Expression of Interest for
Neutrinos Scattering on Glass:
We propose a 3500 ton (3000 ton fiducial volume) neutrino detector with sampling calorimetry, charged particle tracking, and muon spectrometers to run in a Tevatron Fixed Target Program. Improvements to the Fermilab accelerator complex should allow substantial increases in the neutrino flux over the previous NuTeV quad triplet beamline. With 4 10 protons on target/year, a 5 year run would achieve event statistics more than 100 times higher than NuTeV. With 100 times the statistics of previous high energy neutrino experiments, the purely weak processes and (inverse muon decay) can be measured with high accuracy for the first time. The inverse muon decay process is independent of strong interaction effects and can be used to significantly improve the flux normalization for all other processes. The high neutrino and antineutrino fluxes also make new searches for lepton flavor violation and neutral heavy leptons possible. In this document, we give a first look at the physics opportunities, detector and beam design, and calibration procedures.
T. Adams, L. Bugel, J.M. Conrad, P.H. Fisher,
A. de Gouvêa, W.A. Loinaz, G. Karagiorgi, T.R. Kobilarcik, S. Kopp,
G. Kyle, D.A. Mason, R. Milner, J. G. Morfín, M. Nakamura,
D. Naples, P. Nienaber, F.I Olness, J.F. Owens, W.G. Seligman,
M.H. Shaevitz, H. Schellman, M.J. Syphers, C.Y. Tan,
R.G. Van de Water, R.K. Yamamoto, G.P. Zeller
Amherst College, Amherst, MA 01002
Columbia University, New York, NY 10027
Fermi National Accelerator Laboratory, Batavia IL 60510
Florida State University, Tallahassee, FL 32306
Los Alamos National Accelerator Laboratory, Los Alamos, NM 87545
Massachusetts Institute of Technology, Cambridge, MA 02139
Nagoya University, 464-01, Nagoya, Japan
New Mexico State University, Las Cruces, NM 88003
Northwestern University, Evanston, IL 60208
University of Pittsburgh, Pittsburgh, PA 15260
Saint Mary’s University of Minnesota, Winona, MN 55987
Southern Methodist University, Dallas, TX 75205
University of Texas, Austin TX 78712
- 1 Introduction
2 Physics Opportunities
- 2.1 Electroweak Precision Measurements
- 2.2 The NuTeV Anomaly
- 2.3 Direct Searches for New Physics
- 2.4 Measurement of Parton Distribution Functions
3 Neutrino Flux and Event Rates
- 3.1 The Neutrino Flux
- 3.2 Event Rates
- 3.3 Precision Measurement of the Flux from Events in the Detector
- 4 Preliminary Design
- 5 Summary
The Neutrino Scattering on Glass (NuSOnG) experiment will consist of four detector modules, each composed of a finely segmented calorimeter followed by a muon spectrometer. The detector will be illuminated by a neutrino or antineutrino beam from the Tevatron. In its five-year data acquisition period, NuSOnG will make precise measurements of three types of neutrino scattering and will accumulate the world’s largest sample of electron-neutrino scatters. These data will provide unique opportunities to discover physics beyond the Standard Model (including, inter alia, lepton flavor violation and new particles) as well as determine structure functions over a wide range of and . The breadth of anticipated measurements makes NuSOnG a program rather than an experiment; the design heritage ensures that the approach is low-risk and cost-effective.
This Expression of Interest arises from our view that an experiment probing the high energy interactions of neutrinos is a necessary complement to the LHC and an important lead-in to the ILC. In the next few years, the LHC will reveal the nature of electroweak symmetry breaking; the Higgs mass will cease being a prediction of the electroweak theory and will become an input to the theory. Without the Higgs mass as a fit parameter, precision electroweak data, including neutrino scattering data, will be much more powerful as a tool for constraining that physics beyond the Standard Model which directly influences the electroweak sector. More important still, precision neutrino scattering will probe areas of phenomenology that may be inaccessible to the LHC and ILC. NuSOnG is not a precision test of the Standard Model; NuSOnG is a discovery experiment aimed at the terrain not covered by the collider experiments.
This Expression of Interest presents the physics case and initial design for NuSOnG. The detector draws on the heritage of FMMF, CDHS, CHARM and CCFR/NuTeV. The design uses an SiO target in one-quarter radiation length panels interleaved with active detector elements (proportional tubes and/or scintillator). This will provide the very high segmentation needed to ensure good separation between different classes of events. We will develop these ideas in the coming months and submit a proposal to the Fermilab Directorate.
2 Physics Opportunities
The physics opportunities of the experiment arise from NuSOnG’s uniquely high statistics: 20k neutrino-electron scatters and 100M neutrino-quark scatters. Roughly equal statistics will be obtained from antineutrino scattering. More information on the event rates for various processes is given in Sec. 3. These rates present a wide range of physics opportunities including precision electroweak measurements, direct searches for new physics, and parton distribution studies.
2.1 Electroweak Precision Measurements
NuSOnG’s considerable discovery potential derives from its ability to do precision electroweak tests through two independent channels: electron scattering and quark scattering. These measurements probe for new particles and new neutrino properties beyond the present Standard Model. As examples, NuSOnG will be sensitive to extra bosons with masses beyond the 1 TeV scale (depending on the model), and to compositeness scales above 5 TeV. Thus the energy scales explored by this experiment overlap the LHC, and we present the discovery potential for the new physics we will explore within this context. This experiment also directly addresses questions raised by the “NuTeV anomaly,” an electroweak precision measurement in disagreement with the Standard Model.
2.1.1 Electroweak Measurements in Neutrino Scattering
NuSOnG is sensitive to new physics through neutral current (NC) scattering. The exchange of the boson between the neutrino and fermion leads to the effective interaction:
where the Standard Model values of the couplings are:
Here, and are the weak isospin and electromagnetic charge of fermion , respectively. In these formulae, is the relative coupling strength of the neutral to charged current interactions ( at tree level in the Standard Model). The weak mixing parameter, , is related (at tree level) to to , and by
NuSOnG is unique in its ability to test the NC couplings by studying scattering of neutrinos from both electrons and quarks. A deviation from the Standard Model predictions in both the electron and quark measurements will present a compelling case for new physics.
Neutrino Electron Scattering
The differential cross section for muon neutrino and antineutrino scattering from electrons, defined using the coupling constants described above, is:
The upper and lower signs corresponding to the neutrino and anti-neutrino cases, respectively. In this equation, is the incident energy and is the electron recoil kinetic energy.
More often in the literature, the cross section is defined in terms of the parameters , which are defined as
In terms of these parameters, we can write:
When , the third terms in these expressions can be neglected. If we introduce the variable , then
Integrating over the region , we obtain the total cross sections which are
The ratio of the integrated cross sections for neutrino to antineutrino electron scattering is
Many systematics, including flux errors, cancel in this ratio, as does the dependence. Fig. 1(top) shows the results for from many past experiments.
NuSOnG will make independent measurements of the electroweak parameters for both and -electron scattering. We can achieve this via ratios or by direct extraction of the cross section. In the case of -electron scattering, we will use the ratio of the number of events in neutrino-electron elastic scattering to inverse muon decay:
Because the cross section for IMD events is well determined by the standard model, this ratio should have low errors and will isolate the EW parameters from NC scattering. In the case of running, the ratio is more complex because there is no equivalent process to inverse muon decay (since there are no positrons in the detector). In this case, we use the fact that, for low exchange energy in Deep Inelastic Scattering, the cross sections in neutrino and antineutrino scattering approach the same constant, , as is explained in Sec. 3.3.2. Thus, for Deep Inelastic events with low energy transfer and hence low hadronic energy ( GeV), and . The result is that we can extract the electroweak parameters to high precision using the ratio:
The first ratio cancels the DIS cross section, leaving the energy-integrated to flux ratio. The IMD events in the denomenator of the second term cancel the integrated flux. The NC elastic events cancel the integrated flux. Alternatively, because we will have accurate knowledge of the flux as a function of the energy (see Sec. 3.3) we could directly measure the cross sections.
An important point is that the two independent measurements, one in neutrino and the other in antineutrino mode, will in turn allow independent extraction of and . The previous best measurement from and cross-section measurements is from CHARM II, which used 267782 events in neutrino mode and 275288 events in antineutrino mode  to find
This can be compared to electroweak measurements from LEP provide a very precise prediction of these parameters :
The CHARM II results are in agreement with LEP, but with large errors. Errors on the neutrino measurement must be substantially reduced in order to meaningfully probe for physics beyond the Standard Model. The goal of NuSOnG is to measure the neutrino-electron and antineutrino-electron cross sections to .
18.104.22.168 Neutrino Quark Scattering
Substantially higher precision has been obtained using neutrino-quark scattering, which compares neutral-current (NC) to charged-current (CC) scattering to extract . However, these experiments are subject to issues of modeling in the quark sector. Fig. 1(bottom) reviews the history of these measurements.
The lowest systematic errors come from implementing a “Paschos-Wolfenstein style”  analysis, which would be the technique used by NuSOnG. This requires separated and beams, for which the following ratios could be formed:
Paschos and Wolfenstein  recast these as:
where . In many systematics cancel to first order, including the effects of the quark and antiquark seas for , and . Charm production only enters through (which is Cabbibo suppressed) and at high ; thus the error from the charm mass is greatly reduced. The cross section ratios can be written in terms of the effective neutrino-quark coupling parameters and as
NuTeV fit for and simultaneously to extract obtaining the value . The goal of NuSOnG is to improve on this error by a factor of two. Table 1 lists the errors which NuTeV identified and indicates those for which NuSOnG expects improvement. Many of the largest experimental systematics of NuTeV came from the method of separating CC and NC events, which relied on length. NuSOnG will have a more sophisticated model for differentiating CC and NC events, using shower shape and identification of Michel-electron followers from low energy pion decays.
|Error||Reduction in NuSOnG|
|Statistics||0.00135||100 times the statistics|
|, flux prediction||0.00039||see Sec. 3.3.6|
|Interaction vertex position||0.00030||Better detector segmentation and|
|more sophisticated shower identification.|
|Shower length model||0.00027||Better segmentation and|
|more sophisticated shower identification.|
|Counter efficiency and noise||0.00023||Better, Minos-style counter design|
|Energy Measurement||0.00018||Likely to be at a similar level.|
|Charm production, strange sea||0.00047||See Sec. 2.4.4|
|0.00032||Likely to be at a similar level.|
|0.00022||See Sec. 2.4.5|
|Higher Twist||0.00014||Likely to be at a similar level.|
|Radiative Corrections||0.00011||Likely to be at a similar level.|
|Charm Sea||0.00010||Under study|
|Non-isoscalar target||0.00005||Glass is isoscalar|
From Fig. 1, it is apparent that the NuTeV measurement is in agreement with past neutrino scattering results, although these have much larger errors. However, the NuTeV result is in disagreement with the global fits to the electroweak data which give a Standard Model value of . Expressed in terms of the couplings, NuTeV measures:
which can be compared to the Standard Model values of and , respectively. Sec. 2.2 (below) considers possible sources for this disagreement, both within and outside the Standard Model.
2.1.2 NuSOnG and New Physics
NuSOnG will provide important probes of physics beyond the Standard Model distinct from and complementary to those of the LHC. NuSOnG will seek indirect evidence for new physics by addressing anomalies in the precision electroweak data, and by providing unique information about neutrino coupling to the . In addition, precision measurements from NuSOnG will help to disentangle the complicated set of observations that will be present at the LHC and, in doing so, elucidate the mechanism of electroweak symmetry breaking. NuSOnG and the LHC provide distinct probes of new physics because new physics enters collider and neutrino scattering processes differently: neutrino physics measures different combinations of couplings to light quarks; neutrino scattering probes new physics at space-like momentum transfer (versus the time-like scattering at colliders); and systematics are very different between low and high energy experiments. Finally, NuSOnG will directly search for new particles and interactions in the lepton sector that might be missed by the LHC and must otherwise await discovery by the ILC.
22.214.171.124 New Physics Observed through Coupling to the
NuSOnG is unique among experiments in its ability to address the nature of the neutrino couplings to the boson in the near future. In the Standard Model, the neutrino coupling to the - and -bosons is purely left-handed. Indeed, the fact that the neutrino coupling to the -boson and an electron is purely left-handed is, experimentally, a well-established fact (evidence includes precision measurements of pion and muon decay, nuclear processes, etc.). By contrast, the nature of the neutrino coupling to the boson is, experimentally, far from being precisely established .
The best measurement of the neutrino coupling to the -boson is provided by indirect measurements of the invisible -boson width at LEP. In units where the Standard Model neutrino–-boson couplings are , , the LEP measurement  translates into . Note that this result places no meaningful bound on .
Precise, model-independent information on can be obtained by combining scattering data from CHARM II and LEP and SLD data. Assuming model-independent couplings of the fermions to the -boson, scattering measures , while LEP and SLD measure the left and right-handed couplings of the electron to the . The CHARM II result translates into , assuming that the charged-current weak interactions produce only left-handed neutrinos. In spite of the good precision of the CHARM II result (around 3.5%), a combination of all available data allows at the two confidence level .
Significant improvement in our understanding of can only be obtained with more precise measurements of scattering, or with the advent of a new high intensity collider, such as the ILC. By combining ILC running at the -boson pole mass and at GeV, could be constrained at the two level after analyzing missing energy events .
At NuSOnG, we estimate that can be measured at around the 0.86% level. This estimate is obtained by combining the statistical uncertainty (20,000 elastic scattering events) with an estimated 0.5% systematic uncertainty from the flux estimate. Fig. 2 (left) depicts an estimate of how precisely could be constrained if the NuSOnG result, assumed to agree with the Standard Model prediction, is combined with the indirect LEP constraints. One can clearly see that this measurement ( at the two sigma level) compares favorably with the ILC capabilities described above. If the NuSOnG result is incompatible with Standard Model expectations but still in agreement with the CHARM II experiment, a combined NuSOnG–LEP analysis should be able to establish that , as depicted in Fig. 2 (right).
126.96.36.199 New Physics Observed through Oblique Corrections
Precision neutrino scattering measurements made at NuSOnG can reveal new physics even when new particles are not created in the final state, through the effects of these particles in loops. For models of new physics in which the dominant loop corrections are vacuum polarization corrections to the gauge boson propagators (“oblique” corrections), the parameterization introduced by Peskin and Takeuchi  provides a convenient framework in which to describe the effects of the new physics.
The parameterization begins with a reference Standard Model, including reference values for the Higgs and top masses, and predictions for observables in this reference Standard Model. Differences between predicted and experimental values of the observables are then parameterized by and used to fit for and , which can then be compared to predictions from new physics. The full set of precision electroweak data can then be used to constrain and , as shown in Fig. 3. The parameter is sensitive to new physics that violates isospin and is zero for new physics that conserves isospin. Isospin-breaking new physics such as heavy non-degenerate fermion doublets or scalar multiplets would affect the parameter. The parameter is sensitive to isospin-conserving physics, such as heavy degenerate fermion doublets.
The status of electroweak measurements are shown in Fig. 3 . The combined analysis of the LEP and SLD data by the LEP Electroweak Working Group (EWWG)  indicates an allowed region shown by the small oval, centered at and . A different choice of reference Higgs or top mass changes Standard Model predictions for observables and thus shifts the center of the plot ; setting the Higgs mass to 1000 GeV would shift the center of the oval to roughly . Measurements of the mass, which are not shown, are also consistent with the LEP measurements. The highest precision neutrino result comes from and scattering by the NuTeV experiment. This result clearly disagrees with the other measurements, as discussed in Sec. 2.2.
The goal of NuSOnG is to make measurements which are competitive with or better than past electroweak measurements. These goals are indicated by the magenta ellipse and orange band on Fig. 3. The magenta ellipse shows the area in space which can be probed if a 0.7% measurement of the and NC electron-scattering cross sections is achieved. The orange band shows the improvement in the neutrino-quark, “Paschos-Wolfenstein”-style measurement which is expected from NuSOnG.
Disregarding the NuTeV offset for the moment, one can now ask: how will this plot look in the era of LHC and what will NuSOnG add? We consider this question in light of three scenarios:
a light Higgs (115-200 GeV)
a heavy Higgs (200-1000 GeV)
no Higgs signal.
188.8.131.52 NuSOnG Impact for a Light Higgs (115-200 GeV) Scenario
A light Higgs is consistent with LEP/SLD and mass data. The fit to the electroweak data excluding NuTeV indicates a mass less than 144 GeV at 95% CL. This is also consistent with the current best direct-search limit which finds GeV . In the case of the lightest Higgs masses, where the cleanest signal may be in , a clear observation above background will be experimentally difficult and may take some time.
Once the LHC measurement of the Higgs mass is made, the center of the ellipse (Fig. 3) will be fixed at a point (modulo any remaining uncertainty in the top mass). Our experiment is especially interesting if the NuSOnG result disagrees with this LEP+SLD+LHC point. If the LHC measurement is high, i.e. GeV, the result would be marginally inconsistent with the analysis, which is GeV. In this case, comparison with the scattering results from NuSOnG could resolve the question of a discrepancy between these measurements.
If all other electroweak results are in good agreement, but disagree with NuSOnG, this would indicate new properties associated exclusively with the neutrino. An example would be decreased coupling of the neutrino to the boson, where suppression of the coupling comes from intergenerational mixing of the light neutrino with a moderately heavy neutrino:
The coupling is modified by and the coupling is modified by . This model, inspired by the NuTeV anomaly (see Sec. 2.2), would yield a measurement in NuSOnG with a low NC-to-CC ratio in both the case of electron and quark scattering.
These moderately heavy right-handed states, dubbed “neutrissimos” , could have masses as low as just above the current bound of the mass. They may well be within the reach of the LHC and may appear as missing energy in events . Some models allow for neutrissimos as light as GeV . The neutrissimos decay very quickly, but not always invisibly. For example, in the reaction , the may decay to either two jets or a neutrino–charged-lepton pair; only the latter case has missing energy. This may make recognition of the neutrissimo at LHC rather difficult. In the case of GeV, a dominant decay mode of the Higgs (along with ) could be into , where the neutrissimo subsequently decays. Reconstructing the Higgs in this case may be difficult at LHC; if neutrissimos exist, the result from NuSOnG may significantly improve our understanding of LHC results.
With a large tuning among the neutrino Yukawa couplings  neutrissimos could be the seesaw right-handed neutrinos. Relatively “large” mixing is marginally consistent with other constraints, including neutrinoless double-beta decay, which constrains to be less than a few for a 100 GeV right-handed neutrino, and rare pion and tau decays, which constrain to be less than, most conservatively, 0.004 and to be less than 0.006. Other bounds come from conversion in nuclei and other charged-lepton-flavor violation. A new experiment to search for has been proposed at Fermilab  should also be sensitive to neutrissimos. The combination of NuSOnG and this experiment will be powerful in identifying the existence of these particles.
If the neutrissimo is a Majorana particle, it could be instrumental in elucidating the mechanism for leptogenesis. The present models of leptogenesis require very high mass scales for the neutral lepton, but theorists are pursuing ways to accommodate lower masses . There also may be a wide mass spectrum for these particles, with one very heavy state required by standard leptogenesis models and others with masses in the range observable at LHC .
184.108.40.206 NuSOnG Contribution in a Heavy Higgs ( GeV) Scenario
While present electroweak data excluding NuTeV favor a light Higgs ( GeV), as indicated in Fig. 3, the Higgs mass can extend up to about 1000 GeV without violating unitarity . Thus, if LHC finds that the Higgs is between 200 and 1000 GeV and the LEP+SLD ellipse has no major systematic error, then new physics must explain the discrepancy. Candidate models of new physics may well affect the neutrino scattering and scattering differently, so the high-precision neutrino scattering measurements from NuSOnG will provide an important piece of the puzzle if the Higgs mass found at LHC is genuinely inconsistent with LEP+SLD predictions.
Introduction of a fourth family would compensate for a modestly heavy ( GeV) Higgs by shifting the LEP+SLD allowed region back up in and . This family would need to exist above the bounds of direct searches, which is GeV. Mixing must be confined within the allowed bounds of the CKM matrix measurements . A nice feature of this model is that a fourth-generation Majorana neutrino could play the role of dark matter. Depending on the underlying physics, evidence of a fourth family would be apparent in a shift of the NuSOnG result on the plot. This could be especially important if the physics introducing the fourth family is from a mechanism like “Top See Saw” , which will not be observable at LHC. The impact of this particular model on neutrino scattering is not yet thoroughly explored, but could prove interesting .
A classic method for masking a heavy Higgs is to introduce heavy bosons , which, as shown in ref. , tend to move the LEP-SLD ellipse upward in , compensating for the heavy Higgs. Introduction of a tends to increase NC rate in neutrino scattering and also to move the neutrino result upward on the plot (although with a different dependence than the LEP-SLD result).
There are good theoretical reasons for considering the existence of additional neutral heavy gauge bosons. Extra bosons appear in various GUT and string-motivated extensions to the Standard Model . For example, the breakdown to results in the . The break down to yields the . Thus the new exchange boson could be: , where the mixing angle is an arbitrary parameter. Extra bosons also appear in other beyond Standard Model theories, including extra dimensions with gauge fields in the bulk ; little Higgs theories , which use heavy s to cancel divergences in the Higgs mass; and topcolor in which they drive electroweak symmetry breaking . Heavy s provide a mechanism for new SUSY theories to evade the LEP bound of GeV . These models all produce new physics signatures at LHC. The precision measurement from NuSOnG can aid in differentiating models.
Models which introduce new physics to mask a heavy Higgs may seem contrived until one looks at the LEP+SLD data more closely. Up to this point we have considered the LEP+SLD measurements as a single result, however, many measurements enter this fit, and larger than expected inconsistencies between these measurements exist . For example, there is a 3.2 discrepancy between the forward-backward () and left-right () asymmetry measurements. Excluding the result, the LEP+SLD fit yields GeV at 95%, with the best fit at 42 GeV – i.e. a range already excluded by direct searches, which require GeV at 95% CL.
There are several ways to interpret this deviation. It may simply be that there are systematics involved in the measurement which have yet to be identified and which would bring this result into agreement with the others. In this case, we are in the dramatic situation of having already ruled out the Higgs. The scenario of no Higgs is considered in the next section. Alternatively, new physics is involved. This result is dominated by purely leptonic measurements. On the other hand, the fit to the hadronic asymmetries, dominated by has two minima, at 450 and 3000 GeV. Thus, one may either introduce new physics which produces a 20% shift on alone; or introduce new physics which would indicate apparently low values of in the lepton-based measurements, when actually the value is large. Within any of these scenarios, new precision results from NuSOnG will be valuable for understanding the underlying physics.
220.127.116.11 NuSOnG and the Case of No Higgs
Higgsless models do not employ the Higgs mechanism to render the Standard Model renormalizable ; instead they introduce some other scheme. The Higgs mechanism enforces unitarity in the scattering amplitudes of longitudinally polarized gauge bosons, , for example. A requirement that the transition probability remains less than one gives the energy scale at which a new mechanism must come into play,
Higgsless theories generally contain new mass bosons with masses on the TeV scale that act to cancel the divergences in gauge boson scattering. Cancelling the amplitudes while respecting bounds from current electroweak couplings typically give small couplings:
for =700 GeV.
At the LHC, the typical cross sections for are hundreds of femtobarns, so, after cuts, the LHC experiments will record tens to hundreds of events in the first years of data taking. Since the resonances serve the same purpose as the Higgs boson, additional information will be necessary to determine whether these resonances originate from spontaneous symmetry breaking or from strong coupling between the known gauge bosons. The electroweak measurements from NuSOnG will play a role in understanding the origin of such events, en route to a more complete explanation provided by the ILC.
2.2 The NuTeV Anomaly
The NuTeV anomaly is a deviation of from the Standard Model prediction . NuTeV employed the PW-inspired method discussed in Sec. 18.104.22.168, which resulted in a 0.75% measurement of the weak mixing angle (see Tab. 1). Two systematic adjustments to the NuTeV result have been identified since the result was published. The first is the new measurement of the branching ratio from KTeV, which does not significantly reduce the error, but introduces a correction moving the result away from the Standard Model. The second is the final measurement of the difference between the strange and antistrange seas (called “the strange sea asymmetry”, see Sec. 2.4.4), which will pull the NuTeV result toward the Standard Model. A new analysis of the NuTeV data which will include these two corrections is expected be available in late summer, 2007 . It should be noted that while an error from the strange sea appeared in the NuTeV analysis, no error on a strange sea asymmetry appeared in the original NuTeV analysis; this will be included in the upcoming re-analysis.
NuTeV is one of a set of experiments measuring . It was performed at 1 to 140 GeV, GeV, GeV, which is also the expected range for NuSOnG. Two other precision low measurements are from atomic parity violation (APV), which samples ; and SLAC E158, a Møller scattering experiment at average GeV . Using the measurements at the -pole with to fix the value of , and evolving to low , Fig. 4, from ref. , shows that APV and SLAC E158 are in agreement with the Standard Model. However, the radiative corrections to neutrino interactions allow sensitivity to high-mass particles which are complementary to the APV and Møller-scattering corrections. Thus, these results may not be in conflict with NuTeV. The NuSOnG measurement will provide valuable additional information on this question.
Since the NuTeV result was published, more than 300 papers have been written which cite this result. Various Beyond-the-Standard-Model explanations have been put forward; those which best explain the result require a follow-up experiment which probes the neutral weak couplings specifically with neutrinos, such as NuSOnG. Several “within-Standard-Model” explanations have also been put forward, based on the inherent issues involving scattering off quarks. NuSOnG can address these criticisms in two ways. First, we will provide better constraints of the quark-related distributions at issue. Second, we perform the measurement of the weak mixing angle in both a purely leptonic mode (scattering from electrons) and via the PW method. Agreement between the two results would address the questions which have been raised.
2.2.1 Explanations Within the Standard Model
Four explanations for the NuTeV anomaly that are “within the Standard Model” have been proposed. These are: electromagnetic radiative corrections; higher order QCD corrections; isospin (or charge symmetry) violation; and the strange sea asymmetry. The radiative corrections will be disregarded here, since the results of this paper  are not reproducible.
The effect of the possible explanations is illustrated in Fig. 5. On this plot, the solid horizontal line indicates the deviation of NuTeV from the Standard Model. The thick vertical lines, which emanate from the NuTeV deviation, show the range of pulls estimated for each explanation, as discussed below. The dashed horizontal line shows the estimated shift due the new branching ratio. We do not yet have an estimated shift due to the new NuTeV strange sea measurement, but it is expected that this will move the dashed line toward the Standard Model .
Three “Standard Model” explanations may be considered next [37, 38]. First, the NuTeV analysis was not performed at a full NLO level; NuSOnG will need to undertake a full NLO analysis. But the effect of going to NLO on NuTeV can be estimated , and the expected pull is away from the Standard Model, as shown on Fig. 5. Second, the NuTeV analysis assumed isospin symmetry, that is, and . Isospin violation can come about from a variety of sources and is interesting in its own right. NuSOnG’s contribution to this study is discussed in Section 2.4.3. Various models for isospin violation have been studied and their pulls range from less than away from the Standard Model to toward the Standard Model . We have chosen three examples  for illustration on Fig. 5: the full bag model, the meson cloud model, and the isospin QED model. These are mutually exclusive models, so only one of these can affect the NuTeV anomaly. Third, variations in the predicted strange sea asymmetry can either pull the result toward or away from the Standard Model expectation [41, 42, 43]. This issue is considered in detail in Sec. 2.4.4.
2.2.2 Beyond Standard Model Interpretations
Chapter 14 of the APS Neutrino Study White Paper on Neutrino Theory  is dedicated to “the physics of NuTeV” and provides an excellent summary. The discussion presented here is drawn from this source.
The NuTeV measurements of and , the NC-to-CC cross sections, are low. If one is assumes that the Higgs is light, then this must be interpreted as Beyond-Standard-Model physics that suppresses the NC rate with respect to the CC rate. Two types of models produce this effect and remain consistent with the other electroweak measurements: 1) models which affect only the couplings, e.g., the introduction of a heavy boson which interferes with the Standard Model ; or 2) models which affect only the neutrino couplings, e.g., the introduction of moderate mass neutral heavy leptons which mix with the neutrino.
As discussed in Sec. 22.214.171.124, introduction of bosons tend to increase the NC rate rather than suppress it. Thus there is only a small subset of models which produce the destructive interference needed to explain the NuTeV result. Models which introduce a which selectively suppresses neutrino scattering, without significantly affecting the other electroweak measurements, include cases where the couples to  or to . In the former case, fitting the NuTeV anomaly requires that TeV. From the bounds from direct searches, this sets a limit on GeV if the coupling is on the order of unity, but as low as 2 to 10 GeV if the coupling is . The latter case is an example which improves the agreement between NuTeV and other results, but does not entirely address the problem. Its effectiveness in solving the NuTeV anomaly is limited by the data constraining lepton universality. This model addresses more than just the NuTeV anomaly. It is inspired by attempts to address bimaximal mixing in the neutrino sector. It has the nice features of also addressing the muon measurement and producing a distinctive dimuon signature at LHC.
The case of models involving moderate-mass neutral heavy leptons, a.k.a. neutrissimos, have been discussed in the Sec. 126.96.36.199 and examples of viable models appear in ref. . Eq. 45 described how the muon neutrino couplings might be modified by mixing. This idea can be extended to all three flavors, leading to a suppression factor for the coupling which is expressed as and for the by , where or . This addresses the NuTeV anomaly and at the same time suppresses the invisible width of the , describing the LEP I data.
If the NuTeV anomaly is due to Beyond Standard Model physics, then the effect will be visible in the neutrino-electron elastic scattering measurement also. Thus, if the NuTeV anomaly is borne out, NuSOnG would observe an plot similar to Fig. 6.
2.3 Direct Searches for New Physics
2.3.1 Light Neutrino Properties
Evidence for three light neutrino masses has now been established through neutrino oscillations in solar, atmospheric, and reactor experiments (see references  through ). Furthermore, although the MiniBooNE experiment recently refuted the LSND two-neutrino oscillation scenario at eV , the question of the existence of multiple light sterile neutrinos still remains open . These observations already require beyond-the-Standard-Model physics, and consequently raise phenomenological questions, such as: what are the mass and mixing parameters still allowed in sterile neutrino models? What do sterile neutrinos imply about neutrino mixing? Is the neutrino mixing matrix unitary, or is there effective freedom of mixing parameters? As we illustrate in the following sections, these are some of the questions that NuSOnG can potentially address.
188.8.131.52 Matrix Freedom
Perhaps the most interesting study of light neutrino properties which can be performed at NuSOnG is the search for evidence of “matrix freedom” or “nonunitarity.” For example, in the case of existence of sterile neutrinos, the neutrino mixing matrix is extended to an matrix, where 3. Under that assumption, it has been suggested that the 33 part of the matrix describing the three active (SM) neutrinos is not necessarily unitary; or, equivalently, the three flavor eigenstates are non-orthogonal (the 33 neutrino mixing matrix is free) .
This introduces striking changes to the probability formula for neutrino flavor transitions. Assuming unitarity, the survival probability formula for a neutrino produced as flavor is
where one has made use of , and . In the case of matrix freedom, the mixing matrix is no longer unitary. The level at which unitarity is violated can be defined as , where
with being small. Under that assumption, the survival probability formula is then found to be
As implied by Eq. 50 one of the main consequences of such scenario is instantaneous (0) flavor transitions in a neutrino beam. This occurs regardless of the size of the mass splitting between the mostly sterile and mostly active states, and thus allows for a full-mass-range search for evidence of sterile neutrinos. A recent study  suggests that current experimental data limit such an effect to up to the order of a few percent.
As a result, several interesting and potentially observable phenomena can occur. Extending the argument of ref. , for instance, the non-orthogonality of and that matrix freedom introduces, results in an instantaeous transition at from to . Thus one could observe an excess of events in a pure beam.
The trick to searching for this instantaneous transition is to focus on an energy range where the background is low and well constrained. In the case of NuSOnG, this is on the high energy tail of the flux, above E GeV. For the limits on transformation to , which are at the level, NuSOnG would see an excess of events in this high energy region. Fig. 7 shows the ratio of flux with transitions to flux without transitions. The abrupt cutoff is due to Monte Carlo statistics; higher energies can be explored. Assuming that such transitions indeed happen at the level, one would expect up to a 10% increase in flux for E GeV. In that high energy region, the flux is mainly from decay, which is well constrained by the events. Such an excess should therefore be measurable.
Other interesting effects of matrix freedom  include the oscillatory behavior in the total (flavor-summed) CC event rate as a function of , and (fake) CP-violating effects in the and neutral-current event rates (the two rates oscillate differently with ). Potential observation of those effects at NuSOnG has not been explicitly considered at this stage, although it would be interesting to address this and we are planning to do so in the near future. Regardless of that, evidence of contamination in a beam above expected background levels, something for which NuSOnG can search, would strongly support the matrix freedom hypothesis.
184.108.40.206 Sterile Neutrino Oscillations
Direct observation of sterile neutrino oscillations may also be possible in NuSOnG, depending on the mass and mixing parameters. Oscillations of active to light sterile neutrinos have been introduced to explain the LSND anomaly, as dark matter candidates, and in describing the supernova collapse models. These ideas span a wide range of values. The LSND anomaly requires a sterile neutrino in the range of eV with moderate mixing (), while dark matter candidates and supernova collapse models require . These models also require tiny mixing (). NuSOnG probes an intermediate range of , between the LSND and astrophysical allowed regions. However, since sterile neutrinos may come in families, it is worth exploring this previously uncharted territory.
The NuSOnG experimental design consists of a 30-600 GeV muon neutrino beam, peaked at 100 GeV, incident on a -meter long detector located at L1.5km from the neutrino source. This detector design allows for disappearance studies across the detector length by examining the scattering rate variation across the detector. Such searches would be limited by the detector energy resolution. Preliminary studies have shown that, assuming a 10% energy resolution, 600eV regions with mixing of can be probed easily. NuSOnG may also be able to explore smaller mixings and higher s, depending on the final experimental design.
NuSOnG can also probe for and disappearance in the range of , thus in the range of eV. This is a range which has been covered by past experiments including CCFR , CHDS , and NOMAD . However, the improved quality of the first principles prediction due to the new SPY secondary production data , discussed in sec. 3.3, should allow improvement of these limits.
2.3.2 New Interactions
220.127.116.11 Lepton Number Violation Searches
The NuSOnG experiment possesses two valuable characteristics for the search for lepton number violation. First, it relies upon a high purity, high intensity beam as its source of neutrinos; secondly, it employs an instrumented detector optimized to measure inverse muon decay with high accuracy. An experiment with these two features naturally lends itself to searches for the process:
This interaction is forbidden by the Standard Model since it violates lepton family number conversation (). As such, observation of this reaction would immediately constitute direct observation of physics beyond the Standard Model.
A number of theories beyond the Standard Model predict that lepton number is not a true conserved quantum number; this means that processes that violate lepton number are allowed to occur. Theories which incorporate multiplicative lepton number conservation [71, 72], left-right symmetry , or the existence of bileptons  fall under this category.
The differential cross-section for lepton-violating processes can be parametrized in the following form:
where is the fractional energy carried by the outgoing lepton, the weak coupling constant, the square of the center of mass energy of the system, and the threshold factor, defined as . The parameters and describe the strength of the reaction and whether the process is vector or scalar in nature. It is typical to compare this process to that of inverse muon decay:
The signature for such a reaction is the tagging of an during antineutrino running with the same signature as expected from inverse muon decays. The main backgrounds to this reaction include (a) contamination, (b) contamination, and (c) charge misidentification of candidate events. Our current estimates place a very small beam contamination during antineutrino running: about 0.4% contamination of s and a 2.3% contamination of and neutrinos (See Sec. 3.1). Charge misidentification is expected to be very small, on the order of 10. If we assume a conservative knowledge of the backgrounds at the 5% level, this would imply a limit on the lepton number violation cross-section ratio of better than 0.2% (at 90% C.L.) for V-A couplings and less than 0.06% for scalar couplings. Previous searches, based on protons on target and smaller target masses, have placed limits on this cross-section ratio to less than 1.7% at 90% C.L. for V-A couplings and less than 0.6% for scalar couplings . The NuSOnG experiment can therefore reach an improvement of over an order of magnitude compared to previous searches. This limit can be improved if further selection criteria are used in removing unwanted beam impurities or the quasi-elastic background contamination.
18.104.22.168 Inverse Muon Decay
The study of inverse muon decay, provides access to the helicity structure of the weak interaction distinct from muon decay experiments. The weak interaction polarizes the incident , making inverse muon decay an excellent place to study departures from couplings. For inverse muon decay,  where and is the helicity of the incident muon. Ref.  has measured and the current limit on . For a measurement of the total cross section scaled to the predicted cross section, the uncertainty on the coupling is .
For NuSOnG, we expect k inverse muon decay events, which would give a statistical uncertainty of 0.002 on . However, we will need to determine the neutrino flux. Taking the cross section as known gives the neutrino flux to 0.7%. Since we plan to use the inverse muon decay events for determining the flux for the electroweak measurements, NuSOnG will need to measure the efficiency and fiducial volume for both processes to better than 0.7%. Combined with other systematics, we should be able to achieve an total uncertainty of about 1-2% on , an improvement by a factor of four.
The key background will come from CCQE events that have small hadronic energy. We expect our high granularity will allow us to keep the systematic error from this source well below 1%, but this needs study.
Obviously, the manner of analysis described above is somewhat questionable. Ultimately, one would want to carry out a combined analysis of both neutrino elastic scattering on electrons and quarks and of inverse muon decay in the context of a specific model which relates the charged and neutral current coupling constants. For such an analysis, 1-2% uncertainty should still be achievable.
2.3.3 New Particles
22.214.171.124 Long-lived, Light Neutral Heavy Leptons
Another interesting NuTeV result arose from the search for long-lived, light ( GeV) neutral heavy leptons. This was performed in a helium-filled decay region located upstream of the calorimeter. In the mass region of 2.2-15 GeV, NuTeV has a small expected background (0.07 0.01 events), but observed three events. All events had two muons originating from a vertex within the helium decay region and missing energy. .
Since publication in 2001, no widely accepted explanation has been found. In 2006, D published a search for a similar decay signature in proton-antiproton interactions . No events were found and some production models were excluded. The most viable remaining model is by Dedes et al., which hypothesizes that the events are from decay of long-lived neutralinos. These are produced in the NuTeV beam dump through hadron decays . No other experiment has been able to match NuTeV’s running conditions to further explore this intriguing result.
NuSOnG can address the question by including a low-mass (helium-filled) decay region between the calorimeter segments. Assuming parameters similar to those of NuTeV (except for a 20-fold increase in the number of protons on target), NuSOnG would expect to see 60 events with an expected background of 1-2 events. The sensitivity would scale directly with the decay volume, so the increased length compared to NuTeV (26 40 ) would increase this to 90 signal events over a 2-3 event background. Observing no signal would finally settle this outstanding question.
These decay regions allow exploration for a signal from a beyond-the-Standard-Model particle in other decay modes as well; other interesting modes include , , and . NuSOnG’s sensitivity to other new particles is similarly improved over NuTeV by the increase in beam intensity and decay volume, allowing us to study new regions of phase space.
126.96.36.199 Muonic Photons
In the mid-1990’s there was interest in searching for “leptonic photons” – massless vector particles that couple according to flavor. Electronic, muonic, and tauonic photons, , , and were introduced . Production occurs in secondary meson decays such as , and detection can proceed through , where is the charged nucleus. These events have small missing compared to the “trident” background, . The search by CHARM II sets the best limit at .
Since this time, neutrino oscillations have been confirmed (see references  through ). This complicates the theory of “muonic photons,” since, in this case, lepton flavor-charge is not conserved. As pointed out in reference , a theory with a non-conserved charge cannot have massless vector particles and a Coulomb-like potential. It appears very difficult to evade this problem.
Nevertheless, NuSOnG should search for these events. With higher rate and better segmentation than CHARM II, NuSOnG should have sensitivity in the range of . A significant excess would be quite startling.
2.4 Measurement of Parton Distribution Functions
The Deeply Inelastic Scattering (DIS) process provides crucial information about the structure of the proton which is used to determine the Parton Distribution Functions (PDFs). For example, in the recent CTEQ6HQ analysis, DIS data accounted for more than two-thirds of the data points used in the analysis.111Specifically, there were 1333 DIS data points used out of the 1925 total. As such, the DIS measurements form the foundation for the many calculations which make use of the PDFs.
In the basic DIS process, leptons scatter from hadrons via the exchange of an intermediate vector boson: . Different boson probes couple to the hadrons with different factors, and it is important to combine data from these different probes to separate the different flavor components in the hadron. Unfortunately, three of the four DIS probes have a (relatively) large mass and couple only weakly; this introduces a number of complications:
The statistics for these weak processes are limited as compared with the photon-exchange processes.
To compensate for the weak cross section, typically heavy nuclear targets (e.g., Fe and Pb) are used; this introduces nuclear corrections when the results are scaled from the heavy target back to proton or isoscalar targets.
The NuSOnG experiment will generate high statistics (M DIS events) measurements on an intermediate atomic-weight nuclear target (SiO). This will provide precise information on the linear combinations of PDFs which couple to the weak charged currents (), which can significantly improve the parton distribution fits. In this section, we first introduce the basics of DIS and the connection to parton distribution functions. Then we concentrate on three aspects of parton distribution studies where NuSOnG can make a unique contribution to the physics:
Improved understanding of nuclear effects in neutrino scattering.
Study of Charge Symmetry Violation
Measurement of the Strange Sea
Measurement of and
The latter two items are directly relevant to the electroweak studies proposed for NuSOnG (see Sec. 2.2.1).
2.4.1 Deep Inelastic Scattering and Parton Distribution Functions
The differential cross section for neutrino DIS depends on three structure functions: , and . It is given by:
where the is for scattering. In this equation, is the Bjorken scaling variable, the inelasticity, and the squared four-momentum transfer.
The function is unique to the DIS cross section for the weak interaction. It originates from the parity-violating term in the product of the leptonic and hadronic tensors. For an isoscalar target, in the quark-parton model,
Defining , at leading order in QCD,
To the level that the sea quark distributions have the same dependence, and thus cancel, can be thought of as probing the valence quark distributions. The difference between the neutrino and antineutrino parity violating structure functions, , probes the strange and charm seas.
Analogous functions for and appear in both the cross section for charged lepton ( or ) DIS and the cross section for DIS. At leading order,
where is the charge associated with the interaction. In the weak interaction, this charge is unity. For charged-lepton scattering mediated by a virtual photon, the fractional electromagnetic charge of each quark flavor enters. Thus and are analogous but not identical and comparison yields useful information about specific parton distributions . is the longitudinal to transverse virtual boson absorption cross-section ratio. The best measurements for this come from charged lepton scattering rather than neutrino scattering. In the past, neutrino experiments have used the charged lepton fits to as an input to the measurements of and . This, however, is just a matter of the statistics needed for a global fit to all of the unknown structure functions in and bins . With the high statistics of NuSOnG, precise measurement of will be possible from neutrino scattering for the first time.
In addition to fitting to the inclusive DIS sample, neutrino scattering can also probe parton distributions through exclusive samples. A unique and important case is the measurement of the strange sea through opposite sign dimuon production. When the neutrino interacts with an or quark, it produces a charm quark that fragments into a charmed hadron. The charmed hadron’s semileptonic decay (with branching ratio ) produces a second muon of opposite sign from the first: