Sonia Bouchiba - Indico · HNL is a spin 1/2 particle, its decay is helicity dependent Z usual way...

Simulating inclusively produced HNL at physics level

Sonia Bouchiba

supervised byFederico Redi and Inar Timiryasov

28th May 2019

Sonia Bouchiba (EPFL) LLP Workshop 28th May 2019 1 / 14

Search for HNL at LHCb

Search for Majorana neutrinos in the exclusive production modeB− → π+µ−µ− decay for Run 1 3 fb−1 data. [arXiv:1401.5361]Model-independant constraint on the rate of SS muonic decays + upperlimits set on coupling |Uµ4|2 based on a theoretical model for the B decaywidth to N and the N lifetime.Peskin & Shuve correction: claim the used model is unsound (BR missed am4

N/m4B factor), recomputation of the |Uµ4|2 limits [arXiv:1607.04258]

Figure: Corrected upper limit on |Uµ4|2 @ 95% CL from the LHCb experiment


https://arxiv.org/abs/1401.5361

https://arxiv.org/pdf/1607.04258

Method

Using Pythia framework (part of LHCb complete simulation framework Gauss):

Input: BRs of the inclusive production channels from B mesons(b → `N/P`N/V `N) and the exclusive decay into interesting channels, inparticular: SS muons process b → Xµ+N(→ µ+π−).Use decay width expression from phenomenology paper [arXiv:1805.08567]

Simulate by adapting the already existing framework for tau decays.

Transpose the piece of code to Gauss, apply right cuts and produce signal.



HNL decay using Pythia 8: Tau Decay framework

HNL is a spin 1/2 particle, its decay is helicity dependent

Z usual way to decay a particle: choose a channel weighted by BR, assessesmomentum isotropically in phase space.

Z use already existing framework developped by Ph.Ilten in Pythia[arXiv:1401.5361], taking helicity dependency into consideration for τ decays.

Z main difference: momenta weight computed differently in function ofhelicity combinations between initial and final states1.

1Collins & Knowles algorithmSonia Bouchiba (EPFL) LLP Workshop 28th May 2019 4 / 14


Helicity dependancy in HNL decay I

τ → ντπ+

ND → µ+π−

With Dirac spinors: for a given τ/N helicityλ1 = ±1/2, summing over µ2 polarizations.

M∝ u/v 2(p2, λ2)γµ(1− γ5)u/v 1(p1, λ1)

|M|2 ∝ (E2 +− 2λ1p2 cos θ)E2m2−−−−→ (1 +− 2λ1 cos θ)

75 50 25 0 25 50 75* [ ]

0

d d

( ) = + 12 / (N) = 1

2

( ) = 12 / (N) = + 1

2sum


Helicity dependancy in HNL decay II

Z Can identify ND ↔ τ for λ(τ) = −λ(N)

And use the fact differential decay widths are the same for polarized ND and N 2:

dΓ±dΩ

(ND → µ−π+) =dΓ∓dΩ

( ND → µ+π− )︸︷︷︸Dirac

=dΓ±dΩ

(N → µ−π+) =dΓ∓dΩ

( N → µ+π− )︸︷︷︸Majorana

Z Same distribution for our Majorana HNL than for an anti-Dirac HNL simulable inPythia.

2see also [arXiv:1905.00284]Sonia Bouchiba (EPFL) LLP Workshop 28th May 2019 6 / 14


Results I

Once the equivalence τ ↔ N is done, the only sanity checks are (1) the correcthandle of the angular decay width (2) the correct handling of the mass

Distribution of θ(µ2) in N rest frame @ fixed λ(τ) = −λ(N)

80− 60− 40− 20− 0 20 40 60 80) [deg]

2µ(

*θ

20

40

60

80

100

120

) = +1/2τ(λ, τHNL ~

) = -1/2τ(λ, τHNL ~

Z Can observe a difference for the 2 pol, to compare with analytical.


Results II

Distribution of θ(µ2) in B rest frame for fixed λ(τ) = −λ(N)

0 20 40 60 80 100 120 140 160 180Angle between muons [deg]

0

100

200

300

400

500 = 0λHNL ~ Higgs,

) = +1/2τ(λ, τHNL ~

) = -1/2τ(λ, τHNL ~


Results III

Comparing angle between muons in B rest frame τ → ντπ− and → µ+π−

processes: handling of the lepton daughter mass.


0

50

100

150

200

250

300

350

400

450-π +µ →' τ'-π τν →' τ'

Figure: mN = 0.5 GeV/c2, E2 ∼ m2,clear difference


0

20

40

60

80

100

-π +µ →' τ'-π τν →' τ'

Figure: mN = 3.0 GeV/c2, E2 m2


Conclusion on simulation model

Not more to check!... By only comparing the vertices: N ↔ τ but withopposite helicity, . Angular dependency and daughter mass correctly takeninto account.

New Pythia code for HNL easily transposable to Gauss (physics level+LHCbdetector) framework.

Soon production of MC signal and apply LHCb cuts, to reproduce results ofPeskin-Shuve and set prospects.


BACKUP SLIDES


HNL production from B mesons BRs

Figure: Dominant branching ratios of HNL production from different beauty mesons. Forcharged mesons two-body leptonic decays are shown, while for the neutral mesons decaysare necessarily semi-leptonic. For these plots we take Ue = 1, Uµ = Uτ = 0. See figure 5of [arXiv:1805.08567]



HNL production from B mesons BRs

0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50q2[MeV2] 1e7

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

f0 (q2 )

B mesons form factor f0(q2) for semileptonically produced HNLs B0 + N

B0 + N

B0 D + N

B0 D * + N

B + D0 * + N

B + D0 + N

B + 0 + N

B + 0 + N

B0s Ds

+ N

B0s Ds

* + N

B0s K + N

0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50q2[MeV2] 1e7

0.0

0.5

1.0

1.5

2.0

2.5

3.0

f+(q

2 )

B mesons form factor f + (q2) for semileptonically produced HNLs

B0 + N

B0 + N

B0 D + N

B0 D * + N

B + D0 * + N

B + D0 + N

B + 0 + N

B + 0 + N

B0s Ds

+ N

B0s Ds

* + N

B0s K + N

Figure: Transfer energy-dependant form factors of B mesons


Helicity decays handling algorithm (Collins & Knowles)1 Generation of momenta of the particles in the hard process

2 Random choice of outgoing particles spin density matrix computationnormalisation for this particle’s decay.

3 Choose a decay mode among those available; compute daughters momentaaccording to the weight (0: decayer and 1, . . . , n: decay products. )

W = ρλ0,λ′0Mλ0;λ1...λnM

∗λ′0;λ

′1...λ

′n

n∏i=1

D iλiλ

′i

4 Repeat until stable particle.

This handling is applied for the tau coming from: electroweak (Drell-Yan, W ),Higgs, and B/D mesons.


Sonia Bouchiba - Indico · HNL is a spin 1/2 particle, its decay is helicity dependent Z usual way...

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