Novel neutrino interactions at IceCube

Novel neutrino interactions at IceCube

Alex FriedlandLos Alamos

Dec 17, 2013

1Tuesday, December 17, 13

Collaborators

JJ Cherrypostdoc, Los Alamos

Ian Shoemakerpostdoc, Los Alamos

-> CP3, Denmark


Generalities: new physics searches and neutrinos

• I’d like to pick up on a point made yesterday by Heather Ray

• We don’t understand where new physics is hiding -> cast a wide net!

• LHC

• Dark matter searches (direct, indirect)

• Axion searches (ADMX, CAST, etc)

• Precision low-energy stuff

• Electric dipole moments, rare decays, Kaon mixing ...

• Cosmological fits

• Neutrino sector?3Tuesday, December 17, 13

Why think about neutrinos?

• Because the neutrino sector has been getting some amazing data over the last two decades

• There was something new almost every year!

• Because this is where we have already discovered physics beyond the standard model (oscillations)

• Leptonic flavor mixing results greatly surprising for model-builders

• See talk by Pierre Ramond from yesterday

• Because in the next 10-15 years, we should expect more precision data


PDG 1996http://pdg.lbl.gov/1996/www_2ltab.ps


http://pdg.lbl.gov/1996/www_2ltab.ps

http://pdg.lbl.gov/1996/www_2ltab.ps

For comparison, around the same time ...

hep-ph/9810316

(TASI lectures by J. Hewlett)

Fig. 1880

80.1

80.2

80.3

80.4

80.5

80.6

130 140 150 160 170 180 190 200Mtop (GeV/c2)

MW

(GeV

/c2 )100

250

500

1000

Higgs Mass (G

eV/c2 )

INDIRECTLEP + SLC

World Av.

80

80.1

80.2

80.3

80.4

80.5

80.6

130 140 150 160 170 180 190 200


What else could be hiding in the neutrino sector?

• Generally speaking, ideas in the literature fall into two categories:

• New interactions (“NSI”)

• New states (“sterile neutrinos”)

• Both of these ideas have decades of theoretical work behind them


New neutrino-matter interactions

• Could appear at oscillation experiments, for example:

• Solar neutrino survival probability

• Atmospheric neutrino oscillations

• Neutrino beams

• Non-oscillation experiments, for example

• LHC, Tevatron

pep

NSI

Std. MSW

0.00 0.02 0.04 0.06 0.08 0.100.00

0.02

0.04

0.06

0.08

0.10

P�⇧⌅⌥⇧e⇥

P�⇧ ⌅⌥⇧ e⇥

NO⇧A, ⇤⇤e⌃⇤�0.4, ⇥⇧�0


Here, I wish to speculate about neutrino self-interactions

• That’s the hardest of them all to constrain

• Scattering neutrino beams is not easily accomplished

• On the other hand, in the universe this experiment does happen over and over. Hence, this interaction could have profound astrophysical and cosmological implications

• For example, it is responsible for collective flavor oscillations in supernova environments

• Neutrino free-streaming in the early universe

• Neutrino-dark matter interactions?


• Bardin, Bilenky, Pontecorvo (1970)

• Barger, Keung, Pakvasa (1982)

• Manohar (1987)

• Kolb & Turner (1987)

• Fuller, Mayle, Wilson (1988)

• Bilenky, Bilenky, Santamaria (1993)

• ...

V o l u m e 32B. n u m b e r 2 P H Y S I C S L E T T E R S 8 J u n e 1970

O N T H E v - v I N T E R A C T I O N

Do Yu. BARDIN, S. M. B I L E N K Y , B. P O N T E C O R V O Joint Institute for Nuclear Research, Dubna, USSR

Received 28 April 1970

A n e w h y p o t h e t i c a l i n t e r a c t i o n b e t w e e n n e u t r i n o s is c o n s i d e r e d . It is s h o w n tha t e v e n r e l a t i v e l y s t r o n g v e - v e , vtz - v/. t and Pe - v t l i n t e r a c t i o n s a r e not in c o n t r a d i c t i o n wi th e x i s t i n g d a t a and u p p e r l i m - i t s f o r the c o r r e s p o n d i n g i n t e r a c t i o n c o n s t a n t a r e o b t a i n e d . New e x p e r i m e n t s a r e s u g g e s t e d w h i c h m i g h t g i v e i n f o r m a t i o n on ~, - v i n t e r a c t i o n s .

I t i s t a k e n f o r g r a n t e d t h a t the on ly i n t e r a c - t i o n w h i c h n e u t r i n o s u n d e r g o i s the c l a s s i c a l w e a k i n t e r a c t i o n . N e v e r t h e l e s s , t he q u e s t i o n c a n be pu t a s to w h e t h e r the n e u t r i n o m a y u n d e r - go a d d i t i o n a l i n t e r a c t i o n s . Our w o r k i s c o n - c e r n e d w i th a p o s s i b l e i n t e r a c t i o n b e t w e e n n e u - t r i n o s . Of c o u r s e , t h e r e i s a n i n t e r a c t i o n b e - t w e e n n e u t r i n o s a r i s i n g in the s e c o n d o r d e r of the u s u a l w e a k i n t e r a c t i o n , bu t h e r e we s h a l l c o n s i d e r a new ( h y p o t h e t i c a l ) v - v i n t e r a c t i o n . As i t t u r n s out , e v e n a r e l a t i v e l y s t r o n g v - v i n t e r a c t i o n i s not in c o n t r a d i c t i o n w i t h e x i s t i n g da ta . We s u g g e s t t h e n new e x p e r i m e n t s w h i c h m i g h t g ive i n f o r m a t i o n on the v - v i n t e r a c t i o n .

In the p r e s e n c e of n o n - w e a k v - v i n t e r a c - t i o n s w i l l a p p e a r m a n y p h e n o m e n a , a m o n g w h i c h we s h a l l c o n s i d e r i) s o m e new t y p e s of d e c a y s ( s ee , f o r e x a m p l e , fig. l a ) , i i) s o m e new t y p e s of n e u t r i n o - i n d u c e d p r o c e s s e s a t h i g h e n e r g y

C.L. g.

F i g . 1.

( s ee , f o r e x a m p l e , fig. l b ) , i i i ) n e u t r i n o " f o r m f a c t o r s " ( see f ig. l c ) .

In a d d i t i o n to the u s u a l w e a k d e c a y s wi th e m i s s i o n of l e p t o n s , a v - v i n t e r a c t i o n c l e a r l y i m p l i e s d e c a y s w i th the e m i s s i o n of a n a d d i - t i o n a l v - ~ p a i r . L e t us f i r s t c o n s i d e r the d e c a y

~ + - e + + r e + Ve + ~e " (1)

In a po l e a p p r o x i m a t i o n we o b t a i n f o r the e l e c - t r o n s p e c t r u m in p r o c e s s (1) the e x p r e s s i o n

dW 1 G2F2 if~l mTr × ~ e 3 v - 27~ 5 VeVe

× ( l + r 2 - 2 x ) ( x 2 - r 2 ) 1/2 [ ( 1 - 2 x ) x + r 2] , (2)

w h e r e G ~ 10 -5 mp 2 i s the w e a k i n t e r a c t i o n c o n s t a n t . If~l ~ 0.92 rnTr i s the F - d e c a y c o n s t a n t , r = rne/m~, x E / m ~ (E i s the e l e c t r o n e n e r g y ) , a n d FVeVe i s the v e - v e i n t e r a c t i o n c o n s t a n t .

To be c o n c r e t e , we s e l e c t e d fo r the v e - v e e f - f e c t i v e H a m i l t o n i a n the v e c t o r f o r m ~VeVe =

= F½ ~e (PeVa Ve)(~eVa re)" N e g l e c t i n g the e l e c -

t r o n m a s s we o b t a i n f o r the t o t a l p r o b a b i l i t y of p r o c e s s (1)

1 G2F 2 If~12m 7 o (3) Wn ~ e 3 v - 157T5211 ~eVe

F o r c o m p a r i s o n we g ive a l s o the w e l l - k n o w n e x p r e s s i o n of W~ ~ lv (l i s a c h a r g e d l ep ton) :

_ 1 2 m2m (1 m2 2 Wrr_.g v 23~G Ifzr[ 2 - ~ - ) o (4)

7r

121

V o l u m e 32B. n u m b e r 2 P H Y S I C S L E T T E R S 8 J u n e 1970

O N T H E v - v I N T E R A C T I O N

Do Yu. BARDIN, S. M. B I L E N K Y , B. P O N T E C O R V O Joint Institute for Nuclear Research, Dubna, USSR

Received 28 April 1970

A n e w h y p o t h e t i c a l i n t e r a c t i o n b e t w e e n n e u t r i n o s is c o n s i d e r e d . It is s h o w n tha t e v e n r e l a t i v e l y s t r o n g v e - v e , vtz - v/. t and Pe - v t l i n t e r a c t i o n s a r e not in c o n t r a d i c t i o n wi th e x i s t i n g d a t a and u p p e r l i m - i t s f o r the c o r r e s p o n d i n g i n t e r a c t i o n c o n s t a n t a r e o b t a i n e d . New e x p e r i m e n t s a r e s u g g e s t e d w h i c h m i g h t g i v e i n f o r m a t i o n on ~, - v i n t e r a c t i o n s .

I t i s t a k e n f o r g r a n t e d t h a t the on ly i n t e r a c - t i o n w h i c h n e u t r i n o s u n d e r g o i s the c l a s s i c a l w e a k i n t e r a c t i o n . N e v e r t h e l e s s , t he q u e s t i o n c a n be pu t a s to w h e t h e r the n e u t r i n o m a y u n d e r - go a d d i t i o n a l i n t e r a c t i o n s . Our w o r k i s c o n - c e r n e d w i th a p o s s i b l e i n t e r a c t i o n b e t w e e n n e u - t r i n o s . Of c o u r s e , t h e r e i s a n i n t e r a c t i o n b e - t w e e n n e u t r i n o s a r i s i n g in the s e c o n d o r d e r of the u s u a l w e a k i n t e r a c t i o n , bu t h e r e we s h a l l c o n s i d e r a new ( h y p o t h e t i c a l ) v - v i n t e r a c t i o n . As i t t u r n s out , e v e n a r e l a t i v e l y s t r o n g v - v i n t e r a c t i o n i s not in c o n t r a d i c t i o n w i t h e x i s t i n g da ta . We s u g g e s t t h e n new e x p e r i m e n t s w h i c h m i g h t g ive i n f o r m a t i o n on the v - v i n t e r a c t i o n .

In the p r e s e n c e of n o n - w e a k v - v i n t e r a c - t i o n s w i l l a p p e a r m a n y p h e n o m e n a , a m o n g w h i c h we s h a l l c o n s i d e r i) s o m e new t y p e s of d e c a y s ( s ee , f o r e x a m p l e , fig. l a ) , i i) s o m e new t y p e s of n e u t r i n o - i n d u c e d p r o c e s s e s a t h i g h e n e r g y

C.L. g.

F i g . 1.

( s ee , f o r e x a m p l e , fig. l b ) , i i i ) n e u t r i n o " f o r m f a c t o r s " ( see f ig. l c ) .

In a d d i t i o n to the u s u a l w e a k d e c a y s wi th e m i s s i o n of l e p t o n s , a v - v i n t e r a c t i o n c l e a r l y i m p l i e s d e c a y s w i th the e m i s s i o n of a n a d d i - t i o n a l v - ~ p a i r . L e t us f i r s t c o n s i d e r the d e c a y

~ + - e + + r e + Ve + ~e " (1)

In a po l e a p p r o x i m a t i o n we o b t a i n f o r the e l e c - t r o n s p e c t r u m in p r o c e s s (1) the e x p r e s s i o n

dW 1 G2F2 if~l mTr × ~ e 3 v - 27~ 5 VeVe

× ( l + r 2 - 2 x ) ( x 2 - r 2 ) 1/2 [ ( 1 - 2 x ) x + r 2] , (2)

w h e r e G ~ 10 -5 mp 2 i s the w e a k i n t e r a c t i o n c o n s t a n t . If~l ~ 0.92 rnTr i s the F - d e c a y c o n s t a n t , r = rne/m~, x E / m ~ (E i s the e l e c t r o n e n e r g y ) , a n d FVeVe i s the v e - v e i n t e r a c t i o n c o n s t a n t .

To be c o n c r e t e , we s e l e c t e d f o r the v e - v e e f - f e c t i v e H a m i l t o n i a n the v e c t o r f o r m ~VeVe =

= F½ ~e (PeVa Ve)(~eVa re)" N e g l e c t i n g the e l e c -

t r o n m a s s we o b t a i n f o r the t o t a l p r o b a b i l i t y of p r o c e s s (1)

1 G2F 2 If~12m 7 o (3) Wn ~ e 3 v - 157T5211 ~eVe

F o r c o m p a r i s o n we g ive a l s o the w e l l - k n o w n e x p r e s s i o n of W~ ~ lv (l i s a c h a r g e d l ep ton) :

_ 1 2 m2m (1 m2 2 Wrr_.g v 23~G Ifzr[ 2 - ~ - ) o (4)

7r

121


• Beam: ultra-high energy neutrinos, originating at cosmological distances (z~1-4) in astrophysical sources such as GRBs or AGNs

• Target: cosmic neutrino background, 336 cm-3 at the current epoch

• Detector: IceCube

• “A large-volume Cherenkov detector made of 5160 photomultipliers (PMTs) at depths between 1450 and 2450 m in natural Antarctic ice”

We propose to test this interaction at IceCube

From IceCube, Science 342, 1242856 (2013)

Evidence for High-Energy Extraterrestrial Neutrinos at the IceCube DetectorIceCube Collaboration*

Introduction: Neutrino observations are a unique probe of the universe’s highest-energy phe-nomena: Neutrinos are able to escape from dense astrophysical environments that photons cannot and are unambiguous tracers of cosmic ray acceleration. As protons and nuclei are accelerated, they interact with gas and background light near the source to produce subatomic particles such as charged pions and kaons, which then decay, emitting neutrinos. We report on results of an all-sky search for these neutrinos at energies above 30 TeV in the cubic kilometer Antarctic IceCube obser-vatory between May 2010 and May 2012.

Methods: We have isolated a sample of neutrinos by rejecting background muons from cosmic ray showers in the atmosphere, selecting only those neutrino candidates that are fi rst observed in the detector interior rather than on the detector boundary. This search is primarily sensitive to neutri-nos from all directions above 60 TeV, at which the lower-energy background atmospheric neutrinos become rare, with some sensitivity down to energies of 30 TeV. Penetrating muon backgrounds were evaluated using an in-data control sample, with atmospheric neutrino predictions based on theo-retical modeling and extrapolation from previous lower-energy measurements.

Results: We observed 28 neutrino candidate events (two previously reported), substantially more than the 10.6 expected from atmospheric backgrounds, and ranging in energy from 30 to 1200 TeV. With the current level of statistics, we did not observe signifi cant clustering of these events in time or space, preventing the identifi cation of their sources at this time.

Discussion: The data contain a mixture of neutrino fl avors compatible with fl avor equipartition, originate primarily from the Southern Hemisphere where high-energy neutrinos are not absorbed by Earth, and have a hard energy spectrum compat-ible with that expected from cosmic ray accelerators. Within our present knowledge, the directions, ener-gies, and topologies of these events are not compatible with expectations for terrestrial processes, deviating at the 4σ level from standard assumptions for the atmo-spheric background. These properties, in particular the north-south asymmetry, generically disfavor any purely atmospheric explanation for the data. Although not compatible with an atmospheric explanation, the data do match expectations for an origin in uniden-tifi ed high-energy galactic or extragalactic neutrino accelerators.

FIGURES IN THE FULL ARTICLE

Fig. 1. Drawing of the IceCube array.

Fig. 2. Distribution of best-fi t deposited energies and declinations.

Fig. 3. Coordinates of the fi rst detected light from each event in the fi nal sample.

Fig. 4. Distributions of the deposited energies and declination angles of the observed events compared to model predictions.

Fig. 5. Sky map in equatorial coordinates of the TS value from the maximum likelihood point source analysis.

Fig. 6. Distribution of deposited PMT charges (Qtot).

Fig. 7. Neutrino effective area and volume.

SUPPLEMENTARY MATERIALS

Materials and MethodsEvent Displays 1 to 28Neutrino Effective Areas

A 250 TeV neutrino interaction in IceCube. At the neutrino interaction point (bottom), a large particle shower is visible, with a muon produced in the interaction leaving up and to the left. The direction of the muon indicates the direction of the original neutrino.

READ THE FULL ARTICLE ONLINEhttp://dx.doi.org/10.1126/science.1242856

Cite this article as IceCube Collaboration, Science 342, 1242856 (2013). DOI: 10.1126/science.1242856

www.sciencemag.org SCIENCE VOL 342 22 NOVEMBER 2013 947

RESEARCH ARTICLE SUMMARY

*The list of author affi liations is available in the full article online.Corresponding authors: C. Kopper ([email protected]); N. Kurahashi ([email protected]); N. Whitehorn ([email protected])

Published by AAAS


• IceCube reported 28 events with energies between 20 TeV and 2 PeV that stand above the atmospheric background (4 sigma)

• Science 342, 1242856 (2013)

• Two PeV events are affectionately named “Bert” and “Ernie”

• Phys. Rev. Lett. 111, 021103 (2013)

• The third one, at 2 PeV, is in the pipeline (“Big Bird”)

• Some features of this data could be pointing to the presence of new interactions (our speculation!)

We propose to test this interaction at IceCube

A102

102 103

101

100

10-1

Eve

nts

per

662

days

Deposited EM-equivalent energy in detector (TeV) sin(Declination)

10

From IceCube, Science 342, 1242856 (2013)


Peculiarity of the data

• The observed spectrum lines up with E-2 expectation from astrophysics, except that

• there are no events above ~ 2 PeV (one would expect 3-6 in the 2-10 PeV window from a continuing E-2 spectrum)

• no events in the gap between 0.3 and 1 PeV

• relative paucity of muon events (none at PeV, one reported between 0.15 to 0.3 PeV)

• Leptoquarks at the detection point?

• Barger, Keung, arXiv:1305.6907

• Oscillations of pseudo-Dirac neutrinos with Δm2~10-15eV2

• Joshipura, Mohanty, Pakvasa, arXiv:1307.5712


Our speculation

• We propose that something happens in propagation, but not an oscillation!

• What if the universe is not transparent to neutrinos at certain energies (~PeV)?

• That’s a crazy thing to say, because it is well known that the universe is transparent to neutrinos with energies below ~1022 eV

• At those ~1022 eV, the neutrinos finally get scattered/absorbed because of the s-channel Z-boson resonance

• T. Weiler, PRL 1982

116 P. Gondolo, G. Ge/mini / Cosmic neutrinos

II I I

10 —~ --\ 6

--158— -

6— —--10

— NCs - Cl)-~ 4- N

N —5N2— 2\

- scattering ‘~ annihilatio \ -- 3

0 0

H Hi H H III

—5 0 5 10 15log E~ [TeV]

Fig. 1. The absorption redshift Za (line 1) for cosmic neutrinos as a function of the neutrino energy atemission E, taking 120h

2 = 1. The other lines indicate: (2) the boundary between the two regions whereabsorption due to annihilation and scattering dominate; (3) the present epoch; (4) the Z-boson pole; (5)

the epoch ofmatter-radiation equality; (6) the epoch of light—neutrino decoupling.

Approximate expressions for the absorption redshift Za(Ee) can be obtained for1 ~Z Ze <Zeq and Ze >> Zeq• In these cases, the result of the integration simplifies to

3.5 x 1017(fl0h2)’/

2(1 +ze)5~2(Ee/TeV), for 1 ~Ze <Zeq,(2.20)

0.81 x 10’~(1+ze)2(Ee/TeV), for Ze >>Zeq•

The absorption redshift Za(Ee) is then obtained by setting s~= 1:

1 +Za(Ee)

= 3.8 x 106(12t1h2)l/S(Ee/TeV)_

2/S, Ec 5.2 X i0~TeV(fl0h2)

2, (2.21)

1.1 x 10~(Ee/TeV)~’~2, Ee~5.2X i0~TeV(fl0h2)

2.

3. Neutrino spectrum

We now determine the present energy spectrum of neutrinos originating fromthe decay of an unstable heavy particle x with decay lifetime i-s. The number of

Gondolo, Gelmini, 1993

Ec.m. ⇠p

(10�1 eV)(1023 eV) ⇠ 102 GeV ⇠ mZ


Our speculation

• The standard transparency conclusion is based on standard physics only

• What if we have a light mediator particle?

• resonant condition

• “Dark force”

• Could be a vector or scalar

m2� = s ⇡ 2m⌫E⌫

=) m� ⇠p(10�1 eV)(1015 eV) ⇠ 107 eV


Some rough estimates

• Resonant cross section is bigger than that on the Z pole, since ɸ is lighter

• Given relic neutrino number density ~ 103 (we assume astrophysical sources at z of several), we can (first very roughly) estimate that

• Therefore, there is plenty of room for the numerical coefficient in the cross section formula to be small (due to small coupling and/or small mixing)

• Also, there is room for the redshift effects to work (see later)

�res ⇠ (#)m�2� ⇠ (#)10�24 cm2

�intersting ⇠ (l ⇥ n)�1 ⇠ (Gpc⇥ 103 cm�3)�1 ⇠ 10�31cm2


Framework

• How to get such new interaction into the neutrino sector?

• We don’t want to build specific models here, just outline a framework

• We don’t want to break the weak SU(2)

• And we don’t have to. It is well-known that our standard neutrinos could oscillate into a sterile state. Let’s give that state new interactions

• Then our familiar 3 light neutrino mass eigenstates would acquire new interaction thanks to the mixing with the new state

• The amount of mixing could be different for each of the states, hence rich phenomenological possibilities

• + a state that is predominately “sterile”


Framework

• A new fermion in the “dark sector”, which couples via a ɸ-mediated interaction. The only way this state interacts with the Standard Model is via mixing with neutrinos. “Neutrino Portal”

• The dark sector has its own Higgs mechanism with a field that gives ɸ its mass

• Simple renormalizable see-saw Lagrangian. Upon integrating out the heavy right-handed , one gets a light “sterile” mixing with the usual active neutrinos in

• Akin to “baryonic neutrino” in Pospelov, arXiv:1103.3261, only we don’t want the hidden gauge group to directly couple to the SM baryon number (which could induce large NSI)

L ⇠ LH⌫R + ⌫D⌘⌫R +M⌫R⌫R

⌘

⌫R ⌫D L


Constrains?

• Schematically:

• Laboratory constraints, a la Pontecorvo, are completely avoided!

• Neutrinos in laboratory are produced as flavor states, don’t have the νD component. For example, processes of the type considered by Laha, Dasgupta & Beacom, arXiv:1304.3460 (a la Barger et al 1982) don’t occur in the detector

• In dense environments such as supernova, large matter potential reduces the admixture of the “sterile” state -- details beyond the scope of this talk

4

V

�µ

µ�

as

as

fK W �usK�

�

FIG. 3. Feynman diagram for K�(us) decay to a muon wherea V is radiated from the final state antineutrino. We also takeinto account another diagram where the V is also radiatedfrom the muon. The hadronic matrix element h0|u�↵(1 ��5)s|K�i = fK p↵K is denoted by the shaded circle.

C. Kaon decay

An even stronger constraint can be obtained fromkaon decay, again assuming that V couples to both theneutrinos and charged leptons. The basic idea is the sameas above, but instead of the decay width, we look at thedistortion of the charged lepton spectrum due to excessmissing energy in kaon decays. Kaons dominantly decay(branching ratio ⇠ 65%) via the 2-body leptonic channelK� ! µ� ⌫µ, for which the muon energy spectrumis a delta function in the kaon rest frame. If a newvector boson couples to leptons as assumed, then therecan be V -boson emission from the final states if mV .mK �mµ ⇡ 388MeV; the 3-body decay K� ! µ� ⌫µV ,has a dramatically di↵erent muon spectrum.

We consider the 3-body decay K� ! µ� ⌫µ V , asshown in Fig. 3. Much of the calculation is similarto that for a related limit on parity-violating muonicforces [18]. In Fig. 4, we show the muon spectrum fromkaon decay in two cases: when V emission is forbidden(K� ! µ�⌫µ) and when it is allowed (K� ! µ�⌫µV ).In both cases, we plot d�/dEµ normalized by the total(all modes) decay width �

tot

. For the 2-body decay,the muons have a monoenergetic spectrum with Eµ =258MeV; we show the measured result (including energyresolution) [106]. For the 3-body decay, the muons havea continuum spectrum; we show this for g⌫ = 10�2 andmV = 0.5MeV. This produces events at energies whereno excess events above the Standard Model backgroundwere observed (shaded region) [107]. We also show theapproximate upper limit that we derive (in the energyrange used for the search) from the upper limit presentedin Ref. [107].

To obtain our constraint, we use the resultsfrom a search for missing-energy events in kaondecays with muons having kinetic energies between60MeV to 100MeV (Eµ between 165.5MeV and205.5MeV). We integrate our calculated di↵erentialdecay rate, d�/dEµ, over this range of Eµ toobtain the partial decay width �(K� ! µ� ⌫µ V ).

1/K

totdK

/dE µ

[MeV

-1]

Eµ [MeV]

10-4

10-3

10-2

10-1

100 200 300

2-bodydecay

3-bodydecay

no e

xces

s ev

ents

uppe

r lim

it: 6

× 1

0-8 M

eV-1

FIG. 4. Muon spectra from kaon decay for the standard 2-body decay K� ! µ� ⌫µ (solid blue) measured in [106] alongwith the hypothetical 3-body decay K� ! µ� ⌫µ V (dashedred) with g⌫ = 10�2 and mV = 0.5MeV. The shaded regionshows the search region of Ref. [107], where no excess eventswere found. From this we derive an upper bound on the 3-body di↵erential decay rate that is ⇠104 times lower than thedashed red line.

The measured constraint on the branching ratio�(K�! µ� + inv.)/�(K�! µ� ⌫µ) 3.5 ⇥ 10�6 [107]leads to the limit on g⌫ shown in Fig. 1. If the V bosonwere to couple only to the neutrino, then the limit on g⌫would naively be a factor of ⇠ 3 stronger than what ispresented here.The constraints from W and kaon decays do not apply

directly to purely neutrinophilic models, e.g., Ref. [8],because no gauge-invariant implementation of the basicidea is available. An important issue that must be notedis that the longitudinal mode of V couples to the anomalyin the fermion current, and results in a contributionproportional to the charged lepton mass-squared to thedecay rate. These lepton masses cannot be written downusing renormalizable gauge-invariant operators unlessone makes modifications to the Higgs sector or couplesthe right-handed leptons to V . The lepton masses mayalso be generated by nonrenormalizable operators, as inRef. [108], which would then provide a natural UV cuto↵to the calculations. Since in this e↵ective model, theV -boson mass, mV , is proportional to the UV cuto↵ ofthe theory, it is not possible to take to take the limit ofmV ! 0 in this model.

III. CONSTRAINT FROM SCATTERING

A very strong constraint can be obtained byconsidering neutrino-electron scattering at very low


Resonant absorption

• As neutrinos oscillate in vacuum, however, they go into mass eigenstates and gain the new interaction

• Applies to both beam UHE neutrinos and the cosmic neutrino background

• Neutrinos could scatter resonantly when the energies are right

• The resonance condition is determined by the absolute neutrino masses, which could in principle leave imprints in the spectrum

• cf Eberle, Ringwald, Song, Weiler, hep-ph/0401203 in the standard case (which requires however neutrinos of > 1022 eV)


s-channel: A few physics considerations

• Breit-Wigner

• cross section on resonance dependents on the new mixing angle θ

• the width Γtot depends on the coupling g of the “sterile” neutrino to the “dark force” φ

• As the universe expands, the resonance line sweeps through the spectrum

• The net effect then depends on the distribution of astrophysical sources (GRBs) with z

�BW

⇠ 12⇡

m2�

�in

�out

4(s�m2�

) + �2tot

! �res

⇠ 12⇡

m2�

�in

�tot

⇠⇠ 12⇡

m2�

sin4 ✓


Example calculationSources are GBRs (Waxman-Bahcall) + AGNs at high E


Discussion of the results

• The plot shows four absorption bands, with the one at highest energies broadened by thermal motion of the lightest neutrinos

• Assumed normal mass hierarchy + 1 eV “sterile” state

• Assumed that the lightest neutrino is still relativistic at T ~ 1.9 K

• Assumed equal sterile mixing with all light states assumed for illustration

• Assume mφ=10 MeV for the mediator mass


Discussion of the results

• Notice the width of the absorption band between 0.3 and 1 TeV. This is where IceCube sees no events

• This width is obtained automatically, as a consequence of the distribution of GRBs with redshift!

• The absorption line sweeps through that part of the spectrum as the universe expands

Bert, Ernie,Big Bird “Gap”

Lower energy events

Atmospheric BG

Hi energy cutoff


t-channel scattering

• Notice also that some of the curves show decay with energy

• Effect of the t-channel scattering

• t-channel depends on g4 sin4θ, which is different from t-channel

• Depending on the choice of parameters, one can have domination by s-channel (bands), t-channel (continuum), or both


Selective absorption possible

• Amounts of “sterile” mixing to different mass eigenstates could be different. This has observable consequences.

• Example: Imagine we have our “sterile” state mixing mostly with ν3. If that state is absorbed as a result, ν1 and ν2 still make it to Earth.

• In this scenario, with more data, IceCube would fill in some events in the “gap” between 0.3 and 1 TeV, but there would still be a dip


Selective absorption: flavor effects

• In the standard case, the prediction is to have equal numbers of flavors at the detector. That’s because the muon neutrino projects equally onto the three mass eigenstates.

• Imagine we have our “sterile” state mixing mostly with ν3. If that state is absorbed as a result, the resulting flavor composition on earth will be different.

• Because ν3 has almost no electron neutrino component (suppressed by theta13), the observed flux would have more electron neutrinos than muon. More “blobs” vs “tracks”


Broad range of physical options

• In general, one can vary:

• Different mixing angles and couplings

• Overall mass scale of light neutrinos

• Mass hierarchy

• Cosmological abundance of “sterile” neutrinos ( generally model-dependent)

• It could be a theorist’s dream

• ...and an experimentalist’s nightmare!


Possible cosmological implications

• If the sterile neutrino is also coupled to dark matter, a whole host of possibilities open up

• Recently, it was suggested that neutrino-dark matter coupling could solve the missing satellites/too-big-to-fail problems with structure

• It was separately proposed that dark matter self-interactions could alleviate problems with cores vs cusps.

• Mediator masses in the 10 MeV range are optimal

• Our framework easily and naturally accommodates neutrino-dark matter coupling that would impact both the cutoff halo sizes and the core profiles

Loeb & Weiner, PRL 2011

van den Aarssen, Bringmann, Pfrommer, PRL 2012


Conclusions

• Neutrino sector could still contain many surprises

• The universe could be opaque to neutrinos in certain energy ranges. This can be easily achieved in a framework combining the ideas of sterile neutrinos and nonstandard interactions.

• The IceCube experiment could be probing this physics.

• The range of physical scenarios is broad. This could turn into an experimentalist’s nightmare.

• On the other hand, there is a possibility that the IceCube is probing “a portal” into the dark sector!


Novel neutrino interactions at IceCube

Documents

Transcript of Novel neutrino interactions at IceCube