mohammad sajjad athar m honda - indian institute of ... · mohammad sajjad athar1 m honda2 1aligarh...

Atmospheric Neutrino Flux

Mohammad Sajjad Athar1

M Honda2

1Aligarh Muslim University, India

2University of Tokyo, Japan

M. Sajjad Athar (AMU, India) DAE-HEP @ IIT, Guwahati 2014 1 / 54

Outline

1 Introduction

2 Atmospheric Model

3 Effect of the earth’s magnetic field

4 Muon flux at INO

5 Neutrino Flux

6 Conclusions

Sites for the Atmospheric Neutrino Experiment

Kamioka Lat 36.426 Long 137.310

INO Lat 9.967 Long 77.267

South Pole -90.0 0.0

Pyhasalmi mine Lat 63.661 Long 26.035

PRIMARY COSMIC RAY SPECTRUM

For us the region of interest is up to 1014−1015 eV

PRIMARY COSMIC RAY SPECTRUM

For us the region of interest is up to 1014−1015 eV

The primary cosmic rays interact with the air nuclei mainly in the altituderange from 10km to 20km.

p+Aair→ n+π++Xn+Aair→ p+π−+X

π+→ µ++νµ

π−→ µ−+ νµ

µ+→ e++ νµ +νe

µ−→ e−+νµ + νe

Since the energy of the neutrons created by the first interaction in the abovereaction is lower than that of incident protons, therefore, the number andaverage energy of the π+ are larger than that of the π−.

π+→ µ++νµ

Proton is dominant in the cosmic ray composition, therefore, there is alwaysan excess of π+ to π− by 20%. Consequently we expect 20% excess of νe toνe.

The atmospheric neutrino flux is a convolution ofΦp : the primary cosmic ray flux of proton(p) or nuclei of mass A outside theinfluence of the geomagnetic fieldRp: takes care of the filtering effect of geomagnetic fieldY : yield of neutrinos per primary particle

Φνi = Φp⊗Rp⊗Yp→νi +∑A [ΦA⊗RA⊗YA→νi ]

Discrepancies in the observed spectra below 10 GeV for protons and 5 GeV/Nfor helium nuclei come from the difference of solar activity (around minimumin 1998 and around maximum in 2002).

Physics Letters B 594 (2004) 35.

The overall uncertainties including both statistical and systematic errors areexpected to be less than 15% for protons, helium nuclei and muons.

Discrepancies in the observed spectra below 10 GeV for protons and 5 GeV/Nfor helium nuclei come from the difference of solar activity (around minimumin 1998 and around maximum in 2002).

Physics Letters B 594 (2004) 35.

The overall uncertainties including both statistical and systematic errors areexpected to be less than 15% for protons, helium nuclei and muons.

Solar Modulation

1 The sun emits a magnetized plasma with a velocity of 400km/sec in thesolar equatorial region and about twice as fast over the solar poles.

2 To reach earth and interact in the atmosphere, galactic cosmic rays mustdiffuse into the inner heliosphere against the outward flow of theturbulent solar wind, a process known as solar modulation.

3 Particles of very low energy outside the heliosphere are almostcompletely excluded, and higher energy particles loose energy as theydiffuse in.

4 During periods of high solar activity corresponding to solar maximum,the turbulence in the solar wind is higher than during solar minimum,and the low energy portion of the spectrum is more suppressed.

Solar Modulation

Proton spectra

1997 −→ 2000 Year in the order of increasing Solar Activity

Proton Spectra measured by BESS and AMS experiments.M. Sajjad Athar (AMU, India) DAE-HEP @ IIT, Guwahati 2014 9 / 54

It may be noted that there are large seasonal variation of atmosphere in polarregions (South Pole and Pyhasalmi).

In both the regions, with the increase in altitude, the air density gets higher inthe summer and lower in the winter.

Accordingly, we expect some seasonal variation of atmospheric neutrino fluxespecially in the polar regions.

We study the seasonal variation of neutrino flux, dividing one year into fourseasons, March – May, June – August, September – November, andDecember – February.

Atmospheric Model

MSISE-00 is a new atmospheric model, which is an empirical, globalmodel of the Earth’s atmosphere from ground to space. In this model thedensity, pressure and the composition is expressed as the function of theposition on the earth, as well as it takes into account altitude and the timevariation in a year.

Earlier U. S. Standard Atmosphere 1976 were being used but this givesthe atmospheric density profile as the function of altitude only.

MSISE-00 takes care of positional and seasonal variations ofatmospheric profile.

Using this new code one can study the time variation of atmosphericneutrino flux in a year, and azimuth angle dependence of it at highenergies, which is not expected from US-standard’76.

A. E. Hedin http://ccmc.gsfc.nasa.gov/models/modelinfo.php?model=MSISEM. Sajjad Athar (AMU, India) DAE-HEP @ IIT, Guwahati 2014 11 / 54

Atmospheric Model

The ratio of air density in NRLMSISE-00 model to that of US-standard’76, andthe variation for four seasons in a year for SK-site(KAM) and INO site(INO).

The ratio of air density in NRLMSISE-00 model to that of US-standard’76,and the variation for four seasons in a year for South pole(SPL), andPyhasalmi(PYH).

New target nuclei like Ne, Mg, Ar,etc. are produced in the earth’s atmospherethrough the interaction of primary cosmic rays(p, He).For this we have used JAM which is a hadronic interaction model. JAM is alsoresponsible for the production of Pions, Kaons, etc.

All particle spectrum as a function of E (energy/A) from air showermeasurements.

For the interaction of Primary Cosmic Ray Particles with Air Nuclei:JAM, has been used for the kinetic energy of primary cosmic ray fluxsmaller than 32GeV.

The JAM interaction model agrees with the HARP experiment and hasbeen found to be better than DPMJET-III in this energy range.

For primary cosmic ray flux energies greater than 32GeV DPMJET-III isbeing used.

We have used DPMJETIII for energies > 32 GeV because JAM isunstable at around 100GeV.

Earlier this code has been applied to study the muon flux as well as theatmospheric neutrino flux for the Gran Sasso, Frejus, Kamioka andother sites where atmospheric muon flux at sea level, at mountainaltitudes, and at balloon altitudes have been measured and found to beconsistent with the Monte Carlo generator.

Steps to obtain atmospheric neutrino flux

First step is to get primary cosmic ray flux, which has been obtained usingBESS and AMS data.

The next step is to allow p.c.r. to interact with the atmosphere. For thisNRLMSISE-00 atmosphere model has been used. It expresses air density asthe function of position on the Earth and the time of the year.

The interaction of p.c.r. with atmosphere has been taken into account usingJAM interaction for the kinetic energy of p. c. r. flux less than 32GeV andDPMJET-III for energies greater than 32GeV. These interactions wouldproduce heavier seed nuclei as well as secondary cosmic ray particles.

Another big task that is left is to consider Geomagnetic field of the Earth.

In spite of using the same primary flux model and the interaction model forthe different sites, the calculated atmospheric neutrino fluxes are different dueto the variation in the geomagnetic field.

The Earth has a magnetic field, which is generated by electric currents in itscore. If the Earth were located in empty space, the magnetic field outside itsbody would be similar to that of a bar magnet, a dipole, located somewhat offthe center of the Earth, and inclined to its axis of rotation.This off axis is responsible for the major effect due to the geomagnetic field inthe equatorial region where INO lies.

Different Atmospheric Neutrino Sites

Lat 36.426 Long 137.310 KamiokaLat 43.490 Long -81.180 SNOLat 42.750 Long 13.650 GranSassoLat 45.142 Long 6.689 FrejusLat 9.967 Long 77.267 INO-90.0 0.0 South PoleLat 44.360 Long -103.760 HomestakeLat 63.661 Long 26.035 Pyhasalmi mine

IGRF2010 Model for the Geomagnetic Field has been used

Horizontal component of magnetic field

↑ Latitude −→ LongitudeM. Sajjad Athar (AMU, India) DAE-HEP @ IIT, Guwahati 2014 19 / 54

Effect of Geomagnetic field

The geomagnetic field affects cosmic rays both inside and outside of the atmo-sphere.

Firstly it acts as a filter for low energy cosmic rays, and secondly, it deflectsthe charged particles in the atmosphere.

These two effects are mainly controlled by the horizontal component of thegeomagnetic field. Whether a particle is allowed or forbidden is determined byits position, direction and radius of curvature.

Only particles that interact with the atmosphere before curving back into spacecan contribute to the flux of atmospheric neutrinos.

For example, the INO site is close to the region where the strength of the hor-izontal component of the magnetic field is maximum in comparison to all theother ongoing or proposed neutrino experiments, and the South Pole site hasthe minimum.

Geomagnetic Field

Cosmic ray particle travels through empty space until it encounters the mag-netosphere at some distance from the Earth. It depends upon E0, geomagneticcutoff energy where no particle gets access to the atmosphere.

If the incoming cosmic ray proton has avery high energy, it will travel along anearly straight line.

If E< E0, its trajectory will be bent by themagnetic field into a semi-circle withsuch a small radius that the proton willnot reach the atmosphere.

Particles at intermediate energies reachthe atmosphere along a curved path. Thecurvature is stronger for the lower energy.

Red shading at the borders of the map is for regions where protons with energybelow 125 MeV can penetrate to the atmosphere (20 km above the ground),while energies above 15 GeV (green colour within the closed contour) are re-quired in equatorial regions above Southern Asia.

As one approaches the magneticequator, the minimum energy cutoff required for cosmic rays toreach the atmosphere becomeslarger.

The cutoff energies are higherwithin the closed contour abovesouthern Asia, because the Earthsdipole is located somewhat outsidethe center of the Earth.

Comparison of JAM(solid line) and DPMJET-III(dashed line)interaction models with HARP data. The change of the hadronicinteraction model mainly results in a change in the prediction of lowenergy neutrino flux(E < 1GeV).

Comparison of muon flux observed at Tsukuba(30m a.s.l.), Mt.Norikura(2770 a.s.l.) and balloon altitudes at Fort Summer.

Fractional contribution of pions and kaons to the flux of muons andneutrinos. Solid lines indicate the vertical and dashed lines indicate600.

Convention

In the particle simulation, we use the earth-coordinate system. We haveconsidered origin to be at the center of the earth, and treat Earth to be asphere of radius Re=6378.14km.

The Z-axis is the line from the origin to North pole, the X-axis is the linefrom the origin to (lat, lon) = (00, 00) direction and the Y-axis is the linefrom the origin to (lat, lon) = (00,900) direction.

At an observation site with (X,Y,Z) in earth-coordinate system, the localcoordinate system at the site is defined as

the Z-axis directed towards the Zenith

the X-axis directed to South, parallel to the latitude decreasing direction,

the Y-axis directed to East, parallel to the longitude increasing direction.

The azimuth angle is measured in the anticlockwise direction from theSouth(φ=00), East(φ=900), North(φ=1800) and West(φ=2700);x = r sin(θ) cos(φ); y = r sin(θ) sin(φ); z = r cos(θ), where θ is the zenithangle for a point (x,y,z) in local coordinate system.

Convention

Muon flux in the different zenith angle bin: at INO

Muon flux vs Azimuthal angle: at INO

We find that

The variation of the atmospheric neutrino flux has complex structures at1GeV due to the rigidity cutoff and muon bending in the geomagnetic field.

The variation of upward going neutrinos −0.2 > cosθ is much morecomplicated than the variation for the downward going neutrinos cosθ > 0.2.

This is because the upward going neutrinos are produced in a far larger areaon Earth than the downward going neutrinos, and are affected by largevariation of rigidity cutoff and geomagnetic field.

Because of the muon bending due to earth’s geomagnetic field the neutrinoflux shows strong azimuthal dependence.

The geomagnetic field deflects µ+ towards the same direction as p.c.r.Therefore, it enhances the difference between East and West for νµ and νe

fluxes.

While the geomagnetic field acts in the opposite direction on µ− to that ofp.c.r. Therefore, it reduces the difference between East and West for νe and νµ

fluxes.

We find that

fluxes.

We find that

fluxes.

We find that

fluxes.

We find that

fluxes.

We find that

fluxes.

Conclusions

1 Fluxes are almost larger by a factor of 3 at lower energies(<1GeV) at theSouth Pole and Pyhasalmi than at INO. Beyond 5GeV the differencebecomes smaller.

2 The calculated atmospheric neutrino flux at tropical site (INO) has astrong effect due to the horizontal component of the geomagnetic field.

One is due to the rigidity cutoff that reduces the vertically down goingneutrino flux, which is significant even at 3.2 GeV.

Second reason is the muon bending that causes a large azimuthalvariation of neutrino flux. Also it reduces the neutrino flux for thehorizontal direction.

3 Using NRLMSISE-00, we find the variation of the production height ofatmospheric neutrinos. The variation is small at SK site, and is almostinvisible at INO site.

4 We find that the production height has large azimuth variations for thehorizontal direction.

Conclusions

mohammad sajjad athar m honda - indian institute of ... · mohammad sajjad athar1 m honda2 1aligarh...

Documents