Measuring the mass, width, and couplings of semi-invisible - - PowerPoint PPT Presentation

Measuring the mass, width, and couplings of semi-invisible resonances with the matrix element method

Prasanth Shyamsundar

University of Florida

based on work done with (arXiv:1708.07641)

Amalia Betancur

• Dr. Dipsikha Debnath
• Dr. James Gainer
• Dr. Konstantin Matchev

7 May, 2018

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The problem

W could be a charged Higgs scalar or a new W ′ heavy guage boson. To find: MW, Mν, ΓW, and the chirality of the couplings. gq = gq

LPL + gq RPR

gl = gl

LPL + gl RPR

where PL,R = (1 ∓ γ5)/2 tan(ϕq) ≡ gq

R

gq

L

tan(ϕl) ≡ gl

R

gl

L

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End point methods for mass measurements

The end point of the PlT distribution is given by µ = M2

W − M2 ν

2MW

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Matrix Element Method

Likelihood of an event {Pvis

j } under a set of parameter values α

P({Pvis

j }|α) = 1

σα

• Nf
• j=1

∫ d3pj (2π32Ej)

• W({Pvis

j }, {pvis j })

×

• a,b

fa(x1) fb(x2) 2sx1x2 |Mα({pi}, {pj})|2 × (2π)4δ4

• 2
• i=1

pi −

Nf +2

• i=1

pj

• Likelihood of set of N events

Lα =

N

• n=1

P({Pvis

j }n|α)

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“Mass difference” µ

Endpoint µ = M2

W − M2 ν

2MW

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Mass scale Mν

50 100 150 200 250 300 350 400

P T (GeV)

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035

M = 0 GeV, MW = 750 GeV M = 250 GeV, MW = 826 GeV M = 500 GeV, MW = 1000 GeV M = 1000 GeV, MW = 1443 GeV M = 2000 GeV, MW = 2410 GeV

1 σ dσ dPlT = 3 4 + 3ρ PlT µ

• µ2 − P2

lT

• 2 −

P2

lT

µ2 + ρ

• where ρ = 2M2

ν /(M2 W − M2 ν )

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Mass scale Mν

χ2 per d.o.f. fit from Plz templates

100 200 300 400 500 600 700 800 900 1000

P z (GeV)

0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030

M = 0 GeV, MW = 750 GeV M = 250 GeV, MW = 826 GeV M = 500 GeV, MW = 1000 GeV M = 1000 GeV, MW = 1443 GeV M = 2000 GeV, MW = 2410 GeV

200 300 400 500 600 700 800 900 1000

Mν (GeV)

2 4 6 8 10 12 14 16

χ2/nd

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Width ΓW

χ2 per d.o.f. fit from PlT templates (10000 events)

200 400 600 800 1000

M (GeV)

2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 W/MW (%) 12 24 36 48 60 72

Flat direction ΓW Γtrue

W

= 1 + (Mtrue

ν

/Mtrue

W

)2 1 + (Mν/MW)2

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Masses and width using MEM

Negative log likelihood fit for masses and width (1000 events) Including both PlT and Plz eliminates the flat direction

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Chirality (ϕl, ϕq)

100 200 300 400 500 600 700 800 900 1000

Pℓz (GeV)

0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030

ϕℓ = ϕq = 0 ϕℓ = 0, ϕq = 90◦ ϕℓ = ϕq = 45◦

u ¯ d → W+ → ¯ lν |M|2 ∝ {(gq

Lgl L)2 + (gq Rgl R)2}(pu.p¯ l)(p ¯ d.pν)

+ {(gq

Rgl L)2 + (gq Lgl R)2}(p ¯ d.p¯ l)(pu.pν)

The dependence on (ϕl, ϕq) is through cos(2ϕl) cos(2ϕq)

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Chirality (ϕl, ϕq)

Dependence of matrix element on chirality has a degeneracy. Matrix element depends on cos(2ϕl) cos(2ϕq) = cos2(ϕl − ϕq) − sin2(ϕl + ϕq) Negative log likelihood fit for 1000 events assuming values of other

• parameters. True value: ϕq = ϕl = 0

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Simultaneous measurement

Extent to which different components of the visible momenta are affected by the parameters PℓT Pℓz mass difference

• ∼

mass scale ∼

• width

∼ ∼ chirality ×

• For 100 events produced at

MW = 1000 GeV, Mν = 500 GeV, ΓW = 50 GeV, ϕq = ϕq = 45◦, multivariate minimization of the log likelihood function yielded MW = 998 GeV, Mν = 502 GeV, ΓW = 43 GeV, ϕq = ϕq = 46.5◦

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Pair production of W like resonances

Log likelihood minimization with 500 events

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Thank You!

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