vector vs. scalar nsi’s, light mediators,
TRANSCRIPT
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!