Vector vs. Scalar NSIs, Light Mediators, and other considerations - - PowerPoint PPT Presentation

Vector vs. Scalar NSI’s, Light Mediators, and other considerations

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

Collaborators

v 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 operators v 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

• perators are electrons

Fierz Identities

Fierz Identities for Chiral Fields

v 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’s Scalar NSI’s

Further points to consider:

v The Ge-Parke analysis assumes Dirac masses v 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 Model

v 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? εqC

µτ ∼ 0.005

→ εµτ ∼ 0.06

Farzan-Shoemaker Model : Fermion Content

v SU(3)C × SU(2)L × U(1)Y × U(1)’ gauge theory v 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 Content

v Higgses: v Yukawa couplings:

H = H+ H0

• ∼

✓ 1, 2, +1 2, 0 ◆ , H++ =  H+

++

H0

++

• ∼

✓ 1, 2, +1 2, +2ζ ◆ , H−− =  H+

−−

H0

−−

• ∼

✓ 1, 2, +1 2, −2ζ ◆ .

3

X

i=1 3

X

j=1

⇣ ijdRiH†Qj + ˜ ijuRi e H†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 Breaking

v Higgs VEV’s: v Assume (no Z-Z’ or !-Z’ mixing at tree-level) v Gauge boson masses:

hH0i = v p 2 , hH0

++i = v+

p 2 , hH0

−−i = v−

p 2 ,

v+ = v− = w √ 2

MW = g2 2 p v2 + w2 , MZ = p g2

1 + g2 2

2 p v2 + w2 , MZ0 = 2ζg0w

Farzan-Shoemaker Model : Z’ Mass & Coupling

v The mass of the Z’ is chosen to be: so that the decays cannot occur v 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: 135 MeV < MZ0 < 200 MeV π0 → γ + Z0 , Z0 → µ+ + µ τ → µ + Z0

Farzan-Shoemaker Model : Problems

v 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 coupling v 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 ± δ(A, Z) EC = 3 5 Q2 R = 3 5 (eZ)2 (r0A1/3) = (0.691 MeV)(1.25 fm) r0 Z2 A1/3

Z’ potential energy:

v Z’ potential energy term: where

EZ0 = 3 5 Q02 R f(mR) = 3 5 (3g0A)2 (r0A1/3)f(mr0A1/3) = (0.691 MeV)(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 + · · ·

2 4 6 8 10 x 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 fm r0=1.22 fm r0=1.25 fm r0=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

0.0 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 electrons v 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 2.0 0.1 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

• bservable, 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!