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H→ τ+τ− at Muon ColliderMurugeswaran Duraisamy & Alakabha Datta
Department of Physics and Astronomy
University of Mississippi
H→ τ+
τ− at Muon Collider – p. 1
Motivation
• SM Higgs can have Non-Standard Couplings.
• Many extensions of SM have extra Higgs e.g.SUSY, 2HDM, there are 3 neutral Higgs h, H,A (pseudo-scalar).
• There is interest in Higgs models wherecertain Higgs only couple to leptons (Leptonic Higgs H.S. Goh., L. J. Hall & P. Kumar
arXiv:0902.0814[hep-ph] ).H→ τ
+τ− at Muon Collider – p. 2
Motivation cont...
• Most general couplings of Higgs to τ τ pairneed to be measured.
• Measurements of these couplings willindicate the nature of the Higgs.
• Muon Collider will be Higgs factory⇒ these couplings can be measured
precisely.
H→ τ+
τ− at Muon Collider – p. 3
H → τ+τ−
• We study µ+µ− → H → τ+(π+ν̄τ)τ−(π−ντ)
process.
H
τ+
τ −
h(π ,ρ,a)
ντ
ν_
h(π ,ρ,a)_
τ
µ +
µ −
µ −
µ+Z,γ
Background τ −
τ+
• SM background: µ+µ− → Z, γ → τ+τ−.• Angular distributions (AD) can distinguish
Higgs decays and backgrounds(V.Barger hep-ph/0002042 ). H→ τ
+τ− at Muon Collider – p. 4
Non-standard couplings
• Non-standard Higgs couplings to τ lepton
L = τ̄(a + bγ5)τ.
• Various cases• SM (scalar Higgs): a = mτ/v (v =
VEV), b=0.• Pseudo-scalar (A) Higgs: a = 0, b 6= 0.• General case: a 6= 0, b 6= 0 and complex
⇒ possible CPV
H→ τ+
τ− at Muon Collider – p. 5
Full ADs
φ
H
θ+
π+
τ+z
τ −
x
θ −π −
• Let z-axes lie along ~pτ± in Higgs rest frame.• Polar angles in tau rest frame: π± - θτ±.• Azimuthal angles: π± - φτ± s.t
φ = φτ− + φτ+.H→ τ
+τ− at Muon Collider – p. 6
Full ADs
1
Γ
dΓ(H → τ+τ−)
d cos θτ−d cos θτ+dφ
=1
8π
(
1 − cos θτ− cos θτ+
−βτ2Re[aτb
∗τ ]
(β2τ |aτ |2 + |bτ |2)
(cos θτ− − cos θτ+)
+(−β2
τ |aτ |2 + |bτ |
2)
(β2τ |aτ |2 + |bτ |2)
sin θτ− sin θτ+cos φ
+βτ2Im[aτb
∗τ ]
(β2τ |aτ |2 + |bτ |2)
sin θτ− sin θτ+sin φ
)
,
where βτ =√
1 − 4m2τ
m2H
.H→ τ
+τ− at Muon Collider – p. 7
Full ADs
• For scalar Higgs bτ = 0
1
Γ
dΓ(H → τ+τ−)
d cos θτ−d cos θτ+dφ
=1
8π
(
1 − cos θτ− cos θτ+
− sin θτ− sin θτ+cos φ
)
.
• For pseudo-scalar Higgs aτ = 0
1
Γ
dΓ(A → τ+τ−)
d cos θτ−d cos θτ+dφ
=1
8π
(
1 − cos θτ− cos θτ+
+ sin θτ− sin θτ+cos φ
)
.H→ τ
+τ− at Muon Collider – p. 8
Full ADs
• Relative phase between couplings aτ and bτ
can be probed through coefficients Re[a∗τbτ ]and Im[a∗τbτ ]
Re[a∗τbτ ] = |aτ |2rτ cos δτ ,
Im[a∗τbτ ] = −|aτ |2rτ sin δτ ,
where rτeiδτ = bτ/aτ .
• Re[a∗τbτ ] related to forward-backwardasymmetry( AFB) and τ polarization (PT ).
H→ τ+
τ− at Muon Collider – p. 9
Full ADs
• Im[a∗τbτ ] indicates CP violations.
• In fact, the coefficient of Im[a∗τbτ ] is the Tripleproduct term.
T.P = p̂τ−.(n̂π− × n̂π+) = sin θHτ− sin θH
τ+ sin φ,
⇒ T.P 6= 0 indicates CPV.• T.P is odd under naive time reversal.
♦ unit vectors
n̂π± =~pπ±
|~pπ± |, p̂τ− =
~pτ−
|~pτ− |,
♦ θHτ± polar angles in Higgs rest frame.
H→ τ+
τ− at Muon Collider – p. 10
Kinematics in Higgs rest frame
• Relation between polar angles in Higgs andtau rest frames
cos θH± =
(βH(1 + ǫ2) + (1 − ǫ2) cos θτ±)
((1 − ǫ2) + βH(1 + ǫ2) cos θτ±).
• Polar angles in tau rest frame can be shownas
cos θτ± =
2EH
π±
Eτ
− (1 + ǫ2)
βτ (1 − ǫ2), ǫ = mπ/mτ
H→ τ+
τ− at Muon Collider – p. 11
Kinematics in Higgs rest frame
δHπ π+ −
• cos φ can be expressed in terms of openingangle (δH) between π± momenta
cos φ =m2
h
4m2τ sin θτ−
sin θτ+
(
g1−g1
+ cos δH − g2−g2
2
)
,
where g1∓ = ((1 ± βτβπ cos θτ∓)2 − 16m2
π
m2h
)1/2
g2∓ = (βπ cos θτ∓ ± βτ ).
• Hence AD can be expressed in terms ofmeasurable quantities at Muon collider.
H→ τ+
τ− at Muon Collider – p. 12
AFB and tau polarization
• τ± polar angular distributions can be obtainedas
W± =1
Γ
dΓ(H → τ+τ−)
d cos θτ±
=1
2
(
1 ± PT cos θτ±
)
⇒ PT = 2βτ rτ cos δτ
(β2τ+r2
τ )
• The forward-backward asymmetries define
AFB± =∫ 1
0d cos θτ±
W±−∫ 0
−1d cos θτ±
W±∫ 1
0d cos θτ±
W±+∫ 0
−1d cos θτ±
W±
= ±12PT
H→ τ+
τ− at Muon Collider – p. 13
Preliminary results
• AFB and tau polarization measurements canconstrain (rτ , δτ )
0 1 2 3 4 5-1.0
-0.5
0.0
0.5
1.0
rΤ
AFB
0 50 100 150-1.0
-0.5
0.0
0.5
1.0
∆Τ@DegD
AFB
PΤ=0.8
PΤ=0.85PΤ=0.90PΤ=0.95
-40 -20 0 20 400.0
0.5
1.0
1.5
2.0
2.5
∆Τ@DegD
r Τ
H→ τ+
τ− at Muon Collider – p. 14
Preliminary results
0 50 100 150 200 250 300 350
0.10
0.15
0.20
0.25
Φ@DegD
1 G
dG dΦ
rτ = 0, δτ = 0, rτ = 0.5, δτ = 0, π/4, π/2 , rτ = 1, δτ = 0, π/4, π/2
• Azimuthal angular distribution can be obtained as1Γ
dΓ(H→τ+τ−)dφ
= 12π
„
1 − π2
16(c1 cos φ + c2 sin φ)
«
,
c1 =1−r2
τ
1+rτ
, c2 = − 2rτ sin δτ
1+r2τ
.
• This distribution is sensitive to phase δτ .
H→ τ+
τ− at Muon Collider – p. 15
H → τ−τ+ at LHC
• Problems at LHC are difficult to reconstruct• τ rest frame in τ → πντ decays.• Higgs rest frame (pp → HX).
• Muon Collider is preferable for our analysis.
H→ τ+
τ− at Muon Collider – p. 16
Conclusion
• H → τ−τ+ can be used to study the mostgeneral couplings of Higgs to tau lepton.
• Measurements of these couplings can revealthe true nature of the Higgs.
• Future plan: general realistic study (withexperimentalists) to see how well we canmeasure these coupligs at Muon Collider.
H→ τ+
τ− at Muon Collider – p. 17