Spin measurements in cascade decays at the LHC

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Spin measurements in cascade decays at the LHC

• hep-ph/0605296
• SangHui Im
• 2009.1.30 Seminar

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Contents

• Angular correlation of decay products to a
  polarized particle
• Application to cascade decays of various channels
  for spin determination
• Determining spin in decay channels of no leptonic
  partner
• Concluding remarks

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1. Angular correlation of decay products to
a polarized particle

• Scalar decayA scalar doesnt peak any special
  direction in space and so its decay is isotropic.
  i.e. No angular correlation
• Fermion decay1. fermion(?1) ? fermion(?2)
  scalar(f) If initial ?1 is polarized, there is
  angular correlation if ?2 is produced as
  polarized by chiral interaction (yL ? yR)

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• Fermion decay2. fermion(?1) ? fermion(?2)
  gauge-boson(Aµ) If Aµ is longitudinally
  polarized ? same as fermion(?2)
  scalar(f) If Aµ is transversely polarized
  ? opposite to fermion(?2) scalar(f)
  i.e. same helicity sin2(?/2),
  opposite helicity cos2(?/2)
• Chiral vertex is needed for angular
  correlation.
• The most important feature of the fermions
  decay is the linear dependence of the decay
  probability on cos(?).

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• Gauge-boson decay1. gauge-boson(Aµ) ?
  2-fermion2. gauge-boson(Aµ) ? 2-scalar, or
  2-gauge-boson
• The vertex need not be chiral for angular
  correlation in this case.
• Note the quadratic dependence on cos(?).
  There are finite mass effects when the products
  are not highly boosted, which wash out any
  angular dependence of the amplitude. The
  contribution scale m2/E2 ?
  appreciable mass difference between the decaying
  particle and its products is
  needed to suppress this.

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• Higher spin j particle decayBy noting that a
  rotation by ? of a state of spin j is given by
  exp(i ? jsy),the amplitude for the decay of a
  particle with spin j is as follows.The
  coefficient ai are such that when we sum over all
  polarization ?,so that an unpolarized particle
  has no preferred direction. Higher-spin
  consideration can be important when it comes to
  the physics of graviton and its partner,
  though we wont consider them here.

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2. Application to cascade decays of various
channels for spin determination

• Well apply the previous knowledge to determining
  the spin of new particles in SUSY and Same Spin
  senario (like UED or little Higgs models) in
  various decay channels.
• The typical decay channel we will consider has
  the following topology and structure.
• Since we dont know the missing particles
  momentum, construction of Cs rest frame is
  impossible.
• However, the cos(?) information in Cs rest
  frame can be obtained by measuring invariant
  mass of two visible particles.
• So, by investigating the invariant mass
  distributions, we can measure the cos(?)
  dependence of matrix elements and thereby spin
  determination of the intermediate particle C is
  possible.

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2.1 Weak decay with ql final state

• SUSY model
• Chargino Dirac fermion
• For spin correlation, the chargino and lepton
  should be polarized as mentioned before.
• In SUSY, the two vertices are both (at least
  partially) chiral so that the chargino and lepton
  are both indeed polarized. And as shown in
  section 1, the matrix element has linear
  dependence on cos(?).
• cos(?) information is included in the invariant
  mass of q and l as follows.

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• Same Spin model
• We assume that W couples like a Standard Model
  W.
• If masses of q and W are not too degenerate,
  then in the rest frame of W, both q and q are
  boosted and mostly left-handed.? Then W should
  be longitudinally polarized mostly by angular
  momentum conservation.
• Another way of seeing the above factin the
  rest frame of W
• Since W is longitudinally polarized, its
  subsequent decay into two fermion is governed by
  1-cos2(?) as mentioned in section 1.
• So the matrix element turns out to be a quadratic
  function of tql with a negative coefficient in
  front of the leading power.
• Note that a gauge-boson does not require the
  vertices to be chiral for spin correlation.
  However, its more susceptible to mass
  difference than SUSY model case sincethe fermion
  finite mass effect mq2/Eq2 is larger because
  of the large mq mass.

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• Another decay channel in SUSY model
• Neutralino Majorana fermion
• By Majorana nature, there is always pair of
  vertices with opposite lepton charges.
• The squark-quark-neutralino vertex is chiral, so
  the neutralino becomes polarized.
• By definite opposite helicities of l and l-,
  charge asymmetry in the invariant mass
  distributions is appeared, which can be used to
  uncover spin information.
• Note that the charge asymmetry does not appear in
  the case of Dirac fermion intermediate particle
  like chargino.
• However, a further complication due to the
  Majorana nature arises. There is always another
  diagram starting from anti-squark with opposite
  sign of its charge which contribute the same
  process but with the opposite helicity structure.
  
• In a proton-proton collider, squarks and
  anti-squarks are produced unevenly so that the
  angular correlation are not washed out
  completely.

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2.2 Weak decay with
final state

• In principle, it could contain similar spin
  correlation since it just replace the leptons in
  the previous decay chains with quarks.
• However, in general we cannot determine the
  charge of the initial jet.
• Then for example, in the Majorana case
  considered just before, all angular correlations
  are washed out once we are forced to average over
  the two final states with opposite charges.
• On the other hand, if the decay products of the
  second decay are a third generation quark and
  quark partner, we could recover some charge
  information, in principle.
• Careful studies taking into account the
  efficiency of identifying charge of the third
  generation quarks are required.

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2.3 Weak decay with q W final state

• If the charged gauge-boson partner is lighter
  than the leptonic partner, then its decay into a
  W and LSNP(Lightest Stable Neutral Particle)
  through a non-Abelian vertex is usually the
  dominant decay mode.

• SUSY model
• If masses of squark and chargino are not too
  degenerate, quark is boosted and
  chargino becomes polarized.
• chargino-neutralino-W coupling is at least
  partially chiral if tan ß ? 1 and the
  higgsino is not much heavier than the gauginos.
• So there exists spin correlation between the
  quark and W, which gives a linear dependence
  on the variable tqW.
• Up-type squark contribution can be canceled by
  anti-down-type squark. Fortunately, thanks
  to the initial asymmetry between them in pp
  collisions, the signal is not washed out.

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• Same Spin model
• In the rest frame of W, both q and q are
  boosted and are mostly left-handed or mostly
  right-handed. Hence W becomes longitudinally
  polarized.
• As a result, this decay exhibits a quadratic
  dependence on tqW with a positive coefficient.
• This channel will be studied more detailedly
  later. It deserves to be focused since it is a
  more generic channel comparing with the channel
  requiring on-shell lepton partner in the decay
  chain.
• Actually, if the spectrum does not even allow
  for this decay chain, we will not be able to
  extract any information from weak decays.

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2.4 Weak decay with q Z final state

• A similar channel to the previous one with a
  neutralino as the intermediate particle and Z in
  the final state (higgsino-higgsino-Z coupling).
• This could be a potentially golden channel
  considering the leptonic decay of the Z.
• Unfortunately, therere no angular correlation
  since the vertex is not even partially chiral.
• In Same Spin models, if the intermediate particle
  is a heavy scalar partner of the higgs, there are
  no correlations.
• If the intermediate particle is some heavy Z,
  this might be the easiest channel to discover.
  But this is not a very generic case.
• When Z decays into quarks, this process can be
  problematic since its indistinguishable from the
  previous qW case if W decays into quarks.
• Fortunately, in most models, it is suppressed
  by a factor of 10-50 with respect to the chargino
  channel owing to the higgsino origin of the
  coupling.

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2.5 Weak decay with q h final state

• The neutralino could also decay into a Higgs and
  LSP (because of mixing with the higgsino).
• But the vertex is not chiral, and no correlation
  exists.
• In the Same-Spin senario, a correlation between
  the higgs and the quark exists and follow the
  same as those for a massive gauge-boson decay
  into two bosons. Note Z is longitudinally
  polarized. So the amplitude has a quadratic
  dependence on tqh with a positive coefficient.
• This channel is quite generic and it is important
  to investigate it further. In certain cases,
  replacing the quark with a lepton might be
  possible (heavy leptonic partner case).

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2.6 Decay of gluon partner

• This would certainly be the dominant channel of
  producing new physics particles if gluon partners
  are present in the spectrum. This diagram might
  prove to be the dominant decay mode into missing
  energy.
• But no spin effects at all in on-shell decays in
  both SUSY and Same-Spin senario cases. (SUSY
  scalar intermediate, Same-Spin not chiral
  vertex)
• If the spectrum is such that the gluon partner
  must decay into the LSNP via an off-shell quark
  partner, the situation can be quite different as
  we will discuss it later.

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2.7 Strong decay of quark partner

• Slightly specialized as it relies on the
  existence of a squark heavier than the gluino,
  but its still generic enough to warrant
  consideration.
• If such a quark partner indeed exist, this will
  be its dominant decay mode.
• The gluon partner is polarized by left-right
  asymmetric spectrum.
• In SUSY model, still no angular correlations
  owing to our experimental limitations that we
  cannot measure jets charge, which makes the
  charge asymmetry due to Majorana gluino useless.
  However, if we can know the charge of the third
  generation quarks, there can be a hope to see
  correlations.
• In Same-Spin model, the gluon partner becomes
  longitudinally polarized as discussed so far,
  and we expect the decay to be a quadratic
  function of the variable tq1q2.
• Significant SM background can be removed by hard
  cuts on missing E.

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2.8 Decay from leptonic initial states

• If lepton partners are heavy enough, all
  previous channels can be initiated by a lepton
  partner decay instead of a quark partner decay.
• The angular correlations are the same, only we
  replace an outgoing jet with an outgoing lepton.
• It has advantages than quark partner initial
  states in that we can gain a lot more information
  because charge and flavor is now available to us,
  and jet combinatorics is not a problem.
• On the other hand, a lepton partner at the
  beginning of a cascade is harder to come by. It
  could come from the decay of heavy electroweak
  gauge boson partner Z coupled to leptons. That
  is more model dependent.
• It also requires rather special arrangements
  among parameters. For example, in the MSSM,
  This looks promising in certain regions of
  parameter space.

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2.9 Off-shell decays

• In the case of intermediate fermion, if it is
  off-shell, then one of the helicities dominates
  over the other simply because m2/q2 ? 1 (q is the
  fermion 4-momenta).
• For example, consider gluon partner decay
  through an off-shell quark partner.
• In SUSY channel, obviously no correlations since
  the squark is a scalar.
• In Same-Spin channel, however, the correlations
  are indeed present. The amplitude is
• Notice that when the quark partner is off-shell
  (q2 ? mq2), the coefficient of tqq is non-zero.
  So it can be distinguished from the SUSY case.
• Similar considerations apply for the other case
  of a gauge-boson partner decay to LSNP via an
  off-shell slepton.
• Further study is needed to explore the
  observability of this effect in different models.

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3. Determining spin in decay channels of no
leptonic partner

• Deeper look at qW process in which channel no
  on-shell leptonic partner is required.
• Explicit matrix element calculations shows the
  same angular behavior as the one analyzed before.
• The first equation is for the SUSY case. And the
  second one is for the Same-Spin senario with F2gt0
  and F1lt0 as anticipated.

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3.1 Experimental observable jet-lepton
correlation
W is not observed directly and only its decay
products can be measured. Consider W ? neutrino
lepton decay. (full reconstruction of W is
impossible by missing neutrino.)
? Correct pairing tql distribution
2 jets and 1 lepton events
2 jets and 2 leptons events (i.e. both branches
decaying into leptons)
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3.2 Experimental observable jet-jet correlation
Consider W ? 2 jets decay. (full reconstruction
of W is now possible. But background is enhanced
and momentum determination involves some amount
of smearing.)
Irreducible background
Evaded by W reconstruction
Spin determination still works.
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3.3 Scanning M1 and M2

• F1 and F2 are the cumulative distribution
  functions(CDF) for the two data sets.
• Kolmogorov-Smirnov test The p-value assigned
  to the D-statistics is low when the two data
  sets come from different underlying
  distributions.

mq1000 GeV

• If the spectrum is not too degenerate (like M2
  ? M1 or M2 ? mq), this rough estimation seem
  to indicate that spin determination in qW decay
  channel is possible in generic parameter
  space.

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Concluding remarks

• Even though spin correlations are present in a
  variety of decay channels, the viability of any
  particular channel is always confined to certain
  kinematical regions.
• We should explore the effective range of all
  possible decay channels and devise techniques for
  using them efficiently.
• One of the most important challenges is to
  measure the spin of gluon quark partners where
  decay products are usually jets, missing the
  charge information. Also larger combinatorial
  background and SM background are present.
• Notice that decay channels involving leptons are
  generally more promising than those involving
  only jets since we have charge and flavor
  information form the lepton.
• Other than kinematic variables constructed out of
  just two objects of the decay products, the
  possibility of using more complicated kinematic
  variables deserves to be considered.
• The possibility of measuring spin in the
  production is to be investigated carefully.