# Why is the top quark mass reconstructed too high when the bottom quarks were swapped (semileptonic decay of a ttbar pair)?

I use a dataset containing simulated events of semileptonic $t\bar{t}$ decays ($t\bar{t} \rightarrow W⁺b W⁻ \bar{b} \rightarrow q\bar{q}bl\nu_l\bar{b}$) at CMS, LHC. For each event, the four-momenta of the particles in the final state are stored in the dataset. The algorithm to reconstruct the event now has 24 possibilities to assign (match) the jets originating from the quarks in the final state. As I have simulated data, I know whether this worked out or not. Events can be classified into correctly matched (the algorithm managed to assign each jet to its original particle) or wrong matched. The wrong matched events can be further classified into those, were the two $b$ quarks were swapped, those, where the two other quarks were swapped or some other combinations.

When I sort the events by the matching type of the jets - all jets correctly matched, $b$ quarks swapped, hadronic branches from one of the $W$ bosons swapped, other stuff mixed up,... - and plot their $m_t$ distributions I see, that:

• those events have clearly a much broader $m_t$ distribution even than those, where some of the jets were not matched at all
• those events have top masses reaching far higher on the scale, than other events (again, even than those completely unmatched).

Does someone have a clue, why this is so?

Or, maybe firstly more important: Is it a physical problem? Or does it maybe arise from the reconstruction algorithm.

• As long as there is nobody around who is familiar with naming conventions in the CMS collaboration, you need to be more precise. What is "matching type of jets", how do you define "correctly matched"? Jan 19 '16 at 18:40
• To emphasize @asdfex's point, I'm a experimental particle physicist, but of the neutrino kind. Now I've worked in the same group with people from both big Tevetron experiments a couple of RHIC experiments and ATLAS so I've gone to their talks and chatted with them about their analyses (and I went to the CTEQ summer school one year), which gives me only a basic grasp of the specialized nomenclature of collider analysis. Why don't you start by telling us what the basic diagram(s) you're working with is (are)? Jan 19 '16 at 21:55
• Thanks a lot for the comments @asdfex,@dmckee, I wasn't aware that I'm using some specialized nomenclature. I hope it is more clear now, if not please ask further. Jan 19 '16 at 22:35
• I probably won't be able to explain this very clearly, but imagine two particles with different masses which decay to the same 2-body final state. If the decays are boosted by the same amount, the angle between the particles from the heavier parent will be larger than that of the lighter one. When you swap the b quarks, the angle between it and the wrong W is likely to be larger than the right one, so your reconstructed invariant mass is likely to be higher. Jan 19 '16 at 22:46
• So, you get four jets (two of which are b-tagged) and a charged lepton. Then the question the analyzer has to answer is "which b-tagged jet goes with the lepton (and the missing $p_T$) and which goes with the non-b-tagged jets?", and you see a systematic bias toward higher reconstructed masses for a "wrong" answer to the question. That right? I assume you see that in MC, too, yes? If so, I suspect that @dukwon is on the right track. I'll think about it, but I'm a bit out of my depth. Jan 20 '16 at 4:17

$m_t^2 = p_t^2 = (p_W + p_b)^2 = p_W^2 + p_b^2 + 2p_Wp_b = m_W^2 + m_b^2 + 2 E_W E_b(1-\beta_W\beta_bcos(\gamma))$
with $p$ denoting the four-momenta and $\gamma$ beeing the angle between the $W$ three-momentum and the $b$ three-momentum. In the $t\bar{t}$ center of mass system, top and antitop travel back to back. As the decay products ($W$, $b$) are much lighter, they will be boosted in the direction of the top-momenta and $\gamma$ will be rather small for both of the top quarks. If the bottom quarks are swapped in the reconstruction process, $\gamma$ will be rather in the region of $180$ degrees, leading to a higher mass.