Razor kinematic variables

Chapter III: Supersymmetry and searches at the LHC

3.7 Razor kinematic variables

physics [94]. We describe here the derivation of the razor variables and discuss their utility in SUSY searches.

To begin, we consider pair production of heavy squarks at the LHC. Each squark decays to a quark, which is observed as a jet; and the LSP, which escapes without being detected. This is the situation in, e.g., the T2bb model shown in Figure 3.6.

Let the squark and LSP masses bem_Q andmχ, and assume the quarks to be mass- less. We have access to measurements of the lab-frame momenta of the jets, denoted p1 and p2, and top~_T^miss, but not to the LSP momenta. We consider the problem of how to estimate the SUSY particle masses in this situation of imperfect information.

In the center-of-mass reference frame of each produced squark, the visible quark has momentum

q_i = M∆

2 {1,uˆ_i}, (3.25)

wherei =1,2, ˆu_iare unit 3-vectors, and

M∆ = m_Q² −m²_χ

m_Q (3.26)

carries information about the masses of the SUSY particles. If we knew what Lorentz boosts to perform to go from the lab frame to the squark rest frames, we could apply those boosts to p1,2, recoverq1,2, and thus measure M∆.

Due to the missing kinematic information (the LSP momenta), the true boosts can- not be recovered exactly. We instead find approximations to the correct boosts by relying on the fact that the rest-frame energy of quark 1 equals that of quark 2 (both have value M∆/2). Consider a boost in the z-direction, β~_L, which is applied to bothp₁andp₂; and a transverse boost,±β~_R, which is applied in opposite directions to the two particles. This is illustrated in Figure 3.10. The longitudinal boost β~_L takes us from the lab frame into an approximation of the center-of-mass frame of the ppcollision. The subsequent transverse boosts±β~_R take us from the collision frame to the approximate rest frames of the produced squarks. LetγL andγRbe the Lorentz factors associated with β~_L and ~β_R.

We obtain the values of the boosts β~_L and β~_R as follows. Let unprimed, primed, and double-primed variables indicate quantities measured in the lab frame, the ap- proximate collision frame, and the approximate squark rest frames, respectively, and letEi, piz, and ~piT represent the observed energies, longitudinal momenta, and transverse momenta of the jets. We have

E⁰⁰_1,2= γ_R(E_1,2⁰ ∓ β~_R· ~p⁰_1,2) (3.27)

Figure 3.10: Diagram illustrating the reference frames considered in the derivation of M_R. Left: the lab frame, with observed jet momentap₁andp₂, and unobserved LSP momentapχ1 andpχ2. Center: the collision center-of-mass frame, which can be reached by a longitudinal boost that we approximate by ~β_L. Right: the individual squark decay frames, where true quark momentaq₁andq₂are each proportional to M∆/2. The boosts±β~_Rapproximate the true boosts from the collision frame to the squark decay frames.

and

E_1,2⁰ =γ_L(E_1,2− β~_L ·~p_1,2). (3.28) The equal energy condition, E⁰⁰₁ = E₂⁰⁰, can be expressed in terms of the collision- frame quantities as

E₁⁰ −E₂⁰ = β~_R·

~

p⁰_1T +~p⁰_2T

. (3.29)

Noting that the boost β~_L is alongz, we have ~p⁰_iT = ~p_iT. We write Eq. 3.29 in terms of lab-frame quantities and find an expression for the magnitude of the transverse boost:

~β_R= γ_L

(E₁− E₂)− |β~_L|(p_1z− p_2z)

~p1T +~p2Tcosφ_R , (3.30) whereφ_R is the azimuthal angle betweenp~_1T +p~_2T and the boost β~_R.

We define the razor variable M_Rby

M_R =γ_R(E₁⁰⁰+E₂⁰⁰). (3.31) M_R is an estimator for the SUSY-sensitive quantity M∆. Because we have im- perfect information about the event kinematics, two additional constraints must be imposed in order to uniquely specify the boosts β~L,R and hence the value of M_R. Having in mind the context of massive SUSY particles produced near threshold,

we first choose to make the transverse boost β~_R as small as possible. This choice corresponds to cosφ_R =1, i.e., a boost along the direction of~p_1T +~p_2T.

For the second constraint, we choose ~β_L so that M_Ris extremized. This is satisfied by

~β_L = p_1z +p_2z E1+E2

z.ˆ (3.32)

After expressing M_R in terms of lab-frame quantities and using Eqs. 3.30 and 3.32 for the boosts, we obtain the simple formula

M_R =q

(E₁+E₂)²− (p_z1+p_z2)², (3.33) which is equal to the transverse energy in the event.

The second razor variable, R², is obtained by considering a different estimator for M∆ as follows:

M∆ ≈ q

m²_Q −m²_χ

=q

(E1,2+Eχ1,2)²−(p~1,2+~pχ1,2)²−m²_χ

=q

2Eχ1,2E1,2−2~pχ1,2· ~p1,2

=q

(E_χ1E1− ~pχ₁ ·~p1)+(E_χ2E2− ~pχ₂ ·~p2),

(3.34)

whereEχ_i and~pχ_i are the energies and momenta of the LSPs. The second and third lines are true for the decay products of either squark; in the fourth line we average over the two squarks. The approximation in the first line assumes that the LSP is light compared with the squark.

To evaluate this expression, we must estimate the (unknown) LSP momenta. We do this via the rough approximation that the LSPs are transverse and each carry half of the missing energy: Eχ₁ = Eχ₂ = E_T^miss/2 andp~χ₁ = ~pχ₂ = ~p_T^miss/2. The above expression then becomes

M_T^R ≡ s

E_T^miss

2 (E₁+E₂)− p~_T^miss

2 ·(p~_T1+p~_T2). (3.35) We have neglected the longitudinal LSP momenta, so the variable M_T^R is less than M∆, with a kinematic endpoint at that value.

We defineR²as the dimensionless ratio R²≡



M_T^R M_R





2

. (3.36)

For signal events,M_RandM_T^Rboth approximateM∆(each using different kinematic information from the event) and R² will be approximately 1/4. Events with little E_T^miss or fakeE_T^miss from mismeasured jets have smaller values ofR².

To search for SUSY using the razor variables, we select events with M_R near the mass scale of the signal under consideration, and apply a cut on R² to reduce the background from events whose kinematics are not consistent with the signal. Fig- ure 3.11 shows typicalM_RandR² distributions for SUSY signal events.

Figure 3.11: Left: MR distributions for several squark production scenarios. Right:

two-dimensional distributions ofM_R andR²for the same signal models [95].

The above derivations assume that there are only two visible jets in the event. If there are more than two jets (or leptons), we enforce a two-jet event topology by clustering the observed physics objects (jets and leptons) into two ‘megajets’ (see Figure 3.12). Each object is assigned to one megajet or the other, and the four- momentum of the megajet is taken to be the sum of the four-momenta of the objects assigned to it. Assignment of objects to megajets is performed in such a way as to minimize the sum of the squared megajet masses,

m²_j1+m²_j2. (3.37)

This condition encourages objects near one another inηandφto be assigned to the same megajet.

An inclusive SUSY search using razor variables was carried out on the full 8 TeV CMS dataset [71, 72]. It yielded limits on the masses of third-generation squarks and gluinos that are among the best obtained with the Run I data (see Figures 3.7 and 3.8).

49

M _R and New Physics Scale

I What if topology differs from ‘canonical’ di-jet SUSY topology? ) Force di-jet topology

I Consider pair-produced gluinos, undergoing 3-body decays to 2 jets and an LSP

+ Calculation of Razor Variables

!

Start from the jets on the event

!

Group the jets in two mega- jets, minimizing the sum of the invariant masses

!

Compute MR and R2

6

R2

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Entries

10 102 103 104 105

Mass Balance

Top Mass

!

Good performance for the considered final state, tested against specific algorithms (min mass distance from top hypothesis)

[GeV]

MR

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Entries

1 10 102 103 104

Mass Balance

Top Mass

highest pT megajet other megajet

Similar performances in Mass reconstruction

11

[GeV]

M

R

600800100012001400160018002000220024002600

Entries

1 10 102

103

104

Number of TCHEM B-tags

[Incl.]

[1 TCHEM]

[2 TCHEM]

[GeV]

MR

600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 )INCL TCHEM / Ni TCHEMR(N ^-1

-0.8 -0.6-0.4 -0.20.20.40.60 0.81

R

2

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Entries

1 10 102

103

104

105

Number of TCHEM B-tags

[Incl.]

[1 TCHEM]

[2 TCHEM]

R2

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

)INCL TCHEM / Ni TCHEMR(N ^-1

-0.8 -0.6-0.4 -0.20.20.40.60 0.81

Figure 3: Distribution of M

_R

(left) and R

²

(right) for different TCHE b-tag multiplicities, for events from the BJet and BVeto boxes. The normalised ratio of these distributions to the inclu- sive distribution are shown in the bottom part of each plot.

Hemisphere mass [GeV]

0 100 200 300 400 500 600 700

Entries

0 5000 10000 15000 20000 25000 30000

Mass Balance

Top Mass

Hemisphere mass [GeV]

0 100 200 300 400 500 600 700

Entries

0 2000 4000 6000 8000 10000

Mass Balance

Top Mass

Hemisphere mass [GeV]

0 100 200 300 400 500 600 700

Entries

0 50 100 150 200 250 300 103

×

Mass Balance

Top Mass

Figure 4: Distribution of the megajet mass for the hemisphere with the highest p

_T

(solid line) and second highest (dashed line) for t t ¯ MC (left), QCD MC (centre), and data (right). The default Razor hemisphere algorithm is labelled as Mass Balance, while the algorithm based on Eq. 2 is labelled Top Mass.

R2

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Entries

10 102

103

104

105

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Top Mass

R2

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Entries

1 10 102

103

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105

Mass Balance

Top Mass

R2

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Entries

10 102

103

104

105

106 Mass Balance

Top Mass

[GeV]

MR

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Entries

1 10 102

103

104

Mass Balance

Top Mass

[GeV]

MR

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Entries

10 102

103

Mass Balance

Top Mass

[GeV] MR

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Entries

10 102

103

104

105

Mass Balance

Top Mass

Figure 5: Distributions of R

²

and M

_R

for t t ¯ MC (left), QCD MC (centre), and data (right). The colour scheme is the same as in Fig. 4. It can be seen that the Razor hemisphere algorithm produces fewer events in the tail of the R

²

distribution.

ttbar MC Faster bkg drop in kinematic variables

g ˜ g ˜ ! ( qq ˜ ⁰ ₁ )( qq ˜ ⁰ ₁ )

+ M _R and new physics scale ⁶

M = M _{q ˜} ² M _˜ ² M _{q ˜}

What happens to M _R for topologies that differ from the one where it was derived?

For di-gluino pair-production (SMS T1), the M _R distribution peaks at the characteristic scale:

[GeV]

M

R

500 1000 1500 2000 2500

a.u.

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

0.09 _{= 900 GeV}

!"

= 1150 GeV, m

~g

m

= 750 GeV

!"

= 1150 GeV, m

~g

m

= 500 GeV

!"

= 1100 GeV, m

~g

m

= 50 GeV

!"

= 1150 GeV, m

~g

m

˜

g g ˜ ! (qq ˜ ⁰

1 )(qq ˜ ⁰

1 )

Here, gluinos are pair-produced and undergo 3-body decays to two jets and an LSP

I gluino pair-production M _R distribution peaks at

characteristic scale

M = M _{g ˜} ² M ² _˜ M _{g ˜}

Figure 3.12: Diagram illustrating the clustering of jets into megajets for the calcu- lation of M_Rand R².

The beauty of the moment is a beauty sadly lost.

Belle andSebastian, “We are theSleepyheads”

P art II:

T owards T rigger -B ased S earches : D ata S couting

50

C h a p t e r 4

DATA SCOUTING TRIGGER DEVELOPMENT

In this chapter we describe data scouting, a paradigm for collider data analysis based on trigger-level event reconstruction. Data scouting complements the tradi- tional analysis paradigm in which events are selected by the trigger and are sent offline to undergo an expensive reconstruction procedure. By taking advantage of the reconstruction that already takes place at the HLT level, we were able to use scouting to dramatically increase the number of CMS physics events stored for analysis while having negligible impact on available computing resources.

After motivating data scouting and describing the history of its use in CMS, we provide details on a framework for scouting that was designed and deployed for data taking during CMS Run II, and give information on the datasets collected using the framework. In the next chapter, we describe the impact of the scouting framework on the CMS physics program.