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$T$ -parity violation by anomalies

Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, Illinois 60510, USA

Phys. Rev. D 76, 115014 – Published 27 December, 2007

DOI: https://doi.org/10.1103/PhysRevD.76.115014

Abstract

Little Higgs theories often rely on an internal parity (“ $T$ -parity”) to suppress nonstandard electroweak effects or to provide a dark matter candidate. We show that such a symmetry is generally broken by anomalies, as described by the Wess-Zumino-Witten term. We study a simple $S U (3) \times S U (3) / S U (3)$ Little Higgs scheme where we obtain a minimal form for the topological interactions of a single Higgs field. The results apply to more general models, including $[S U (3) \times S U (3) / S U (3)]^{4}$ , $S U (5) / S O (5)$ , and $S U (6) / S p (6)$ .

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References (32)

B. A. Dobrescu and C. T. Hill, Phys. Rev. Lett. 81, 2634 (1998); R. S. Chivukula, B. A. Dobrescu, H. Georgi, and C. T. Hill, Phys. Rev. D 59, 075003 (1999).
D. B. Kaplan and H. Georgi, Phys. Lett. B 136, 183 (1984); D. B. Kaplan, H. Georgi, and S. Dimopoulos, 136, 187 (1984); H. Georgi, D. B. Kaplan, and P. Galison, 143, 152 (1984); H. Georgi and D. B. Kaplan, 145, 216 (1984); M. J. Dugan, H. Georgi, and D. B. Kaplan, Nucl. Phys. B254, 299 (1985).
N. Arkani-Hamed, A. G. Cohen, and H. Georgi, Phys. Lett. B 513, 232 (2001).
J. Wess and B. Zumino, Phys. Lett. B 37, 95 (1971).
C. T. Hill and R. J. Hill, Phys. Rev. D 75, 115009 (2007).
E. Witten, Nucl. Phys. B223, 422 (1983).
J. S. Bell and R. Jackiw, Nuovo Cimento A 60, 47 (1969).
S. L. Adler, Phys. Rev. 177, 2426 (1969).
W. A. Bardeen, Phys. Rev. 184, 1848 (1969).
H. C. Cheng and I. Low, J. High Energy Phys. 08 (2004) 061.
H. C. Cheng and I. Low, J. High Energy Phys. 09 (2003) 051.
For example, the instanton becomes a worldline (particle) in $D = 5$ and has two associated conserved topological currents. These currents can only be generated if Chern-Simons terms are appended to the theory [24].
In a more precise language, Chern-Simons operators arise only in odd $D$ , as in $ϵ^{A B C D E} A_{A} d_{B} A_{C} d_{D} A_{E}$ . Here we use the pejorative meaning for $D = 4$ operators such as $ϵ_{μ ν ρ σ} A^{μ} B^{ν} d^{ρ} B^{σ}$ or $ϵ_{μ ν ρ σ} Tr (A^{μ} B^{ν} B^{ρ} B^{σ})$ .
Note that we can also include a matrix $Ω$ with $Ω^{2} = 1$ into the definition of $T$ -parity: $\tilde{π} \to - Ω \tilde{π} Ω$ , etc. For example, $Ω = diag (1, 1, - 1)$ will allow the $K$ to be defined as scalar, whereas the $π$ and $η$ are pseudoscalar. As in the $S U (3)$ QCD chiral Lagrangian, this has no physical consequences until isospin-violating interactions are added.
N. Arkani-Hamed, A. G. Cohen, and H. Georgi, Phys. Rev. Lett. 86, 4757 (2001); C. T. Hill, S. Pokorski, and J. Wang, Phys. Rev. D 64, 105005 (2001).
O. Kaymakcalan, S. Rajeev, and J. Schechter, Phys. Rev. D 30, 594 (1984).
N. Arkani-Hamed, A. G. Cohen, E. Katz, and A. E. Nelson, J. High Energy Phys. 07 (2002) 034.
Alternatively, the low-energy theory can be arrived at by embedding inside of $S U (5) \times S U (5) / S U (5)$ with the extraneous NGB’s removed by a strongly coupled gauge field.
I. Low, W. Skiba, and D. Smith, Phys. Rev. D 66, 072001 (2002).
Note that in contrast to the $U (1)$ charges advocated in Ref. [19], it is possible to choose generators that do not induce additional $U (1) / color$ anomalies—e.g., in the coordinates of Ref. [19], $Y_{1} \propto (1, 1, 1, 1, 1, - 5)$ , and $Y_{2} \propto (1, 1, - 5, 1, 1, 1)$ .
D. E. Kaplan and M. Schmaltz, J. High Energy Phys. 10 (2003) 039.
N. Arkani-Hamed, A. G. Cohen, E. Katz, A. E. Nelson, T. Gregoire, and J. G. Wacker, J. High Energy Phys. 08 (2002) 021.
The mechanism of [22] used to stabilize a flat direction in the Higgs potential breaks the $U_{2} \leftrightarrow U_{4}$ symmetry.
C. T. Hill, Phys. Rev. Lett. 88, 041601 (2002); C. T. Hill and P. Ramond, Nucl. Phys. B596, 243 (2001).
An explicit model is studied in E. Katz, J. Y. Lee, A. E. Nelson, and D. G. E. Walker, J. High Energy Phys. 10 (2005) 088.
M. Carena, J. Hubisz, M. Perelstein, and P. Verdier, Phys. Rev. D 75, 091701 (2007).
A. Birkedal, A. Noble, M. Perelstein, and A. Spray, Phys. Rev. D 74, 035002 (2006).
A. Birkedal-Hansen and J. G. Wacker, Phys. Rev. D 69, 065022 (2004).
C. T. Hill, Phys. Rev. D 73, 126009 (2006); 73, 085001 (2006); C. T. Hill and C. K. Zachos, 71, 046002 (2005).
K. Agashe, R. Contino, and R. Sundrum, Phys. Rev. Lett. 95, 171804 (2005).
C. Csaki, C. Grojean, H. Murayama, L. Pilo, and J. Terning, Phys. Rev. D 69, 055006 (2004); R. Sekhar Chivukula, D. A. Dicus, and H. J. He, Phys. Lett. B 525, 175 (2002). For further references, see, e.g., R. Sekhar Chivukula, E. H. Simmons, H. J. He, M. Kurachi, and M. Tanabashi, Phys. Rev. D 71, 035007 (2005).
G. Servant and T. M. P. Tait, Nucl. Phys. B650, 391 (2003); G. Bertone, D. Hooper, and J. Silk, Phys. Rep. 405, 279 (2005); H. C. Cheng, J. L. Feng, and K. T. Matchev, Phys. Rev. Lett. 89, 211301 (2002).

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$T$ -parity violation by anomalies

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T-parity violation by anomalies

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$T$ -parity violation by anomalies