Bottom Forward-Backward Asymmetry at High Mass

Abstract:

We measure the forward-backward asymmetry in \(b\bar{b}\) pairs at large \(b\bar{b}\) mass using jet-triggered data and jet charge to identify \(b\) from \(\bar{b}\). As a function of \(m(b\bar{b})\), the asymmetry is consistent with both zero and with the standard model predictions.

More details about the analysis can be found in CDF Note 11092.

Monte Carlo model:

We use dijet Monte Carlo generated with pythia to describe both our signal and the light-jet background. This model reproduces the overall kinematics of the data well.

A full set of model validation plots can be found in the Model validation section.

b b-bar pt in the lowest mass bin
\(b\bar{b}~p_T\) in the lowest mass bin
Number of jets in the middle mass bin
\(N_\mbox{jet}\) in the middle mass bin
Number of jets in the highest mass bin
\(m_{jj}\) in the highest mass bin
Number of jets in the highest mass bin
\(\Delta y\) in the highest mass bin

Sample purity:

We estimate the purity of the sample by studying the rate at which light jets are \(b\) tagged. This rate is found from a fit to the mass of the vector sum of tracks associated with the identified secondary vertex. The templates in the fit are produced from our pythia Monte Carlo. The per-jet mistag rates are then used to calculate the per-event \(b\bar{b}\) fraction, or the sample purity.

Fit to vertex mass for low-significance b tags
Fit to vertex mass for low-signifiance \(b\) tags
Fit to vertex mass for high-significance b tags
Fit to vertex mass for high-signifiance \(b\) tags

Jet charge

In order to define the forward-backward asymmetry, we need to be able to identify \(b\) from \(\bar{b}\). We do this using the momentum-weighted sum of the charges of tracks associated with the jets. This provides some separation between \(b\) and \(\bar{b}\), but there is still some charge confusion.

We quantize the individual jet charges, and take the difference between the two quantized charges. From the rates of single-jet charge confusion, we can derive the per-event rates of charge confusion.

Jet charge for Monte Carlo b and anti-b jets
Jet charge for Monte Carlo \(b\) and \(\bar{b}\) jets

Background asymmetry

We use a data sideband to estimate the asymmetry of the light-jet background. To do this, we look for jets with \(b\) tags derived from a looser version of our tagging algorithm. These jets are kinematically similar to the jets in our signal region, but they are depleted in signal.

Background asymmetry
Asymmetry of the backgrounds in each mass bin, as a function of the quantized jet charge difference.

Mass smearing

Because we measure the energies of the jets with a finite resolution, our estimate of the \(b\bar{b}\) mass is also limited in resolution. We estimate this resolution using \(b\bar{b}\) events in our pythia dijet Monte Carlo. We produce a matrix which describes the probability that an event with a \(b\bar{b}\) mass in one bin will be measured with a dijet mass in a different bin.

Mass smearing matrix
Dijet mass smearing matrix

Results:

We use a Bayesian technique to extract the hadron-jet level asymmetry result. We use a formula to relate the background asymmetry, the charge confusion rate, the sample purity, the mass smearing, and the signal asymmetry to the observed number of forward and backward events in the data. This likelihood, along with prior probability distributions representing our estimate of each parameter with its uncertainty, is sufficient according to Bayes' theorem to define the posterior probability distribution. We estimate this posterior using Markov chain Monte Carlo.

We marginalize the posterior over all parameters except for the signal asymmetry. The marginal posterior probability density is compared to the SM theory prediction and to the prediction of a model containing a low-mass axigluon. The result is consistent with zero, the SM, and the axigluon model with a mass of 345 GeV\(/c^2\). The 200 GeV\(/c^2\) axigluon model is inconsistent with our measurement at more than 95%.

marginal posterior probability density for AFB
Marginalized posterior probability density for the signal asymmetry in each mass bin. The green region represents the 68% credible interval (highest posterior density), and the yellow region represents the 95% credible interval. The listed value is the maximum a posteriori point.
Central value and 68% credible interval for AFB as
						a function of b b-bar mass
Maximum a posteriori points for the signal asymmetry in each mass bin. The error bars represent the 68% credible intervals.

Model validation:

Because we employ a Monte Carlo simulation for calibrations and in the correction to the particle-jet level, we must verify that the model adequately describes our data. The model is quite good, and we verified that it was adequate by reweighting the model to match the data and verifying that this produced only a negligible shift in the results.

\(b\bar{b}~p_T\)

All tag categories together

b b-bar pt in the lowest mass bin
\(b\bar{b}~p_T\) in the lowest mass bin
b b-bar pt in the middle mass bin
\(b\bar{b}~p_T\) in the middle mass bin
b b-bar pt in the highest mass bin
\(b\bar{b}~p_T\) in the highest mass bin

Tag categories separate

b b-bar pt in lowest
						mass bin and LL tag bin
\(b\bar{b}~p_T\) in lowest mass bin and LL tag bin
b b-bar pt in lowest
						mass bin and LH tag bin
\(b\bar{b}~p_T\) in lowest mass bin and LH tag bin
b b-bar pt in lowest
						mass bin and HH tag bin
\(b\bar{b}~p_T\) in lowest mass bin and HH tag bin
b b-bar pt in middle
						mass bin and LL tag bin
\(b\bar{b}~p_T\) in middle mass bin and LL tag bin
b b-bar pt in middle
						mass bin and LH tag bin
\(b\bar{b}~p_T\) in middle mass bin and LH tag bin
b b-bar pt in middle
						mass bin and HH tag bin
\(b\bar{b}~p_T\) in middle mass bin and HH tag bin
b b-bar pt in highest
						mass bin and LL tag bin
\(b\bar{b}~p_T\) in highest mass bin and LL tag bin
b b-bar pt in highest
						mass bin and LH tag bin
\(b\bar{b}~p_T\) in highest mass bin and LH tag bin
b b-bar pt in highest
						mass bin and HH tag bin
\(b\bar{b}~p_T\) in highest mass bin and HH tag bin

Number of jets

All tag categories together

Number of jets in the lowest mass bin
\(N_\mbox{jet}\) in the lowest mass bin
Number of jets in the middle mass bin
\(N_\mbox{jet}\) in the middle mass bin
Number of jets in the highest mass bin
\(N_\mbox{jet}\) in the highest mass bin

Tag categories separate

Number of jets in lowest
						mass bin and LL tag bin
\(N_\mbox{jet}\) in lowest mass bin and LL tag bin
Number of jets in lowest
						mass bin and LH tag bin
\(N_\mbox{jet}\) in lowest mass bin and LH tag bin
Number of jets in lowest
						mass bin and HH tag bin
\(N_\mbox{jet}\) in lowest mass bin and HH tag bin
Number of jets in middle
						mass bin and LL tag bin
\(N_\mbox{jet}\) in middle mass bin and LL tag bin
Number of jets in middle
						mass bin and LH tag bin
\(N_\mbox{jet}\) in middle mass bin and LH tag bin
Number of jets in middle
						mass bin and HH tag bin
\(N_\mbox{jet}\) in middle mass bin and HH tag bin
Number of jets in highest
						mass bin and LL tag bin
\(N_\mbox{jet}\) in highest mass bin and LL tag bin
Number of jets in highest
						mass bin and LH tag bin
\(N_\mbox{jet}\) in highest mass bin and LH tag bin
Number of jets in highest
						mass bin and HH tag bin
\(N_\mbox{jet}\) in highest mass bin and HH tag bin

Dijet mass

All tag categories together

Number of jets in the lowest mass bin
\(m_{jj}\) in the lowest mass bin
Number of jets in the middle mass bin
\(m_{jj}\) in the middle mass bin
Number of jets in the highest mass bin
\(m_{jj}\) in the highest mass bin

Tag categories separate

Dijet mass in lowest
						mass bin and LL tag bin
\(m_{jj}\) in lowest mass bin and LL tag bin
Dijet mass in lowest
						mass bin and LH tag bin
\(m_{jj}\) in lowest mass bin and LH tag bin
Dijet mass in lowest
						mass bin and HH tag bin
\(m_{jj}\) in lowest mass bin and HH tag bin
Dijet mass in middle
						mass bin and LL tag bin
\(m_{jj}\) in middle mass bin and LL tag bin
Dijet mass in middle
						mass bin and LH tag bin
\(m_{jj}\) in middle mass bin and LH tag bin
Dijet mass in middle
						mass bin and HH tag bin
\(m_{jj}\) in middle mass bin and HH tag bin
Dijet mass in highest
						mass bin and LL tag bin
\(m_{jj}\) in highest mass bin and LL tag bin
Dijet mass in highest
						mass bin and LH tag bin
\(m_{jj}\) in highest mass bin and LH tag bin
Dijet mass in highest
						mass bin and HH tag bin
\(m_{jj}\) in highest mass bin and HH tag bin

Rapidity difference

All tag categories together

Number of jets in the lowest mass bin
\(\Delta y\) in the lowest mass bin
Number of jets in the middle mass bin
\(\Delta y\) in the middle mass bin
Number of jets in the highest mass bin
\(\Delta y\) in the highest mass bin

Tag categories separate

Rapidity difference in lowest
						mass bin and LL tag bin
\(\Delta y\) in lowest mass bin and LL tag bin
Rapidity difference in lowest
						mass bin and LH tag bin
\(\Delta y\) in lowest mass bin and LH tag bin
Rapidity difference in lowest
						mass bin and HH tag bin
\(\Delta y\) in lowest mass bin and HH tag bin
Rapidity difference in middle
						mass bin and LL tag bin
\(\Delta y\) in middle mass bin and LL tag bin
Rapidity difference in middle
						mass bin and LH tag bin
\(\Delta y\) in middle mass bin and LH tag bin
Rapidity difference in middle
						mass bin and HH tag bin
\(\Delta y\) in middle mass bin and HH tag bin
Rapidity difference in highest
						mass bin and LL tag bin
\(\Delta y\) in highest mass bin and LL tag bin
Rapidity difference in highest
						mass bin and LH tag bin
\(\Delta y\) in highest mass bin and LH tag bin
Rapidity difference in highest
						mass bin and HH tag bin
\(\Delta y\) in highest mass bin and HH tag bin