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 0 / 12

The problem W could be a charged Higgs scalar or a new W ′ heavy guage boson. To find: M W , M ν , Γ W , and the chirality of the couplings. g q = g q L P L + g q g l = g l L P L + g l R P R R P R where P L , R = ( 1 ∓ γ 5 )/ 2 tan ( ϕ q ) ≡ g q tan ( ϕ l ) ≡ g l R R g q g l L L 1 / 12

End point methods for mass measurements The end point of the P lT distribution is given by M 2 W − M 2 ν µ = 2 M W 2 / 12

Matrix Element Method Likelihood of an event { P vis j } under a set of parameter values α ∫ � � � N f d 3 p j j }| α ) = 1 � � P({ P vis W ({ P vis j } , { p vis j }) ( 2 π 3 2 E j ) σ α � � j = 1 � f a ( x 1 ) f b ( x 2 ) |M α ({ p i } , { p j })| 2 × 2 sx 1 x 2 a , b � � × ( 2 π ) 4 δ 4 � p j � N f + 2 2 � � p i − � � i = 1 i = 1 Likelihood of set of N events � N P({ P vis L α = j } n | α ) n = 1 3 / 12

“Mass difference” µ Endpoint M 2 W − M 2 ν µ = 2 M W 4 / 12

Mass scale M ν 0.035 M = 0 GeV, M W = 750 GeV 0.030 M = 250 GeV, M W = 826 GeV M = 500 GeV, M W = 1000 GeV 0.025 M = 1000 GeV, M W = 1443 GeV M = 2000 GeV, M W = 2410 GeV 0.020 0.015 0.010 0.005 0.000 0 50 100 150 200 250 300 350 400 P T (GeV) � � P 2 � 1 d σ 3 P lT lT 2 − µ 2 + ρ = 4 + 3 ρ σ dP lT µ 2 − P 2 µ lT where ρ = 2 M 2 ν /( M 2 W − M 2 ν ) 5 / 12

Mass scale M ν χ 2 per d.o.f. fit from P lz templates 0.0030 M = 0 GeV, M W = 750 GeV M = 250 GeV, M W = 826 GeV 0.0025 16 M = 500 GeV, M W = 1000 GeV M = 1000 GeV, M W = 1443 GeV 14 0.0020 M = 2000 GeV, M W = 2410 GeV 12 0.0015 10 χ 2 /n d 8 0.0010 6 0.0005 4 2 0.0000 0 100 200 300 400 500 600 700 800 900 1000 0 P z (GeV) 200 300 400 500 600 700 800 900 1000 M ν (GeV) 6 / 12

Width Γ W χ 2 per d.o.f. fit from P lT templates (10000 events) 20.0 72 17.5 60 15.0 48 12.5 W / M W (%) 36 10.0 7.5 24 5.0 12 2.5 0 0 200 400 600 800 1000 M (GeV) Flat direction 1 + ( M true / M true ) 2 Γ W ν W = Γ true 1 + ( M ν / M W ) 2 W 7 / 12

Masses and width using MEM Negative log likelihood fit for masses and width (1000 events) Including both P lT and P lz eliminates the flat direction 8 / 12

Chirality ( ϕ l , ϕ q ) 0 . 0030 ϕ ℓ = ϕ q = 0 0 . 0025 ϕ ℓ = 0 , ϕ q = 90 ◦ ϕ ℓ = ϕ q = 45 ◦ 0 . 0020 0 . 0015 0 . 0010 0 . 0005 0 . 0000 0 100 200 300 400 500 600 700 800 900 1000 P ℓz (GeV) d → W + → ¯ u ¯ l ν �|M| 2 � ∝ {( g q L ) 2 + ( g q L g l R g l R ) 2 }( p u . p ¯ l )( p ¯ d . p ν ) + {( g q L ) 2 + ( g q R g l L g l R ) 2 }( p ¯ d . p ¯ l )( p u . p ν ) The dependence on ( ϕ l , ϕ q ) is through cos ( 2 ϕ l ) cos ( 2 ϕ q ) 9 / 12

Chirality ( ϕ l , ϕ q ) Dependence of matrix element on chirality has a degeneracy. Matrix element depends on cos ( 2 ϕ l ) cos ( 2 ϕ q ) = cos 2 ( ϕ l − ϕ q ) − sin 2 ( ϕ l + ϕ q ) Negative log likelihood fit for 1000 events assuming values of other parameters. True value: ϕ q = ϕ l = 0 10 / 12

Simultaneous measurement Extent to which different components of the visible momenta are affected by the parameters P ℓ T P ℓ z mass difference � ∼ mass scale ∼ � width ∼ ∼ chirality × � For 100 events produced at M W = 1000 GeV , M ν = 500 GeV , Γ W = 50 GeV , ϕ q = ϕ q = 45 ◦ , multivariate minimization of the log likelihood function yielded M W = 998 GeV , M ν = 502 GeV , Γ W = 43 GeV , ϕ q = ϕ q = 46 . 5 ◦ 11 / 12

Pair production of W like resonances Log likelihood minimization with 500 events 12 / 12

Thank You! 12 / 12