Analysis of semileptonic decays of someb−baryons within the SM and beyond

C P Haritha

School of PhysicsUniversity of Hyderabad

Dec 16, 2020

C P Haritha XXIV DAE-BRNS HEP SYMPOSIUM 2020 Dec 16, 2020 1

Outline

I Introduction

I Theoretical Framework

I Constraints on New Couplings

I Results

I Summary

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Introduction

Motivation

I Flavor anomalies in b-hadron decays - BSM physics.

I Discrepancies seen in decays: b→ sl+l−

b→ cτ−ντ

I Lepton flavor universality violation

C P Haritha XXIV DAE-BRNS HEP SYMPOSIUM 2020 Dec 16, 2020 3

I The world average value of RD and RD∗ reported by HFLAV is[Y.S.Amhis et al.(HFLAV)(2019); arXiv:1909.12524]

RExptD =B(B → Dτ−ντ )

B(B → Dl−νl)= 0.340± 0.027± 0.013

RExptD∗ =B(B → D∗τ−ντ )

B(B → D∗l−νl)= 0.295± 0.011± 0.008

RSMD = 0.299± 0.003 , RSMD∗ = 0.258± 0.005.

I LHCb measured the value of RJ/ψ [R. Aaij et al.(LHCb Collaboration);

Phys.Rev.Lett. 120, 121801(2018)]

RExptJ/ψ

=B(B → J/ψτ−ντ )

B(B → J/ψl−νl)= 0.71± 0.17± 0.18

RSMJ/ψ

= 0.289± 0.01.

I New Physics in b→ cτ−ντ decays.

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Theoretical Framework

Effective HamiltonianThe most general effective Hamiltonian for b→ clνl transitionincluding NP contributions [C.Murgui, A.Penuelas, M.Jung, A.Pich; JHEP09 (2019) 103]

Hb→clνeff =4GFVcb√

2

[OVL +

∑i

CiOi

],

Ci −→ CVL,R , CSL,R , CT Wilson coefficients.

The fermionic operators are:

OVL,R = (cγµbL,R)(lLγµνlL )

OSL,R = (cbL,R)(lRνlL )

OT = (cσµνbL)(lRσµννlL )

I NP only in the τ mode.

I NP couplings are assumed to be real.

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B1(p1,mB1) −→ B2(p2,mB2) + l(pl,ml) + νl(pν , 0)

Hadronic matrix elements :

MVµ = 〈B2, λ2|V µ|B1, λ1〉 = u2(p2, λ2)

[f1(q2)γµ + if2(q2)σµνqν+

f3(q2)qµ]u1(p1, λ1)

MAµ = 〈B2, λ2|Aµ|B1, λ1〉 = u2(p2, λ2)

[g1(q2)γµ + ig2(q2)σµνqν+

g3(q2)qµ]γ5u1(p1, λ1)

qµ −→ four-momentum transfer,λ1, λ2 −→ helicities of the parent and daughter baryon,

σµν =i

2[γµ, γν ].

I We use the form factors obtained in the relativistic quark model.[D.Ebert, R.N.Faustov, V.O.Galkin; Phys.Rev.D 73,094002(2006)]

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Helicity Amplitudes

I The helicity amplitudes relevant for our calculations are thevector and axial−vector helicity amplitudes.

HV/Aλ2,λW

= MV/Aµ (λ2)ε†

µ

(λW ),

λ2 −→ helicity of the daughter baryon,λW −→ helicity of the W−off−shell,

εµ −→ polarization of the W−off−shell.

I Total helicity amplitude

Hλ2,λW = HVλ2,λW −H

Aλ2,λW .

I The helicity amplitudes are obtained in terms of form factors andthe NP couplings.

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Angular Decay distribution

The two-fold angular distribution for the B1 → B2lνl decay[S.Shivashankara, W. Wu, A. Datta; Phys.Rev.D 91,115003(2015)]

dΓ

dq2dcosθl=G2F |Vcb|

2q2|pB2|

512π3m2B1

(1−

m2l

q2

)2 [A1 +

m2l

q2A2 + 2A3 +

4ml√q2A4

],

where

A1 = 2 sin2θl

(H

212

0+H

2

− 12

0

)+ (1− cos θl)

2H

212

1+ (1 + cos θl)

2H

2

− 12−1,

A2 = 2 cos2θl

(H

212

0+H

2

− 12

0

)+ sin

2θl

(H

212

1+H

2

− 12−1

)+ 2

(H

212t

+H2

− 12t

)− 4 cos θl

(H 1

2tH 1

20

+H− 12tH− 1

20

),

A3 =

(HSP12

0

)2

+

(HSP

− 12

0

)2

,

A4 = − cos θl

(H 1

20HSP12

0+H− 1

20HSP

− 12

0

)+

(H 1

2tHSP12

0+H− 1

2tHSP

− 12

0

).

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Differential decay rate

After integrating out cos θl ,

dΓ

dq2=G2F |Vcb|

2q2|pB2|

192π3m2B1

(1−

m2l

q2

)2 [B1 +

m2l

2q2B2 +

3

2B3 +

3ml√q2B4

],

where

B1 =

(H

212

0

)+

(H

2

− 12

0

)+

(H

212

1

)+

(H

2

− 12−1

),

B2 =

(H

212

0

)+

(H

2

− 12

0

)+

(H

212

1

)+

(H

2

− 12−1

)+ 3

(H

212t

+H2

− 12t

),

B3 =

(HSP12

0

)2

+

(HSP

− 12

0

)2

,

B4 = H 12tHSP12

0+H− 1

2tHSP

− 12

0.

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q2− dependent observables

I Differential branching fraction

DBR(q2) =

(dΓ

dq2

)/Γtot

I Ratio of branching fractions

R(q2) =DBR(q2)(B1 → B2τντ )

DBR(q2)(B1 → B2lνl)

I Forward-backward asymmetry of the charged lepton

AlFB(q2) =

(∫ 0

−1−∫ 1

0

)dcosθl

dΓ

dq2dcosθl

/dΓ

dq2

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I Convexity parameter

ClF (q2) =1

Htot

d2W (θ)

d(cos θ)2,

where

W (θ) =3

8

[A1 +

m2l

q2A2 + 2A3 +

4ml√q2A4

],

Htot =

∫d(cos θ)W (θ),

d2W (θ)

d(cos θ)2=

3

4

(1−

m2l

q2

)2 [H2

121

+H2− 1

2−1− 2

(H2

120

+H2− 1

20

)].

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I Longitudinal polarization of the daughter baryon

PB2L (q2) =

dΓλ2=1/2/dq2 − dΓλ2=−1/2/dq2

dΓλ2=1/2/dq2 + dΓλ2=−1/2/dq2

I Longitudinal polarization of the charged lepton

P τL(q2) =dΓλτ=1/2/dq2 − dΓλτ=−1/2/dq2

dΓλτ=1/2/dq2 + dΓλτ=−1/2/dq2

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Constraints on New Couplings

I NP couplings are constrained from the observables RD∗ , RJ/ψand B(B+

c → τ+ντ ).

I The world average value of RD∗ reported by HFLAV is

RExptD∗ =B(B → D∗τ−ντ )

B(B → D∗l−νl)= 0.295± 0.011± 0.008

I LHCb measured the value of RJ/ψ

RExptJ/ψ

=B(B → J/ψτ−ντ )

B(B → J/ψl−νl)= 0.71± 0.17± 0.18

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I The differential branching fraction of B → D∗(J/ψ)l−νl is givenby [Y.Sakaki, M.Tanaka, A.Tayduganov, R.Watanabe, Phys.Rev.D 88, 094012(2013);

R.Watanabe, Phys.Lett.B 776, 5(2018)]

dBR(B → D∗(J/ψ)l−νl)

dq2= τB

G2F |Vcb|

2q2|pD∗(J/ψ)|192π3m2

B1

(1−

m2l

q2

)2

×

(|1 + CVL |2

+ |CVR |2)

[(1 +

m2l

2q2

)(H

2V,0 +H

2V,+ +H

2V,−

)

+3

2

m2l

q2H

2V,t

]− 2Re

[(1 + CVL

)C∗VR

] [(1 +

m2l

2q2

)(H

2V,0 + 2HV,+HV,−

)+

3

2

m2l

q2H

2V,t

]+

3

2|CSL − CSR |

2H

2S

+ 3Re[(

1 + CVL − CVR) (C∗SL− C∗SR

)] ml√q2HSHV,t

,

where HV,0, HV,±, HV,t and HS are the hadronic helicity amplitudes.

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I The branching fraction of B+c → τ+ντ decay is given by

[P.Biancofiore, P.Colangelo, F.DeFazio; Phys.Rev.D 87, 074010(2013)]

B(B+c → τ+ντ ) =

G2F |Vcb|

2m2τ

8πτBcmBcf

2Bc

(1−

m2τ

m2Bc

)2

×∣∣∣∣(1 + CVL − CVR )−

m2Bc

mτ (mb +mc)(CSL − CSR )

∣∣∣∣2

I The experimental upper limit on B(B+c → τ+ντ ) is [A.G.Akeroyd,

C.H.Chen; Phys.Rev.D 96, 075011(2017)]

B+c → τ+ντ . 30%

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I The best-fit values are obtained using χ2 fitting.

NP Coupling Best-fit value 1σ rangeCVL 0.072 [0.051, 0.093]CVR -0.048 [-0.063, -0.034]CSL 0.549 [0.402, 0.685]CSR -0.549 [-0.685, -0.402]

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Results for the

Ωb → Ωcτ−ντ Decay Mode

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Differential branching fraction DBR(q2)

Figure 1: The differential branching fraction DBR(q2) for the Ωb → Ωcτ−ντ in different NP

scenarios.

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Ratio of branching fractions R(q2)

Figure 2: The ratio of branching fractions RΩc(q2) for the Ωb → Ωcτ

−ντ in different NP scenarios.

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Forward-Backward Asymmetry AlFB(q2)

Figure 3: The Forward-Backward Asymmetry of the charged lepton AτFB(q2) for the Ωb → Ωcτ−ντ

in different NP scenarios.

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Convexity parameter ClF (q2)

Figure 4: Convexity parameter CτF (q2) for the Ωb → Ωcτ−ντ in different NP scenarios.

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Longitudinal Polarization of the daughter baryon PB2L (q2)

Figure 5: Longitudinal Polarization of the daughter baryon PΩcL

(q2) for the Ωb → Ωcτ−ντ in

different NP scenarios.

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Longitudinal Polarization of the charged lepton P τL(q2)

Figure 6: Longitudinal Polarization of the charged lepton PτL(q2) for the Ωb → Ωcτ−ντ in different

NP scenarios.

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Results for the

Ξb → Ξcτ−ντ Decay Mode

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Differential branching fraction DBR(q2)

Figure 7: The differential branching fraction DBR(q2) for the Ξb → Ξcτ−ντ in different NP

scenarios.

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Ratio of branching fractions R(q2)

Figure 8: The ratio of branching fractions RΞc(q2) for the Ξb → Ξcτ

−ντ in different NP scenarios.

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Forward-Backward Asymmetry AlFB(q2)

Figure 9: The Forward-Backward Asymmetry of the charged lepton AτFB(q2) for the Ξb → Ξcτ−ντ

in different NP scenarios.

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Convexity parameter ClF (q2)

Figure 10: Convexity parameter CτF (q2) for the Ξb → Ξcτ−ντ in different NP scenarios.

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Longitudinal Polarization of the daughter baryon PB2L (q2)

Figure 11: Longitudinal Polarization of the daughter baryon PΞcL

(q2) for the Ξb → Ξcτ−ντ in

different NP scenarios.

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Longitudinal Polarization of the charged lepton P τL(q2)

Figure 12: Longitudinal Polarization of the charged lepton PτL(q2) for the Ξb → Ξcτ−ντ in different

NP scenarios.

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Summary

I Ωb → Ωcτ−ντ and Ξb → Ξcτ

−ντ decay modes are analyzed within theSM and beyond.

I The best-fit values of the NP couplings are obtained using a χ2

analysis.

I Predictions for various q2 dependent observables such as DBR(q2),R(q2), AlFB(q2), ClF (q2), PB2

L (q2) and P τL(q2) are presented in the SMand in various NP scenarios.

I The observables are sensitive to NP effects. Deviations from the SMprediction is more pronounced in case of scalar NP couplings than thatwith the vector NP couplings.

I The b−baryon decay modes mediated by b→ clνl can act ascomplementary decay channels to b−meson decays with regards to NP.

I Search for physics beyond SM will be enriched by studies of such

modes also.

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Thank You

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