Tes tj ng minimal seesaw models at hadron co lm iders Arindam Das - - PowerPoint PPT Presentation
Tes tj ng minimal seesaw models at hadron co lm iders Arindam Das Korea Neutrino Research Center, Seoul National University, Korea Institute for Advanced Study 18th July, 2017 Neu ts inos at ti e High Energy Fron tj er Wolfgang Pauli, Enrico
Arindam Das Korea Neutrino Research Center, Seoul National University, Korea Institute for Advanced Study 18th July, 2017 Neutsinos at tie High Energy Frontjer
more care needed amongst many open questions
Wolfgang Pauli, Enrico Fermi ‘Little neutral one’ going to be the most attractive key now a days energy momentum conservation
Homestake experiment site at Homestake gold mine in Lead, South Dakota Raymond Davis Jr. (1914-2006) John Bahcall (1934-2005)
Kamiokande, Japan; SAGE, former Soviet Union; GALLEX, Italy; Super Kamiokande, Japan; Sudbury Neutrino Observatory, Canada Development of the neutrino oscillation experiments
Super['Kamiokande,'Sudbury'Neutrino'Observatory''1999',' Neutrino'oscilla$on'between'mass'and'flavor'eigenstates' Neutrinos'are'very'special''
∆m2
21
7.6 × 10−5eV2 SNO |∆m31|2 2.4 × 10−3eV2 Super − K sin2 2θ12 0.87 KamLAND, SNO sin2 2θ23 0.999 T2K 0.90 MINOS sin2 2θ13 0.084 DayaBay2015 0.1 RENO 0.09 DoubleChooz
Neutrino'oscilla$on'data'
νe νµ ντ ⇥ ⌅ =
⇥ ⌅
ν1 ν2 ν3 ⇥ ⌅
= ⇤ ⌥ ⌥ ⌥ ⌥ ⌥ ⌥ ⌥ ⇧ c12c13 s12c13 s13e−iδ −s12c23 − c12s23s13eiδ c12c23 − s12s23s13eiδ s23c13 s12s23 − c12c23s13eiδ −c12s23 − s12c23s13eiδ c23c13 ⌅
⇥
×diag
,
and''
?' Tes$ng'the'UNITARITY'of''''UP MNS ''''Bruno'' Pontecorvo' Ziro'Maki' 'Masami'''''' Nakagawa' Shoichi'Sakata'
2
Eeore'Majorana','(1906['?')' Paul'Dirac,'FRS'(1902[1984)'
LνL +'H.'c.'
Fermion'Number'Viola$ng'
L → r
µ ←
L → r
µ ←
R →
← ←
→
L → r
µ ←
L → r
µ ←
R → R →
← ← 'Fermion'Number'Conserving'
m1 < m2 < m3 : Normal Hierarchy m3 < m1 < m2 : Inverted Hierarchy
Normal Hierarchy Inverted Hierarchy
Weinberg'Operator''in'SM'(d=5),'PRL'43,'1566(1979)' ⇥LH⇥c
L TH
within'the'Standard' 'Model' The'dimension'5'operator'can'be'realized'in'the'following'ways'
Majorana'mass'term'is'generated'by'the'breaking'of'the'lepton'numbers'by'2'units.'
Seesaw'Mechanism'
Minkowski(1977),'Yanagida'(1979),'Gell[Mann,'Ramond,' Slansky'(1979),''Glashow'(1980),'Mohapatra'and'Senjanovic' (1980)'
SU(3) SU(2) U(1)Y L =
eL
2 −1
2
eR 1 1 −1 H =
H−
2 −1
2
NR 1 1
L ⊃ −Y αβ
D α LHNβ R − 1
2mαβ
N NαC R Nβ R + H.c..
MD = YDv √2 .
Mν =
MT
D
mN
N MT D.
Naturally'explains'the'small' neutrino'mass''
Gell-Mann, Glashow, Minkowski, Mohapatra, Ramond, Senjanovic, Slansky, Yanagida
Inverse(Seesaw(Mechanism(:(Mohapatra(1986),(Mohapatra(&(Valle((1986)((((
SU(2) U(1)Y L 2 −1/2 H 2 −1/2 Nj
R
1 Nj
L
1
Lmass ⊃ −µij((NL)c)iN
j L − mijNi RN j L − YDiji LHN j R + H.c.
Relevant(Part(of(the(Lagrangian(
νL →t mD NR → v M NL → r µ ← NL v M ← NR t mD ← νL mD = YD √2v
D
−1)µ(mDM −1)T
ll, O (mν),
−1 ∼ O(1)
LightS(heavy(mixing(could(be(large(and(Heavy(neutrino(can(be( produced(at(LHC(
−1 1, b
s ⌫ ' N⌫m + RNm,
= ⇣ 1 1
2✏
⌘ UMNS
N
h ✏ = R∗RT
U T
MNSmνUMNS = diag(m1, m2, m3)
In the presence of ✏, the mixing matrix N is not unitary, namely N †N 6= 1.
Nonunitarity: JHEP 10 (2006) 084 JHEP 12(2007) 061
LNC = g 2 cos ✓W Zµ h ⌫miµPL(N †N)ij⌫mj + NmiµPL(R†R)ijNmj + n ⌫miµPL(N †R)ijNmj + H.c.
,
UMNS = c12c13 s12c13 s13eiδ −s12c23 − c12s23s13eiδ c12c23 − s12s23s13eiδ s23c13 s12s23 − c12c23s13eiδ −c12s23 − s12c23s13eiδ c23c13 ×diag(1,eiρ,1)
12 = m2 2 − m2 1
23 = |m2 3 − m2 2|
For the minimal scenario we consider the Normal Hierarchy(NH) and Inverted Hierarchy(IH) cases as
DNH = diag ✓ 0, q ∆m2
12,
q ∆m2
12 + ∆m2 23
◆
DIH = diag ✓q ∆m2
23 ∆m2 12,
q ∆m2
23, 0
◆
we assume degenerate case
as MN = m 1
N = m 2 N ,
mν = 1 MN mDmT
D = U ∗ MNSDNH/IHU † MNS,
Light neutrino mass matrix for type-I seesaw can be simplified
mD = p MNU ∗
MNS
p DNH/IH O,
p p DNH = B B B @ (∆m2
12)
1 4
(∆m2
23 + ∆m2 12)
1 4
1 C C C A , p DIH = B B B @ (∆m2
23 ∆m2 12)
1 4
(∆m2
23)
1 4
1 C C C A
⇥ O = @ cos(X + iY ) sin(X + iY ) sin(X + iY ) cos(X + iY ) 1 A = @ cosh Y i sinh Y i sinh Y cosh Y 1 A @ cos X sin X sin X cos X 1 A
Due to non unitarity, the elements of N are highly constrained by the precession experiments of the W, Z decays and the LFV processes
µ → e B( < 4.2 × 10−13) EPJ C 76, (2016) no.8, 434 ⌧ → e B (< 4.5 × 108) PLB 666, (2008)16-22 ⌧ → µ B (< 12.0 × 10−8) PLB 666, (2008)16-22
µ− N e− W + W + γ
Application Casas- Ibarra Conjecture Phenomenologies: JHEP 09 (2010) 108 PRD 84, 013005 (2011) JHEP 08 (2012) 125 JHEP 09 (2013) 023(E) Lee and Shrock:
(1977).
|NN †| = B B B @ 0.994 ± 0.00625 1.288 ⇥ 10−5 8.76356 ⇥ 10−3 1.288 ⇥ 10−5 0.995 ± 0.00625 1.046 ⇥ 10−2 8.76356 ⇥ 10−3 1.046 ⇥ 10−2 0.995 ± 0.00625 1 C C C A .
'
B B B @ 0.006 ± 0.00625 < 1.288 ⇥ 10−5 < 8.76356 ⇥ 10−3 < 1.288 ⇥ 10−5 0.005 ± 0.00625 < 1.046 ⇥ 10−2 < 8.76356 ⇥ 10−3 < 1.046 ⇥ 10−2 0.005 ± 0.00625 1 C C C A
✏(, ⇢, Y ) = (R∗RT)NH/IH = 1 M 2
N
mDmT
D
= 1 mN UMNS p DNH/IHO∗OTp DNH/IHU †
MNS.
O∗OT = @cosh2 Y + sinh2 Y −2i cosh Y sinh Y 2i cosh Y sinh Y cosh2 Y + sinh2 Y 1 A
@ A Now we perform a scan for the parameter set {, ⇢, Y } and identify an allowed region for which ✏(, ⇢, Y ) satisfies the experimental constraints in Eq. (17).
set MN = 100 GeV a
−⇡ ≤ , ⇢ ≤ ⇡ with the interval of
π 20 and 0 ≤ y ≤ 14 with the interval of 0.01875.
1 2 3 10-18 10-15 10-12 10-9 10-6 0.001
d »V11 2
1 2 3 10-22 10-18 10-14 10-10 10-6
d »V12 2
2 4 6 8 10 12 14 10-18 10-15 10-12 10-9 10-6 0.001
Y »V11 2
2 4 6 8 10 12 14 10-21 10-17 10-13 10-9 10-5
Y »V12 2
Das, Okada: arXiv:1702.04688
Mixing parameters vary between 10-5-10-20, similar behavior is obtained for the other elements
1 2 3 10-18 10-15 10-12 10-9 10-6 0.001
d »V11 2
1 2 3 10-22 10-18 10-14 10-10 10-6
d »V12 2
2 4 6 8 10 12 14 10-18 10-15 10-12 10-9 10-6 0.001
Y »V11 2
2 4 6 8 10 12 14 10-21 10-17 10-13 10-9 10-5
Y »V12 2 Mixing parameters vary between 10-5-10-19, similar behavior is obtained for the other elements
1 2 3 10-30 10-25 10-20 10-15 10-10 10-5
d VeN VmN* 2 VeN 2 + VmN 2
2 4 6 8 10 12 14 10-22 10-18 10-14 10-10 10-6
Y VeN VmN* 2 VeN 2 + VmN 2
1 2 3 10-30 10-25 10-20 10-15 10-10 10-5
d VeN VmN* 2 VeN 2 + VmN 2
2 4 6 8 10 12 10-18 10-15 10-12 10-9 10-6 0.001
Y VeN VmN* 2 VeN 2 + VmN 2
NH Case IH Case
Implication in collider physics
u
¯ d
W +
Ni
Riα(δ, ρ,
y)
, y)†
Riβ(δ, ρ,
W +
ν
l+
γ
l−
β
l+
α
tri-le
q0 ! `Ni (u ¯ d ! `+
αNi and ¯
ud ! `
αNi) i
(q¯ q0 ! `αNi) = LHC|Rαi|2,
Phenomenological works by Atre, Antusch, Chen, Das et. al., Del-Aguila, Dev et. al., Fischer, Han, Mohapatra et. al., Okada
BR( )
mN 1 A
u
¯ d
W + Ni
Riα(δ, ρ,
y)
, y)†
Riβ(δ, ρ,
W +
ν
l+
γ
l−
β
l+
α
tri-le
tr
j l+ l+ + j j
(q¯ q0 ! `αNi) = LHC|Rαi|2,
|2
11(22)
|
12(21)
| |2
Many modes/ many ways to produce the heavy neutrinos at the colliders but (very small) mixings can spoil the game
Light neutrino mass matrix for inverse seesaw can be simplified
M →
M
µ
MNSDNH/IHU † MNS
−1)µ(mDM −1)T
DNH = diag
12,
12 + ∆m2 23
23 − ∆m2 12,
23,0
mD mT
D
M MT µ
mν = µ M2mDmD = U
∗ MNSDNH/IHU † MNS
mD = M √ µ U
∗ MNS
FND(:(2(generaRons(( NRj, NLj; j = 1, 2
(
a)((
mD ∼ nondiag(mD) (
Flavor(nonSdiagonal((FND)( (Flavor(diagonal((FD)(
(∆m2
12)
1 4
(∆m2
23 + ∆m2 12)
1 4
(∆m2
23 − ∆m2 12)
1 4
(∆m2
23)
1 4
b)(
M )2µ
MNSDNH/IHU † MNS
we use
FND( FD(
D
m
MNS
d µminNH = 525eV
u
¯ d
W +
Ni
Riα(δ, ρ,
y)
, y)†
Riβ(δ, ρ,
W +
ν
l+
γ
l−
β
l+
α
tri-le
=
ri
→ β →
R(δ,ρ,x,y) = 1 √µ U∗
MNS
O =
sin(x + iy) −sin(x + iy) cos(x + iy)
R∗RT(δ, ρ, y) = 1 µUMNS
DNH/IH
T
U†
MNS
O∗OT(y) =
−2icoshysinhy 2icoshysinhy cosh2y + sinh2y
R∗RT is constrained by the LFV and LEP data.
CasasSIbarra,(NPB(618(2001)171S204(
Das, Okada: arXiv:1207.3734
ee IH
µµ NH
µµ IH
FND:(Cross(secRon(is(enhanced( by(the(general(parameterizaRon(
with ffiffiffi s p ¼ 14 TeV.M=(100(GeV,(Luminosity(=(30(nS1(
ee µµ NH 15.5 178.5 IH 17.3 14.3 SMBG 116.4 45.6
6 fb
(SM(background,(F.(del(Aguila,(J.(A.(A.(Savedra( NPB(813((2009)(22S90,(PLB(672((2009)(158S165(
Diagonal (FD)
Signal Example: pp → Nµ, N → W µ, W → ανα
The cross section is twice larger than that of the SF case.
ProducRon(of(the(heavy(neutrino(
AD, PSB Dev, N Okada: PLB 735(2014)364-370
(i) The transverse momentum of each lepton: p
T > 10 GeV.
(ii) The transverse momentum of at least one lepton: p,leading
T
> 20 GeV. (iii) The jet transverse momentum: pj
T > 30 GeV.
(iv) The pseudo-rapidity of leptons: |η| < 2.4 and of jets: |ηj| < 2.5. (v) The lepton-lepton separation: ∆R > 0.1 and the lepton-jet separation: ∆Rj > 0.3. (vi) The invariant mass of each OSSF lepton pair: a) m+− < 75 GeV and b) m+− > 105 GeV. (vii) The scalar sum of the jet transverse momenta: HT < 200 GeV. (viii) The missing transverse energy: / E T < 50 GeV.
expectation 560±87 events . Upper limit of 510 − (560 − 87) =37 events.
expectation 200±35 events. Upper limit of 178 − (200 − 35) =13 events.
neutrino mass.
expected.
CMS(search(for(the(triSlepton+(MET((matches(with(our(signal(state)(
PHYSICAL REVIEW D 90, 032006 (2014)
Upper(bound(on(the(Mixing(angle(from(triSleptonSlepton( search(from(the(pseudoSDirac(heavy(neutrino((inverse(seesaw()(
Low(mass(region(is(in(good(comparison(to(the(EWPD(
mN=100 GeV -200 GeV will be good to study see also, arXiv:1510.04790
Production of heavy neutrino at the NLO-QCD order
AD, P Konar, S Majhi: JHEP 1606(2016) 019 Majorana heavy neutrino can display distinct same sign dilepton mode plus dijet Pseudo-Dirac heavy neutrino can display trilepton mode
µNLO
F
= µNLO
R
= ξ ∗ mN µNLO
F
= mN, µNLO
R
= ξ ∗ mN µNLO
F
= ξ ∗ mN, µNLO
R
= mN.
EWPDΤ EWPDe EWPDΜ EWPDe old EWPDΜ old Higgs L3 ATLAS8 CMS8 LO, Ξ0.1, 14TeV LO, Ξ1.0, 14TeV LO, Ξ10.0 14TeV
NLO, Ξ0.1, 14TeV NLO, Ξ1.0, 14TeV NLO, Ξ10.0 14TeV
100 200 300 400 500 106 105 104 0.001 0.01 0.1 1
mNGeV VΜN 2
s 14 TeV, 300 fb1
Prospective bounds on the mixing angle as a function of the Majorana heavy neutrino mass
EWPDΤ EWPDe EWPDΜ EWPDeold EWPDΜold Higgs ATLAS7 L3 ATLAS8 CMS8 Ξ0.1, SF75 Ξ1.0, SF75 Ξ10.0 SF75 Ξ0.1, FD75 Ξ1.0, FD75 Ξ10.0, FD75 Ξ0.1, SF105 Ξ1.0, SF105 Ξ10.0 SF105 Ξ0.1, FD105 Ξ1.0, FD105 Ξ10.0, FD105
100 150 200 250 300 350 400 106 105 104 0.001 0.01 0.1 1
mN GeV VlN 2
s 14 TeV, 300 fb1
Prospective bounds on the mixing angle as a function of the pseudo-Dirac heavy neutrino mass
Z N N
(a) (b) (c) (d) (e) (f) (g) (h)
Production of heavy neutrino pair at the NLO-QCD order
Majorana heavy neutrinos can display distinct same sign dilepton mode plus W, W can decay into leptons / jets Pseudo-Dirac heavy neutrinos can decay opposite sign dileptons plus W, W can decay into leptons/ jets However, heavy neutrinos can decay into Z but that is not the dominant mode AD : arXiv:1701.04946, more to come in the updated version
µNLO
F
= µNLO
R
= ξ ∗ mN µNLO
F
= mN, µNLO
R
= ξ ∗ mN µNLO
F
= ξ ∗ mN, µNLO
R
= mN.
EWPD-e EWPD-m EWPD-t EWPD-eHoldL EWPD-mHoldL Higgs ATLAS7 LEP2 ATLAS8 CMS8 xLO=0.1 xLO=1.0 xLO=10.0 xNLO=0.1 xNLO=1.0 xNLO=10.0
100 120 140 160 180 200 220 240 10-8 10-6 10-4 0.01 1
mNHGeVL »VeN 2
s =13 TeV, 3000 fb-1 EWPD-e EWPD-m EWPD-t EWPD-eHoldL EWPD-mHoldL Higgs ATLAS7 LEP2 ATLAS8 CMS8 xLO=0.1 xLO=1.0 xLO=10.0 xNLO=0.1 xNLO=1.0 xNLO=10.0
100 120 140 160 180 200 220 240 10-8 10-6 10-4 0.01 1
mNHGeVL »VmN 2
s =13 TeV, 3000 fb-1 EWPD-e EWPD-m EWPD-t EWPD-eHoldL EWPD-mHoldL Higgs ATLAS7 LEP2 ATLAS8 CMS8 xLO=0.1 xLO=1.0 xLO=10.0 xNLO=0.1 xNLO=1.0 xNLO=10.0
100 120 140 160 180 200 220 240 10-11 10-9 10-7 10-5 0.001 0.1
mNHGeVL »VeN 2
s =100 TeV, 3000 fb-1 EWPD-e EWPD-m EWPD-t EWPD-eHoldL EWPD-mHoldL Higgs ATLAS7 LEP2 ATLAS8 CMS8 xLO=0.1 xLO=1.0 xLO=10.0 xNLO=0.1 xNLO=1.0 xNLO=10.0
100 120 140 160 180 200 220 240 10-11 10-9 10-7 10-5 0.001 0.1
mNHGeVL »VmN 2
s =100 TeV, 3000 fb-1
Prospective bounds on the mixing angle as a function of the Majorana heavy neutrino mass
mN=100 GeV -200 GeV will be good to study
x=0.1, FDLO75 x=1.0, FDLO75 x=10.0 FDLO75 x=0.1, FDNLO75 x=1.0, FDNLO75 x=10.0, FDNLO75
100 120 140 160 180 200 220 240 10-5 10-4 0.001 0.01 0.1
mNHGeVL »VlN 2
3l û
s =13 TeV, 3000 fb-1 x=0.1, FDLO75 x=1.0, FDLO75 x=10.0 FDLO75 x=0.1, FDNLO75 x=1.0, FDNLO75 x=10.0, FDNLO75
100 120 140 160 180 200 220 240 10-6 10-5 10-4 0.001 0.01
mNHGeVL »VlN 2
3l û
s =100 TeV, 3000 fb-1 x=0.1, FDLOoff-Z x=1.0, FDLOoff-Z x=10.0 FDLOoff-Z x=0.1, FDNLOoff-Z x=1.0, FDNLOoff-Z x=10.0, FDNLOoff-Z
100 120 140 160 180 200 220 240 10-5 10-4 0.001 0.01
mNHGeVL »VlN 2
4l û
s =13 TeV, 3000 fb-1 x=0.1, FDLOoff-Z x=1.0, FDLOoff-Z x=10.0 FDLOoff-Z x=0.1, FDNLOoff-Z x=1.0, FDNLOoff-Z x=10.0, FDNLOoff-Z
100 120 140 160 180 200 220 240 1 ¥ 10-5 5 ¥ 10-5 1 ¥ 10-4 5 ¥ 10-4 0.001 0.005 0.010
mNHGeVL »VlN 2
4l û
s =100 TeV, 3000 fb-1
Prospective bounds on the mixing angle as a function of the pseudo-Dirac heavy neutrino (FD case) mass
mN=100 GeV -200 GeV will be good to study
Higgs doublets, breaking by the
doublet, hϕ0i ¼ v, the Yukawa
term MD ¼ vYD. neutrino to the SM Higgs
YD ¼ VMN=v, which is also suppressed by V. For simplicity, we will assume that only the
Mixing
wed: N → l−Wþ, νlZ, boson (the only physical
SM Higgs boson, physical remnant of
doublet ϕ). vely,
ΓðN → l−WþÞ ¼ g2jVlNj2 64π M3
N
M2
W
W
M2
N
2 1 þ 2M2
W
M2
N
ΓðN → νlZÞ ¼ g2jVlNj2 128π M3
N
M2
W
Z
M2
N
2 1 þ 2M2
Z
M2
N
128π M3
N
M2
W
h
M2
N
2 :
Antusch, Atre, Chen, Deppisch, Dev, Drewes, Franceschini, Gao, Kamon, Kim, Mohapatra, Fischer, Han, Pascoli, Pilaftsis, Senjanovic Decay Widths Das, Okada; Das, Konar, Majhi; Deppisch, Dev, Pilaftsis: Review arXiv:1502.06541
kinematically allowed.
ΓðN → l−
1 lþ 2 νl2Þ ≃ jVl1Nj2G2 FM5 N
192π3 ;
ΓðN → νl1lþ
2 l− 2 Þ ≃ jVl1Nj2G2 FM5 N
96π3 ðgLgR þ g2
L þ g2 RÞ
ðN → → l−WþÞ ¼
leptons
ΓðN → νllþl−Þ ≃ jVlNj2G2
FM5 N
96π3 ðgLgR þ g2
L þ g2 R þ 1 þ 2gLÞ;
ΓðN → νl1νl2 ¯ νl2Þ ≃ jVl1Nj2G2
FM5 N
96π3 ðN →
→ νlZ
leptons
ΓðN → l−jjÞ ≃ 3 jVlNj2G2
FM5 N
192π3 ;
ΓðN → νljjÞ ≃ 3 jVlNj2G2
FM5 N
96π3 ðgLgR þ g2
L þ g2 RÞ;
ðN → → l−WþÞ ¼
hadrons
ðN →
→ νlZ
hadrons
where gL ¼ − 1
2 þ sin2 θw, gR ¼ sin2 θw,
All three body decays Gorbunov and Shaposhnikov: arXiv:0705.1729 Atre, Han, Pascoli and Zhang: arXiv: 0901.3589 Dib and Kim : arXiv: 1509.05981 Das, Dev, Kim: arXiv:1704.0880 Das, Gao, Kamon: arXiv:1704.00881
Production cross section of the heavy neutrinos in from different initial states
N l+X ggF Enhancement due to prompt Higgs decay into ‘Nv’ as mN < mH
Results in good agreements with the pioneering 1408.0983 by Hessler, Ibarra, Molinaro and Vogl
Nl Nn ggF
200 400 600 800 1000 10-8 10-6 10-4 0.01 1
mN s0HpbL
s =13 TeV, »VNl 2=10-4
Nv+X CTEQ6l1
Production cross section of the heavy neutrinos in from different initial states
Nl Nn ggF
200 400 600 800 1000 10-6 10-5 10-4 0.001 0.01 0.1 1
mN s0HpbL
s =100 TeV, »VlN 2=10-4
CTEQ6l1
Heavy Neutrino Production from Higgs Decay
h v N v Z l l
where ΓSM ≃ 4.1 MeV for Mh ¼ 125 GeV ≃ ¼ Γnew ¼ Y2
DMh
8π
N
M2
h
2 :
Region Mass range 1 MN < MW 2 MW < MN < MZ 3 MZ < MN < Mh 4 MN > Mh
Dev, Franceschini, Mohapatra: PRD86,093010(2012)@8TeV LHC
Same as the previous slide except
leptons: jηl1;2j < 2.47. ferences are jηej < 2.47
eðe¯ μÞ < . ,
j ð Þ are jηej < 2.47, jημj < 2.4, GeV. j meμ > 10 GeV and ET > 20 GeV.
The transverse mass cut is common in the three cases
4 Mh < mT < Mh.
2mT ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ðEll þ pνν
T Þ2 − j ⃗
pTll þ ⃗ pTννj2 p , ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pll m p , where p νν p ll is
Ell
T ¼
sum of
mT ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðE þ p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðpll
T Þ2 þ ðmllÞ2
p , the neutrino (lepton) ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi j
T
þ
T
where ⃗ pTννð ⃗ pTllÞ transverse momenta
= Vector sum of the neutrino (lepton) transverse momenta
and pνν
T ðpll T Þ is the magnitude
For more detailed analysis of the backgrounds and separation techniques, see
Possible way to screen the signal from the backgrounds Das, Dev and Kim: PRD.95.115013, arXiv:1704.00880
process pp → h → νN → 2l2ν. analysis, we have three types
are opposite-sign,
Final States:
We consider all sorts of charge combinations as Higgs can decay into heavy and anti- heavy neutrinos for Dirac type heavy neutrino or for a Majorana type case the heavy neutrino can decay into both positively and negatively charged leptons
ATLAS
Selection Cuts
(i) Transverse momentum pl2;sub-leading
T
> 10 GeV. (ii) Transverse momentum
pl1;leading
T
> 22 GeV. (iii) Jet transverse momentum
T > 25 GeV.
> 25 GeV. leptons, jηl1;2j < 2.4,
jets, jηjj < 2.4. Lepton-lepton
separation, ΔRll > 0.3; and jet-jet
separation, ΔRlj > 0.3, . .
ΔRjj > 0.3. (vi) Invariant mass
mll > 12 GeV. (vii) Transverse mass
h
(MET): ET > 40 GeV. momentum are sup-
Dilepton transverse momentum is away from the MET
2.
pll
T > 30 GeV.
ee events, similar
After applying the cuts from ATLAS we calculate the yield
N ðMN; jVlNj2Þ ¼ L · σSM
h
lν¯ νÞ ΓSM þ ΓNew X ¯
þ X
j;k
ϵjk Γðh → ¯ νN þ c:c: → lj ¯ lkν¯ νÞ ΓSM þ ΓNew
luminosity, σSM
h ðpp → hÞ
section (which is domi-
= SM Higgs production cross section
,
= efficiencies for the decays mediated by SM and in presence
Calculated using cuts of ATLAS
Γðh → WW → l¯ lν¯ νÞ, ΓSM [106] S. Heinemeyer et al. (LHC Higgs Cross Section Working Group), arXiv:1307.1347.
L · σSM
h
CERNYellowReportPageAt8TeV.
8 TeV 14 TeV, 100 TeV
[123] https://twiki.cern.ch/twiki/bin/view/LHCPhysics/ HiggsEuropeanStrategy. [124] R. Alonso, M. Dhen, M. B. Gavela, and T. Ham
the mixing
¼ 169 denote
N ðMN; jVlNj2Þ < N expt, 95% C.L. upper limit on
Maximal values
j
lNj
here N expt ¼ 169 number of excess 2
[112] G. Aad et al. (ATLAS Collaboration), Phys. Rev. D 92, 012006 (2015).
for Mh ¼ 125 GeV at ffiffi ffi s p ¼ 8 TeV with L ¼ 20.3 fb−1 [112]. We plot this bound on the mixing parameter as a
Excluded by LEP LHC,EWPD, LFV limits from CMS is also included in the lower panel Future limit considering Majorana heavy neutrinos only FCC-ee : Limits from Z decay W-decay @LHC Future limits
μ → eγ combinati
~ future branching ratio O(10 )
CMS, JHEP 09 (2016) 051: 7&8 TeV combined H W W*, upper limit on Yukawa as well as mixing Future sensitivity @100 can go down to 10%precise result at 100 TeV pp collider: arXiv:1606.09408
the W boson produced in the Higgs decay to νN → decays hadronically, it will give rise to the lνjj final
νlW
W Br(jj) : 67% W Br(lv) : 22%,
are opposite-sign,
Chance of a gain due to > 3 times Br. into leptons
Large irreducible backgrounds
Practically, the purely leptonic modes are more clean turning out the signal sensitivity better than those with the jets, however, reconstruction is easier due to one neutrino in the final state.
Apart from the Higgs decay, the heavy neutrino can display the same final states through the CC and NC interactions. Finally after the decays of the W, Z bosons hadronically, we can get same final states.
(a) (b)
(c)
Selection cuts
lepton: pl
T > 20 GeV.
jets: pj > GeV.
T
T
T
j lj jets: jηj1;2j < 2.5 > . and
gauge boson produced after decay: mi − 20 < mi < mi þ 20,
depending on the
i −
where mi ¼ MN; mW or mZ processes given by the Feynman
Depending upon the process
MN ¼ 100 GeV
ffiffi ffi s p ¼ 14 TeV,
T > 30 GeV and pj1;2 T
ffiffi ffi s p ¼ 100 TeV,
j
ffiffi ffi ¼ cuts, pl
T > 53 GeV and pj1;2 T
> cuts remain the same as in the
35 GeV,
Other cuts remain the same
the W → jj final state,
to Z → jj final state.
for MN ¼ 100 GeV.
6. Significance of eV for two differe
at ffiffi ffi s p ¼ 14
TeV
at ffiffi ffi s p ¼ 100 TeV
two different choices of jVlNj2. Two
Neutrinos are NOT massless particles which ensures the necessary extension of the SM Many BSM scenarios can include the possibilities of neutrino mass. Amongst them type-I and inverse seesaw models are the simplest ones which include right handed SM gauge singlet heavy neutrinos. We have studied the various channels to produce such heavy neutrinos at the high energy colliders, such as LHC and 100 TeV pp collider comparing the bounds on the mixing angles. The bounds on the mixing angle coming from the LFV, LEP experiments are very strong so that the production of such heavy neutrinos from the type-I seesaw could be
Casas-Ibarra conjecture. Due to small lepton number violation parameter, on the other hand, the inverse seesaw scenario is still hopeful to us at the colliders. Even the Casas-Ibarra conjecture can help in testing the LFV modes at the LHC. Recently discovered Higgs can be used as a handle to study the properties of the heavy neutrinos where the heavy neutrino can show leptonic or hadronic decays through the SM gauge bosons. Even, the Higgs+ISR can improve the situation (Das, Gao, Kamon: arXiv:1704.00881 [hep-ph]).