non-standard neutrino interactionskth.diva-portal.org/smash/get/diva2:392925/fulltext01.pdf ·...

Non-Standard Neutrino Interactions

Tommy Ohlsson

Department of Theoretical Physics, School of Engineering Sciences, Royal Institute of Technology (KTH) -AlbaNova University Center, Roslagstullsbacken 21,106 91 Stockholm, Sweden

Abstract. In this talk, I will review non-standard interactions in neutrino physics, especially I will emphazise the impact of non-standard interactions on neutrino oscillations. First, I will give a brief introduction about non-standard interactions and what they are. Then, I will present what has been performed in the literature, what I have done in the field, and what could be done in the fiiture. Next, I will discuss how important non-standard interactions are for neutrino cross-sections. Finally, I will give a summary of the field.

Keywords: neutrino physics, non-standard interactions, neutrino cross-sections PACS: 13.15.+g; 14.60.Pq; 14.60.St

I N T R O D U C T I O N TO N E U T R I N O OSCILLATIONS

Indeed, there are now strong evidences that neutrinos are massive and lepton flavors are mixed. The lepton flavor mixing is usually defined through the leptonic mixing matrix V that can be written as

Ve\ Ve2 Vei

V^i V^2 K 3 I I V2 I , (1) Vri V,2 V,3

which relates the weak interaction eigenstates and the mass eigenstates through the leptonic mixing parameters Ou, 013, 023, S (the Dirac CP-violating phase), as weU as p and a (the Majorana CP-violating phases). In the so-caUed standard parameterization, V is given by

cos 012 sin 012 0 V=\0 COS023 sin023 1 I 0 1 0 | | -sin0i2 cos0i2 0 | ( 0 e" O ) . (2)

0 0 1

Furthermore, since in the Standard Model neutrinos are massless particles, the SM must be extended by adding neutrino masses.

The time evolution of the neutrino vector of state v = (Vg v^ Vf) describing neutrino oscillations is given by a Schrodinger-like equation, namely,

.dv ^d7

0 0

0 COS 023

- sin 023

' \ Sin023 cos 023/

/ COS 013

0 \ - s i n 0 i 3 e ' ^

0 1 0

sin0i3e-'^ 0

cos 013

-^MM^ + Vit) (3)

where E is the neutrino energy, M = VAmg{m\,m2,m3)V^ is the neutrino mass matrix, and V{t) = y^GpNe is the effective matter potential (i.e., the charged-current contribution to the matter-induced potential of electron neutrinos). Here, mi, m2, and m^ are the definite masses of the neutrino mass eigenstates and A/g is the electron density of matter Quantum mechanically, the transition probability amplitudes are given as overlaps of different neutrino states, and finally, neutrino oscillation probabilities are defined as squared absolute values of the transition probability amplitudes. Thus, flavor changing happens during the propagation of neutrinos. For example, in a two-flavor illustration (in vacuum) with electron and muon neutrinos, a neutrino state can be in a pure electron neutrino state at one time, whereas it can be in a pure muon neutrino state at another time.

Using global fits on data of neutrino oscillation experiments (and especially, resuhs from long-baseline neutrino experiments including matter effects), the values given in Table 1 have been obtained for the fimdamental neutrino oscillation parameters [1]. Note that these values have been found not taken NSIs into account. Open questions that exist are: Is 0i3 = 0? What is the sign of the large mass-squared difference Amj^l Are neutrinos Dirac or

CPU 89, From Sixth International Workshop on Neutrino-Nucleus Interactions in the Few-GeVRegion, edited by F. Sanchez, M. Sorel, L. Alvarez-Ruso, A. Cervera, and M. Vicente-Vacas

O 2009 American Institute of Physics 978-0-7354-0725-l/09/$25.00

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Am j [10--|Amf J1 [10-

sin^012 sin^ 023 sin^ 013

eV^] -^ eV^]

' • "^ -0 .20 2 40+°-12 ^•^^-0.11

0 304+°-°22 0 50+°-°^ QQ1+0.016 ^•^^-0.011

TABLE 1. Present values of the neutrino oscillation parameters

parameter best-fit value 2(7 3(7

7.25^8.11 7.05^8.34

2.18^2.64 2.07^2.75 0.27^0.35 0.25^0.37 0.39^0.63 0.36^0.67

< 0.040 < 0.056

Majorana particles? What is the absolute neutrino mass scale? Is there leptonic CP violation? Do sterile neutrinos exist? The timeline of the experimental steps to undertake in order to try to find answers to the above questions is the following. First, one has to improve present measurements on "solar" (Amli and Ou) and "atmospheric" (Awjj and 023) parameters. Then, one has to discover the value of the tiny mixing angle 0i3, which will be tried at the Daya Bay and Double Chooz experiments. Next, one should try to obtain some hints about the CP-violating phase 5 in future long-baseline experiments such as a neutrino factory or a /3-beam experiment. However, recently, one has been concerned with the two following questions in the literature: Are there non-standard neutrino interactions? Are there non-unitarity neutrino mixing? The intention of this talk is to bring some insight into these last two questions.

INTRODUCTION TO NON-STANDARD INTERACTIONS

The Super-Kamiokande [2], SNO [3], and KamLAND [4] neutrino oscillation experiments have strong evidences that neutrino oscillations occur In addition, the theory of neutrino oscillations is the leading description for neutrino flavor transitions. From neutrino oscillation experiments, we have received precision measurements for some of the neutrino parameters, i.e., Amli, \Amli |, Ou, 023, whereas other parameters are stfll completely unknown such as sign(A»j3j), 013, and 5, as well as the Majorana CP-violating phases and the absolute neutrino mass scale.

However, other mechanisms could be responsible for transitions on a sub-leading level. Therefore, we will study phenomenologically "new physics" effects due to non-standard neutrino interactions (NSIs).

NON-STANDARD INTERACTIONS IN NEUTRINO PHYSICS

The phenomenological consequences of non-standard neutrino interactions have been investigated in great detail in the literature. The widely studied operators responsible for NSIs can be written as [5, 6, 7, 8]

^Nsi = -2V2GFe{/p^ {v^fPiVp) (fr^iPcf), (4)

where GF is the Fermi weak coupling constant,... Note that these operators are non-renormalizable and they are also not gauge invariant. Using the NSI operators, one finds that the effective NSI parameters are

m w m

(5) X

where niw is the W boson mass and nix is the mass scale of the NSIs. If the new physics scale, i.e., the NSI scale, is of the order 1(10) TeV, then one obtains e„|3 - 10^2(10""^).

Neutrino oscillations

In order to describe neutrino propagation in matter with NSIs, the simple effective matter potential in Eq. (3) needs to be extended by the NSI parameters Eap,. Thus, we obtain

\ f^ v\ 0

[ Vo

0 Am2j

0

0 0

Awjj

^l+Ea t g ^

(6)

17


where A = l^/lEGpNe. The " 1" in the 1 -1 -element of the effective matter potential describes the interaction of electron neutrinos with left-handed electrons through the exchange of W bosons, i.e., the standard interactions, whereas all the other possible NSI parameters in the effective matter potential describe all the non-standard interactions.

The three-flavor neutrino evolution given in Eq. (6) is rather complicated and cumbersome. Hence, in order to illuminate neutrino oscillations with NSIs, we investigate the oscillations using two flavors, e.g., Vg and Vf. In this case, we have the two-flavor neutrino evolution equation

AL

1 2E

V 0 0 0 Anf

V^'+A (7)

where L is the neutrino propagation length that has replaced time in Eq. (6). Using Eq. (7), one can derive the two-flavor neutrino oscillation probability

AMML P{Ve —> Vt) = sin 20Msin "M-

2E (8)

where 9M and Amlf are the effective neutrino oscillation parameters when taking into account NSIs. These parameters are related to the vacuum neutrino oscillation parameters 9 and Am^ and given by

2EA

sin20M -

f Anf-c o s 2 0 - ( l +eee-£T

\2EA

Am^sm29+4EAee Amlj

f Anf-

\2EA sin20 + 2ee. (9)

(10)

In a work by Davidson et al. [8], constraints on NSI parameters using experiments with neutrinos and charged leptons have been derived for the more realistic scenario with three flavors

-0.9 < Egg < 0.75 |ee^|< 3.8x10 -0.05 < e^^ < 0.08

|e .T |<0 .25^

|eMTl<0-25 |eTT|<0.4

Note that these constraints are obtained without taking into account loop effects. Thus, in Ref [9], Biggio, Blennow, and Fernandez-Martinez have performed such an analysis. The result of this analysis is that the model independent bound for the NSI parameter Eg increases by a factor of 10^.

Overview of the field

Past research and literature

In the past, I have been involved together with collaborators in several studies on NSIs. These studies include both more theoretical and phenomenological works. On the more theoretical side, we have investigated NSI Hamiltonian effects on neutrino oscfllations [10, 11], approximate formulas for two-flavor NSIs [12], and mappings for NSIs [13], whereas on the more phenomenological side, we have simulated NSIs at MINOS [14], OPERA [15], and for reactor neutrinos [16]. In addition, we have studied models for NSIs and non-unitarity in a series of papers [17, 18, 19].

In general, interactions and scattering, loop bounds, beyond the SM physics, CP violation, perturbation theory, gauge invariance etc. are topics that have drawn the attention of people in the connection with NSIs. Simulations of setups of a future neutrino factory and MINOS, OPERA, MiniBooNE, and other future experiments as well as supernovas and neutrino telescopes also belong to the most studied topics including NSIs. I will not try to give any specific references to such works in this proceedings, since I will most probably forget some important ones ... In total, the number of papers written so far on NSIs is of the order of 500.

Models for NSIs

How to realize NSIs in a more fundamental framework with some underlying high-energy theory, which would respect and encompass the SM gauge group SU(3) x SU(2) x U(l)? In a toy model including the SM and one heavy


(a)

A++

(c) (d)

(b)

A > <

FIGURE 1. Tree level diagrams with exchange of a heavy triplet Higgs. This figure has been adopted from Ref [17].

SU(2) singlet scalar field S, one can have the following interaction Lagrangian

^L=-KpLa^<y2LpSi. (11)

Now, integrating out the heavy scalar ^ generates an anti-symmetric dimension-6 operator at tree level [20], i.e..

•d=6,as NSI 4j^^^(i'aPLVp){v,P,fs)

m% (12)

Gauge invariance andNSIs

At high energy scales, where NSIs are originated, there exists SU(2) x U( 1) gauge invariance. Therefore, if there is a dimension-6 operator on the form

j^{VafPLVfi){lyYpPd5),

then this operator will lead to NSI parameters such as ef^. However, the above form for a dimension-6 operator must be a part of the more general form

which involves four charged lepton operators. Thus, we have severe constraints from experiments on processes like li -^3)6, i.e.,

B R ( ^ ^ 3 e ) < 10" '^

which leads to the following upper bound on the above chosen NSI parameter

e - < 10-^

A specific example - NSIs from a type-II seesaw model

In a type-II seesaw model, the tree level diagrams with exchange of a heavy triplet Higgs are given in Fig. 1. Integrating out the heavy triplet field (at tree level), we obtain the relations between the neutrino mass matrix and the NSI parameters as [17]

cP^^- WA

8A/2GFV4A^ (mv)a/3 {m\\

ap (13)

Now, using experimental constraints from lepton flavor violations and rare decays, we find upper bounds on the NSI parameters, which are presented in Table 2.

In addition, for OTA = 1 TeV and varying mi, we plotted the upper bounds on some of the NSI parameters in the triplet seesaw model. The resuhs are shown in Fig. 2. For a hierarchial mass spectrum (i.e., mi < 0.05eV), aU the NSI effects are suppressed, whereas for a nearly degenerate mass spectrum (i.e., mi > 0.1 eV), two NSI parameters can be sizeable.


TABLE 2. Constraints on various e's from I iU, one-loop i -^ iy, and fiê • fi e^ processes.

decay

li~ -^ e~eê~ T~ -ê~eê~

T~ ^ fl~fl^fl~

T~ ê~jiê~

T~ ^ fi~e^fi~

T~ ê~ji^ji~

T~ ^ e~e^fi~

ji- ê'Y T~ ^ e~y

T- ^fi-y

fiê~ ^ fi~e^

10-2

10-2

10-^

10-^

10-^

10-^

i n - 8

-,' ICel '/

/

V k"i

\^7^

constraint on

\^fe\ \4I\ l<;l \4l\ l4l Kl\ '"11

\âCa\ ^ a ^ a a 2.aâa

\4l\

^yKr\

k^

IC

bound

3 . 5 x 1 0 - ^ 1 .6x10-4

1 .5x10-4

1 .2x10-4

1 .3x10-4

1 .2x10-4

9 . 9 x 1 0 - ^

1 .4x10-4 3 . 2 x 1 0 - 2 2 . 5 x 1 0 - 2

3 . 0 x 1 0 - ^

m i

0 0.05 0.10 0.15 0.20

FIGURE 2. Upper bounds on NSI parameters in the type-II seesaw model. This figure has been adopted from Ref. [17].

Future?

I am sure that more investigations about NSIs will be conducted in the future, both theoretically and experimentally. In addition, I believe that a future neutrino factory should be the most plausible experiment to find signatures of NSIs, but perhaps also the LHC will shed some light. The power of a neutrino factory is that it has a sensitivity reach for the small mixing angle 613 of the order sin^20i3 ^ 10"^ — 10"^, and it may have the same sensitivity for the NSI parameters.

NON-STANDARD INTERACTIONS FOR NEUTRINO CROSS-SECTIONS

In this section, non-standard interactions for neutrino cross-sections will be investigated in detail. Neutrino NSIs with either electrons or first generation quarks can be constrained by low-energy scattering data. In general, one finds that bounds are stringent for muon neutrino interactions, loose for electron neutrino interactions, and in principle, do not exist for tau neutrino interactions. Note that in the present overview of the upper bounds on the NSI parameters, the results from Biggio, Blennow, and Fernandez-Martinez [21] have not been included.

The best measurement on electon neutrino-electron scattering comes from the LSND experiment, which found the cross-section of this process to be [22]

a{Vee -^ ve) {XAl±OAlf^'^^^\, (14)

20


to 0

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

FIGURE 3. Bounds on flavor conserving NSIs of Vge scattering from the LSND experiment. This figure has been adopted from Ref [8].

where nie is the electron mass and E^ is the neutrino energy, which should be compared with the SM cross-section a{Vee—^ ' ^)lsM — ^-0967GpifieEv/n.

Including NSIs, the expression for this cross-section becomes

2GJ-meEv aivee -^ ve) = —

1 ( l + g ! + e.f)'+ S l4iP + ^fel + ef ) ' + ^ S |e 3

,eRi2 •ae\ (15)

where gf c^ -0.2718 and g | c^ O.IZIG. Using the LSND data and the NSI cross-section for electron neutrino-electron scattering, we obtain 90 % C.L. bounds on the NSI parameters (note that we are only considering one NSI parameter at a time) [8]

-0.07 < e f < 0.11,

- K e f < 0.5

for flavor conserving diagonal NSI parameters and

\efAKOA, | e | f |<0 .7

for flavor changing NSI parameters. Considering both left- and right-handed diagonal NSIs, i.e., two NSI parameters simultaneously, a 90 % C.L. region between two ellipses is obtained

0.445 <(0.7282 + a ^ + l(0.2326 + a ^ < 0.725,

which is shown in Fig. 3. Then, we study electron neutrino-quark scattering. The CHARM collaboration [23] has measured the ratio between

cross-sections and found

R'' = a{VeN -^ vX) + a{VeN -^ vX) a{VeN -^ eX) + a{VeN -^ eX)

Including NSIs, the quantities gLe and gRe can be expressed as

= [gLe 15 )2 = 0.406 ±0.140.

RLe gl + etif-

Uef = {gl + e:!f-

^dL\2

„dR\2 ?R + i^ee

(16)

(17)

(18)

21


Using the CHARM data, we obtain 90 % C.L. bounds on the NSI parameters (only one NSI at a time) [8]

- l < e , f <0.3,

-0.3 < e,f < 0.3,

-0.4 < e,f < 0.7,

-0.6 < ef* < 0.5

for flavor conserving NSIs and e|e I < 0.5, q = u,d andP = L,R

for flavor changing NSIs. Again, a 90 % C.L. region considering several NSI parameters simultaneously can be obtained

0.176 < (0.3493 + e;i )2 + (-0.4269 + ef^)2 + (-0.1551+egf)2 +(0.0775+ eff)2< 0.636.

Next, for muon neutrino-electron scattering, the CHARM II coUaboration [24] has measured gf. = -0.035 ±0.017 andg^ = -0.503 ±0.017, which translate into g£ = -0.269± 0.017 and g | = 0.234± 0.017. Using these values, one can compute 90 % C.L. bounds on the NSI parameters (only one NSI parameter at a time) [8]

-0.025 <e;^^ < 0.03,

-0.027 <£f^ < 0.03

\ef^<0.\, P = L,R for flavor diagonal NSIs and

for flavor changing NSIs. Furthermore, the NuTeV collaboration [25] has measured (gLu)^ = 0.3005 ±0.0014 and igRn)^ = 0.0310 ± 0.0011 that appear in ratios of cross-sections for neutrino-nucleon (muon neutrino-quark) scattering processes. Using these values, we obtain (only one NSI parameter at a time) [8]

-0.009 < e'lf^ < -0.003 or 0.002 < ef.^ < 0.008,

-0.008 <£f^ < 0.003,

-0.008 <,

for flavor diagonal NSIs and

-0.008 <e;J; < 0.015

|e |^ |<0.05, q = u,d

for flavor changing NSIs. Similarly, the 90 % C.L. regions using two NSI parameters simultaneously are presented in Fig. 4.

Finally, we investigate NSIs for the e+e^ -^ vvy cross-section at LEPII. The 90 % C.L. bounds on flavor diagonal NSIs are given by [7]

-0.6 <e|:^ < 0.4,

-0.4 <e|^ < 0.6,

whereas for flavor changing NSIs

\£fp\<OA, P = L,^, a = T,/3 = e,M.

SUMMARY AND CONCLUSIONS

In summary, non-standard neutrino interactions could be responsible for neutrino flavor transitions on a sub-leading level. Indeed, low-energy neutrino scattering experiments measuring neutrino cross-section can be used to set bounds on NSI parameters. Thus, the LHC and a neutrino factory open a new window towards determining the possible NSI parameters.

22


-> 3 - -to 0 7

•-MM "MM

FIGURE 4. Bounds on flavor conserving NSIs of Vy^q scattering from the NuTeV experiment. This figure has heen adopted from Ref [8].

ACKNOWLEDGMENTS

I would like to thank my collaborators He Zhang, Mattias Blennow, Michal Malinsky, Davide Meloni, Francesco Terranova, Walter Winter, and Zhi-zhong Xing for useful collaboration that led to the publications upon which this talk is based. In addition, I would like to thank the organizers of NUINT 2009, especially Sergio Palomares-Ruiz and Michel Sorel, for the invitation.

This work was supported by the Royal Swedish Academy of Sciences (KVA) and the Swedish Research Council (Vetenskapsradet), contract no. 621-2008-4210.

REFERENCES

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