Abstract
Spontaneous dimensional reduction (SDR) is a striking phenomenon predicted by a number of quantum gravity approaches which all indicate that the spacetime dimensions get reduced at high energies. In this work, we formulate an effective theory of electroweak interactions based upon the standard model, incorporating the spontaneous reduction of space-dimensions at TeV scale. The electroweak gauge symmetry is nonlinearly realized with or without a Higgs boson. We demonstrate that the SDR ensures good high-energy behavior and predicts unitary weak boson scattering. For a light Higgs boson of mass 125GeV, the TeV scale SDR gives a natural solution to the hierarchy problem. Such a light Higgs boson can have induced anomalous gauge couplings from the TeV scale SDR. We find that the corresponding WW scattering cross sections become unitary at TeV scale, but exhibit different behaviors from that of the 4d standard model. These can be discriminated by the WW scattering experiments at the LHC.
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S.L. Glashow, Nucl. Phys. 22, 579 (1961).
S. Weinberg, Phys. Rev. Lett. 19, 1264 (1967).
A. Salam, in Elementary Particle Theory, Nobel Symposium No. 8, edited by N. Svartholm (Almqvist & Wiksells, Stockholm, 1968) p. 367.
P.W. Higgs, Phys. Lett. 12, 132 (1964).
P.W. Higgs, Phys. Rev. Lett. 13, 508 (1964).
P.W. Higgs, Phys. Rev. 145, 1156 (1966).
F. Englert, R. Brout, Phys. Rev. Lett. 13, 321 (1964).
G.S. Guralnik, C.R. Hagen, T.W. Kibble, Phys. Rev. Lett. 13, 585 (1964).
G. ’t Hooft, Nucl. Phys. B 35, 167 (1971).
G. ’t Hooft, M. Veltman, Nucl. Phys. B 44, 189 (1972).
G. ’t Hooft, M. Veltman, Nucl. Phys. B 50, 318 (1972).
J.M. Cornwall, D.N. Levin, G. Tiktopoulos, Phys. Rev. Lett. 30, 1268 (1973).
J.M. Cornwall, D.N. Levin, G. Tiktopoulos, Phys. Rev. D 10, 1145 (1974).
C.H. Llewellyn Smith, Phys. Lett. B 46, 233 (1973).
D.A. Dicus, V.S. Mathur, Phys. Rev. D 7, 3111 (1973).
B.W. Lee, C. Quigg, H.B. Thacker, Phys. Rev. Lett. 38, 883 (1977).
B.W. Lee, C. Quigg, H.B. Thacker, Phys. Rev. D 16, 1519 (1977).
ATLAS Collaboration (G. Aad et al.), Phys. Lett. B 716, 1 (2012) arXiv:1207.7214 [hep-ex].
CMS Collaboration (S. Chatrchyan et al.), Phys. Lett. B 716, 30 (2012) arXiv:1207.7235 [hep-ex].
See: Rencontres de Moriond 2013, http://moriond.in2p3.fr, EW Interactions and Unified Theories, March 2–9, 2013, and QCD and High Energy Interactions, March 9–16, 2013, La Thuile, Aosta valley, Italy.
M.S. Chanowitz, M.K. Gaillard, Nucl. Phys. B 261, 379 (1985).
M.S. Chanowitz, arXiv:hep-ph/9812215.
M.S. Chanowitz, Czech. J. Phys. B 55, 45 (2005) arXiv:hep-ph/0412203 and references therein.
M.S. Chanowitz, M.A. Furman, I. Hinchliffe, Nucl. Phys. B 153, 402 (1979).
T. Appelquist, M.S. Chanowitz, Phys. Rev. Lett. 59, 2405 (1987).
D.A. Dicus, H.J. He, Phys. Rev. D 71, 093009 (2005) hep-ph/0409131.
D.A. Dicus, H.J. He, Phys. Rev. Lett. 94, 221802 (2005) hep-ph/0502178.
L. Susskind, Phys. Rev. D 20, 2619 (1979).
R. Dashen, H. Neuberger, Phys. Rev. Lett. 50, 1897 (1983).
C.T. Hill, E.H. Simmons, Phys. Rep. 381, 235 (2003) arXiv:hep-ph/0203079 and references therein.
M.E. Peskin, arXiv:0801.1928 and references therein.
N. Arkani-Hamed, S. Dimopolous, G.R. Dvali, Phys. Lett. B 429, 263 (1998).
I. Antoniadis, N. Arkani-Hamed, S. Dimopolous, G.R. Dvali, Phys. Lett. B 436, 257 (1998).
L. Randall, R. Sundrum, Phys. Rev. Lett. 83, 3370 (1999).
L. Randall, R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999).
N. Arkani-Hamed, A.G. Cohen, H. Georgi, Phys. Rev. Lett. 86, 4757 (2001).
C.T. Hill, S. Pokorski, J. Wang, Phys. Rev. D 64, 105005 (2001).
G. ’t Hooft, Salam-festschrift 4(A), 1 (1993) arXiv:gr-qc/9310026.
S. Carlip, arXiv:1009.1136 [gr-qc] and references therein.
S. Carlip, arXiv:0909.3329 [gr-qc].
O. Lauscher, M. Reuter, Phys. Rev. D 65, 025013 (2002) arXiv:hep-th/0108040.
O. Lauscher, M. Reuter, Phys. Rev. D 66, 025026 (2002) arXiv:hep-th/0205062.
J. Ambjørn, J. Jurkiewicz, R. Loll, Phys. Rev. Lett. 95, 171301 (2005) arXiv:hep-th/0505113.
J. Ambjørn, J. Jurkiewicz, R. Loll, Phys. Rev. D 72, 064014 (2005) arXiv:hep-th/0505154.
L. Modesto, Class. Quantum Grav. 26, 242002 (2009) arXiv:0812.2214 [gr-qc].
J.J. Atick, E. Witten, Nucl. Phys. B 310, 291 (1988).
P. Hořava, Phys. Rev. Lett. 102, 161301 (2009).
P. Hořava, Phys. Rev. D 79, 084008 (2009).
J. Mureika, D. Stojkovic, Phys. Rev. Lett. 106, 101101 (2011) arXiv:1102.3434 [gr-qc].
L. Anchordoqui, D.C. Dai, M. Fairbairn, G. Landsberg, D. Stojkovic, Mod. Phys. Lett. A 27, 1250021 (2012) arXiv:1003.5914 [hep-ph].
L.A. Anchordoqui, D.C. Dai, H. Goldberg, G. Landsberg, G. Shaughnessy, D. Stojkovic, T.J. Weiler, Phys. Rev. D 83, 114046 (2011) arXiv:1012.1870 [hep-ph].
Steven Weinberg, PoS CD 09, 001 (2009) arXiv:0908.1964 [hep-th].
G. Calcagni, Phys. Rev. Lett. 104, 251301 (2010) arXiv:0912.3142 [hep-th].
G. Calcagni, JHEP 01, 065 (2012) arXiv:1107.5041 [hep-th] and references therein.
G. Calcagni, Adv. Theor. Math. Phys. 16, 549 (2012) arXiv:1106.5787 [hep-th].
G. Calcagni, Phys. Lett. B 697, 251 (2011) arXiv:1012.1244 [hep-th].
G. Calcagni, Phys. Rev. D 84, 061501 (2011) arXiv:1106.0295 [hep-th].
M. Arzano, G. Calcagni, D. Oriti, M. Scalisi, Phys. Rev. D 84, 125002 (2011) arXiv:1107.5308 [hep-th].
S. Matsuzaki, K. Yamawaki, Phys. Rev. D 86, 035025 (2012) arXiv:1206.6703.
S. Matsuzaki, K. Yamawaki, Phys. Rev. D 86, 115004 (2012) arXiv:1209.2017.
S. Matsuzaki, K. Yamawaki, Phys. Lett. B 719, 378 (2013) arXiv:1207.5911.
B. Bellazzini, C. Csaki, J. Hubisz, J. Serra, J. Terning, Eur. Phys. J. C 73, 2333 (2013) arXiv:1209.3299.
O. Antipin, J. Krog, E. Molgaard, F. Sannino, arXiv:1303.7213 [hep-ph].
R.S. Chivukula, V. Koulovassilopoulos, Phys. Lett. B 309, 371 (1993) arXiv:hep-ph/9304293.
V. Koulovassilopoulos, R.S. Chivukula, Phys. Rev. D 50, 3218 (1994) arXiv:hep-ph/9312317.
H.J. He, Y.P. Kuang, C.P. Yuan, B. Zhang, Phys. Lett. B 554, 64 (2003) arXiv:hep-ph/0211229.
H.J. He, Y.P. Kuang, C.P. Yuan, B. Zhang, in Proceedings of the ``Workshop on Physics at TeV Colliders’’, Les Houches, France, May 26--June 6, 2003, arXiv:hep-ph/0401209 and references therein.
B. Zhang, Y.P. Kuang, H.J. He, C.P. Yuan, Phys. Rev. D 67, 114024 (2003) arXiv:hep-ph/0303048.
T. Han, D. Krohn, L.T. Wang, W. Zhu, JHEP 03, 082 (2010) arXiv:0911.3656.
W. Siegel, Phys. Lett. B 84, 193 (1979).
G. ’t Hooft, M. Veltman, Nucl. Phys. B 44, 189 (1972).
H.J. He, Y.P. Kuang, C.P. Yuan, DESY-97-056, arXiv:hep-ph/9704276.
T. Appelquist, C. Bernard, Phys. Rev. D 22, 200 (1980).
A.C. Langhitano, Phys. Rev. D 22, 1166 (1980).
A.C. Langhitano, Nucl. Phys. B 188, 118 (1981).
S. Weinberg, Physica A 96, 327 (1979).
R.S. Chivukula, D.A. Dicus, H.J. He, Phys. Lett. B 525, 175 (2002) hep-ph/0111016.
J. Schwinger, Phys. Rev. 128, 2425 (1962).
S. Deser, R. Jackiw, S. Templeton, Ann. Phys. 140, 372 (1982).
S. Weinberg, Ultraviolet Divergences in Quantum Theories of Gravitation, in General Relativity: An Einstein Centenary Survey, edited by S.W. Hawking, W. Israel (Cambridge University Press, 1979) p. 790.
D.F. Litim, Philos. Trans. R. Soc. London Ser. A 369, 2759 (2011) arXiv:1102.4624 [hep-th].
M. Niedermaier, M. Reuter, Living Rev. Relativ. 9, 5 (2006).
M. Soldate, Phys. Lett. B 186, 321 (1987).
J.L. Basdevant, Fortschr. Phys. 20, 283 (1972).
S.N. Gupta, Quantum Electrodynamics (Gordon and Breach, New York, 1981) pp. 191-198.
O. Cheyette, M.K. Gaillard, Phys. Lett. B 197, 205 (1987).
N. Truong, Phys. Rev. Lett. 61, 2526 (1988).
D. Dicus, W. Repko, Phys. Rev. D 42, 3660 (1990) and references therein.
T. Abe, N. Chen, H.J. He, JHEP 01, 082 (2013) arXiv:1207.4103 and references therein.
X.-F. Wang, arXiv:1304.2257 [hep-ph].
C. Du, H.J. He, Y.P. Kuang, B. Zhang, N.D. Christensen, R.S. Chivukula, E.H. Simmons, Phys. Rev. D 86, 095011 (2012) arXiv:1206.6022 and references therein.
H.J. He et al., Phys. Rev. D 78, 031701 (2008) arXiv:0708.2588.
A.S. Belyaev et al., Phys. Rev. D 80, 055022 (2009) arXiv:0907.2662.
R.N. Mohapatra, G. Senjanovic, Phys. Rev. D 23, 165 (1981).
R.N. Mohapatra, G. Senjanovic, Phys. Rev. Lett. 44, 912 (1980).
M.S. Chanowitz, M.K. Gaillard, Nucl. Phys. B 261, 379 (1985).
V.D. Barger, K. Cheung, T. Han, R.J.N. Phillips, Phys. Rev. D 42, 3052 (1990).
J. Bagger et al., Phys. Rev. D 49, 1246 (1994) arXiv:hep-ph/9306256.
J. Bagger et al., Phys. Rev. D 52, 3878 (1995) arXiv:hep-ph/9504426.
M.S. Chanowitz, W. Kilgore, Phys. Lett. B 322, 147 (1994) arXiv:hep-ph/9311336.
M.S. Chanowitz, W. Kilgore, Phys. Lett. B 347, 387 (1995) arXiv:hep-ph/9412275.
H.J. He, Y.P. Kuang, C.P. Yuan, Phys. Rev. D 55, 3038 (1997) arXiv:hep-ph/9611316.
H.J. He, Y.P. Kuang, C.P. Yuan, DESY-97-056, arXiv:hep-ph/9704276.
M.S. Chanowitz, Czech. J. Phys. B 55, 45 (2005) arXiv:hep-ph/0412203 and references therein.
Roshan Foadi, Francesco Sannino, Phys. Rev. D 78, 037701 (2008) arXiv:0801.0663 [hep-ph].
Roshan Foadi, Matti Jarvinen, Francesco Sannino, Phys. Rev. D 79, 035010 (2009) arXiv:0811.3719 [hep-ph].
P. Fischer, D.F. Litim, Phys. Lett. B 638, 497 (2006) arXiv:hep-th/0602203.
D.F. Litim, T. Plehn, Phys. Rev. Lett. 100, 131301 (2008) arXiv:0707.3983.
J. Hewett, T. Rizzo, JHEP 12, 009 (2007) arXiv:0707.3182.
E. Gerwick, Eur. Phys. J. C 71, 1676 (2011) arXiv:1012.1118.
E. Gerwick, D. Litim, T. Plehn, Phys. Rev. D 83, 084048 (2011) arXiv:1101.5548.
X. Calmet, Mod. Phys. Lett. A 26, 1571 (2011) arXiv:1012.5529.
J.A. Casas, J.R. Espinosa, M. Quiros, Phys. Lett. B 382, 374 (1996) arXiv:hep-ph/9603227 and references therein.
T. Hambye, K. Riesselmann, Phys. Rev. D 55, 7255 (1997) arXiv:hep-ph/9610272 and references therein.
C. Quigg, Annu. Rev. Nucl. Part. Sci. 59, 505 (2009) arXiv:0905.3187 and references therein, for a recent review.
For example, P.P. Giardino, K. Kannike, I. Masina, M. Raidal, A. Strumia, arXiv:1303.3570 [hep-ph].
R.S. Chivukula, D.A. Dicus, H.J. He, Phys. Lett. B 525, 175 (2002) hep-ph/0111016.
R.S. Chivukula, H.J. He, Phys. Lett. B 532, 121 (2002) hep-ph/0201164.
R.S. Chivukula, D.A. Dicus, H.J. He, S. Nandi, Phys. Lett. B 562, 109 (2003) hep-ph/0302263.
H.J. He, Int. J. Mod. Phys. A 20, 3362 (2005) hep-ph/0412113.
R.S. Chivukula, H.J. He, M. Kurachi, E.H. Simmons, M. Tanabashi, Phys. Rev. D 78, 095003 (2008) arXiv:0808.1682 and references therein.
G. Calcagni, private communications.
H.-J. He, Z.-Z. Xianyu, Phys. Lett. B 720, 142 (2013) arXiv:1301.4570 [hep-ph].
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He, HJ., Xianyu, ZZ. Unitary standard model from spontaneous dimensional reduction and weak boson scattering at the LHC. Eur. Phys. J. Plus 128, 40 (2013). https://doi.org/10.1140/epjp/i2013-13040-2
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DOI: https://doi.org/10.1140/epjp/i2013-13040-2