jet-physics-notes

Brief notes for the very basics

Theoretical Foundation
Practical Aspects
Jet Clustering Algorithms
Jet Grooming Algorithms
Jet Observables

Theoretical Foundation

Core questions:

Can jet substructure be predicted by first-principle QCD calculations and compared to data in a meaningful way?

How accurately is jet substructure described by state-of-the-art MC tools?

How does the impact of additional p-p collisions limit jet substructure performance at the LHC, now and in future operating scenarios?

How powerful is jet substructure in studies of boosted top production, and how can it be made even more powerful?

NLO Calculation + Resummation

$\sigma(v)=\sigma_0~g(\alpha_s)e^\beta$

$\beta=L~g_1(\alpha_s~L)+g_2(\alpha_s~L)+\alpha_s~g_3(\alpha_s~L)+..$

Jet substructure calculation at high precision, see Larkoski’s talk

Lund Digram Analysis

Practical Aspects

Jet Clustering Algorithms

Sequential Algorithms
- Jet Clustering
$d_{ij}=min(p_{Ti}^{2\alpha},p_{Tj}^{2\alpha})\frac{\Delta~R_{ij}^2}{R^2}$

$d_{iB}=p_{Ti}^2$

alpha=1 -> kt; alpha=0 -> C/A; alpha=1 -> anti-kt
- Qjets (non-deterministic jet clustering)
$P_{ij}\propto~e^{-\alpha(d_{ij}-d_{min})/d_{min}}$
Minimization
- k-means
- deterministic annealing (DA)
- optimal jet finder (OJF)
Alternatives
- Jet Energy Flow: Snowmass 2001: Jet energy flow project, hep-ph/0202207 [inspire]

Jet Grooming Algorithms

Pruning: re-cluster the constituents using C/A algo.. Discard soft branches if

$\frac{min(p_{Ti},~p_{Tj})}{p_{Tij}}<z_{cut}~\textrm{and}~\Delta~R_{ij}>\frac{2m_j}{p_{Tj}}~R_{cut}$
Trimming: re-cluster the constituents into subjets with kt algo.. Discard all subjets with

$p_{Ti}<f_{cut}~p_{TJ}$
Filtering: re-cluster the constituents into subjets with C/A algo.. Re-define the jet using only the hardest N subjets.
Softdrop: re-cluster all the constituents using C/A. Iteratively undo the last stage of C/A clustering from j to subjets j1, j2. Discard the softer subjet if … and repeat.

$\frac{min(p_{T1},~p_{T2})}{p_{T1}+p_{T2}}<z_{cut}\left(\frac{\Delta~R_{12}}{R}\right)^\beta$

Jet Observables

jet area:
jet mass:
jet substructure observables
- Angular Correlation Functions:
- N-subjettiness: $\tau_N^\beta$ quantifies how well the radiation in the jet is aligned along N directions. $\tau_N^\beta=\frac{1}{d_0}\sum_i~p_{Ti}~min(\Delta~R_{1i}^\beta,~...,~\Delta~R_{Ni}^\beta)~\textrm{with}~d_0=\sum_i~p_{Ti}~R^\beta$
- ratio
$\tau_{N,~N-1}^\beta~\equiv~\frac{\tau_N^\beta}{\tau_{N-1}^\beta}$
- Energy correlation functions ECF and the double ratio ( $C_N^\beta$ )
$C_N^\beta~=~\frac{ECF(N+1,~\beta)~ECF(N-1,~\beta)}{ECF(N,~\beta)^2}$

$ECF(N,~\beta)~=~\sum_{i_1<i_2<...<i_N~\in~j}\left(\prod_{a=1}^N~p_{Ti_a}\right)\left(\prod_{b=1}^{N-1}~\prod_{c=b+1}^N~\Delta~R_{i_b~i_c}\right)^\beta$

$e_N^\beta~=~\frac{ECF(N,~\beta)}{p_{TJ}^N}$
- $M_2^\beta,~D_2^\beta$ with power counting [Larkoski, Moult, Neill]
$M_2^\beta~=~\frac{_1e_3^\beta}{e_2^\beta}~D_2^\beta=\frac{e_3^\beta}{(e_2^\beta)^3}$
color flow
jet charge