Using cosmic neutrinos to search for nonperturbative physics at the Pierre Auger Observatory

Luis A. Anchordoqui,1 Haim Goldberg,2 Dariusz Gora,3,4 Thomas Paul,2,3,5 Markus Roth,3

Subir Sarkar,6 and Lisa Lee Winders1

1Department of Physics, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, Wisconsin 53201, USA2Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA

3Karlsruhe Institute of Technology (KIT), D-76021 Karlsruhe, Germany4Institute of Nuclear Physics PAN, 31-342 Krakow, Poland

5University of Nova Gorica, Vipavska 13, POB 301, SI-5001 Nova Gorica, Slovenia6Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, United Kingdom

(Received 21 April 2010; published 5 August 2010)

The Pierre Auger (cosmic ray) Observatory provides a laboratory for studying fundamental physics at

energies far beyond those available at colliders. The Observatory is sensitive not only to hadrons and

photons but can in principle detect ultrahigh energy neutrinos in the cosmic radiation. Interestingly, it may

be possible to uncover new physics by analyzing characteristics of the neutrino flux at the Earth. By

comparing the rate for quasihorizontal, deeply penetrating air showers triggered by all types of neutrinos

with the rate for slightly up-going showers generated by Earth-skimming tau neutrinos, we determine the

ratio of events which would need to be detected in order to signal the existence of new nonperturbative

interactions beyond the TeV scale in which the final state energy is dominated by the hadronic component.

We use detailed Monte Carlo simulations to calculate the effects of interactions in the Earth and in the

atmosphere. We find that observation of 1 Earth skimming and 10 quasihorizontal events would exclude

the standard model at the 99% confidence level. If new nonperturbative physics exists, a decade or so

would be required to find it in the most optimistic case of a neutrino flux at the Waxman-Bahcall level and

a neutrino-nucleon cross section an order of magnitude above the standard model prediction.

DOI: 10.1103/PhysRevD.82.043001 PACS numbers: 95.85.Ry, 13.15.+g, 96.50.S�

I. INTRODUCTION

Ultrahigh energy cosmic neutrinos (UHEC�) are ex-pected to be produced in association with the observedultrahigh energy (charged) cosmic rays (UHECR), either atthe same sites responsible for UHECR acceleration or viainteraction of the UHECR during propagation, particularlywith the cosmic microwave background . These neutrinosare unique probes of new physics as their interactions areuncluttered by the strong and electromagnetic forces and,upon arrival at the Earth, they may experience collisionswith center-of-mass energies up to

ffiffiffis

p& 250 TeV.

However, rates for new physics processes are difficult totest since the flux of cosmic neutrinos is virtually unknown.Interestingly, it is possible in principle to disentangle theunknown flux and new physics processes by using multipleobservables [1–5].

The Pierre Auger Observatory provides a promising wayto detect UHEC� by looking for deeply-developing, largezenith angle ( * 75�) or ‘‘quasihorizontal’’ air showers[6]. At these large angles, hadron-induced showers traversethe equivalent of several times the depth of the verticalatmosphere and consequently their electromagnetic com-ponent is extinguished before reaching the detector. Onlyvery high energy muons survive past about 2 equivalentvertical atmospheres. Therefore, the shape of a hadron-induced shower front is very flat and prompt in time. Incontrast, a neutrino shower exhibits the roughly samemorphology as a vertical shower. It is therefore possible

to distinguish neutrino induced events from backgroundhadronic showers. Moreover, because of full flavor mixing,tau neutrinos are expected to be as abundant as otherspecies in the cosmic flux. ��’s can interact in the Earth’scrust, producing � leptons which may decay above to theAuger detectors; such events will be referred to as ‘‘Earth-skimming’’ events [7–9].Possible deviations of the neutrino-nucleon cross section

due to new nonperturbative interactions1 can be uncoveredat the Auger Observatory by combining information fromEarth-skimming and quasihorizontal showers. In particu-lar, if an anomalously large rate is found for deeply devel-oping quasihorizontal showers, it may be ascribed either toan enhancement of the incoming neutrino flux or an en-hancement in the neutrino-nucleon cross section (assumingnon-neutrino final states dominate). However, these possi-bilities can be distinguished by comparing the rates ofEarth-skimming and quasihorizontal events. For instance,an enhanced flux will increase both quasihorizontal andEarth-skimming event rates, whereas an enhanced interac-tion cross section will also increase the former but suppressthe latter, because the hadronic decay products cannot

1Throughout this paper we use this term to describe neutrinointeractions in which the final state energy is dominated by thehadronic component. We are not considering here new ‘‘pertur-bative’’ physics e.g. (softly broken) supersymmetry at the TeVscale which would have quite different signatures in cosmic rayshowers.

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escape the Earth’s crust. Essentially this approach consti-tutes a straightforward counting experiment, as the detailedshower properties are not employed to search for thehypothesized new physics.

In this paper, we compute how many Earth-skimming vsquasihorizontal showers one would have to collect at theAuger Observatory to convincingly demonstrate new non-perturbative physics in which the final state energy isdominated by the hadronic component. We show thateven a small number of events could be sufficient to ruleout the standard model (SM). Thus the expected lowneutrino ‘‘luminosity’’ is not at all a show-stopper, andthe Observatory has the potential to uncover new physics atscales exceeding those accessible to the LHC.

In order to demonstrate this, we first compute accep-tances for Earth-skimming and quasihorizontal events us-ing detailed models of the terrain in the vicinity of theObservatory as well as detailed simulations of the responseof the surface array to highly inclined air showers. We thenperform a likelihood analysis to determine the event countsneeded to exclude the SM at various confidence levels. Theanalysis includes systematic effects both from theoreticaluncertainties in the (perturbative QCD) SM cross section[10] and from uncertainties associated with the detectorresponse.

The outline of the paper is as follows. In Sec. II wediscuss an example of a new physics scenario which couldmanifest as nonperturbative interactions. Next, in Sec. IIIwe describe the detailed Monte Carlo studies of the accep-tance for Earth-skimming and quasihorizontal showersunder the assumption of SM interactions, including sys-tematic uncertainties. Finally in Sec. IV we perform thestatistical analysis to ascertain the discovery reach of theObservatory. Our conclusions are collected in Sec. V.

II. NEW NON-PERTURBATIVE PHYSICS

The analysis techniques described herein constitute anentirely general approach to searching for nonperturbativeinteractions in which the final state is dominated by had-rons, without any dependence on what hypothetical mecha-nism might actually cause the ‘‘hadrophilia.’’ In order toillustrate possible new physics signals which may be ac-cessible using these techniques, we consider below thecase of TeV-scale black holes.

In D-dimensional scenarios with large-compact-extradimensions (of common linear size 2�rc) the Planck scaleis related to the fundamental scale of gravity (MD) accord-ing to [11]

M2Pl ¼ 8�rD�4

c MD�2D : (1)

If MD * MW ¼ G�1=2F ’ 300 GeV, microscopic black

holes (BH) can be produced gravitationally in particlecollisions with center-of-mass energies s * 1 TeV [12].Subsequently a TeV-scale BH would promptly decay via

thermal Hawking radiation [13] into observable quanta[14]. (For MD ¼ 1 TeV, the lifetime of a BH of mass10 TeV is less than 10�25 s.) Since gravitational couplingis flavor blind, a BH emits all the � 120 SM particle andantiparticle degrees of freedom with roughly equal proba-bility. Accounting for color and spin, we expect � 75% ofthe particles produced in BH evaporation to be quarks andgluons, � 10% charged leptons, � 5% photons or W=Zbosons, and � 5% neutrinos. Thus, TeV BH productionand evaporation constitutes a clear example of beyond SMnonperturbative physics.Although such BH production cross section �M�1

W is 5

orders of magnitude smaller than the QCD cross section���1

QCD, it was proposed [15] that such BHs could be

produced copiously at the LHC, and that these spectacularevents could be easily filtered out of the QCD background.This is possible by triggering on BH events with promptcharged leptons and photons, each carrying hundreds ofGeVof energy.Cosmic ray collisions, with center-of-mass energies

ranging up to 105 GeV, certainly produce BHs if theLHC does. The question is, can they be detected? Mostcosmic rays are protons or heavier nuclei, which collidewith hadrons in the upper atmosphere, producing cascad-ing showers which eventually reach the Earth’s surface. Atenergies of interest, however, the cosmic ray luminosity(L� 7� 10�10 ðE=PeVÞ�2 cm�2 s�1, taking a single nu-cleon in the atmosphere as a target and integrating over 2�sr), is about 50 orders of magnitude smaller than the LHCluminosity, thus making it futile to hunt for BHs in had-ronic cosmic ray interactions. On the other hand, neutrinointeraction lengths are far longer than the Earth’s atmos-pheric depth, although they would be greatly reduced bythe cross section for BH production [16]. Cosmic neutrinostherefore could produce BHs with roughly equal probabil-ity at any point in the atmosphere. As a result, the lightdescendants of the BH may initiate low-altitude, quasihor-izontal showers at rates significantly higher than SMpredictions.Analytic and numerical studies have revealed that gravi-

tational collapse takes place at high energies and smallimpact parameters [17,18]. In the course of collapse, acertain amount of energy is radiated in gravitational waves,

leaving a fraction y � MBH=ffiffiffis

pavailable for Hawking

evaporation. Here, MBH is a lower bound on the final

mass of the BH, andffiffiffis

p ¼ 2xmNE� is the center-of-massenergy of the colliding particles, taken to be partons. Thisratio depends on the impact parameter of the collision aswell as on the dimensionality of space-time.The inclusive production of BHs proceeds through dif-

ferent final states for different classical impact parametersb [18]. These final states are characterized by the fraction

yðzÞ of the initialffiffiffis

pwhich is trapped within the horizon.

Here, z ¼ b=bmax, and bmax ¼ffiffiffiffiF

prs is the maximum im-

pact parameter for collapse, where

LUIS A. ANCHORDOQUI et al. PHYSICAL REVIEW D 82, 043001 (2010)

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rs ¼ 1

MD

� ffiffiffis

pMD

2D�4�ðD�7Þ=2�ðD�12 Þ

D� 2

�1=ðD�3Þ

(2)

is the radius of a D-dimensional Schwarzschild BH [19],and F is the form factor [18].

The y dependence complicates the parton model calcu-lation, since the production of a BH of mass MBH requiresthat s be M2

BH=y2ðzÞ, thus requiring the lower cutoff on

parton momentum fraction to be a function of impactparameter. Because of the complexity of the final state,we assume that amplitude interference effects can beignored, and we take the �N cross section as an impactparameter-weighted average over partonic cross sections,with the lower parton fractional momentum cutoff deter-mined by xmin ¼ Mmin

BH =MD. This gives a lower boundX ¼ ðxminMDÞ2=½y2ðzÞs� on the parton momentum frac-tion x. All in all, the �N ! BH cross section reads [20]

�ð�N ! BHÞ ¼Z 1

02zdz

Z 1

XdxF�r2s

Xi

fiðx;QÞ; (3)

where i labels parton species and the fiðx;QÞ are partondistribution functions (PDF).

As an illustration, we consider the D ¼ 10 string in-spired scenario. For MD ¼ 1 TeV, xmin ¼ 1, and primaryneutrino energy E� ¼ 1010 GeV, we obtain �ð�N !BHÞ � 2� 106 pb [20]. This is about 2 orders of magni-tude above SM predictions. The BH production crosssection by UHEC� scales as

�ð�N ! BHÞ /�

1

M2D

�ðD�2Þ=ðD�3Þ: (4)

A further suppression arises if xmin is increased. For pa-rameters in the semiclassical regime (xmin * 3 [21]) theBH cross section becomes comparable to the SM crosssection at MD � 2 TeV; this determines the multidimen-sional Planck scale to which Auger may be sensitive.However, the LHC will also be sensitive to extra-dimensional effects at a similar scale. It is interesting toconsider whether Auger may have access to new physicsbeyond the reach of the LHC, and we now discuss such apossibility.

III. ACCEPTANCE AND SYSTEMATICUNCERTAINTIES

To calculate the acceptance we perform detailedMonte Carlo simulations. The incoming neutrinos arepropagated through the Earth’s crust, Andes mountains,and the atmosphere using an extended version [22] of thecode ANIS [23]. For fixed neutrino energies, 106 events aregenerated with zenith angles in the range 60�–90� (down-going showers) and 90�–95� (up-going showers) and withazimuth angles in the range 0�–360�. Neutinos are propa-gated along their trajectories of length �L from the gen-eration point on the top of the atmosphere to the detector insteps of �L=1000ð� 6 kmÞ. At each step of propagation,

the �N interaction probability

PðE�; El; �Þ ’ NA��NSMðE�Þ�ðZÞ�L (5)

is calculated using the cross section (��NSMðE�Þ) estimates of

Ref. [10], where �ðZÞ is the local medium density, El theenergy of the outgoing lepton, and NA ’ 6:022�1023 g�1. The outcoming particle spectrum from �N inter-actions is simulated with PYTHIA [24] and tau decays aresimulated using the package TAUOLA [25].The flux of outgoing leptons as well as their energy and

the decay vertex positions are calculated inside a defineddetector volume. The geometrical size of the detectorvolume is set to 3000� 10 km3, and it includes the realshape of the Auger Observatory on the ground. A reliefmap of the Andes mountains was constructed according toa digital elevation data of the Consortium for SpatialInformation (CGIAR-CSI) [26]. The map of the areaaround the Auger site is shown in Fig. 1.The detection volume corresponds to the so-called ac-

tive volume in which potentially detectable neutrino inter-actions are simulated. For a given incoming neutrino withenergy E� the active volume is defined by a particularplane Agen and distance �L. The plane Agen is the cross

sectional area of the detector volume and it is used as areference plane for the generation of incoming neutrinos.The area depends on the zenith angle � of the incomingneutrino. The distance �L is the multiple n of the averagelepton range hLlðElÞi.Earth-skimming events occur in the Earth’s crust, and so

the relevant neutrinos and taus sample only the Earth’ssurface density �s � 2:65 g=cm3. At these energies, thetau’s propagation length is determined not by its decaylength but by its energy loss. The energy loss per unitlength of crossed matter is usually approximated by alinear equation (continuous energy loss approach). The �lepton loses energy in the Earth according to

X (km)

-300-200

-1000

100200

300

Y (km

)

-300

-200

-100

0

100

200

300

Z (

km)

012345

FIG. 1 (color online). Topography of the Auger site accordingto CGIAR-CSI data. The center of the map corresponds to thecenter of the Auger array (latitude ¼ 35:25�S, longitude ¼69:25�W). The Auger position is marked by a circle.

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dE�

dz¼ �ð�� þ ��E�Þ�s; (6)

where the factor �� parametrizes the ionization losses and�� the energy losses through bremsstrahlung, pair produc-tion and hadronic interactions. For E� ¼ 107 GeV, �� isnegligible and �� � 0:8� 10�6 cm2=g [27]. Hadronic in-teractions (i.e., lepton-nucleus inelastic interactions domi-nated by small values of the squared momentum transferQ2) are responsible for the largest and the most uncertaincontribution [28]. Such an uncertainty in �� dominates thesystematic errors in the estimate of the neutrino event rates.

To investigate the response of the Auger detector, wegenerate the lateral profiles of the shower developmentusing the output of PYTHIA and/or TAUOLA as input forAIRES [29]. The showers induced by the products of up-

going decaying tau leptons, with energies from 0.1 EeV to100 EeV and decay position at altitudes ranging from 0 to3500 m above sea level, are simulated in steps of 100 m. Ateach altitude 40 events are generated to cover the tau decaychannels implemented in ANIS [22]. In the case of down-going showers, the decay altitudes range from ground levelup to the upper atmosphere.

The response of the surface detector array is simulated in

detail using the Off line simulation package [30]. Besidesthe standard procedure to simulate the spacial and temporalsignal response we have added the simulation of atmos-pheric background muons to study the impact on theneutrino identification, since such accidental muons mightbe wrongly classified as shower particles. The backgroundfrom hadronic showers above 108 GeV is estimated to beOð1Þ in 20 years. At E� � 1010 GeV the cosmic ray flux is� 106 time smaller, so the expected background for theenergy bin considered here (9:5< log10 ðE�=GeVÞ<10:5) is negligible.

The expected neutrino event rate (of flavor �) in thedetector volume is found to be

N��¼ Fw

�

XNacc

i¼1

Pi; (7)

where Nacc is the number of events triggering the detectorand passing all quality cuts of the cascade analysis. Here,

Fw� ¼ N�1

gen�TZ Emax

Emin

���

0 ðE�ÞdE�

Z �max

�min

Agenð�Þd�; (8)

d� is the solid angle, �T the observation time, Ngen is the

number of generated events from surface Agen, and we take

the neutrino flux ���

0 ðE�Þ to be isotropic. We further

assume �e:�:�� ’ 1:1:1, which is generally thought to

be the case if the neutrinos are produced predominantlythrough pion decay. In order to ascertain the systematicuncertainties associated with our lack of knowledge of thedependence of the flux on energy, we consider three sce-narios which plausibly bracket the range of possibilities:

(1) ���

0 ðE�Þ ¼ ðC=E0ÞE�1� ,

(2) ���

0 ðE�Þ ¼ CE�2� ,

(3) ���

0 ðE�Þ ¼ ðC=E0ÞE�3� ,

(4) ���

0 ðE�Þ ¼ CE�2� exp½�log10ðE�=E0Þ2=ð2�2Þ�,

where C ¼ 2:33� 10�8 GeV s�1 cm�2 sr�1, E0 ¼1010 GeV, � ¼ 0:5 GeV. This normalization (2) consti-tutes the common benchmark, the so-called ‘‘Waxman-Bahcall bound’’ [31]. The factor Fw

� of Eq. (8) is chosento yield the total number of events per year. The expectedrates for the entire range over which Auger is sensitive aregiven in Table I and the rates for the high energy binconsidered in the following study are given in Table II.Hereafter we consider ���

0 ðE�Þ / E�2� as our nominal

spectrum. We then estimate systematic uncertainties asso-ciated with: different assumptions of the spectrum shape,different parton distribution functions (GRV92NLO [32]and CTEQ66c [33]), and different estimates on �� [28].The contribution of different systematic errors are listed inTable III.

TABLE I. Expected events per year (Ni) at Auger, in theenergy range 8< log10 (E�=GeV), for various incident zenithangle (�) ranges, assuming the Waxman-Bahcall flux.

flux up-going down-going ratio

� N��� N�e

N��N�

N�allN�=N�all

(2) 90–95 0.68 60–90 0.134 0.109 0.019 0.262 2.58

(2) 90–95 0.68 75–90 0.075 0.071 0.011 0.157 4.27

TABLE II. Expected events per year (Ni) at Auger, in theenergy range 9:5< log10 ðE�=GeVÞ< 10:5, for various incidentzenith angle (�) ranges and the 4 flux models considered.

flux up-going down-going ratio

� N��� N�e

N��N�

N�allN�=N�all

(1) 90–95 0.14 60–90 0.059 0.049 0.011 0.12 1.14

(2) 90–95 0.15 60–90 0.059 0.049 0.096 0.11 1.33

(3) 90–95 0.23 60–90 0.079 0.062 0.0123 0.15 1.53

(4) 90–95 0.12 60–90 0.046 0.037 0.0080 0.091 1.33

(1) 90–95 0.14 75–90 0.027 0.031 0.0056 0.064 2.14

(2) 90–95 0.15 75–90 0.026 0.029 0.0048 0.060 2.47

(3) 90–95 0.23 75–90 0.036 0.041 0.0062 0.083 2.75

(4) 90–95 0.12 75–90 0.021 0.024 0.0040 0.049 2.45

TABLE III. Contributions to the systematic uncertainty on theEarth-skimming to quasihorizontal event ratio. We have consid-ered the energy range 9:5< log10 ðE�=GeVÞ< 10:5 and thezenith angle range 75� < �< 90�.

ratio flux PDF �� sum

þ11% 0% þ24% þ26%2.47 2.47

�13% �21% �25% �35%

LUIS A. ANCHORDOQUI et al. PHYSICAL REVIEW D 82, 043001 (2010)

043001-4

IV. AUGER DISCOVERY REACH

Consider a flux of neutrinos with energy in the range109:5 GeV<E� < 1010:5 GeV. In the SM, the interactionpath length is

L�CC ¼ ½NA�s�

�CC��1; (9)

where ��CC is the charged current cross section for E� ¼

E0. (We neglect neutral current interactions, which at theseenergies serve only to reduce the neutrino energy by ap-proximately 20%, which is within the systematic uncer-tainty.) For E0 � 1010 GeV, L�

CC �Oð100Þ km.

Supplemented by the possibility of new nonperturbativephysics, the interaction path length is

L�tot ¼ ½NA�sð��

CC þ ��NPÞ��1; (10)

where ��NP is the new physics contribution to the cross

section for E� ¼ E0.The maximal path length for a detectable � is given by

L� ¼ 1

���s

lnðEmax=EminÞ; (11)

where Emax � E0 is the energy at which the tau is created,and Emin is the minimal energy at which a � can bedetected. For Emax=Emin ¼ 10, L� ¼ 11 km.

Given an isotropic �� þ ��� flux, the number of taus thatemerge from the Earth with sufficient energy to be detectedis proportional to an ‘‘effective solid angle’’

�eff �Z

d cos�d cos�Pð�;Þ; (12)

where

Pð�;Þ ¼Z ‘

0

dz

L�CC

e�z=L�tot�½z� ð‘� L�Þ� (13)

is the probability for a neutrino with incident nadir angle �and azimuthal angle to emerge as a detectable �. (InEq. (13), for the reasons noted above, we have neglectedthe possibility of detectable signals from new nonpertur-bative physics by Earth-skimming neutrinos.) Here ‘ ¼2R cos� is the chord length of the intersection of theneutrino’s trajectory with the Earth, with R � 6371 kmthe Earth’s radius. Evaluating the integrals, we find [1]

�eff ¼ 2�L�tot

L�CC

½eL�=L�tot � 1�

���

L�tot

2R

�2 �

�L�tot

2Rþ

�L�tot

2R

�2�e�2R=L�

tot

�: (14)

At the relevant energies, the neutrino interaction lengthsatisfies L�

tot R. In addition, for L�tot � L�, valid when

the cross section enhancement is significant but not solarge as typical hadronic cross section, Eq. (14) simplifiesto [2]

�eff � 2�L�2totL

�

4R2L�CC

: (15)

Equation (15) gives the functional dependence of theEarth-skimming event rate on the new physics cross sec-tion. This rate is, of course, also proportional to the sourceneutrino flux ��all at E0. Given these inputs,

NES � CES

��all

��all

0

��2CC

ð��CC þ ��

NPÞ2; (16)

where CES ¼ 0:15 is the number of Earth-skimming eventsexpected for a fiducial flux ��all

0 in the absence of new

physics.In contrast to Eq. (16), the rate for quasihorizontal

showers has the form

NQH ¼ CQH

��all

��all

0

��CC þ ��

NP

��CC

; (17)

where CQH ¼ 0:06 for the Auger Surface Array, as deter-

mined in Sec. III.Given a flux ��all and new physics cross section ��

NP,bothNES andNQH are determined. On the other hand, given

just a quasihorizontal event rate NQH, it is impossible to

differentiate between an enhancement of the cross sectiondue to new physics and an increase on the flux. However, inthe region where significant event rates are expected thecontours of NQH and NES, given by Eqs. (16) and (17), are

more or less orthogonal and provide complementary infor-mation. With measurements of Nobs

QH and NobsES , both ��

NP

and ��all may be determined independently, and neutrinointeractions beyond the SM may be unambiguouslyidentified.We now turn to determining the projected sensitivity of

Auger to neutrino fluxes and cross sections. The quantitiesNES and NQH as defined in Eqs. (16) and (17) can be

regarded as the theoretical values of these events, corre-sponding to different points in the ��all=��all

0 � �NP=�CC

parameter space. For a given set of observed rates NobsES and

NobsQH, two curves are obtained in the two-dimensional

parameter space by setting NobsES ¼ NES and Nobs

QH ¼ NQH.

These curves intersect at a point, yielding the most prob-able values of flux and cross section for the given obser-vations. Fluctuations about this point define contours ofconstant �2 in an approximation to a multi-Poisson like-lihood analysis. The contours are defined by

�2 ¼ Xi

2½Ni � Nobsi � þ 2Nobs

i ln½Nobsi =Ni�; (18)

where i ¼ ES, quasihorizontal [34]. In Fig. 2, we showresults for three representative cases. Assuming (Nobs

ES ¼ 1,Nobs

QH ¼ 10) (NobsES ¼ 1, Nobs

QH ¼ 7) and (NobsES ¼ 1, Nobs

QH ¼5), we show the 90%, 95%, 99%, and 3� C.L. contours for2 d.o.f. (�2 ¼ 4:61, 5.99, 9.21, and 11.83, respectively).For Nobs

ES ¼ 1 and NobsQH ¼ 10, the possibility of a SM

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043001-5

interpretation along the ��NP ¼ 0 axis (taking into account

systematic uncertainties) would be excluded at greater than99% CL for any assumed flux. The power of the Earth-skimming information is such that the best fit consistentwith the SM would require a flux of about 50 times theWaxman-Bahcall flux, which is already excluded bypresent limits [35].

V. SUMMARY

We have reexamined a technique to search for newphysics at subfermi distances. The strategy involves deter-mining the ratio of quasihorizontal to Earth-skimmingshowers initiated by cosmic neutrinos which would needto be detected by the Pierre Auger Observatory in order tosignal the existence of exotic nonperturbative interactionsbeyond the TeV-scale. We perform Monte Carlo simula-tions of neutrino interactions in the Earth and in the atmo-sphere and realistic simulation of the detector acceptance

using the AugerOff line software. We find that observationof 1 Earth-skimming and 10 quasihorizontal events wouldexclude the standard model at the 99% confidence level. Ifnew nonperturbative physics exists, a decade or so wouldbe required to uncover it in the most optimistic case(cosmic neutrino flux at the Waxman-Bahcall level and

�N cross section about an order of magnitude above thestandard model prediction). The proposed Northern Augersite [36] (which has not been optimized for neutrino stud-ies) would reduce this time by about a factor of 2. Any hintof such an important signal would provide an impetus toinfill the array to increase the neutrino acceptance.

ACKNOWLEDGMENTS

We would like to thank Mandy Cooper-Sarkar for dis-cussions. L. A.A. is supported by the U.S. NationalScience Foundation (NSF) Grant No PHY-0757598, andthe UWM RGI. H.G. is supported by the NSF GrantNo PHY-0757959. D.G. is supported by the HHNG-128grant of the Helmholtz Association and the Polish Ministryof Science and Higher Education under Grant 2008No. NN202 127235. T. P. is supported by the NSF GrantNo PHY-0855388. M.R. is supported by the HHNG-128grant of the Helmholtz association. S. S. acknowledgessupport by the EU Marie Curie Network UniverseNet(HPRN-CT-2006-035863). L. L.W. is supported by theUWM RGI. Any opinions, findings, and conclusions orrecommendations expressed in this material are those ofthe authors and do not necessarily reflect the views of theNational Science Foundation.

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1

2

3

4

5

0 20 40 60 80 100 1200

1

2

3

4

5

FIG. 2 (color online). Projected determination of neutrino fluxes and cross sections atffiffiffis

p � 250 TeV from future Auger data. Thedifferent shaded regions indicate the 90%, 95%, 99%, and 3� confidence level contours in the ��all=��all

0 � �NP=�CC plane, for

NobsES ¼ 1, Nobs

QH ¼ 10 (left), NobsES ¼ 1, Nobs

QH ¼ 7 (middle), and NobsES ¼ 1, Nobs

QH ¼ 5 (right). The dashed line indicates the result of

including the systematic uncertainty on the next to leading order QCD charged current neutrino-nucleon cross section [37].

LUIS A. ANCHORDOQUI et al. PHYSICAL REVIEW D 82, 043001 (2010)

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