Mass Reconstruction Techniques for Resonances in WW Scattering

Mass Reconstruction Techniques for
Resonances in W±W± Scattering
Stefanie Todt
([email protected])
Institut fuer Kern- und Teilchenphysik, TU Dresden
DPG Wuppertal
March 11, 2015
bluu
Vector boson scattering at the LHC
• longitudinal scattering of weak bosons directly connected to
mechanism of electroweak symmetry breaking (EWSB)
• sensitive to BSM physics: aQGCs, heavy resonances
weak-boson self-couplings
Higgs contributions
include non-VBS and
non-resonant diagrams
+
⇒ SM-EW VVjj process
channel of like-charge W± W± scattering favourable in the context of the LHC
experiments
first evidence for Vector Boson Scattering (VBS) in the processes
W± W± −→ W± W± (arXiv:1405.6241)
Stefanie Todt
Institut fuer Kern- und Teilchenphysik, TU Dresden
Mass Reconstruction Techniques for Resonances in W± W± Scattering
1 / 11
Vector boson scattering at the LHC
• longitudinal scattering of weak bosons directly connected to
mechanism of electroweak symmetry breaking (EWSB)
• sensitive to BSM physics: aQGCs, heavy resonances
weak-boson self-couplings
Higgs contributions
include non-VBS and
non-resonant diagrams
+
⇒ SM-EW VVjj process
• first evidence for Vector Boson Scattering (VBS) in the processes
W± W± −→ W± W± (arXiv:1405.6241)
−→ see talk from Ulrike Schnoor T 67.4
Stefanie Todt
Institut fuer Kern- und Teilchenphysik, TU Dresden
Mass Reconstruction Techniques for Resonances in W± W± Scattering
1 / 11
Heavy resonances in VBS
• new physics in EWSB is introduced via an effective field theory approach
• isospin conservation in high energy limit −→ five possible resonances:
type
weak isospin I
spin J
electric charge Q
width Γres /Γ0
σ
0
0
0
6
f
0
2
0
1
5
ρ
1
1
−, 0, +
4 v2
3 M2
φ
2
0
−−, −, 0, +, ++
1
t
2
2
−−, −, 0, +, ++
1
30
• partial widths Γ0 for resonances decaying into longitudinally polarized vector
bosons:
g2 m3
Γ0 =
·
64π v2
• mass m and coupling g of resonances free parameters
−→ variation of resonance mass m ∈ [500 GeV, 1200 GeV]
−→ fixed coupling g = 2.5 (g ∈ [0, 2.5])
blub
blub Institut fuer Kern- und Teilchenphysik, TU Dresden
Stefanie Todt
Mass Reconstruction Techniques for Resonances in W± W± Scattering
2 / 11
Heavy resonances in VBS W± W± jj
• new physics in EWSB is introduced via an effective field theory approach
• isospin conservation in high energy limit −→ five possible resonances:
type
weak isospin I
spin J
electric charge Q
width Γres /Γ0
σ
0
0
0
6
f
0
2
0
1
5
ρ
1
1
−, 0, +
4 v2
3 M2
φ
2
0
−−, −, 0, +, ++
1
t
2
2
−−, −, 0, +, ++
1
30
• resonant scattering of two like-charge W± bosons
→ resonant scattering in s-channel for doubly charged isotensor resonances:
broad scalar
φ resonance
⇒
Stefanie Todt
Institut fuer Kern- und Teilchenphysik, TU Dresden
narrow tensor
t resonance
or
Mass Reconstruction Techniques for Resonances in W± W± Scattering
2 / 11
Mass reconstruction: X±± → W± W± → l± l± νν
Invariant mass from relativity:
µ
2
Pµ WW
= PWW
mX2 = mWW
µ
PWW
: composite four-momentum of W± W± system
µ
µ
µ
+ Pν
= Plµ1 + Plµ2 + Pν
PWW
2
1
Problem:
• separate momenta of neutrinos unknown ~qν1 , ~qν2
→ 6 degrees of freedom
• ~pTmiss measurement: 2 constraints ~pTmiss =
P
~qTνi
Solution:
• perform minimization over free parameters (arXiv:1105.2977)
→ find smallest resonance mass consistent with measured ~pTmiss
→ allows for concrete information from every event
event
⇒ lower mass bound on resonance mass: mX > mWW
⇒ (if true event topology is chosen)
Stefanie Todt
Institut fuer Kern- und Teilchenphysik, TU Dresden
Mass Reconstruction Techniques for Resonances in W± W± Scattering
3 / 11
Mass reconstruction: Transverse projections
Calculation of transverse masses → define projected (2+1)-momenta
analogous to four-momenta:
• four momentum: Pµ = (E, px , py , pz )
• (2+1)-momentum: pα
> = (e> , px , py )
Projection of energy component:
• “mass-preserving” projection
e> =
q
m2 + p2T =
p
E2 − p2z
−→
2
pα
> p>α = m
• “massless” projection
eo = |pT |
−→
pα
o poα = 0wwlwwwwwwwwwww
Transverse mass:
2
m>1
= (p> + q> )α (p> + q> )α
2
mo1
= (po + qo )α (po + qo )α
Stefanie Todt
Institut fuer Kern- und Teilchenphysik, TU Dresden
Mass Reconstruction Techniques for Resonances in W± W± Scattering
4 / 11
Mass variables
Order of operations (summation of particles, projection) does matter for
energy component of Pµ :
2
2
= (Pµ + Qµ )> (Pµ + Qµ )>
= (p> + q> )α (p> + q> )α , m1>
m>1
• projection discards information → early projection weakens bound
• additionally discard mass information (mo1 ) weakens bound even more
=⇒ m1> > m>1 = mo1 > m1o
Additional constraint for heavy resonances:
• one or both W± bosons are produced on mW mass shell −→ m1>Star
(for WW∗ ) and m1>bound (for both W on-shell) (arXiv:1108.3468, arXiv:1110.2452)
Stefanie Todt
Institut fuer Kern- und Teilchenphysik, TU Dresden
Mass Reconstruction Techniques for Resonances in W± W± Scattering
5 / 11
Mass variables
Traditional transverse mass variables:
• mvis − invariant mass of lepton pair (i.e. mll )
• meff − invariant mass of lepton pair + ETmiss (only transverse plane (hep-ph/9610544))
2
meff
(pTl1 , pTl2 , pTmiss ) = (|~pTl1 | + |~pTl2 | + |~pTmiss |)2
2
= mo1
+ (~p1T + ~pTmiss )2
• mvec − invariant mass of lepton pair + ETmiss (with z-component of leptons)
2
mvec
(pl1 , pl2 , pTmiss ) = (|~pl1 | + |~pl2 | + |~pTmiss |)2
− (~pTl1 + ~pTl2 + ~pTmiss )2 − (~pzl1 + ~pzl2 )2
• mcol − collinear approach (R.K. Ellis et al., Nucl. Phys. B 297, 221 (1988))
Stefanie Todt
Institut fuer Kern- und Teilchenphysik, TU Dresden
Mass Reconstruction Techniques for Resonances in W± W± Scattering
6 / 11
Comparison of resonance types: true mWW
cross section / 10 GeV
cross section / 10 GeV
• MC study with event generator WHIZARD and K-matrix unitarisation at
√
s = 8 TeV (CERN-THESIS-2015-018)
10-2
10-3
W± W± jj-EW
10-2
10-3
W±W±jj-EW
t, m=1200, g=2.5
Φ, m=750, g=2.5
10-4
t, m=1000, g=2.5
10-4
Φ, m=500, g=2.5
t, m=750, g=2.5
Φ, m=1000, g=2.5
t, m=500, g=2.5
-5
10 0
-5
200
400
600
800
1000 1200 1400
10 0
mWW
Φ resonance (broader)
m ∈ {500, 750, 1000} GeV
g = 2.5
200
400
600
800
1000 1200 1400
mWW
t resonance (narrow)
m ∈ {500, 750, 1000, 1200} GeV
g = 2.5
• truth mWW : invariant mass of the W± W± system at parton level (w/o parton
shower) reconstructed with true (associated) neutrinos (i.e. ml± νl l± νl )
• reference: SM-EW mWW distribution (in red)
Stefanie Todt
Institut fuer Kern- und Teilchenphysik, TU Dresden
Mass Reconstruction Techniques for Resonances in W± W± Scattering
7 / 11
Comparison of mass variables: reconstructed mWW
Φ resonance, m = 500 GeV, Γ = 64 GeV, g = 2.5
mass bound variables
mass variables without mass bound
×10−3
mass bound variables
Φ , m=500 GeV, g=2.5
mo1
m1o
50
m1T
m1Tstar
40
m1Tbound
dσsignal
fb
30 GeV
dmreco
WW
dσsignal
fb
30 GeV
dmreco
WW
×10−3
60
mvis
meff
mvec
40
mcol
30
30
20
20
10
10
0
mass var. w/o bound
Φ , m=500 GeV, g=2.5
50
100
200
300
400
500
600
700
0
800
100
200
300
400
mreco
WW [GeV]
500
600
700
800
mreco
WW [GeV]
• m1> , m1>bound and mo1 drop around resonance mass → saturated lower mass
bound (respect generic width of resonance)
• m1>bound shifted to higher invariant masses with respect to m1>
• meff , mvec , mcol fail to give lower mass bound
• mvis : unsaturated lower mass bound due to minimal information input (no ~pTmiss )
Stefanie Todt
Institut fuer Kern- und Teilchenphysik, TU Dresden
Mass Reconstruction Techniques for Resonances in W± W± Scattering
8 / 11
Discovery potential
dN
1
60 GeV
dm1T
WW
• events at particle level with simulation of detector resolution for ~ETmiss
• Signal: pp −→ l± νl± νjj final state with resonance
• Background: only SM-EW pp −→ l± νl± νjj final state
(no contribution from W± W± -QCD, WZ)
• optimize for best statistical significance √SB in reconstructed mass window
mWW −→ discovery potential
1
t, m=500 GeV, g=2.5
W± W± jj-EW
10−1
best significance interval
L = 20 fb-1, s = 8 TeV
10−2
10−3
10−4
10−5 0
200
400
600
800
1000 1200 1400
m1T
WW [GeV]
Stefanie Todt
Institut fuer Kern- und Teilchenphysik, TU Dresden
Mass Reconstruction Techniques for Resonances in W± W± Scattering
9 / 11
Comparison of Discovery potential: Mass variables
t resonance, g = 2.5
Φ resonance, g=2.5
mass bound variables
mo1
m1T
m1Tbound
mass var. w/o bound
mvec
2
10
discovery potential S
B
discovery potential S
B
Φ resonance, g = 2.5
mass bound variables
t resonance, g=2.5
m1T
m1Tbound
mass var. w/o bound
meff
mvec
10
500
600
700
800
900
500
1000 1100 1200
600
700
800
900
1000 1100 1200
resonance mass [GeV]
resonance mass [GeV]
Best mass variable in terms of discovery potential:
• for broader resonance (Φ): mo1 (best background rejection)
• for narrow resonance (t): m1>bound or m1> (most kinematic information)
• only small differences between the different mass variables for different
coupling parameters of the resonances
Stefanie Todt
Institut fuer Kern- und Teilchenphysik, TU Dresden
Mass Reconstruction Techniques for Resonances in W± W± Scattering
10 / 11
Summary
• modelling of heavy resonances in W± W± scattering with WHIZARD
(EFT approach with K-matrix unitarisation)
• study of different resonances and mass reconstruction variables
• study discovery potential against SM-EW pp −→ l± l± νν background
• best mass variables:
• for broader resonance (Φ): mo1
• for narrow resonance (t): m1>bound and m1>
Thanks for your attention!
Stefanie Todt
Institut fuer Kern- und Teilchenphysik, TU Dresden
Mass Reconstruction Techniques for Resonances in W± W± Scattering
11 / 11
Summary
• modelling of heavy resonances in W± W± scattering with WHIZARD
(EFT approach with K-matrix unitarisation)
• study of different resonances and mass reconstruction variables
• study discovery potential against SM-EW pp −→ l± l± νν background
• best mass variables:
• for broader resonance (Φ): mo1
• for narrow resonance (t): m1>bound and m1>
Thanks for your attention!
Stefanie Todt
Institut fuer Kern- und Teilchenphysik, TU Dresden
Mass Reconstruction Techniques for Resonances in W± W± Scattering
11 / 11
Backup
Stefanie Todt
Institut fuer Kern- und Teilchenphysik, TU Dresden
Mass Reconstruction Techniques for Resonances in W± W± Scattering
12 / 11
Heavy resonances in VBS
• new physics in EWSB is introduced via an effective field theory
approach
→ effective chiral Lagrangian as perturbative expansion in some new
physics energy scale Λ
→ SM evolves as low-energy limit (= leading term) of the new theory
• model-independent parametrization of high-energy VBS
→ add new degrees of freedom for any possible heavy resonance
X
L = LSM +
Lr
resonances
• effective theory → new resonant scattering amplitudes rise with energy
→ break unitarity at some energy E > Λ
→ add unitarisation formalism manually: K-matrix unitarisation
=⇒ Monte Carlo studies with Whizard event generator (features generic
effective theory with resonances and K-matrix unitarisation) (arXiv:0806.4145)
Stefanie Todt
Institut fuer Kern- und Teilchenphysik, TU Dresden
Mass Reconstruction Techniques for Resonances in W± W± Scattering
12 / 11
Resonances in W± W± → W± W±
• need to be of electrical charge ++ or −−
• Φ: scalar (Spin 0), isotensor (Isospin 2)
• t: tensor (Spin 2), isotensor (Isospin 2)
arXiv:1307.8170 (Simplified Models - Snowmass 2013)
Stefanie Todt
Institut fuer Kern- und Teilchenphysik, TU Dresden
Mass Reconstruction Techniques for Resonances in W± W± Scattering
12 / 11
W± W± jj → l± l± ννjj final state
Signal process:
scalar φ
resonance
with
tensor t
resonance
or
• same kinematic topology as VBS
• two energetic forward jets (initial quarks radiating off Ws)
• both W bosons decay leptonically
→ two same-sign central leptons
→ missing ~pT from 2 neutrinos in the final state
ν
l± (1)
∆y
tagging jet (4)
tagging jet (3)
l± (2)
Stefanie Todt
Institut fuer Kern- und Teilchenphysik, TU Dresden
ν
Mass Reconstruction Techniques for Resonances in W± W± Scattering
12 / 11
Minimization
Example: M1T
2
M1>
= min M21>
pz miss
M21>
=
q
Mll2
+ ~p21T
!2
r
2
p
p
2
2
2
2
2
+
~q1T + q1z + ~q2T + q2z
− (q1z + q2z )
− (~pT + ~pTmiss )2
4 Contraints:
~pTmiss =
X
~qTi
p
mw2 = 2 |~pi | · ~qiT 2 + qiz 2 − ~piT~qiT − ~piz~qiz
Free choices:
• total z-component of invisible particles pmiss
z
→ minimization: equal rapidities of visible and invisible system: y = ymiss
• frame-independence of y → y = 0 → pz = 0
/ ansatz M
/ =χ
• invariant mass of invisible particle collection (ν1 , ν2 ) M:
otherwise minimization sets it to 0
Problems:
• W mass constraint leads to quadratic equation in any constraining parameter
(same
issue as for pz reconstruction
in W
mass measurement)
Stefanie Todt
Institut fuer Kern- und Teilchenphysik,
TU Dresden
Mass Reconstruction Techniques for Resonances in W± W± Scattering
12 / 11
Mass formulas
2
m1>
(pTl1 , pTl2 , pTmiss ) =
q
2
Mll2 + ~p21T + |~pTmiss | − (~p1T + ~pTmiss )2
2
mo1
(pTl1 , pTl2 , pTmiss ) = (|~pTl1 | + |~pTl2 | + |~pTmiss |)2 − (~p1T + ~pTmiss )2
2
= meff
− (~p1T + ~pTmiss )2
2
= m>1
(massless leptons)
2
m1o
(pTl1 , pTl2 , pTmiss ) = (|~pTl1 + ~pTl2 | + |~pTmiss |)2 − (~p1T + ~pTmiss )2
2
mvec
(pl1 , pl2 , pTmiss ) = (|~pl1 | + |~pl2 | + |~pTmiss |)2
− (~pTl1 + ~pTl2 + ~pTmiss )2 − (~pzl1 + ~pzl2 )2
2
meff
(pTl1 , pTl2 , pTmiss ) = (|~pTl1 | + |~pTl2 | + |~pTmiss |)2
2
mvis
(pl1 , pl2 ) = Mll2
Mll − invariant mass of dilepton system
~p1 − vector sum of lepton momenta ~pl1 , ~pl2
~p1T − vector sum of lepton transverse momenta ~pTl1 , ~pTl2
Stefanie Todt
Institut fuer Kern- und Teilchenphysik, TU Dresden
Mass Reconstruction Techniques for Resonances in W± W± Scattering
12 / 11
Collinear mass mcol
• assumption: decay products of W are emitted collinear
• possibility to reconstruct the momentum of both neutrinos
• compute fraction xi of W momentum carried away from its visible decay
product (lepton) (use momentum conservation in transverse plane)
• only 0 < xi < 1 are physical
• → mWWcol cannot always be calculated
~pW
T,i =
~plT,i
xi
2
mWWcol
=(pW1 + pW1 )2
2
2
mWWcol
=2 · (mW
+ pW1 · pW2 )

s
2
mWWcol
=2 ·
2
mW
+
~pl1
2
mW
+ ( T )2 ·
x1
s

l1
l1
l2
·
~
p
~
p
~
p
T
T
T
2

mW
+ ( )2 −
x2
x1 · x2
• mWWcol fomular holds only for onshell W’s which is not true in all the cases
Stefanie Todt
Institut fuer Kern- und Teilchenphysik, TU Dresden
Mass Reconstruction Techniques for Resonances in W± W± Scattering
12 / 11
Comparison of mass variables: reconstructed mWW
t resonance, m = 500 GeV, Γ = 2 GeV, g = 2.5
mass bound variables
mass variables without mass bound
×10−3
t, m=500 GeV, g=2.5
25
mass bound variables
mo1
m1o
m1T
20
m1Tstar
m1Tbound
15
dσsignal
fb
40 GeV
dmreco
WW
dσsignal
fb
40 GeV
dmreco
WW
×10−3
20
t, m=500 GeV, g=2.5
18
mass var. w/o bound
mvis
meff
mvec
16
14
mcol
12
10
10
8
5
4
6
2
0
0
100 200 300 400 500 600 700 800
mreco
WW [GeV]
0
0
100 200 300 400 500 600 700 800
mreco
WW [GeV]
• φ and t resonance: maxima shifted to higher mWW for φ, difference in shape
(spin dependence of mass variables)
• same observations for higher resonance masses and lower coupling parameters
Stefanie Todt
Institut fuer Kern- und Teilchenphysik, TU Dresden
Mass Reconstruction Techniques for Resonances in W± W± Scattering
12 / 11
Comparison of mass variables: mWW,reco − mWW,true
mo1
m1o
m1T
m1Tstar
10−2
m1Tbound
10−1
mass var. w/o bound
Φ , m=500 GeV, g=2.5
mvis
meff
mvec
mcol
10−2
WW
mass bound variables
Φ , m=500 GeV, g=2.5
dσsignal
fb
18 GeV
d(mreco - mtrue
WW)
10−1
WW
dσsignal
fb
18 GeV
d(mreco - mtrue
WW)
Φ resonance, m = 500 GeV, Γ = 64 GeV, g = 2.5
mass bound variables
mass variables without mass bound
10−3
10−3
−200
−100
0
100
200
true
mreco
WW - mWW [GeV]
−200
−100
0
100
200
true
mreco
WW - mWW [GeV]
• difference between reconstructed and true mWW : clear distinction between mass
bound variables and other mass variables
note: not resonance mass - t resonance mtconstr are all those events in the peak here,
were mass was overestimated because there never were two onshell W
Stefanie Todt
Institut fuer Kern- und Teilchenphysik, TU Dresden
Mass Reconstruction Techniques for Resonances in W± W± Scattering
12 / 11
Comparison of mass variables: mWW,reco − mWW,true
m1T
10−2
m1Tstar
m1Tbound
mass var. w/o bound
t, m=500 GeV, g=2.5
mvis
meff
mvec
−2
10
mcol
WW
mo1
m1o
dσsignal
fb
30 GeV
d(mreco - mtrue
WW)
mass bound variables
t, m=500 GeV, g=2.5
WW
dσsignal
fb
30 GeV
d(mreco - mtrue
WW)
t resonance, m = 500 GeV, Γ = 2 GeV, g = 2.5
mass bound variables
mass variables without mass bound
10−3
10−3
−200
−100
0
100
200
true
mreco
WW - mWW [GeV]
−200
−100
0
100
200
true
mreco
WW - mWW [GeV]
• difference between reconstructed and true mWW : clear distinction between mass
bound variables and other mass variables
note: not resonance mass - t resonance mtconstr are all those events in the peak here,
were mass was overestimated because there never were two onshell W
Stefanie Todt
Institut fuer Kern- und Teilchenphysik, TU Dresden
Mass Reconstruction Techniques for Resonances in W± W± Scattering
12 / 11
reco
reco /<m
Comparison of mass variables: relative width σmWW
WW >
t resonance, g = 2.5
1.0
σmreco/<mreco
WW >
mass bound variables
0.9
mo1
m1o
0.8
WW
WW
σmreco/<mreco
WW >
Φ resonance, g = 2.5
m1T
m1Tbound
0.7
1.0
mass bound variables
0.9
m1o
m1T
m1Tbound
0.7
0.6
0.6
0.5
0.5
0.4
0.4
Φ resonance, g=2.5
0.3
0.2
mo1
0.8
500
600
700
800
900 1000 1100 1200
0.3
0.2
t resonance, g=2.5
500
600
700
800
900 1000 1100 1200
resonance mass [GeV]
resonance mass [GeV]
• for both resonance types:
m1> and m1>bound best resolution especially for high resonance masses
• statistical errors are too small to be visible
• mass resolution 25 − 35% for both resonance types
Stefanie Todt
Institut fuer Kern- und Teilchenphysik, TU Dresden
Mass Reconstruction Techniques for Resonances in W± W± Scattering
12 / 11
Comparison of Discovery potential: Resonances
discovery potential S
B
g = 2.5, mo1
Φ resonance, m=500 GeV
t resonance, m=500 GeV
mo1
102
10
1
0.5
1.0
1.5
2.0
2.5
resonance coupling
• φ resonance has higher discovery potential than t resonance due to higher total
cross section
Stefanie Todt
Institut fuer Kern- und Teilchenphysik, TU Dresden
Mass Reconstruction Techniques for Resonances in W± W± Scattering
12 / 11
Object and event selection criteria
Jets
Leptons
• pT > 30 GeV
• pT > 30 GeV
• |η| < 4.5
• |η| < 2.5
Event selection criteria
• exactly two charged dressed leptons,
• a minimum of two jets,
• both leptons have the same electric charge,
• both leptons have to have a minimum distance of ∆R > 0.3 to any
reconstructed jet in the event and to each other.
Stefanie Todt
Institut fuer Kern- und Teilchenphysik, TU Dresden
Mass Reconstruction Techniques for Resonances in W± W± Scattering
12 / 11

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