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Measuring and Seeing – Going to High Energy. Part - II. Precision vertexing. PV. Basic idea : Y ou want to distinguish particles produced in the B decay from those produced & emerging from the interaction point (PV).

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Measuring and Seeing – Going to High Energy

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Measuring and Seeing – Going to High Energy

Part - II

Precision vertexing


Basic idea: You want to distinguish particles produced in the B decayfrom those produced & emerging from the interaction point (PV).

~5-10 times more particles coming from the pp interaction, so keepingthem separate will dramatically reduce the # of possible combinations.

Need to measure trajectories of particles to high precision ~20mm at PV

How do you see particles that you can’t see?

How do we observe/measure the particles we can’t see?



For almost all interesting physics, we do not DIRECTLY see the particle of interest.

  • We see the stable particles that it decays into.

  • Often, go after decays in which we can fully reconstruct all stable decay products.

    • Best case  have “maximal information”

    • Can fully reconstruct the parent particle!

  • But, sometimes we have to deal with only seeing“N-1” of the decay products.

    • E.g Decays with a neutrino … no shot at seeing the neutrino.

    • Less than optimal, but still much can be done.

    • Here, we rely on the high degree of correlation between the parent particle’s mass, and what you do see!

  • Can miss >1 if doing things like jets, since these particles areusually low momentum. So losing them doesn’t hurt too much.

When all particles are reconstructed

  • A central concept in particle physics is the so-called “invariant mass”.

    • You get the same answer in any reference frame!

  • The total energy of a particle is given by (Special Relativity):

  • Now, solve for the rest mass energy (of the particle), given E and p.

  • When dealing with energy, momentum and mass, it is ~universal to just drop the “c”, to obtain the cleaner expression

    (One can recover the factors of “c” by dimensional analysis, if needed)

  • Usually you just use mass == [MeV/c2] or [GeV/c2], p in [GeV/c], etcand fuhhhgettaboutit…

Computing invariant masses

  • Suppose you are searching for a decay, Babc, where a,b,c are charged particles that have lifetimes long enough to be observed in your detector (p±, K±, e ± , m±, p)

  • Of course the B meson decays, so you don’t “see” it.







  • Having only measured (E,p) of a,b,c, how do you know that they came from a B meson? (E.g. many other particles produced in the collision)

  • All you need are the decay products (E,p) to compute the mass of the parent!

  • If they really come from a B meson, “m” will compute to the known mass of the B meson, ~5280 MeV/c2.

A brief tour on how this goes (I)

  • Step 1: Try and “reconstruct” D0K-p+ decays.

  • Combine a K- and p+ that appearto come from the same point inspace (but not from the ppcollision point)

  • Compute the invariant mass.Is there a peak at m(D0)=1865 MeV/c2 ?

  • Let’s search for the decay:








K-p+ invariant mass distribution

  • Have to “work backwards”

  • First search for the D0 meson decay

  • Then, find 3 pions that comefrom the same point in space,but not the pp collision.

  • Combine D0 and p-p+p- to lookfor B- decay (invariant mass)

U-betcha, we havereal D0K-p+

Why don’t we geta spike at 1865 MeV?

What’s this ?

A brief tour on how this goes (II)

Step 2: “Reconstruct” the p-p+p-(No sharp mass peak, since notfrom the decay of a long-lived particle)

Step 3: Combine D0 and p-p+p- andcompute invariant mass. - Is there a peak at the known B- mass of 5280 MeV/c2?

  • Let’s search for the decay:








  • Have to “work backwards”

  • First search for the D0 meson decay

  • Then, find 3 pions that comefrom the same point in space,but not the pp collision.

  • Combine D0 and p-p+p- to lookfor B- decay (invariant mass)

Breaking down an invariant mass plot

  • Whallah!








  • What are all these features?

  • Red: B- signal events

  • Everything else is “not signal”, aka background.

    • Random tracks combined

    • “Other” B decays that look a lot like our signal.

A specific background





D0p0 ( 62% )


D0g ( 38% )

  • If you do not consider the g or p0 in your decay hypothesis, the decay has the identical signature as signal: B-D0ppp.








g or p0


  • Since the g or p0 carries only a small fraction of the D* energy, when it is not included, the invariantmass gets shifted down just a bit.

  • The cyan component is from D*0D0p0 and the brown is from D*0D0g.

  • Similarly B0 D*+ppp, with D*+D0p+, and D0Kp is also included (gray)(here the p+ is not used in the assumed decay hypothesis)

Things to take away


Here, a “real” Z0 boson is created and detected (in decay to m+m-) in pp collision at LHCb.





M(m+m-) (MeV/c2)

To infer a particle’s “existence”, one searches for and measures the (E,p) of the particles it decays into.

You can then compute the “invariant mass”, and you should get a narrow peak at the expected mass (if you’ve measured all the decay products)

You need to understand the backgrounds that may also show up in this invariant mass plot.

But, what if you can’t detectall the decay products?

From momentum conservation



~ Energy of muon should equal about half the W mass


  • Example: In W+m+nm, the neutrino is not detected. Neutrinos almost always escape the detector without a trace.

  • All you have as a single muon from the W decay.

  • Here’s the key:

    • Let’s assume the W+ is produced nearly at rest.

    • It decays almost instantaneously to mn (~11% of the time)

Muon p distributions

  • Shown are the observed muon momentum spectra (m+ and m-)

  • W+ m+n and W- m-n

  • Points = data, yellow = expected signal distribution; the rest are backgrounds.

    • This momentum spectrum is expected (mostly just kinematics).

    • Peaks at ~40 GeV ~ MW/2

    •  Can measure W boson from these, despite not seeing the n

    • Smeared out because the W is not produced at rest!

  • Don’t need to observe the neutrinoto clearly establish you’re seeing the W-boson decay!

Even heavier … the top quark

  • Each top quark decays to W+b (~100%)

  • The W’s can decay to either:

  • So, one can get events with:

  • Dilepton mode: Two missing neutrinos

  • All Jets: Large backgrounds from multi-jet events with no top.

  • Lepton+Jets:High energy lepton  W in event.Only 1 missing n; enough measured infoto still measure top quark mass.

Top quark mass from Atlas

  • Very different than the narrow Gaussian peaks we saw when reconstructing B mesons!

  • Here, we measure each particle in the decay usingthe tracking system (momentum measured to~0.5% precision!)

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