1. Nucleon Decay Search in the Detector on the Earth’s Surface. Background Estimation. J.Stepaniak Institute for Nuclear Studies Warsaw, Poland FLARE Workshop 4-6 October 2004

2. Introduction The decay of the a nucleon is a possible experimental window into fundamental processes at high mass scale. Supersymmetric GUT models generally favour decay modes with strange quark. But e.g. in SUSY S0(10) version the lepton-eta mode is predicted with large branching ratio. The exact nature of the possible nucleon decay is not known. Therefore the search of the decay both protons and neutrons in a variety of channels even exotic is of interest.

3. Present experimental limits on the nucleon lifetime are better than 10 32 for several decay channels. The limit of such order can be achieved in the 1 kton detector in one year for background free channel with selection efficiency close to one. The efficiency for some channels of interest is low in the the water Cherenkov detectors. For example: in Super-Kamiokande selection efficiency in the case of p-> K + was about 5% and for p-> e + η decay 17%. The liquid Argon detector can provide efficiency better than 95% for both channels due to excellent tracking, and particle identification capabilities.

4. In the deep underground detectors the main source of background to the nucleon decays comes from neutrino interactions. The background from the neutrino interactions in liquid Argon was discussed by A.Rubbia (hep-ph/0407297) and generally was found to be small. We discuss here only the background due to interactions of neutral component of the cosmic rays on the surface of the Earth.

5. Decay channels with K + Background is expected from interactions of atmospheric neutrons and neutral kaons. At sea level, about 1/3 of nucleons above 1GeV/c are neutrons. The integral intensity of vertical neutrons above 1GeV/c is 0.5 m -2 s -1 sr -1 It is about 0.7% with respect to atmospheric muons above 1 GeV/c momentum.

6. Strangeness conservation requires associated production of the K + with Lambda or kaon. The reaction involving  is two orders of magnitude more frequent than the kaon pair production. Possible chain of the reaction without additional charge particles in the final state is: with the hyperfragment formation (less than1% of events) and the lambda nonmesonic decay (>99% for A>20). Cross section for the pn->n  K + was not measured. It can be estimated from the pp->p  K +, for which several experimental point exist.

7. The cross section for pp->p  K + grows quickly from threshold at 1.58 GeV to about 50μb and remains stable until at least 12 GeV. From the measurement on the deuteron the ratio of cross sections on neutron to that on proton near threshold σ n /σ p ≈3 (Buscher 2004). It leads to the upper limit for the cross section on the neutron about 150μb. Three rather fast neutrons are produced in addition to K + and their interactions can be searched for. The probability, that non of the three neutrons undergo inelastic interaction within 1m from the interaction point is e -x/Λ ≈ e -3 since x =1

8. 1 m -2 s -1 neutrons at the sea level?. It is an upper limit because one can exclude the events with shower particles In the neighborhood.. about 0.007 m -2 s -1 remains after fiducial cut 5m top layer of Argon. 150 μb / 40 mb = 4 *10 -3 neutrons produce K + Λ The same ratio can be assumed for neutron-Ar: the A 0.6-0.7 dependence has been found for K + production (Buscher nucl-ex/0401031) and cancels with 2/3 for total cross section. About 0.2 K + is in the momentum range compatible with that from p decay taking into account Fermi momentum (0.2-0.5 GeV/c). About 0.5% Lambda can be trapped on the neutron in nucleus.

9. Background for channels with K + from interactions of neutrons N B = 0.007∙4∙10 -3 ∙0.2∙0.005∙0.05 m -2 s -1 = 1.4∙10 -9 m -2 s -1 = ≈4.4∙10 -2 m -2 year -1 About 0.04 /year/m 2 background events for vK +. For the channels with charged lepton and the kaon a few order of magnitude less.

10. Background for the channels with K + from the atmospheric K 0 The approximate flux of K 0 ‘s on the Earth surface is about six order of magnitude less than the muons. Only K 0 L can survive the fiducial cut. Cross section for charge exchange can be estimated from the reverse reaction K + +n -> K 0 +p (σ≈2mb) Fraction of the neutral kaons that produce K + without other charged particles: 2mb/30mb/2=0.033 The interaction of the neutron should not be observed (≈1/e). After fiducial cut at 5m ≈0.0067 N B =7∙10 -5 ∙ 0.033∙6.7 10 -3 ∙0.37 = 5.7 10 -9 m -2 s -1 = =0.18 m -2 y -1

11. If the charged lepton is expected in the final state the background should be at least three order of magnitude smaller. In addition the cut on invariant mass can be applied.

12. Decay channels with η meson In Liquid Argon detector the major η decay channels (γγ, 3π 0 and π + π - π 0 ) can be recognised and reconstructed with efficiency better than 95%. Background expectations are less favourable. The cross section for the η production in neutron-nucleon collision convoluted with the neutron flux energy dependence is of the order of 100 μb. Lower threshold momentum than for K + (1.254 MeV).

13. The main background is from nn ->nnη reaction N B = 0.007∙2.7 ∙10 -3 ∙0.2∙0.14 m -2 s -1 = 5.2∙10 -7 More stringent fiducial cut (10 m) or the presence of charged lepton is needed to achieve better limit than 10 32. N B = 5.2∙10 -7 ∙0.007∙0.001 = 3.6∙10 -12 m -2 s -1

14. Decay channels with K - The background is from the K 0 L charge exchange : the approximate flux of K 0 at earth is about six order of magnitude less than the muons. Cross section for charge exchange from the reverse reaction of the K+ about 2 milibarns. In addition proton from K 0 +n→ K - + p cannot be seen (E<5MeV) The charged lepton should be observed (<0.001 factor). At the momentum below 500 MeV/c minimum angle between photon showers from the  0 →  decay is larger than 30 0. Very small chance to take it for one shower.

15. N B =7∙10 -5 ∙0.02∙0.001= 1.4∙10 -9 m -2 s -1 = 4.4∙10 -2 y -1 m -2 It is similar to the signal if lifetime ≈10 33 y. In addition the cut on invariant mass can be applied. More stringent fiducial cut would also help..

16. The obtained numbers of background events should be compared with the number of nucleons after 1 meter squared: The number of nucleons in 30 m 3 of Argon (1m 3 times height of the detector) is equal to about 0.3∙10 32. It leads to about 0.3 decays per year in such a volume for the lifetime 10 32.

17. Conclusions Approximate calculations of atmospheric backgrounds for nucleon decays search have been performed. The present lifetime limits can be shifted by at least two order of magnitude especially for channels with charged leptons and strange meson. The validity of some assumptions should be checked.

18. To be done: 1. MC calculation of the flux and energy distribution of isolated atmospheric neutrons and neutral kaons. 2.MC study of the K0 and the neutron propagation through the detector including the scanning and reconstruction of the events. The new experimental data on the relevant cross sections have to be included in the code. 3.Distinction between the electron shower and the  0 asymmetric decay has been assumed at the level of 10 -3. It is probably rather pessimistic value. It should be carefully studied as a function of the pion energy.