probing effects of new physics in semi-hadronic three-body...

Probing effects of new physics insemi-hadronic three-body meson decays

by using angular distribution

Dibyakrupa Sahoo

Department of Physics & IPAPYonsei University, Seoul, Korea

In collaboration with Prof. C. S. Kimand Prof. Seong Chan Park

The 8th KIAS Workshop on Particle Physics and Cosmology

1 November 2018

Plan of the talk

SM

Glorioussuccess

Glaringlacunae

BSMPlet

ho

ra of NP models

Model-independent approach:not biased to any particular

NP modelPr

obing BSM

Specific decays

Signatures of NP

Experimental observables

The Standard Model of particle physics is one of the mostsuccessful theories of our times.

The various interactions of elementary particles as observed in manyparticle physics experiments is very well described by the SM.

Some of the most cherished success stories of SM include,

v Prediction and discovery of the Higgs boson, W±, Z0, gluons, top,bottom and charm quarks.

v Quark mixing matrix and CP violation in meson sector.

v Prediction of one electroweak mixing angle.

v Precisely accounting for various decays of Z0.

v Precise prediction of anomalous magnetic dipole moment ofelectron.

SM accomplishes an incomplete description of ourobservable universe at its most fundamental level.

The Standard Model of particle physics (SM) fails to answer,

1. What is the quantum description of gravity?2. What are the constituents of dark matter, and what is dark energy?3. How to explain the matter anti-matter asymmetry observed in our

universe?4. How do neutrinos get such tiny masses?5. How to describe the observed muon anomalous magnetic dipole

moment (g− 2)?6. Why is there no CP violation in strong interaction?7. Is there any physical understanding of the plethora of SM

parameters?8. Why do quarks and leptons appear in three families?9. How to unify the strong and electroweak interactions?

. . . and so on.

Despite its glaring lacunae, SM is our best description of theexperimentally observed zoo of elementary particles except theneutrinos.

With insufficient experimental guidance we are lost inthe rain-forest of Beyond SM scenarios (New Physics).

We have many beyond standard model scenarios (New Physicspossibilities):

v Grand Unified Theories (SU(5), SU(8), SO(10), . . .),

v Supersymmetry (MSSM, NMSSM, . . .),

v Extra dimensions (Large ED, warped ED, universal ED, . . .),

v Neutrino mass models (see-saw, inverse see-saw, . . .),

v Dark matter models (WIMP, SIMP, Axions, . . .),

v Two-Higgs-doublet model,

v Technicolor,

v Preonic models (Rishon model, Quantum Haplodynamics, . . .),

v Quantum gravity (loop quantum gravity, SUGRA, . . .),

v String theory, . . . etc.

Experiment is the touchstone of all new physics possibilities.

Our best strategy to search for new physics isto look for its model-independent signatures.

v With so many new physics (NP) models around, how do we figureout which model is the correct one.

v Besides, how can we ensure that all conceivable NP possibilitieshave already been taken care of by existing NP models.

v We need results from more particle physics experiments, concerningvarious processes that have not been considered so far, to get abetter indication of the nature of NP.

v Would it not be better to know how NP, without considering anyspecific NP model, would affect some processes in a very generalmanner (except enhancing the probability of their occurance)?

v This is precisely the place where a model-independent analysis of NPplays a very significant role.

Heavy flavor physics is a very popular areawhere new physics contributions are favourable.

v Heavy flavor physics, mostly involving B decays have been afavourite hunting ground for various new physics searches.

v Recent experimental results from LHCb† on R(K(∗)), R(D(∗)), R(J/ψ)suggest new physics might just be around the corner.

v Thus analyzing three-body heavy meson decays, in a modelindependent manner, is very interesting for new physics studies.

† JHEP 1708, 055 (2017);PRL 115, no. 11, 111803 (2015),

Erratum: [PRL 115, no. 15, 159901 (2015)];PRL 120, no. 12, 121801 (2018).

We shall consider a fully model independent analysis ofdecays of the type Pi→ Pf f1 f2 and look for genericsignatures of new physics.

An effective model independent probe of effects of new physics in a largenumber of heavy meson decays can be analyzed by studying the decayPi→ Pf f1 f2, where Pi, Pf are well chosen pseudo-scalar mesons and f1,2denote fermions (which may or may not be leptons) out of which at leastone gets detected in experiments.

The masses of particles Pi, Pf , f1 and f2 are denoted by mi, mf , m1 and m2respectively.

The most general Lagrangian for Pi→ Pf f1 f2 decays.

Pi (k)

f1 (k1)

f2 (k2)

P f (k3) Leff =JS

�

f̄1f2�

+ JP

�

f̄1 γ5 f2�

+ (JV)α�

f̄1 γα f2

�

+ (JA)α�

f̄1 γαγ5 f2

�

+�

JT1

�

αβ

�

f̄1 σαβ f2

�

+�

JT2

�

αβ

�

f̄1 σαβγ5 f2

�

+ h.c.,

where JS, JP, (JV)α, (JA)α,�

JT1

�

αβ,�

JT2

�

αβare the different hadronic

currents which effectively describe the Pi→ Pf quark level transitions.

The most general amplitude for Pi→ Pf f1 f2 decays.

Pi (k)

f1 (k1)

f2 (k2)

P f (k3) M�

Pi→ Pf f1f2�

= FS

�

f̄1f2�

+ FP

�

f̄1 γ5 f2�

+�

F+V pα + F−V qα� �

f̄1 γα f2

�

+�

F+A pα + F−A qα� �

f̄1 γα γ5 f2

�

+ FT1pα qβ

�

f̄1 σαβ f2

�

+ FT2pα qβ

�

f̄1 σαβ γ5 f2

�

,

where FS, FP, F±V , F±A , FT1and FT2

are the relevant form factors, withp≡ k+ k3 and q≡ k− k3 = k1 + k2.

In the SM, only vector and axial-vector currents (mediated by photon,W± and Z0 bosons) and the scalar current (mediated by the Higgs boson)contribute.

All new physics information is contained in the form factors.

We analyse the Pi→ Pf f1 f2 decaysin the Gottfried-Jackson frame.

zPi(k)

f1(k1)

f2(k2)

P f (k3)

θ

Notation á la Mandelstam:

s= (k1 + k2)2 = (k− k3)

2,

t= (k1 + k3)2 = at − b cosθ ,

u= (k2 + k3)2 = au + b cosθ .

where

at =m21 +m2

f +12s

�

s+m21 −m2

2

�

�

m2i −m2

f − s�

,

au =m22 +m2

f +12s

�

s−m21 +m2

2

�

�

m2i −m2

f − s�

,

b=12s

r

λ�

s, m21, m2

2

�

λ�

s, m2i , m2

f

�

,

with λ(x, y, z) = x2 + y2 + z2 − 2 (xy+ yz+ zx).

The angular distribution for Pi→ Pf f1 f2 decayshas three distinct parts.

d2Γ

ds d cosθ=

bp

s�

C0 + C1 cosθ + C2 cos2 θ�

128π3 m2i

�

m2i −m2

f + s� .

Here the coefficients C0, C1 and C2 contain all the NP informationthat we can extract from the angular distribution.

Owing to the generalness of the amplitude, these coefficients havegot complicated expressions.

C0 =2

�

−�

�FT1

�

�

2�

−Σm212s2 + 2Σm2

12

�

Σm2�

if s+�

∆m2�2

12 s−∆a2tus− 2

�

∆m2�2

12

�

Σm2�

if −�

∆m2�2

if Σm212 + 2∆atu

�

∆m2�

12

�

∆m2�

if

�

− 2Im�

F+V F∗T1

�

�

−Σm12s2 + 2Σm12

�

Σm2�

if s+∆m12

�

∆m2�

12 s− 2∆m12

�

∆m2�

12

�

Σm2�

if −�

∆m2�2

if Σm12 +∆atu∆m12

�

∆m2�

if

�

+�

�FT2

�

�

2�

∆m212s2 − 2∆m2

12

�

Σm2�

if s−�

∆m2�2

12 s+∆a2tus+ 2

�

∆m2�2

12

�

Σm2�

if +∆m212

�

∆m2�2

if − 2∆atu

�

∆m2�

12

�

∆m2�

if

�

− 2Im�

F+A F∗T2

�

�

∆m12s2 − 2∆m12

�

Σm2�

if s−�

∆m2�

12Σm12s+ 2�

∆m2�

12Σm12

�

Σm2�

if −∆atu

�

∆m2�

if Σm12 +∆m12

�

∆m2�2

if

�

+�

�F+A�

�

2�

s2 − 2�

Σm2�

if s−Σm212s+ 2Σm2

12

�

Σm2�

if +�

∆m2�2

if −∆a2tu

�

+�

�F+V�

�

2�

s2 − 2�

Σm2�

if s−∆m212s+ 2∆m2

12

�

Σm2�

if +�

∆m2�2

if −∆a2tu

�

+�

�F−A�

�

2 �

Σm212s−

�

∆m2�2

12

�

− 2Re�

FPF−∗A

� �

Σm12s−∆m12

�

∆m2�

12

�

−�

�F−V�

�

2 ��∆m2

�2

12 −∆m212s�

− 2Re�

FSF−∗V

� ��

∆m2�

12Σm12 −∆m12s�

− |FS|2 �Σm2

12 − s�

− |FP|2 �∆m2

12 − s�

+ 2Re�

F+A F−∗A

�

�

�

∆m2�

if Σm212 −∆atu

�

∆m2�

12

�

− 2Re�

FPF+∗A

�

�

�

∆m2�

if Σm12 −∆atu∆m12

�

− 2Re�

FSF+∗V

�

�

∆atuΣm12 −∆m12

�

∆m2�

if

�

+ 2Re�

F+V F−∗V

�

�

∆m212

�

∆m2�

if −∆atu

�

∆m2�

12

�

�

,

C1 =8b

�

∆m12

�

Im�

F−V F∗T1

�

s−Re�

FPF+∗A

�

�

+Σm12

�

− Im�

F−A F∗T2

�

s+Re�

FSF+∗V

�

−�

∆m2�

if Im�

F+A F∗T2

��

+∆atu

��

−�

�FT2

�

�

2 −�

�FT1

�

�

2�

s+�

�F+V�

�

2+�

�F+A�

�

2�

+�

Im�

FSF∗T1

�

+ Im�

FPF∗T2

��

s

+�

∆m2�

12

�

Re�

F+V F−∗V

�

+Re�

F+A F−∗A

��

+�

∆m2�

if

�

∆m12Im�

F+V F∗T1

�

+�

∆m2�

12

��

�FT2

�

�

2+�

�FT1

�

�

2��

�

,

C2 =8b2��

�FT2

�

�

2+�

�FT1

�

�

2�

s−�

�F+V�

�

2 −�

�F+A�

�

2�

,

The expressions for the coefficients C0, C1 and C2 become simpler if weconsider the SM contribution alone, as FP = FT1

= FT2= 0 in the SM.

We define three angular asymmetries that are sensitive tothe three distinct parts of the angular distribution.

A0 ≡ A0(s) =− 1

6

�

∫ −1/2

−1 −7∫ +1/2

−1/2 +∫ +1

+1/2

� d2Γ

dsd cosθd cosθ

dΓ/ds=

3C0

6C0 + 2C2,

A1 ≡ A1(s) =−�

∫ 0

−1−∫ +1

0

� d2Γ

dsd cosθd cosθ

dΓ/ds=

3C1

6C0 + 2C2,

A2 ≡ A2(s) =2�

∫ −1/2

−1 −∫ +1/2

−1/2 +∫ +1

+1/2

� d2Γ

ds d cosθd cosθ

dΓ/ds=

3C2

6C0 + 2C2.

The feature of three distinct angular components is alsothe most general feature after integration over s.

We can do the integration over s and define the following normalizedangular distribution,

1Γ

dΓd cosθ

= T0 + T1 cosθ + T2 cos2 θ ,

where

Tj =3cj

6c0 + 2c2,

for j= 0,1, 2 and with

cj =

∫ (mi−mf )2

(m1+m2)2

bp

s Cj

128π3m2i

�

m2i −m2

f + s�ds.

The three angular components can be easily measuredfrom the Dalitz plot distribution for Pi→ Pf f1 f2 decays.

T0 = −16

�

NI − 7 (NII +NIII) +NIV

NI +NII +NIII +NIV

�

,

T1 =(NI +NII)− (NIII +NIV)

NI +NII +NIII +NIV,

T2 = 2�

NI − (NII +NIII) +NIV

NI +NII +NIII +NIV

�

,

where Ni denotes the numberof events in the ith segment ofthe Dalitz plot.

This is an easier methodwhen the Dalitz plot can beconstructed.

0

10

20

30 B→ Dµ−µ+

0

10

20

30

0 10 20 30

B→ Kνν̄

u( G

eV2)

−1

−0.5

0

0.5

1

cosθ

I

II

III

IV

III

III

IV

u( G

eV2)

t(GeV2

)

I

II

III

IV

An example showing the effect of new physicson angular distribution.The example process

v We choose a process for which the construction of Dalitz plot is notpossible. This is especially true if in Pi→ Pf f1 f2 the two fermionsare missing, such as the case when they are neutrino, anti-neutrino(active or sterile) or some long-lived particles or fermionic darkmatter particles.

v We assume that in future with advanced detectors we could at leastmeasure some sort of displaced vertex corresponding to theinteraction of either of the fermions with the detector material sothat one could deduce the angle θ in the Gottfried-Jackson frame.

v As a specific case let us consider B→ Kνν̄. Also, we shall considertwo specific NP contributions: scalar type and vector type NPcontributions, just to illustrate our methodology.

An example showing the effect of new physicson angular distribution.SM contribution

v Only vector and axial vector currents contribute and F±A = −F±V .

v Angular distribution:

d2Γ SM

ds d cosθ=

b3ps

8π3 m2B

�

m2B −m2

K + s�

�

�

�

F+V�

SM

�

�

2sin2 θ .

Or1Γ SM

dΓ SM

d cosθ=

34

sin2 θ ,

which implies that T0 = 3/4= −T2, T1 = 0.

An example showing the effect of new physicson angular distribution.Scalar type NP contribution

v We consider FS 6= 0, FP = F±V = F±A = FT1= FT2

= 0.v Angular distribution (NP only):

d2ΓNP

ds d cosθ=

bp

s

64π3 m2B

�

m2B −m2

K + s�

�

s− 4m2�

|FS|2 .

Or1ΓNP

dΓNP

d cosθ=

12

.

v Angular distribution(SM + NP):

1Γ

dΓd cosθ

=3 sin2 θ + 2ε

4 (1+ ε),

where the effect of NP isparametrized by ε= ΓNP/Γ SM.

0

0.2

0.4

0.6

0.8

−1 −0.5 0 0.5 1

1Γ

dΓd cos θ

cos θ

SM0

0.2

0.4

0.6

0.8

1

ε

An example showing the effect of new physicson angular distribution.Vector type NP contribution

v We consider F+V = FNPV 6= 0 and other form factors are zero.

v Angular distribution (NP only):

d2ΓNP

ds d cosθ=

b�

�FNPV

�

�

2λ�

s, m2B, m2

K

� �

s sin2 θ + 4m2 cos2 θ�

64π3 m2B

�

m2B −m2

K + s�p

s.

Or1ΓNP

dΓNP

d cosθ=

3�

S sin2 θ +C cos2 θ�

2(2S +C ),

where

S =∫ (mB−mK)2

4m2

dΓNP

ds

� ss+ 2m2

�

ds,

C =∫ (mB−mK)2

4m2

dΓNP

ds

�

4m2

s+ 2m2

�

ds.


v Angular distribution (SM + NP):

1Γ

dΓd cosθ

=3 (1+ εs) sin

2 θ + 3εc cos2 θ

4 (1+ εs) + 2εc.

whereεs = S /Γ SM, εc =C /Γ SM,

are the two parameters that describe the effect of vector NP.

v If we consider the mass of the fermion f to be zero, i.e. m= 0, thenC = 0 =⇒ εc = 0. In such a case we get back the SM result, as thissituation is indistinguishable from the SM case.


v Assuming 0¶ ΓNP ¶ Γ SM, we get 0¶ εs ¶ 1 and 0¶ εc ¶ 2(1− εs).

0

0.2

0.4

0.6

0.8

0

0.2

0.4

0.6

0.8

0

0.2

0.4

0.6

0.8

−1−0.5 0 0.5 1 −1−0.5 0 0.5 1 −1−0.5 0 0.5 1

1Γ

dΓ

d cos θ

SM

0

0.5

1

1.5

2

εc

εs = 0

SM

εs = 0.125

SM

εs = 0.25

1Γ

dΓ

d cos θ

SM

εs = 0.375

SM

εs = 0.5

SM

εs = 0.625

1Γ

dΓ

d cos θ

cos θ

SM

εs = 0.75

cos θ

SM

εs = 0.875

cos θ

SM

εs = 1

An example showing the effect of new physicson angular distribution.Discussion

v Both scalar type and vector type new physics effects vanish atcosθ = ±1/

p3. The fundamental reason for this is the absence of

any term linear in cosθ in the angular distribution.

v Vector type of new physics can accommodate much larger variationin angular distribution than the scalar type scenario.

v However, when ε=3εc

2 (1+ εs − εc), both scalar type and vector type

new physics contributions give similar angular distribution.

v In any case, we are able to look into the effects of NP in a way whichis not affected by hadronic uncertainties in form factors etc.

v This provides a methodology to parametrize and constraint NPcontributions in a model independent manner.

Conclusion

v Any NP contribution in Pi→ Pf f1 f2 decays, irrespective of theparticulars of NP model, would leave behind some genericsignatures in the corresponding Dalitz plot or angular distribution,which can be quantified by easily observable angular asymmetriesA0, A1 and A2 (or T0, T1 and T2).

v In certain cases, NP can be searched for and constrained in a fullyexact manner without any hadronic uncertainties.

Thank you

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