Vector vs. Scalar NSI’s,Light Mediators,

and other considerations

Tatsu Takeuchi, Virginia TechApril 27, 2019 Amherst Center for Fundamental Interactions“Neutrino-Electron Scattering at Low Energies”

Collaboratorsv Sofiane M. Boucenna (INFN, Italy)

v David Vanegas Forero (U. of Campinas, Brazil)v Patrick Huber (Virginia Tech)

v Ian Shoemaker (Virginia Tech)

v Chen Sun (Brown)

Non-Standard Interactions:v Effects of new physics at low energies can be expressed via dimension-six four-fermion operatorsv There are five types:

v Operators relevant for neutrino-electron scattering are those in which two of the operators are neutrinos and the other two operators are electrons

Fierz Identities

Fierz Identities for Chiral Fieldsv LL, RR cases

v LR, RL cases

Fierz Transformation Example:

v neutrino-electron interaction from W exchange :

v neutrino-electron interaction from Z exchange :

New Physics:

v Vector exchange:

v Scalar exchange:

Fierz Transformed New Physics:

v Charged vector exchange:

vCharged scalar exchange:

Vector and Scalar NSI:v Vector NSI’s :

v See talk by Chen Sun from yesterday

v Scalar NSI’s :

v Shao-Feng Ge and Stephen J. Parke, arXiv:1812.08376

Effect of Scalar NSI to Neutrino Propagation:v Shao-Feng Ge and Stephen J. Parke, arXiv:1812.08376

v In matter:

v Mass matrix is shifted:

Bounds from Borexino:v Shao-Feng Ge and Stephen J. Parke, arXiv:1812.08376

v electron-neutrino survival probability:

Vector NSI’sScalar NSI’s

Further points to consider:v The Ge-Parke analysis assumes Dirac massesv If neutrino masses are Majorana

v There is also a matter potential effect:

Can we generate large NSI’s?

v Generating large NSI’s from heavy mediators is very difficult

v Can light mediators help us?

Interactions must be SU(2) x U(1) invariant:

v Case 1:

Constrained by ! → #$$ : %&'() < 10-.

v Case 2:

Constrained by µ → $0(0', ! → $0(0&, ! → #0(0( : %&'() < 10-2

Farzan-Shoemaker Modelv Y. Farzan and I. M. Shoemaker, “Lepton Flavor Violating Non-Standard Interactions via Light Mediators,” JHEP07(2016)033, arXiv:1512.09147

v Is the model truely viable?

"qCµ⌧ ⇠ 0.005 ! "µ⌧ ⇠ 0.06

Farzan-Shoemaker Model : Fermion Contentv SU(3)C × SU(2)L × U(1)Y × U(1)’ gauge theoryv Quarks:

v Leptons:

v Extra (heavy) fermions for anomaly cancellation (?)

Qi =

uLi

dLi

�⇠

✓3, 2,+

1

6, 1

◆, uRi ⇠

✓3, 1,+

2

3, 1

◆, dRi ⇠

✓3, 1,�1

3, 1

◆

L0 =

⌫L0

`L0

�⇠

✓1, 2,�1

2, 0

◆, `R0 ⇠ (1, 1,�1, 0) ,

L+ =

⌫L+

`L+

�⇠

✓1, 2,�1

2,+⇣

◆, `R+ ⇠ (1, 1,�1,+⇣) ,

L� =

⌫L�`L�

�⇠

✓1, 2,�1

2,�⇣

◆, `R� ⇠ (1, 1,�1,�⇣) ,

Farzan-Shoemaker Model : Scalar Contentv Higgses:

v Yukawa couplings:

H =

H

+

H0

�⇠

✓1, 2,+

1

2, 0

◆,

H++ =

H

+++

H0++

�⇠

✓1, 2,+

1

2,+2⇣

◆,

H�� =

H

+��

H0��

�⇠

✓1, 2,+

1

2,�2⇣

◆.

3X

i=1

3X

j=1

⇣�ijdRiH

†Qj + �̃ijuRi

eH†Qj

⌘+ h.c.

+X

j=0,+,�

�fj `RjH

†Lj

�+ h.c.

+⇣c�`R+H

†��L� + c+`R�H

†++L+

⌘+ h.c.

Farzan-Shoemaker Model : Symmetry Breakingv Higgs VEV’s:

v Assume (no Z-Z’ or !-Z’ mixing at tree-level)

v Gauge boson masses:

hH0i =vp2, hH0

++i =v+p2, hH0

��i =v�p2,

v+ = v� =wp2

MW =g22

pv2 + w2 , MZ =

pg21 + g222

pv2 + w2 , MZ0 = 2⇣g0w

Farzan-Shoemaker Model : Z’ Mass & Couplingv The mass of the Z’ is chosen to be:

so that the decays

cannot occurv Range of the Z’-exchange force comparable to that of strong interactions → Z’ interactions between quarks can be sizable but still be masked by the strong force (?)v Z’ coupling to the leptons are strongly constrained by:

135MeV < MZ0 < 200MeV

⇡0 ! � + Z 0 , Z 0 ! µ+ + µ�

⌧ ! µ+ Z 0

Farzan-Shoemaker Model : Problemsv U(1) charges are ill defined in models with multiple U(1)’s → They necessarily mix under renormalization group running(See W. A. Loinaz and T. Takeuchi, Phys.Rev. D60 (1999) 115008)

v Constraint on !g’ does not allow the generation of Z’ mass in the 135∼200 MeV range without making the Higgs VEV w too large for the W and Z masses→ Need to introduce a SM-singlet scalar

v Full MNS neutrino mixing matrix cannot be generated.The U(1)’ singlet lepton cannot mix with the non-singlet leptons.→ Need to introduce a more scalars

v Not clear whether the fermions necessary for anomaly cancelation can be made heavy → Even more scalars?

Constraints on the Z’ couplings revisited:v Z’-quark couplingv Z’-lepton coupling

v Semi-Empirical Mass Formula of Nuclei:

v Coulomb term:

EB = aV A� aSA2/3 � aC

Z2

A1/3� aA

(A� 2Z)2

A± �(A,Z)

EC =3

5

Q2

R=

3

5

(eZ)2

(r0A1/3)= (0.691MeV)

(1.25 fm)

r0

Z2

A1/3

Z’ potential energy:v Z’ potential energy term:

where

EZ0 =3

5

Q02

Rf(mR) =

3

5

(3g0A)2

(r0A1/3)f(mr0A

1/3)

= (0.691MeV)(1.25 fm)

r0

✓3g0

e

◆2

A5/3f(mr0A1/3)

f(x) ⌘ 15

4x5

"1� x2 +

2x3

3� (1 + x)2e�2x

#

= 1� 5x

6+

3x2

7� x3

6+ · · ·

0 2 4 6 8 10x

0.2

0.4

0.6

0.8

1.0

Result of Fit:v Our result from fit to stable nuclei (90% C.L. left) compared to Figure from Farzan-Shoemaker paper (JHEP07(2016)033 right)

g'

mZ' [MeV]

r0=1.2 fmr0=1.22 fmr0=1.25 fmr0=1.3 fm

10-6

10-5

10-4

10-3

10-2

10-1

100

1 10 100

Excluded

Result of Fit:

r0=1.30 fm

r0=1.22 fm

-2.0 -1.5 -1.0 -0.5 0.00

50

100

150

200

Log10(g′)

MZ′ /MeV

Coupling to the electron from photon-Z’ mixing:v Recall that ! → #$$ is strongly bounded:

%(!' → #'$'$() < 1.8 × 10',

v At tree level the Z’ does not couple to electronsv But Z’ and the photon can mix!

Optical Theorem:

photon-photon and photon-Z’ correlations:

Separation of Isovector and Isoscalar parts:

Dolinsky Isoscalar + BW resonance

Total R ratio

0.5 1.0 1.5 2.00.1

1

10

100

1000

s /GeV

R

Running of the effective coupling to electrons:

Resulting bounds:

Does this bound apply?v For the Z’ decay into an electron-positron decay to be observable, the Z’ must decay inside the detector

v Belle central drift chamber:Z’ must decay within 0.88 m to 1.7 m

Two-body decay bound:v Argus (1995)

v Belle has 2000 times more statistics and is expected to improve the bound to 1×10$% (Yoshinobu and Hayasaka, Nucl. Part. Phys. Proc. 287-288 (2017) 218-220)

Conclusion :v Both g’ and g’! are more tightly bound than originally assumed

v Constructing viable models that predict sizable neutrino NSI’s is not easy!