Mass measurements at the Large Hadron Collider

Mass measurements at the Large Hadron Collider Priyotosh Bandyopadhyay Helsinki Institute of Physics, Helsinki Seminar Course Lectures J.Phys.G:Nucl. Part. Phys. 37, 123001 February 3, 2012

Plan 1 Mass Measurement: An Introduction 2 Variables for Particle Production at or near threshold 3 Variables for single cascade decay chain 4 Sneak peak for next lecture

Mass Mass of a particle Mass came from Greek µ αζα barley cake, lump (of dough) Classical Definition of mass F = ma, Where F is the force and a is the accelaration and m is defined as mass. Special Theory of relativity defines mass as E 2 = m 2 c 2 + p 2

Mass Mass measurement Kinematic method demands that at least some of the particles are sufficiently close to the mass-shell p µ p µ m 2. Assuming the relation, one can learn about the 4-momenta and hence constraints the masses; which are otherwise not directly observed experimentally. Why? Unstable particles, which decay down Weakly interacting particles which though stable, do not interact with the detectors.

Information Beyond kinematics Non-kinematic method Either known or assumed With sufficient theoretical and experimental understanding and provide the calculation is tractable, one could obtain maximal information about an event by comparing its statistical likelihood under different mass hypothesis. The ability to marginalize over uncertain information (e.g. components of momentas of invisible particle) has made such calculation computationally feasible. Matrix element method has been implemented by CERN, LEP and Tevatron which is ideal when one has some confidence about the underlying theory. Constraint on the Higgs boson mass from the loop contribution to EW observables.

Information Beyond kinematics Kinematic method Very few assumptions about the detailed underlying theory. Robust

Phases in mass measurement techniques Most of the techniques have three-phases The postulation of a hypothesis or hypotheses about the decay topology. The sequence of decays which involve the particles whose masses are to be determined. Identification of most appropriate final state. Construction of constraints or measurements of the target particle masses, using those observables.

Decay topologies or hypothesis Topology Indicate a sequence of decays of heavy objects to lighter ones. Constituents of topology Final state Which could be Distinguishable with some non-trivial dynamics: Showering and hadronization of quarks or gluon to jets. Or, Indistinguishable Leptons or unobserved (e.g. neutrinos)

Observables and hypothesis Hypothesis 1 Hypothesis 2 A X,Y,Z A B,X X,Y,Z More detailed. Main information from collider Momentum, Energy with smearing effects. Need to know Smearing effects modelled by experiments. Detector response for precision measurements.

Observables Unobserved: Neutrinos, WIMPs, particles with small angle to the beam pipe. LHC At LHC measurement is restricted to a fiducial pseudorapidity of η 5, where η = logtanθ θ: angle relative to one of the beam pipe. Being a pp collider, at LHC the center of mass energy and the longitudinal boost of CM frame are not known. Invisible Momenta p inv T p T p vis T

Additional Information Decay length Most of the particle decay rapidly and do not travel macroscopic distance. But τ lepton and B hadron travel macroscopic distances. Detection of secondary vertex gives you additional information. Identities More precise angle, momenta and energy Identities. Muon detector outside the hadron calorimeters. Typical Observable Observable consisting of 4-momemta of group of particles. Each such observable with the associated hypothesis about the topology can be used to make inferences about the properties (e.g. mass)

Additional Information Invariant Observable Observable invariant under Lorentz boosts and lack of knowledge about CM frame of primary interaction Secondary derived quantities (invariant under boost, etc, e.g. invariant mass, transverse mass). Non-invariant Observable Contralinear invariant mass (m c ): Decidedly deviant under Lorentz boost nonetheless useful. This is equivalent to m T2 but without the missing momentum. Ref:arXiv:0802.2879 [hep-ph]

Constraints and quantities Per-dataset Observables that are formed from samples coming from large number of events. e,g. Kinematic end points, Differential distribution. Hybrid-dataset Mixes per-event and per-dataset to something more powerful and defined as per-event.

Ambiguities Ambiguities Identical particle in the final state. ISR Alternative internal particle in a decay chain: q q χ 0 2 l l q χ 0 1 l l q Lack of certainty as to whether the decay topology hypothesised reflects actual reality. If slepton is heavier than the χ 0 2, it would have been a three-body decay.

Variables for particle production at or near threshold Variables with least assumption Type of interaction Decay topology Types of particle involved. The scale, which approximately gives the center of mass-energy of the collision.

Variables @threshold Pdf are largely rapidly falling functions of momentum fraction x. So above the threshold the cross-section tend to decrease with C.M.E of parton-parton system as ŝ Heavy particles expected to be produced at or near threshold. Energy of collision can be expected to give good indication of the mass scale of the particle produced. Most of the variables are sensitive to the overall mass-energy scale involved. Momentum of parton-parton CM is not known and when invisible particles are produced, then only estimate we can have, are the variables perpendicular to the beam pipe; as pt = 0 pt vis = pt invs

Effective Mass The scalar sum of the four highest p jets T and missing transverse momentum. M eff = p Ti + p T (1) i=1,4 But this can be extended to n-jets depending on the analysis channel. The peak of such distribution was found to correlate O(10%) level with a characteristic SUSY mass scale. M SUSY min(m g,m qr ) from cmssm. ATLAS

Effective Mass Table: SUGRA parameters for the five LHC points. Point m 0 m 1/2 A 0 tanβ sgn µ (GeV) (GeV) (GeV) 1 400 400 0 2.0 + 2 400 400 0 10.0 + 3 200 100 0 2.0 4 800 200 0 10.0 + 5 100 300 300 2.1 +

Effective Mass 10-7 10-8 LHC Point 5 ID 11147 dσ/dm eff (mb/400 GeV) 10-9 10-10 10-11 10-12 10-13 0 1000 2000 3000 4000 M eff (GeV) Figure: SUSY signal and Standard Model backgrounds for LHC Point 5. See Figure 1 for symbols. Figure 1 shows the resulting scatterplot of M susy vs. M eff. The ratio is constant within about ±10%, as can be seen from Figure 2

Effective Mass 1250 1000 25 20 3.378 / 8 Constant 15.76 Mean 1.926 Sigma.1945 M SUSY (GeV) 750 500 No. Models 15 10 250 5 0 0 500 1000 1500 2000 M eff (GeV) 0 0 1 2 3 4 M eff / M SUSY Figure 1 shows the resulting scatterplot of M susy vs. M eff. The ratio is constant within about ±10%, as can be seen from Figure 2

Effective Mass LHC Point M eff () M SUSY () Ratio 1 1360 926 1.47 2 1420 928 1.53 3 470 300 1.58 4 980 586 1.67 5 980 663 1.48

Effective Mass A more general MSSM study found that scalar sum over all jet given by, M est = p Ti + p T (2) i=1 had a peak position correlates with a cross-section weighted SUSY mass-scale. hep-ph/0006276 CMS has three different definitions. H T = E T2 + E T3 + E T4 + p T (3) where E T(i) is the transverse energy of i th jet and E T = E sinθ Other definition: Scalar sum of transverse energy of all jets excluding the missing momentum. H T = E T1 + E T2 + E T3 + E T4 +... (4)

Effective Mass 3rd one: Scalar sum of transverse momentum of all jets. H T = P T1 + P T2 + P T3 + P T4 +... (5) Regardless of the definition, the implicit assumption is that in hadron collider particles tend to be produced near threshold. Particle produced at rest when decay semi-invisibly in two-body decay, the visible daughter has transverse momentum less than the two-body decay momentum, A B, C p T p = λ 1 2(m A,m B,m C ) 2m A where, λ 1 2(a,b,c) = [a 2 (b + c) 2 ][a 2 (b c) 2 ]

Ŝ 1 2 When invisible particles are produced, the sufficient information to reconstruct Ŝ 1 2 for any event is at most, Ŝ 1 2 = (E 2 p 2 Z ) 1 2 + ( p T 2 + M 2 inv ) 1 2 where, M inv is the sum of all invisible particle masses thought to be produced. KP,KK,MK, JHEP03(2009)085 The variable gets modified under initial state radiation effects but the effects are calculable.

Invariant Mass Simple two-body decay: A B, C of following types. (a) Visible (b) Semi-invisible Figure: Two very simple decay topologies. In case of visible decay we talk about Invariant mass of the final states. Construction of the invariant mass comes from the square of the sum of the visible four-momenta: m 2 bc = (p b + p c ) 2

Invariant Mass As an example: consider dileton invariant mass in Z-decay. (a) Dilepton invariant mass Figure: (a) Dilepton invariant mass distribution for the process +

Transverse Mass When decays to a visible and an invisible particle, e.g. W lν A B + /C /p is not an observable. But p T may typically inferred from the energy-momentum conservation in the transverse plane, if there is no other ivisible particle. Transverse Mass: M 2 T = m2 B + m2 /C + 2(e C e /C B T./C T ) e 2 = m 2 + pt 2 = Transverse energy

Transverse Mass Figure: Transverse mass distribution for p p W eν. The W boson mass is determined from a fit to the range indicated with the double-headed horizontal arrow.

Fully visible Three-body decay Figure: A single particle A decaying to three visible particles B, C and D. This kind of decay can be analysed using tried and tested method od Dalitz Plot.

Dalitz Plot 1 + 2 3 + 4,+5 A given incident energy, two of the three possible two-body invariant masses of the final state fully describe the system. m 2 34 = (p 3 + p 4 ) 2 m 2 45 = (p 4 + p 5 ) 2 The third invarinat mass lies at 45 0 as, m 2 34 + m2 45 + m2 35 = m2 12 + m2 3 + m2 4 + m2 5 = const.

Dalitz Plot For fixed p 1, p 2, i.e. for fixed total energy, the physical region of a Dalitz plot inside a well-defined area. Absence of any resonaces or interferences can be shown to be uniformly populated. Resonant behaviour of two final state particles givse rise to band of higher density, parallel to one of the co-ordinate axes or line 45 0. Figure: In this projection various f 0 and f 2 resonances are clearly visible.

sneak peek: Two successive two-body decays One part of the event topology: Figure: The dilepton decay topology. The particle labelled Z is assumed to be unobserved by the detector. In supersymmetric decays we often have: q q χ 0 2 llq χ 0 1 llq

The di-lepton edge Figure: An example dilepton distribution (taken from [?]) for the topology shown in??. In this example, the kinematic endpoint is at approximately 100 GeV.

Conclusions

Thank you