Unlocking the Structure of New Physics at the LHC Natalia Toro - PowerPoint PPT Presentation

Unlocking the Structure of New Physics at the LHC Natalia Toro hep-ph/0703088: Arkani-Hamed et al 0810.3921: Alwall, Schuster, NT work in progress: UCSB CMS group (special thanks: S.A. Koay)

Hadron Collider 101 A x 1 , x 2 : fraction of beam energy x 1 E 1 x 2 E 2 carried by each parton B � dx 1 x 1 f g ( x 1 , Q ) x 2 f q ( x 2 , Q ) d ˆ σ ( qg → AB ) d σ inc dx 2 d Vars = d Vars x 1 x 2

Hadron Collider 101 A x 1 , x 2 : fraction of beam energy x 1 E 1 x 2 E 2 carried by each parton B � dx 1 x 1 f g ( x 1 , Q ) x 2 f q ( x 2 , Q ) d ˆ σ ( qg → AB ) d σ inc dx 2 d Vars = d Vars x 1 x 2 � = d ˆ s s d ¯ y ˆ uu arbit. u ¯ u/ug u ¯ u/ug arbit. scale scale uu gg gg parton E 2 (1 TeV) cm (300 GeV) CM boost y (CM boost) ¯ y (CM boost) ¯ CM-frame boost ⇒ multi-particle Lorentz invariants and p T ’s

Multi-Particle Mass Invariants Edge/endpoint: Full reconstruction and m T2 : ℓ ℓ q χ 0 χ 0 ˜ ˜ ℓ q 2 1 Many more variables: – precision mass measurement at hadron colliders! To construct invariants, must pair/group particles. To pair, must know decay topology. Not known a priori . ...100 fb -1 What can be learned from simpler p T ’s? (and lower statistics)

Using Transverse Momenta H T = � | p T | , � E T = � � Useful combinations: p T 1) H T bump ~ 1–2 x produced particle mass: H T for Models with (depends on decay chain, LSP mass) M=650–700 GeV (after cuts) H T (GeV) 2) Locations of p T bumps ~ relative mass scales Leading Lepton p T +jet jet p T +lepton & counts are search variables → understood early. p T , H T , � E T They suffice to build good hypotheses for mass spectra, cascades, then isolate decay modes for precision mass measurement.

Outline 1. Hadron Collider Observables and Ambiguities - Goal: “Basis of Parameters” for new physics to model most relevant observables and address (subset of) theoretical questions. - p T in Pair Production (mostly independent of M.E!) - p T ’s and counts insensitive to complex decay chains 2. Designing Robust and General New-Physics Searches (results from UCSB CMS group) 3. Building up from very simple description of new physics

p T Distributions Simple and instructive to calculate p T distribution for 2 → 2 product with general matrix element: � dx 1 x 1 f g ( x 1 , Q ) x 2 f q ( x 2 , Q ) d ˆ σ ( qg → AB ) d σ inc dx 2 d Vars = d Vars x 1 x 2 � � � = d ˆ s ∼ (1 − x ) p x − q parton cross-section PDF’s s d ¯ y ˆ � → parton luminosity d ¯ y s, Q 2 ) ∝ (ˆ s/S tot ) − q ρ (ˆ ( q ~1–1.5) parton E 2 cm CM boost s/S tot , Q 2 ) gg ρ (ˆ s 2 � � s = 1 s 2 d ˆ d σ Q 2 = (500 GeV) 2 σ ug uu s 2 0 s, Q 2 ) s 2 ρ (ˆ ˆ 0 d ˆ d ˆ ˆ ˆ s td ˆ t u ¯ u � 1 s, ˆ t ) | 2 8 π |M (ˆ (1 TeV) (300 GeV) s 0 = 2 M 2 ( : threshold s ) s/S tot τ = ˆ

p T Distributions s 2 d σ 1 s 2 0 s, Q 2 ) |M| 2 s = s 2 ρ (ˆ s/S tot ) − q ρ (ˆ s, s 0 ) ≈ A (ˆ 0 d ˆ td ˆ ˆ s s & ˆ s & p 2 CM-frame Lorentz invariants: or or s & ξ ˆ ˆ ˆ t T u − M 4 t = − 1 ˆ t ˆ ˆ ⇒ dp 2 s = ξ d ˆ p 2 related by: 2 [ˆ s (1 − ξ ) − s 0 ] T d ˆ td ˆ s T = s ˆ “pure angular” variable linearly related to ξ ∼ β cos θ CM : → good variable for M.E. expansion

p T Distributions � 1 S tot S tot s 2 d σ d σ � = 1 d ˆ s s 2 s 2 0 s, Q 2 ) |M| 2 s = s 2 ρ (ˆ d ˆ s s/S tot ) − q ρ (ˆ s, s 0 ) ≈ A (ˆ 0 0 d ˆ dp 2 ξ td ˆ ξ s ˆ T s 0 + 4 p 2 s 0 + 4 p 2 T T s & ˆ s & p 2 CM-frame Lorentz invariants: or or s & ξ ˆ ˆ ˆ t T u − M 4 t = − 1 ˆ t ˆ ˆ ⇒ dp 2 s = ξ d ˆ p 2 related by: 2 [ˆ s (1 − ξ ) − s 0 ] T d ˆ td ˆ s T = s ˆ “pure angular” variable linearly related to ξ ∼ β cos θ CM : → good variable for M.E. expansion

p T Distributions � 1 S tot S tot s 2 d σ d σ � = 1 d ˆ s s 2 s 2 0 s, Q 2 ) |M| 2 s = s 2 ρ (ˆ d ˆ s s/S tot ) − q ρ (ˆ s, s 0 ) ≈ A (ˆ 0 0 d ˆ dp 2 ξ td ˆ ξ s ˆ T s 0 + 4 p 2 s 0 + 4 p 2 T T s & ˆ s & p 2 CM-frame Lorentz invariants: or or s & ξ ˆ ˆ ˆ t T u − M 4 t = − 1 ˆ t ˆ ˆ ⇒ dp 2 s = ξ d ˆ p 2 related by: 2 [ˆ s (1 − ξ ) − s 0 ] T d ˆ td ˆ s T = s ˆ “pure angular” variable linearly related to ξ ∼ β cos θ CM : → good variable for M.E. expansion |M| 2 = � C m,n (ˆ s/s 0 ) m ξ n Expand near threshold (usually dominated by low m , n ) � s 0 � d ˆ S tot � − q � d σ s s 2 s/s 0 ) m − q − 2 ξ n = C m,n s (ˆ 0 dp 2 S tot ξ ˆ T m,n s 0 + 4 p 2 T

p T Distributions � 1 S tot S tot s 2 d σ d σ � = 1 d ˆ s s 2 s 2 0 s, Q 2 ) |M| 2 s = s 2 ρ (ˆ d ˆ s s/S tot ) − q ρ (ˆ s, s 0 ) ≈ A (ˆ 0 0 d ˆ dp 2 ξ td ˆ ξ s ˆ T s 0 + 4 p 2 s 0 + 4 p 2 T T s & ˆ s & p 2 CM-frame Lorentz invariants: or or s & ξ ˆ ˆ ˆ t T u − M 4 t = − 1 ˆ t ˆ ˆ ⇒ dp 2 s = ξ d ˆ p 2 related by: 2 [ˆ s (1 − ξ ) − s 0 ] T d ˆ td ˆ s T = s ˆ “pure angular” variable linearly related to ξ ∼ β cos θ CM : → good variable for M.E. expansion |M| 2 = � C m,n (ˆ s/s 0 ) m ξ n Expand near threshold (usually dominated by low m , n ) � s 0 � d ˆ S tot � − q � d σ s s/s 0 = 1 + 4 p 2 T /s 0 s 2 s/s 0 ) m − q − 2 ξ n = C m,n s (ˆ ˆ 0 dp 2 S tot ξ ˆ 1 − ξ 2 T m,n s 0 + 4 p 2 T � s 0 ≈ 1 � − q � 2 d ξ � 1 − ξ 2 (1 − ξ 2 ) − m + q +2 ξ n × (1 + 4 p 2 T /s 0 ) m − q − 2 = C m,n S tot m,n 0

p T Distributions � 1 S tot S tot s 2 d σ d σ � = 1 d ˆ s s 2 s 2 0 s, Q 2 ) |M| 2 s = s 2 ρ (ˆ d ˆ s s/S tot ) − q ρ (ˆ s, s 0 ) ≈ A (ˆ 0 0 d ˆ dp 2 ξ td ˆ ξ s ˆ T s 0 + 4 p 2 s 0 + 4 p 2 T T s & ˆ s & p 2 CM-frame Lorentz invariants: or or s & ξ ˆ ˆ ˆ t T u − M 4 t = − 1 ˆ t ˆ ˆ ⇒ dp 2 s = ξ d ˆ p 2 related by: 2 [ˆ s (1 − ξ ) − s 0 ] T d ˆ td ˆ s T = s ˆ “pure angular” variable linearly related to ξ ∼ β cos θ CM : → good variable for M.E. expansion |M| 2 = � C m,n (ˆ s/s 0 ) m ξ n Expand near threshold (usually dominated by low m , n ) � s 0 � d ˆ S tot � − q � d σ s s/s 0 = 1 + 4 p 2 T /s 0 s 2 s/s 0 ) m − q − 2 ξ n = C m,n s (ˆ ˆ 0 dp 2 S tot ξ ˆ 1 − ξ 2 T m,n s 0 + 4 p 2 T � s 0 ≈ 1 � − q � 2 d ξ � 1 − ξ 2 (1 − ξ 2 ) − m + q +2 ξ n × (1 + 4 p 2 T /s 0 ) m − q − 2 = C m,n S tot m,n � 0 Euler B -function shape independent of n

p T Universality pT variables are useful because they are simple, single-particle Lorentz invariants and insensitive to production matrix element! d σ |M| 2 ∼ (ˆ ∼ (1 + p 2 T /M 2 ) m − q − 2 s/s 0 ) m ξ n , ρ (ˆ s ) ∼ ˆ s − q for dp 2 T Typical p T ~ 0.5 M • Not completely universal - Depends on m (different for p-wave and contact operators) - Depends on q (sensitive to init. state) - Observable p T ’s depend on decay M.E. • But easy to get similar effects (after cuts) by changing s 0 – simple analysis can’t distinguish • Similarly, η distribution indep. of m – even different n – convolved with y distribution have similar shape “Shape invariance” Arkani-Hamed et al, hep-ph/0703....

Why bother? • Shape invariance: a clear guide to information that can be stripped out & still do meaningful analysis • Why understand these? - Important (approximate) ambiguities to be aware of in any description of positive signal at LHC - Allows predictions, MC generation, simulation of detector response w/o full knowledge of model Lagrangian - Suggest search/interpretation strategies with wide reach compared to no. of parameters

How much do you need to say about model to predict LHC signals? Specialize to models like SUSY – pair production, no fully-reconstructed decays • Masses and quantum numbers of produced particles • Production cross-sections (and near-threshold behavior) • Branching fractions to different final states • To predict invariant mass distributions , also need to know intermediate spins. First three: O n- S hell E ffective T heory – hep-ph/0703088 Much less detail than full Lagrangian – but even at this level data can be ambiguous...

Squarks + Gluino Example ˜ q L,R ˜ q L,R +jet +jet ˜ g Mass ˜ g +2j +2j +2j Extreme spectra well +2j χ 0 χ 0 described by fewer 2 2 χ 0 χ 0 particles –> can’t 1 1 resolve squark mass q − m ˜ g ≫ m ˜ q − m ˜ g ≪ m ˜ m ˜ m ˜ in these cases g g ⇓ ⇓ g ≪ σ ˜ jet from squark decay σ ˜ q , σ ˜ q ˜ q ˜ g ˜ g very soft can ignore squarks can ignore squarks

� � � � � � � � � � � � � � � � � Overlapping Lepton Sources Many handles: frequency of n -lepton events, flavor & sign correlations. G E T � T E T E T * ℓ � T ν or ℓ ℓ q ν q ℓ G ℓ or ν q q q q G G q q G G G G q q q q q q q G G G G G q q q q G G G G G q q q ℓ q q q q /Z ( ∗ ) Lepton Cascades ℓ or ν ℓ ℓ * ℓ ν or ℓ * E T E T G E T E T G Two decay modes Just 2 flavor-uncorrelated populate 0, 2, 4 leptons, leptons flavor correlation distinguishable but.... Q Q Q Q Q q q Q q ν Q q Q Q ℓ Q ℓ ℓ q q q ℓ ℓ Q Q