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

THANK YOUH→ τ

+τ− at Muon Collider – p. 18