Alessandro Fois

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Detection of h particles in B meson decay

• Alessandro Fois

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What are h particles?

• h (pronounced eta) particles are mesons
  consisting of a quark anti-quark pair
• i.e. uu, dd, ss
• We will try to detect them here in simulated
  data as a product of the rare decay
• B ? hln

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How do we detect the h particles?

• h particles have a very short mean lifetime
• (approximately 10-18 seconds). They decay too
  soon to reach the detector!!!
• We reconstruct them from their products when
  they decay the main decay mode is
• h ? 2g (approximately 28)

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A typical B decay
Particle 1 id 13 Px
1.6650 Py 0.2804 Pz 2.6981 E
3.1847 mass 0.1057 Particle 2
id 211 Px 0.5850 Py 0.3135 Pz
-0.5261 E 0.8584 mass 0.1396
Particle 3 id -211 Px 0.0012 Py
-0.4991 Pz 1.1310 E 1.2441 mass
0.1396 Particle 4 id 211 Px
0.2274 Py 0.1597 Pz 0.0386 E
0.3133 mass 0.1396 Particle 5
id 211 Px 0.2504 Py -0.0573 Pz
0.2075 E 0.3585 mass 0.1396
Particle 6 id -211 Px 0.1456 Py
-0.0747 Pz 0.1264 E 0.2495 mass
0.1396 Particle 7 id 22
Px 0.0110 Py -0.0160 Pz 0.0173 E
0.0260 mass 0.0000 Particle 8
id 22 Px 0.0033 Py -0.1451 Pz
0.1128 E 0.1838 mass 0.0000
Particle 9 id 22 Px 0.0178
Py -0.1115 Pz 0.0870 E 0.1426 mass
0.0000 Particle 10 id 22 Px
0.0283 Py 0.0084 Pz 0.0206 E
0.0360 mass 0.0000 Particle 11
id 22 Px 0.0398 Py 0.1004 Pz
0.0636 E 0.1254 mass 0.0000
Particle 12 id 22 Px -0.1659 Py
0.3464 Pz 0.1286 E 0.4051 mass
0.0000 Particle 13 id 22 Px
-0.0383 Py 0.0631 Pz 0.0012 E
0.0738 mass 0.0000 Particle 14
id 22 Px -0.0240 Py 0.0235 Pz
0.0021 E 0.0336 mass 0.0000
Particle 15 id 22 Px -0.0756 Py
0.0514 Pz 0.0050 E 0.0916 mass
0.0000 Particle 16 id 22 Px
-0.4086 Py -0.3953 Pz -0.1300 E 0.5832
mass 0.0000 Particle 17 id
22 Px -0.1085 Py -0.1177 Pz -0.0594 E
0.1707 mass 0.0000 Particle 18
id 22 Px 0.0103 Py -0.0236 Pz
-0.0076 E 0.0269 mass 0.0000
Particle 19 id 22 Px -0.3842 Py
-0.1175 Pz -0.1586 E 0.4319 mass
0.0000 Particle 20 id 22 Px
-0.5621 Py -0.1833 Pz -0.3246 E 0.6745
mass 0.0000 Particle 21 id
22 Px -0.0249 Py 0.0285 Pz -0.0193 E
0.0425 mass 0.0000 Particle 22
id -14 Px -1.0172 Py 0.3658 Pz
1.0798 E 1.5279 mass 0.0000

• Which are the right photons? Does the sum have to
  have the etas mass? Energy? In which frame of
  reference?

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Invariant Mass

• We use the quantity invariant mass which is
  conserved across frames of reference
• inv. mass (E2 p2c2)1/2
• The h particle has invariant mass 0.547GeV
  hence we seek photon pairs with combined
  invariant mass of this value.

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Photon pairs

• We consider the invariant masses of all possible
  pairs of photons in an event lots of background!
• Two salient peaks - 0.1 GeV (p0)
• - 0.55 GeV (h)

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Reconstructing the B

• As, mentioned before, B ? hln
• Now consider invariant masses of all pairs of
  photons combined with the lepton and neutrino for
  each event

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Reconstructing the B

• There is no peak! Maximum is at about 4 GeV B
  has invariant mass 5.29 GeV.
• Clearly too much background can we isolate the
  real decays?

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Cuts

• To isolate the real decays, we can take cuts
  set criteria for the decay to be accepted as
  real.
• Obviously, the photon pairs must have invariant
  mass of about 0.5-0.6 GeV to be h candidates.
• Energy cuts there are many photons with tiny
  energies. We only accept photon pairs with each
  photon above a certain energy, E.
• The result?

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Energy Cuts before and after

• E gt 0.2 GeV
• Peak at 5.3 GeV!

No energy cut
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Further Cuts Momentum

• Since the h only has invariant mass 0.55GeV,
  while the B has invariant mass 5.27 GeV, the hs
  must be fast for invariant mass (and energy) to
  be conserved in the decay.
• So, we cut on momentum in the centre of mass
  frame. But what is the best cut for momentum?

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Determining the best momentum cut

• Consider the 2D histogram of momentum of h vs.
  invariant mass of h (no cuts)

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• There is no obvious clustering around the h
  window of invariant mass near 0.55GeV.
• But, if we use our previous energy cuts

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Determining best h momentum

• E gt 0.2 GeV

E gt 0.1 GeV
Clustering between 0.5 and 0.6 GeV!
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Select a window

• Accept only photon pairs in this window i.e.
• combined momentum gt 1.0 GeV/c, combined
  invariant mass between 0.5 and 0.6 GeV.

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The Result

• Spike at 5.3 GeV!!!

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How good are the cuts?

• Do our cuts filter well when applied to random
  data?
• Run our cuts on Phils data (no hs)

Looks similar, but Much smaller and broader
distribution (maximum only 250 (c.f. 500 when run
on hs), and there are 3 times as many events in
Phils file. Distribution is centred about 4.9
GeV (c.f. 5.3 GeV when run on hs)
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Another Trick Beam Constrain

• We know that our reconstructed B will have 0
  momentum and 5.27 GeV of energy in its own frame
  of reference (it is stationary in its own
  reference frame!!)
• In fact, we set E 5.29 (a correction, since the
  Bs frame is not the CoM frame), and calculate
  the invariant mass of our reconstructed B in the
  centre of mass frame.
• Upon plotting a frequency histogram of this
  quantity

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Another Trick Beam Constrain

• Data with no h particles, with cuts

Without cuts
With cuts
In all cases, we get a distribution around about
5.27GeV, but the less background, the sharper the
spike.
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One Last Trick DE

• Since energy is conserved, we can also make use
  of the quantity
• DE SEi 5.29, where the Ei are the energies
  in the centre of mass frame of the pair of
  photons, lepton and neutrino that reconstruct the
  B.
• Since the Ei should add to the centre of mass
  frame energy of the B, 5.29 GeV, for the actual
  decay products, we should get a distribution with
  a spike at DE 0.

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One Last Trick DE
With cuts Background cut, peak at DE 0
Without cuts Background distribution, no spike
Data with no h particles, with cuts More
background, peak at DE -0.3GeV
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The real candidates

• If we plot a 2D histogram of DE vs. the beam
  constrained invariant mass, we should have the
  real Bs separating from the background and
  clustering about DE 0 and inv. mass 5.29 GeV

Data with no h particles, with cuts
With cuts
Without cuts
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Conclusions and Beyond

• Our cuts yield a peak at the required value for
  the reconstructed B, but only 7304 candidates
  remain from an original sample of 163384 hs, thus
  giving a 2 efficiency.
• Our cuts also isolate the real decays using the
  2D plots.
• Our cuts preferentially select hs, filtering out
  4 times as much background as hs.
• To go further, more work would need to be done
• making the cuts more precise and efficient.
• For example, we could select only the fastest
  photon in each event as one candidate for the
  reconstructed h.

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Acknowledgements

• Paul Harrison, Natures flawed mirror, Physics
  World, July 2003
• K. Hagiwara et al. (Particle Data Group), Phys.
  Rev. D 66, 010001 (2002)
• Young and Freedman, University Physics, 10th ed.,
  2002, p. 1032-42
• Kevin Varvell, for putting (and keeping) me on
  the right track.

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