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Neutrino Physics and the Standard Model: Precision Measurements with High Intensity Future Beams
Nuclear Physics B (Proc. Suppl.) 188 (2009) 46–48 www.elsevierphysics.com
Neutrino Physics and the Standard Model: Precision Measurements with High Intensity Future Beams V. Antonellia a
∗
Dipartimento di Fisica, Universit` a di Milano and I.N.F.N. Sez. Milano, Via Celoria 16, Milano, Italy
Future experiments, planned to improve our knowledge of neutrino physics, will use neutrino beams of high intensities, never reached before. Hence, they will also offer the possibility of doing precision tests of the Standard Model at relatively low energies. We performed a full analysis of this possibility for superbeams and partially also for beta beams and here we report the main steps of the analysis and some results.
1. Physical Motivations of the Analysis Neutrinos played already in the past an essential role to prove the validity and perform precision tests of the Standard Model. The experimental evidences obtained in the recent years that they are massive and oscillating particles are the first clear indications of the need to go beyond the usual version of the Standard Model. In the near future the search for new physics will probably follow two parallel paths, exploring not only the higher energy, but also the high-intensity frontier. A very important contribution could come by future neutrino experiments and in particular by the ones that will use dedicated high intensity neutrino beams to fully determine the pattern of masses and mixing and to look for signals of mixing in appearance experiments or for CP violation. It has been shown already in literature that interesting studies of the electroweak and strong interactions could be performed at high energy neutrino factories. Here we present the first results of a similar analysis we performed for a low energy but high intensity neutrino beam, like the ones planned for superbeams [1] and eventually for beta beams[2]. We focused our attention on the possibility of using these beams to study neutrino nucleon interactions and to extract a com∗ I am deeply grateful to the organizers for the invitation, the perfect organization and for their kindness and professionality. I also would like to thank G. Battistoni, P. Ferrario and S. Forte who collaborated with me in the analysis on which this paper is mainly based.
0920-5632/$ – see front matter © 2009 Published by Elsevier B.V. doi:10.1016/j.nuclphysbps.2009.02.010
petitive estimate of the electroweak mixing angle at low energies. The Weinberg angle value is very well known at high energies, but it would be useful to improve our knowledge of this parameter at energies of the order of GeV or lower. This would be also a test of consistency of the theory over a wide range of energy. In the case of neutrino factories (in which neutrinos are produced at relatively high energies) the neutrinoelectron elastic scattering is a competitive process to measure the Weinberg angle. At lower energies, of the order of 1 GeV, typical for instance of superbeams, an interesting possibility is offered, instead, by the study of the quasi elastic contribution to neutrino-nucleon interactions. In this energy region the quasi elastic contribution is of the order of 50% of the total neutrino-nucleon cross section and it is not affected by the uncertainties typical of the inelastic contribution (mainly related to the knowledge of parton distributions and to the difficulties of a low energy perturbative treatment). This suggested us the idea to study in detail the possibility of recovering a low energy determination of the weak mixing angle from quasi elastic neutrino nucleon interaction. The analytical study showed the feasibility of this research project[3]. However, real experimental situations require a numerical analysis, that we performed. To estimate the accuracy reachable with the high intensity neutrino beams at future experiments, we generated a set of data that we used as our fictitious “experimental data” and,
V. Antonelli / Nuclear Physics B (Proc. Suppl.) 188 (2009) 46–48
by means of a χ2 analysis, we studied how well the results of the fit reproduce the experimental values we adopted for the Weinberg angle and the unknown hadronic form factors. 2. Guidelines of the Analysis and Experimental Set-up One of the main problems to face to get a good fit is to disentangle the dependence on the Weinberg angle from the one on the eight hadronic form factors entering the cross sections, which are only partially known [4]. The experimental observables would be in principle six (the different channels for quasi elastic neutrino-nucleon scattering), but they are reduced to four, because in the case of neutral currents only recoiling protons can be measured in real experimental situations (neutral currents on neutrons will not be detected). We investigated different angular bins (corresponding to different Q2 values). Hence it is important to consider an experimental set-up that can guarantee a satisfactory kinematic reconstruction of the event and, at the same time, to have a good control of the theoretical dependence of the form factors on Q2 value. This last requirement is one of the most tricky points of the analysis. In our study we assumed that the two electrical and the strange electric form factors are well known and we considered a one sigma variation for the pair of axial isotriplet and strange form factors (which have only a weak impact on the result of the Weinberg angle fit). We were, therefore, left with three form factors: the magnetic form factors for the nucleons (GnM (Q2 ) and GpM (Q2 )) and the strange magnetic one GSM (Q2 ) and we studied the possibility of fitting simultaneously the Weinberg angle and these form factors (or an appropriate subsystem of them). The analysis confirmed that a good fit requires first of all the knowledge of the form factor values at Q2 = 0 (forward region). In addition to this, one has to take into account also different Q2 values. For what concerns the experimental set-up, the natural choice of the detector is a Liquid Argon Time Projection Chamber (TPC), which offers the possibility, in principle, to identify protons with values of the momentum down to 50 MeV.
47
To be conservative we put a kinematic cut of 300 MeV for proton momentum, corresponding to values of Q2 ≥ 0.1 GeV2 ; even with this cut about 75% of the events survive. The main problem for this kind of detector is, instead, the difficulty to assemble large masses, in addition to the fact that nuclear reinteractions in Argon are more important than in water. In order to study the quasi elastic contribution, it is essential to select the energy region around 1 GeV; hence we focused our analysis on the study of neutrino beams having these energy vaules. This is a region of particular interest for the superbeams, like the T2K experiment (Tokai-to-Kamioka long baseline oscillation experiment). We showed that, with the typical T2K beam parameters, a liquid Argon near detector with a mass of the order of 1 kton can be sufficient to extract from the fit of the data a competitive low energy determination of the Weinberg angle. Most of the results we are going to report in this paper have been obtained in analyses done assuming to use a 10 ktons detector. 3. Possible Strategies and Main Results Different possible strategies and the consequent results will be discussed in a detailed way in [5]. Here we just report the main results we obtained using two alternative approaches. In a first kind of analysis we assumed that the exact Q2 functional dependence of the 3 form factors is known and adopted the expressions recently given in literature [6] for the two magnetic form factors of the nucleons (GpM (Q2 ) and GnM (Q2 )) and for the strange magnetic form factor (GSM (Q2 )). The study is quite difficult, due to the fact that the function giving the χ2 is essentially flat in the region of the minimum. Nevertheless it is possible to obtain a reasonable fit. The difference between the value of sin2 θW corresponding to χ2 minimum and the one we used to generate our set of data is of the order of 1% (or even lower), while the uncertainties in the fit is of a few permille [5]. We also tried to vary the functional form we adopted for the form factors we used to generate the data. In this way we studied the impact on the fit of our ignorance of the exact expressions for the form factors. Also the results of this
48
V. Antonelli / Nuclear Physics B (Proc. Suppl.) 188 (2009) 46–48
analysis are encouraging, as described in detail in [5]. Assuming that one of the two magnetic nucleon form factors is known and considering a global fit of the other form factor together with the strange magnetic one and the Weinberg angle, one gets very accurate estimates of the angle. For instance, by fitting the weak mixing angle together with GpM (Q2 ) and GSM (Q2 ) one gets the value sin2 (θW ) = 0.23040 ± 0.00046, to compare with the value sin2 (θW ) = 0.23120 used in data generation. The figures 1 and 2 show that in this case also the 2 form factors are well reproduced.
Figure 1. The 2 curves refer to the proton magnetic form factor GpM (Q2 ) versus Q2 and reproduce the experimental expression (full line) and the one obtained by the fit (dashed line).
Figure 2. Same of fig.1 but for GSM (Q2 ). The “experimental” curve is the lower one. We also performed a sort of “blind analysis”, without assuming any knowledge of the form fac-
tors and we reproduced them by using a neural network. The network succeeds very well in reproducing separately the different form factors. For instance, in the case of simultaneous fit of GSM (Q2 ) and sin2 (θW ), we generated the data with sin2 (θW ) = 0.23120 and the result of the fit is sin2 (θW ) = 0.23129 ± 0.00018. The analysis remains satisfactory also in the case of simultaneous fit of the Weinberg angle and two form factors (for instance GSM (Q2 ) and GpM (Q2 ) or GnM (Q2 )), despite a few problems in the reproduction of GpM (Q2 ) in the low Q2 bins. A particular attention must be paid to the correlation between the different form factors, which can be responsible of the existence of “fake solutions” of the fit, that is particular combinations of values of the Weinberg angle and the form factors which separately are different from the “experimental” values used to generate the data, but reproduce these data very well. This is the main difficulty we found in the study of the simultaneous fit of the three form factors and of the Weinberg angle. This case is still under investigation and it will probably require the use of complicate algorithms for the fit (like, for instance, genetic algorithms). REFERENCES 1. Y. Itow et al., arXiv: hep-ex/0106019; D.S. Ayres et al., hep-ex/0503053. 2. See, for instance: M. Mezzetto, J. Phys. Conf. Ser. 39 (2006) 329 and C. Volpe, J. Phys. G 34 (2007) R1-R44. 3. V. Antonelli, G. Battistoni, P. Ferrario and S. Forte, Nucl. Phys. Proc. Suppl. 168 (2007) 192; V. Antonelli, contribution to IFAE 2007Italian Meeting on High Energy Physics, pagg.271-275; P. Ferrario, Laurea Thesis, Milan University (July 2005). 4. I.C. Cloet et al, arXiv:nucl-th/0812.0416; J. Arrington, C.D. Roberts and J.M. Zanotti, J. Phys. G 34, S23 (2007); G.A. Miller, E. Piasetzky, G. Ron, arXiv:nucl-th/0711.0972. 5. V. Antonelli, G. Battistoni, P. Ferrario and S. Forte, work in progress. 6. R. Bradford et al., Nucl. Phys. Proc. Suppl. 159 (2006) 127; W.M. Alberico, S.M. Bilenky and C. Maieron, Phys. Rept. 358 (2002) 227.
Neutrino Physics and the Standard Model: Precision Measurements with High Intensity Future Beams V. Antonellia a
∗
Dipartimento di Fisica, Universit` a di Milano and I.N.F.N. Sez. Milano, Via Celoria 16, Milano, Italy
Future experiments, planned to improve our knowledge of neutrino physics, will use neutrino beams of high intensities, never reached before. Hence, they will also offer the possibility of doing precision tests of the Standard Model at relatively low energies. We performed a full analysis of this possibility for superbeams and partially also for beta beams and here we report the main steps of the analysis and some results.
1. Physical Motivations of the Analysis Neutrinos played already in the past an essential role to prove the validity and perform precision tests of the Standard Model. The experimental evidences obtained in the recent years that they are massive and oscillating particles are the first clear indications of the need to go beyond the usual version of the Standard Model. In the near future the search for new physics will probably follow two parallel paths, exploring not only the higher energy, but also the high-intensity frontier. A very important contribution could come by future neutrino experiments and in particular by the ones that will use dedicated high intensity neutrino beams to fully determine the pattern of masses and mixing and to look for signals of mixing in appearance experiments or for CP violation. It has been shown already in literature that interesting studies of the electroweak and strong interactions could be performed at high energy neutrino factories. Here we present the first results of a similar analysis we performed for a low energy but high intensity neutrino beam, like the ones planned for superbeams [1] and eventually for beta beams[2]. We focused our attention on the possibility of using these beams to study neutrino nucleon interactions and to extract a com∗ I am deeply grateful to the organizers for the invitation, the perfect organization and for their kindness and professionality. I also would like to thank G. Battistoni, P. Ferrario and S. Forte who collaborated with me in the analysis on which this paper is mainly based.
0920-5632/$ – see front matter © 2009 Published by Elsevier B.V. doi:10.1016/j.nuclphysbps.2009.02.010
petitive estimate of the electroweak mixing angle at low energies. The Weinberg angle value is very well known at high energies, but it would be useful to improve our knowledge of this parameter at energies of the order of GeV or lower. This would be also a test of consistency of the theory over a wide range of energy. In the case of neutrino factories (in which neutrinos are produced at relatively high energies) the neutrinoelectron elastic scattering is a competitive process to measure the Weinberg angle. At lower energies, of the order of 1 GeV, typical for instance of superbeams, an interesting possibility is offered, instead, by the study of the quasi elastic contribution to neutrino-nucleon interactions. In this energy region the quasi elastic contribution is of the order of 50% of the total neutrino-nucleon cross section and it is not affected by the uncertainties typical of the inelastic contribution (mainly related to the knowledge of parton distributions and to the difficulties of a low energy perturbative treatment). This suggested us the idea to study in detail the possibility of recovering a low energy determination of the weak mixing angle from quasi elastic neutrino nucleon interaction. The analytical study showed the feasibility of this research project[3]. However, real experimental situations require a numerical analysis, that we performed. To estimate the accuracy reachable with the high intensity neutrino beams at future experiments, we generated a set of data that we used as our fictitious “experimental data” and,
V. Antonelli / Nuclear Physics B (Proc. Suppl.) 188 (2009) 46–48
by means of a χ2 analysis, we studied how well the results of the fit reproduce the experimental values we adopted for the Weinberg angle and the unknown hadronic form factors. 2. Guidelines of the Analysis and Experimental Set-up One of the main problems to face to get a good fit is to disentangle the dependence on the Weinberg angle from the one on the eight hadronic form factors entering the cross sections, which are only partially known [4]. The experimental observables would be in principle six (the different channels for quasi elastic neutrino-nucleon scattering), but they are reduced to four, because in the case of neutral currents only recoiling protons can be measured in real experimental situations (neutral currents on neutrons will not be detected). We investigated different angular bins (corresponding to different Q2 values). Hence it is important to consider an experimental set-up that can guarantee a satisfactory kinematic reconstruction of the event and, at the same time, to have a good control of the theoretical dependence of the form factors on Q2 value. This last requirement is one of the most tricky points of the analysis. In our study we assumed that the two electrical and the strange electric form factors are well known and we considered a one sigma variation for the pair of axial isotriplet and strange form factors (which have only a weak impact on the result of the Weinberg angle fit). We were, therefore, left with three form factors: the magnetic form factors for the nucleons (GnM (Q2 ) and GpM (Q2 )) and the strange magnetic one GSM (Q2 ) and we studied the possibility of fitting simultaneously the Weinberg angle and these form factors (or an appropriate subsystem of them). The analysis confirmed that a good fit requires first of all the knowledge of the form factor values at Q2 = 0 (forward region). In addition to this, one has to take into account also different Q2 values. For what concerns the experimental set-up, the natural choice of the detector is a Liquid Argon Time Projection Chamber (TPC), which offers the possibility, in principle, to identify protons with values of the momentum down to 50 MeV.
47
To be conservative we put a kinematic cut of 300 MeV for proton momentum, corresponding to values of Q2 ≥ 0.1 GeV2 ; even with this cut about 75% of the events survive. The main problem for this kind of detector is, instead, the difficulty to assemble large masses, in addition to the fact that nuclear reinteractions in Argon are more important than in water. In order to study the quasi elastic contribution, it is essential to select the energy region around 1 GeV; hence we focused our analysis on the study of neutrino beams having these energy vaules. This is a region of particular interest for the superbeams, like the T2K experiment (Tokai-to-Kamioka long baseline oscillation experiment). We showed that, with the typical T2K beam parameters, a liquid Argon near detector with a mass of the order of 1 kton can be sufficient to extract from the fit of the data a competitive low energy determination of the Weinberg angle. Most of the results we are going to report in this paper have been obtained in analyses done assuming to use a 10 ktons detector. 3. Possible Strategies and Main Results Different possible strategies and the consequent results will be discussed in a detailed way in [5]. Here we just report the main results we obtained using two alternative approaches. In a first kind of analysis we assumed that the exact Q2 functional dependence of the 3 form factors is known and adopted the expressions recently given in literature [6] for the two magnetic form factors of the nucleons (GpM (Q2 ) and GnM (Q2 )) and for the strange magnetic form factor (GSM (Q2 )). The study is quite difficult, due to the fact that the function giving the χ2 is essentially flat in the region of the minimum. Nevertheless it is possible to obtain a reasonable fit. The difference between the value of sin2 θW corresponding to χ2 minimum and the one we used to generate our set of data is of the order of 1% (or even lower), while the uncertainties in the fit is of a few permille [5]. We also tried to vary the functional form we adopted for the form factors we used to generate the data. In this way we studied the impact on the fit of our ignorance of the exact expressions for the form factors. Also the results of this
48
V. Antonelli / Nuclear Physics B (Proc. Suppl.) 188 (2009) 46–48
analysis are encouraging, as described in detail in [5]. Assuming that one of the two magnetic nucleon form factors is known and considering a global fit of the other form factor together with the strange magnetic one and the Weinberg angle, one gets very accurate estimates of the angle. For instance, by fitting the weak mixing angle together with GpM (Q2 ) and GSM (Q2 ) one gets the value sin2 (θW ) = 0.23040 ± 0.00046, to compare with the value sin2 (θW ) = 0.23120 used in data generation. The figures 1 and 2 show that in this case also the 2 form factors are well reproduced.
Figure 1. The 2 curves refer to the proton magnetic form factor GpM (Q2 ) versus Q2 and reproduce the experimental expression (full line) and the one obtained by the fit (dashed line).
Figure 2. Same of fig.1 but for GSM (Q2 ). The “experimental” curve is the lower one. We also performed a sort of “blind analysis”, without assuming any knowledge of the form fac-
tors and we reproduced them by using a neural network. The network succeeds very well in reproducing separately the different form factors. For instance, in the case of simultaneous fit of GSM (Q2 ) and sin2 (θW ), we generated the data with sin2 (θW ) = 0.23120 and the result of the fit is sin2 (θW ) = 0.23129 ± 0.00018. The analysis remains satisfactory also in the case of simultaneous fit of the Weinberg angle and two form factors (for instance GSM (Q2 ) and GpM (Q2 ) or GnM (Q2 )), despite a few problems in the reproduction of GpM (Q2 ) in the low Q2 bins. A particular attention must be paid to the correlation between the different form factors, which can be responsible of the existence of “fake solutions” of the fit, that is particular combinations of values of the Weinberg angle and the form factors which separately are different from the “experimental” values used to generate the data, but reproduce these data very well. This is the main difficulty we found in the study of the simultaneous fit of the three form factors and of the Weinberg angle. This case is still under investigation and it will probably require the use of complicate algorithms for the fit (like, for instance, genetic algorithms). REFERENCES 1. Y. Itow et al., arXiv: hep-ex/0106019; D.S. Ayres et al., hep-ex/0503053. 2. See, for instance: M. Mezzetto, J. Phys. Conf. Ser. 39 (2006) 329 and C. Volpe, J. Phys. G 34 (2007) R1-R44. 3. V. Antonelli, G. Battistoni, P. Ferrario and S. Forte, Nucl. Phys. Proc. Suppl. 168 (2007) 192; V. Antonelli, contribution to IFAE 2007Italian Meeting on High Energy Physics, pagg.271-275; P. Ferrario, Laurea Thesis, Milan University (July 2005). 4. I.C. Cloet et al, arXiv:nucl-th/0812.0416; J. Arrington, C.D. Roberts and J.M. Zanotti, J. Phys. G 34, S23 (2007); G.A. Miller, E. Piasetzky, G. Ron, arXiv:nucl-th/0711.0972. 5. V. Antonelli, G. Battistoni, P. Ferrario and S. Forte, work in progress. 6. R. Bradford et al., Nucl. Phys. Proc. Suppl. 159 (2006) 127; W.M. Alberico, S.M. Bilenky and C. Maieron, Phys. Rept. 358 (2002) 227.