**10. Overview of the neutrino effective dose at a tau collider**

A third generation tau collider has not been evaluated. In order to provide an estimate of the effective dose consequences of a tau collider, a modification of the muon collider methodology is utilized. The decay characteristics of a tau are considerably more complex than muon decay. The muon essentially decays with a branching ratio of 100 % into a lepton and neutrinos via Eq. 1. For example, tau decays involve 119 decay modes with specified branching fractions with six modes accounting for 90% of the decays (Particle Data Group 2010). The dominant tau decay mode is:

110 Particle Physics

constructed such that the individual muon beams collide in air well above the earth's

For Option 1, the accelerator could either be constructed at an elevated location or at an isolated area. The area will need to be large, perhaps having a site boundary with a diameter greater than 100 km (King, 1999a). This size requirement restricts the available locations, and would normally require that the facility have access to the resources of an existing accelerator facility such as CERN or Fermilab. Alternatively, the facility could be located in an isolated area and scientific personnel relocated to that area with the establishment of a self-sufficient site. The final decision regarding facility location will involve funding and political considerations that are part of new facility development, licensing, and

Option 2 would be technically feasible, and could be located at a smaller site. However, design considerations for both Options 1 and 2 would need to address a number of potential radiation issues associated with accelerator operation (Bevelacqua, 2008, 2009, and 2010a) that could lead to significant, unanticipated radiation levels in controlled as well as uncontrolled areas. Radiation protection issues include beam alignment errors, design errors, unauthorized changes, activation sources, and control of miscellaneous radiation sources (Bevelacqua, 2008, 2009, 2010a). These operational issues require close control because they have the potential to produce large and unanticipated effective dose values. Beam alignment errors could direct the beam in unanticipated directions. Given the long range of the muon effective dose profile, these errors could have a significant impact on licensing and accident analysis. Beam alignment errors are caused by a variety of factors including power failures, maintenance errors, and magnet failures. Both human errors and

Changes in the beam energy or beam current, that exceed the authorized operating envelope, lead to elevated fluence rates, the creation of unanticipated particles, or the creation of particles with higher energy than anticipated. Changes to beam parameters must

The control of secondary radiation sources, radio-frequency equipment, high-voltage power supplies, and other experimental equipment merits special attention. These sources of radiation are more difficult to control than the primary or scattered accelerator radiation because health physicists may not be aware of their existence, the experimenters may not be aware of the hazard, or the radiation source is at least partially masked by the accelerator's radiation output. These miscellaneous radiation sources will include x-rays as well as other

A third generation tau collider has not been evaluated. In order to provide an estimate of the effective dose consequences of a tau collider, a modification of the muon collider methodology is utilized. The decay characteristics of a tau are considerably more complex than muon decay. The muon essentially decays with a branching ratio of 100 % into a lepton and neutrinos via Eq. 1. For example, tau decays involve 119 decay modes with specified branching fractions with six modes accounting for 90% of the decays (Particle Data Group

be carefully evaluated for their impact on the radiation environment of the facility.

**10. Overview of the neutrino effective dose at a tau collider** 

surface.

construction.

types of radiation.

2010). The dominant tau decay mode is:

mechanical failures lead to beam alignment issues.

$$
\pi^- \to \pi^- + \pi^0 + \nu\_\pi \text{ (25.51\%)}\tag{29}
$$

However, the negative pion dominantly decays into a muon and antimuon neutrino, and the neutral pion decays primarily into photons.

$$
\pi^- \to \left(\mu^- + \overline{\nu}\_{\mu}\right) + \left(\gamma + \gamma\right) + \nu\_\tau \tag{30}
$$

Subsequently, the muon decays following Eq. 1. Eq. 30 then yields:

$$
\tau^- \to \left(\varepsilon^- + \nu\_\mu + \overline{\nu}\_e + \overline{\nu}\_\mu\right) + \left(\gamma + \gamma\right) + \nu\_\tau \tag{31}
$$

The net result of the decay is that multiple neutrinos are produced from the tau and subsequent decay of particles. The factor ξ described in subsequent discussion incorporates the effects of the multiple tau decay modes and their effects on the neutrino effective dose.

Subsequent discussion assumes no annihilation of particles and antiparticles in the beam produced by the tau decay products. In addition, the narrow beam approximation is assumed.

The neutrino dose from tau decays is determined by comparing the number of neutrinos emitted from an equal number of tau and muon decays. ξ defines the ratio of the number of neutrinos contributing to the tau collider to muon collider effective doses:

$$\xi = \frac{\sum\_{i=1}^{N} Y\_i \sum\_{j=1}^{3} \left( a n\_i \left( \nu\_j \right) + b n\_i \left( \overline{\nu}\_j \right) \right)}{a n \left( \nu\_\mu \right) + b n \left( \overline{\nu}\_\epsilon \right)} \tag{32}$$

In the numerator of Eq. 32, i labels the various decay modes of the tau, N is the number of tau decay modes, Yi is the branching fraction of the ith tau decay mode, ni(υj) is the number of generation j neutrinos emitted from decay mode i, and *ni <sup>j</sup>* is the number of generation j antineutrinos emitted from decay mode i. In the denominator of Eq. (32), n(υμ) is the number of muon neutrinos emitted in a muon decay, and *n<sup>e</sup>* is the number of antielectron neutrinos emitted in a muon decay. The j sum counts the three neutrino generations, and a and b are the cross-section factors of King (1999a) for neutrinos and antineutrinos which are 1.0 and 0.5, respectively.

The ratio of tau neutrino to muon neutrino effective doses is obtained by utilizing the value of ξ and the calculated ratio of tau and muon neutrino cross-sections (β) (Jeong & Reno, 2010). The discussion is applicable to circular and linear muon and tau colliders. For equivalent accelerator operating conditions (e.g., beam energy and number of beam particle decays) and receptor conditions (e.g., distance and ambient conditions), the ratio of neutrino effective doses from a tau collider and muon collider is given by:

$$\frac{H\_{\text{g}^{-}}(E)}{H\_{\text{g}^{-}}(E)} = \xi^{\prime}\mathcal{J}\mathcal{J}(E) \tag{33}$$

health physics concerns. Keeping public and occupational neutrino effective doses below regulatory limits will require careful and consistent application of dose reduction methods. When compared to muon colliders, initial scooping calculations for tau colliders suggest that higher effective doses and affected areas will result from their operation. Although, the tau collider calculations are initial estimates, they suggest that significant radiation

Autin, B; Blondel, A. & Ellis, J. (1999). Prospective Study of Muon Storage Rings at CERN, CERN 99-02, European Laboratory for Particle Physics, Geneva, Switzerland Bevelacqua, J. (2004). Muon Colliders and Neutrino Dose Equivalents: ALARA Challenges for the 21st Century, *Radiation Protection Management*, Vol.21, No. 4, pp. 8-30. Bevelacqua, J. (2008). *Health Physics in the 21st Century*, Wiley-VCH, ISBN 9783527408221,

Bevelacqua, J. (2009). *Contemporary Health Physics: Problems and Solutions* (Second Edition),

Bevelacqua, J. (2010a). *Basic Health Physics: Problems and Solutions* (Second Edition), ISBN

Bevelacqua, J. (2010b). Standard Model of Particle Physics-A Health Physics Perspective,

Cossairt, J.; Grossman, N. & Marshall, E. (1996). Neutrino Radiation Hazards: A Paper Tiger,

Cossairt, J.; Grossman, N. & Marshall, E. (1997). Assessment of Dose Equivalent due to

Cossairt, J. & Marshall, E. (1997). Comment on "Biological Effects of Stellar Collapse

Collar, J. (1996). Biological Effects of Stellar Collapse Neutrinos, *Physical Review Letters*,

Geer, S. (2010). From Neutrino Factory to Muon Collider, *FERMILAB-CONF-10-024-APC,* Accessed on July 14, 2011, Available from: < http://arxiv.org/abs/1006.0923> Griffiths, D. (2008). *Introduction to Elementary Particle Physics* (Second Edition), Wiley-VCH,

ICRP Report No. 60. (1991). *1990 Recommendations of the International Commission on* 

ICRP Report No. 107. (2007). *The 2007 Recommendations of the International Commission on* 

Jeong, Y. & Reno, M. (2010). Tau neutrino and antineutrino cross sections, Accessed on July

Johnson, C.; Rolandi, G. & Silari, M. (1998). Radiological Hazard due to Neutrinos from a

Muon Collider, *Internal Report CERN/TIS-RP/IR/98*, European Laboratory for

*Fermilab-Conf-96/324*, Accessed on July 11, 2011, Available from:

<http://lss.fnal.gov/archive/1996/conf/Conf-96-324.pdf>

Neutrinos, *Physical Review Letters,* Vol.78, No.7, pp.1394.

<http://arxiv.org/PS\_cache/arxiv/pdf/1007/1007.1966v1.pdf>

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Butler, D. (2011a). Radioactivity Spreads in Japan, *Nature*, Vol.471, No.7340, pp. 555-556 Butler, D. (2011b). Fukushima Health Risks Scrutinized, *Nature*, Vol.472, No.7341, pp. 13-14 Cottingham, W. & Greenwood, D. (2007). *An Introduction to the Standard Model of Particle* 

challenges are also presented by these machines.

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**12. References** 


The results of calculations utilizing Eq. 33 are summarized in Table 8.

Table 8. Ratio of Tau and Muon Collider Neutrino Effective Doses.

The tau collider neutrino effective doses are generally larger than those encountered in a muon collider, and the tau dose profile is also larger. The larger tau profile is demonstrated by considering Eqs. 3 and 4 for equivalent tau and muon collider configurations:

$$\frac{r\left(\pi^{-}\right)}{r\left(\mu^{-}\right)} = \frac{m\_{r-}}{m\_{\mu^{-}}} = \frac{1777\text{ MeV}}{105.7\text{ MeV}} = 16.8\tag{34}$$

Using Eq. 34 and the Table 7 results for circular tau collider conditions, the neutrino effective dose profile radius at the earth's surface is 60.5, 30.2, 16.8, and 13.4 m for 1, 2, 5, and 10 TeV beams. These affected areas and associated effective doses suggest that the tau collider is a more significant radiation hazard than the muon collider. Therefore, larger effective doses and affected areas are anticipated during tau collider operations.

An improved calculation of the neutrino effective dose from a tau collider requires a better specification of neutrino properties. For example, previous calculations were based on the Standard Model assumption that neutrinos have zero mass. Neutrino masses can be calculated assuming the alternative gauge group <sup>2</sup> 2 1 *<sup>L</sup> <sup>R</sup> SU SU U* instead of the Standard Model <sup>2</sup> 1 *<sup>L</sup> SU U* . This gauge group leads to a neutrino generation i mass:

$$m\_i = \frac{M\_i^2}{\mathcal{g}\,m\_{W\_R}}\tag{35}$$

where Mi is the generation i lepton mass (e, μ, and τ), WR is the right-handed W boson mass (≥ 300 GeV), and g is a coupling constant with a value of 0.585 (Mohapatra & Senjanović, 1980). Using these values in Eq. 35 leads to electron, muon, and tau neutrino upper bound masses of 1.5 eV, 64 keV, and 18 MeV, respectively. These masses affect the input values used to calculate the neutrino effective dose in Eqs. 14 and 23. As an alternative, better crosssection data and dose conversion factors would refine the neutrino effective dose.
