 GeV R* > 0.0 R* > 0.5 R* > 0.30 R* > 0.35 R* > 0.40 R* > 0.45 R* > 0.50 R* > 0.55 R* > M R γ M R* R* Events / 3.5 GeV R* > 0.0 R* > 0.5 R* > R* > 0.35 R* > 0.40 R* > R* > 0.50 R* > 0.55 R* > M R γ M R* R* SM backgrounds are modeled in the M R /R D plane with a specific type of function: f(m R,R )=(b(m R M 0 R)(R R 0) )e b(m R M 0 R )(R R 0 )

13 10 4 ttbar+jets simulated events 13 Events / 3.5 GeV R* > 0.0 R* > 0.5 R* > 0.30 R* > 0.35 R* > 0.40 R* > 0.45 R* > 0.50 R* > 0.55 R* > M R γ M R* R* Events / 3.5 GeV R* > 0.0 R* > 0.5 R* > R* > 0.35 R* > 0.40 R* > R* > 0.50 R* > 0.55 R* > M R γ M R* R* This means that iso-yield contours for the background are shaped like: b(m R M 0 R)(R R 0) = constant

14 10 4 ttbar+jets simulated events 14 Events / 3.5 GeV R* > 0.0 R* > 0.5 R* > 0.30 R* > 0.35 R* > 0.40 R* > 0.45 R* > 0.50 R* > 0.55 R* > M R γ M R* R* Events / 3.5 GeV R* > 0.0 R* > 0.5 R* > R* > 0.35 R* > 0.40 R* > R* > 0.50 R* > 0.55 R* > M R γ M R* R* The least steep nd background component wins going higher in R/M R the majority of the signal sensitive region is dominated by this component s shape

15 15 The least steep nd background component is measured to be nearly identical between different final states and backgrounds Here, for illustration, we assume that the nd component is all the of the background (good approximation at high M R ) we use example values of the functional parameters from the MU box data fit

16 Numbers indicate background yield, relative to the 1 iso-yield contour e e-08 1.e-10.0e e With only one background component, the background isoyield contours look like this R Signal events falling at high R/M R will have more significance (less background) M R

17 A variable which gives an indication of how much background there is in the R/M R region for a given signal is log(1/pdf nd ) PDF nd f bkg (M R,R ) where PDF nd is the one component background function, a function of R/M R 17 a.u = 900 GeV = 1100 GeV, m = 750 GeV = 500 GeV = 50 GeV ( 0 1)( 0 1) a.u Signal events falling at m high ~ = 1150 GeV, m = 900 GeV R/M R will = 750 GeV have m more ~ = 1100 GeV, m = 500 GeV significance = 1150 GeV, m = 50 GeV (less background) M R log(1/pdf nd ) (Arbitrary scale)

18 a.u. a.u. + Sensitivity to new physics 0.09 g = 900 GeV 0.08 g = 750 GeV = 900 GeV M R g g ( 0 1 )( 0 1 ) g = 1100 GeV, m = 500 GeV g = 50 GeV = 750 GeV = 1100 GeV, m = 500 GeV = 50 GeV a.u. a.u ( 0 1)( 0 1) g = 900 GeV g = 750 GeV g = 1100 GeV, m = 500 GeV g = 50 GeV nd log(1/pdf ) = 900 GeV = 750 GeV = 1100 GeV, m = 500 GeV = 50 GeV 18 Even though suark-suark and gluino-gluino production have similar M R distribution for a given scale, the difference in R mean the suarksuark events are more significant (have less background) on average M R nd log(1/pdf )

19 19 Even though suark-suark and gluino-gluino production have similar M R distribution for a given scale, the difference in R mean the suark-suark events are more significant (have less background) on average ( 0 1)( 0 1) g g ( 0 1 )( 0 1 ) e e-08 1.e-10.0e-13 ( 0 1)( 0 = 900 GeV 1) = 1150 GeV, m m ~ m ~ m ~ 3.3e-16 = 1150 GeV, m = 750 GeV = 1100 GeV, m = 500 GeV = 1150 GeV, m = 50 GeV e e-08 1.e-10.0e e-16 g = 1150 GeV, m = 900 GeV g = 1150 GeV, m = 750 GeV m g ~ m g ~ = 1100 GeV, m = 1150 GeV, m = 500 GeV = 50 GeV R 0.5 R M R M R

20 The mean value of our illustrative metric over the signal region for a given model point maps closely to the final x-section limit 0 ] [GeV/c m The more significant a model s events are, the fewer events that model needs to produce in order to be observed/excluded m g ~ [GeV/c g g ( 0 1 )( 0 1 ) ] > nd < 1 / PDF ] m [GeV/c CMS Preliminary pp g ~ g ~, g ~ + -1 s = 7 TeV L dt = 4.4 fb Razor Inclusive σ σ σ prod prod prod NLO-QCD = σ = 3 x σ = 1/3 x σ NLO-QCD NLO-QCD m g ~ [GeV/c ] ) 95% CL upper limit on σ (pb) (CL S

21 The cross-section upper limit for a given model has a very similar scale dependence to the it s NLO x-section This is not a coincidence the background rate has a similar dependence on scale to the NLO x-section (signal and background have the same parton distr. func. s) 1

22 Even as the model efficiency begin to plateau at high scale, the cross-section upper limit continues to drop since the effective background to the signal continues to drop with increasing scale ] [GeV/c m CMS Simulation s = 7 TeV >=1 TCHEM b-tag All Boxes pp ~ g ~ g, ~ g t + ; m( ~ t) >> m(g ~ ) m g ~ [GeV/c ] Signal Region Efficiency (%)

23 Looking at the mean value of our event significance metric over the CMSSM, we see that different parts of the plane correspond to different R/M R regions This is also why the the observed limit, relative to the expected, changes over parameter space (since it is effectively probing different parts of the R/M R distribution) M 1/ CMSSM tanβ= M ) > nd < log(1/pdf m 1/ CMS Preliminary = LSP τ tan(β)=10 A 0 = 0 GeV µ > 0 m t = 173. GeV m( ~ ) = 1500 m( ~ ) = 1000 ~ ± LEP l LEP ± 1 m( ~ ) = 000 m( ~ ) = 500 m(g ~ ) = 500 s = 7 TeV m(g ~ ) = 000 Razor Inclusive Hybrid CLs 95% C.L. Limits Median Expected Limit m(g ~ ) = 1500 Expected Limit ±1 σ Observed Limit m(g ~ ) = 1000 m L dt = 4.4 fb No EWSB Non-Convergent RGE's

24 suark-suark production dominates, with high R and very high scale è low expected signal yields but almost no background M 1/ CMSSM tanβ= M 0 gluino-gluino production dominates, with lower R and hence more background, on average, for a given scale than for suarks one needs more events to observe/exclude ) > nd < log(1/pdf m 1/ CMS Preliminary = LSP τ tan(β)=10 A 0 = 0 GeV µ > 0 m t = 173. GeV m( ~ ) = 1500 m( ~ ) = 1000 ~ ± LEP l LEP ± 1 m( ~ ) = 000 m( ~ ) = 500 m(g ~ ) = 500 s = 7 TeV m(g ~ ) = 000 Razor Inclusive Hybrid CLs 95% C.L. Limits Median Expected Limit m(g ~ ) = 1500 Expected Limit ±1 σ Observed Limit m(g ~ ) = 1000 m L dt = 4.4 fb No EWSB Non-Convergent RGE's

25 suark-suark production dominates, with high R and very high scale è low expected signal yields but almost no background gluino-gluino production dominates, with lower R è more background, on average, for a given scale than for suarks è needs more events to observe/exclude e e-08 1.e-10.0e e-16 5 R M R M 0 = 00 GeV, M = 700 GeV 1/ M 0 = 1800 GeV, M = 300 GeV 1/ m 1/ = LSP CMS Preliminary τ tan(β)=10 A 0 = 0 GeV µ > 0 m t = 173. GeV m( ~ ) = 1500 m( ~ ) = 1000 ~ ± LEP l ± LEP 1 m( ~ ) = 000 m( ~ ) = 500 m(g ~ ) = 500 s = 7 TeV m(g ~ ) = 000 Razor Inclusive Hybrid CLs 95% C.L. Limits Median Expected Limit m(g ~ ) = 1500 Expected Limit ±1 σ Observed Limit -1 L dt = 4.4 fb m(g ~ ) = m 0 No EWSB Non-Convergent RGE's

26 gluino e e-08 1.e-10.0e-13 EWK-inos stops/sbottoms suark/gluino 3.3e M 0 = 00 GeV, M 1/ M 0 = 1800 GeV, M 1/ = 700 GeV = 300 GeV 0.6 R M R