Supersymmetry. Theory, Experiment, and Cosmology

Exercises 489

in loop momenta. This is the dimensional reduction scheme (DR corresponding to

M S) [85, 340].

Since DR is compatible with supersymmetry, we have as expected g = gˆ in this

A complication arises in dimensional reduction: from the point of view of D dimensions, local invariance applies only to the components Aa0 , · · · , AaD−1 of the vector fields. The remaining 2 components AaD, · · · , Aa3 are scalars under the Lorentz group in D dimensions: they are called -scalars. They induce additional renormalization counter terms and care must be taken at higher orders to take these fields into account.

Finally, we note that, in the DR scheme, heavy thresholds e ects are very simply taken into account in renormalization group analyses: they are properly described by a simple step function localized precisely at the mass of the heavy field [7].

Exercises

Exercise 1 Show that ξ1 defined in (E.24) satisfies

and solve this equation.

Hints: The equations for the first two families are read from (E.19)–(E.23) by neglecting the Yukawa couplings.

Solution: ξ1(µ) = g12(µ)ξ1(µ0)/g12(µ0).

Bibliography

[1]I. A eck, M. Dine, and N. Seiberg. Dynamical supersymmetry breaking in supersymmetric QCD. Nucl. Phys., B241:493–534, 1984.

[2]I. A eck, M. Dine, and N. Seiberg. Dynamical supersymmetry breaking in four dimensions and its phenomenological implications. Nucl. Phys., B256:557–599, 1985.

[3]I. A eck and M. Dine. A new mechanism for baryogenesis. Nucl. Phys., B249:361, 1985.

[4]Y. Aharonov and D. Bohm. Proc. Phys. Soc. (London), B62:8, 1949.

[5]A. Albrecht and P.J. Steinhardt. Cosmology for Grand Unified Theories with radiatively induced symmetry breaking. Phys. Rev. Lett., 48:1220–1223, 1982.

[6]G. Altarelli and R. Barbieri. Vacuum polarization e ects of new physics on electroweak processes. Phys. Lett., B253:161–167, 1991.

[7]I. Antoniadis, C. Kounnas, and K. Tamvakis. Simple treatment of threshold e ects. Phys. Lett., 119B:377–380, 1982.

[8]T. Appelquist and J. Carazzone. Infrared singularities and massive fields. Phys. Rev., D11:2856, 1975.

[9]N. Arkani-Hamed and S. Dimopoulos. Supersymmetric unification without low energy supersymmetry and signatures for fine-tuning at the LHC. JHEP, 0506:073, 2005.

[10]N. Arkani-Hamed, J. March-Russell, and H. Murayama. Building models of gauge-mediated supersymmetry breaking without a messenger sector. Nucl. Phys., B509:3–32, 1998.

[11]C. Armendariz-Pico, V. Mukhanov, and P.J. Steinhardt. A dynamical solution to the problem of a small cosmological constant and late time cosmic acceleration. Phys. Rev. Lett., 85:4438–4441, 2000.

[12]T. Asaka, K. Hamaguchi, M. Kawasaki, and T. Yanagida. Leptogenesis in inflationary universe. Phys. Rev., D61:083512, 2000.

[13]J. Atick, L. Dixon, and A. Sen. String calculation of Fayet-Iliopoulos D-terms in arbitrary supersymmetric configurations. Nucl. Phys., B292:109–149, 1987.

[14]M.F. Atiyah and I.M. Singer. The index of elliptic operators 1.3. Ann. Math., 87:484–530,546–604, 1968.

[15]M.F. Atiyah and I.M. Singer. The index of elliptic operators 4. Ann. Math., 93:119–138, 1971.

Bibliography 491

[16]B. Aubert, et al. [BABAR Collaboration]. Measurement of the B → Xsγ branching fraction and photon spectrum from a sum of exclusive final states. Phys. Rev., D72, 052004, 2005.

[17]K.S. Babu, J.C. Pati, and F. Wilczek. Fermion masses, neutrino oscillations, and proton decay in the light of SuperKamiokande. Nucl. Phys., B566:33–91, 2000.

[18]H. Baer and M. Brhlik. Neutralino dark matter in minimal supergravity: direct detection versus collider searches. Phys. Rev., D57:567–577, 1998.

[19]J. Bagger, T. Moroi, and E. Poppitz. Anomaly mediation in supergravity theories. JHEP, 0004:009, 2000.

[20]T. Banks and M. Dine. Coping with strongly coupled string theory. Phys. Rev., D50:7454–7466, 1994.

[21]T. Banks and A. Zaks. On the phase structure of vector-like gauge theories with massless fermions. Nucl. Phys., B196:189–204, 1982.

[22]R. Barbieri, F. Caravaglios, and M. Frigeni. The supersymmetric higgs for heavy superpartners. Phys. Lett., B258:167–170, 1991.

[23]R. Barbieri and G.F. Giudice. Upper bounds on supersymmetric particle masses. Nucl. Phys., B306:63, 1988.

[24]R. Barbieri and G.F. Giudice. b → s gamma decay and supersymmetry. Phys. Lett., B309:86–90, 1993.

[25]R. Barbieri and A. Strumia. About the fine tuning price of LEP. Phys. Lett., B433:63–66, 1998.

[26]R. Barbieri and A. Strumia. The LEP Paradox. Fourth Rencontre du Vietnam: International conference on physics at extreme high energies, Hanoi, 2000.

[27]R. Barbier et al. R-parity violating supersymmetry. Phys. Rep., 420:1–195, 2005.

[28]M. Beck et al. Searching for dark matter with the enriched Ge detectors of the Heidelberg-Moscow ββ experiment. Phys. Lett., B336:141–146, 1994.

[29]G. Belanger, F. Boudjema, A. Pukhov, and A. Semenov. Micromegas: a program for calculating the relic density in the MSSM. Comput. Phys. Commun., 149: 103–120, 2002.

[30]G.W. Bennett et al. [E821 Collaboration]. Measurement of the negative muon anomalous magnetic moment to 0.7 ppm. Phys. Rev. Lett., 92:161–802, 2001.

[31]L. Bergstrom, P. Ullio, and J.H. Buckley. Observability of gamma rays from dark matter neutralino annihilation in the Milky Way halo. Astropart. Phys., 9:137–162, 1998.

[32]S. Bertolini, F. Borzumati, A. Masiero, and G. Ridolfi. E ects of supergravityinduced electroweak breaking on rare B-decays and mixings. Nucl. Phys., B353:591–649, 1991.

[33]J. Bijnens and C. Wetterich. Fermion masses from symmetry. Nucl. Phys., B283:237, 1987.

[34]P. Bin´etruy, S. Dawson, M. K. Gaillard, and I. Hinchli e. Supersymmetry breaking in superstring inspired models. Phys. Rev., D37:2633, 1988.

[35]P. Bin´etruy, S. Dawson, and I. Hinchli e. Gaugino masses in superstring models. Phys. Rev., D35:2215, 1987.

492Bibliography

[36]P. Bin´etruy and E. Dudas. Gaugino condensation and the anomalous U (1). Phys. Lett., B389:503–509, 1996.

[37]P. Bin´etruy and G. Dvali. D-term inflation. Phys. Lett., B388:241, 1996.

[38]P. Bin´etruy, G. Girardi, R. Grimm, and M. M¨uller. K¨ahler transformations and the coupling of matter and Yang-Mills fields to supergravity. Phys. Lett., B189:83–88, 1987.

[39]P. Bin´etruy, G. Girardi, and R. Grimm. Supergravity couplings: a geometric formulation. Phys. Rep., 343:255–462, 2001.

[40]P. Bin´etruy, G. Girardi, and P. Salati. Constraints on a system of two neutral fermions from cosmology. Nucl. Phys., B237:285, 1984.

[41]P. Bin´etruy, N. Irges, S. Lavignac, and P. Ramond. Anomalous U(1) and lowenergy physics: the power of D flatness and holomorphy. Phys. Lett., B403:38–46, 1997a.

[42]P. Bin´etruy, S. Lavignac, S. Petcov, and P. Ramond. Quasi-degenerate neutrinos from an abelian family symmetry. Nucl. Phys., B496:3–23, 1997.

[43]P. Bin´etruy, S. Lavignac, and P. Ramond. Yukawa textures with anomalous horizontal abelian symmetry. Nucl. Phys., B477:353–377, 1996.

[44]P. Bin´etruy and P. Ramond. Yukawa textures and anomaly. Phys. Lett., B350: 49–57, 1995.

[45]P. Bin´etruy and C.A. Savoy. Higgs and top masses in a non-minimal supersymmetric theory. Phys. Lett., B277:453–458, 1992.

[46]P. Bin´etruy. Models of dynamical supersymmetry breaking and quintessence. Phys. Rev., D60:063502, 1999.

[47]E.B. Bogomol’nyi. The stability of classical solutions. Sov. J. Nucl. Phys., 24:449–454, 1976.

[48]A. Bouquet, J. Kaplan, and C.A. Savoy. Low-energy constraints on supergravity parameters. Nucl. Phys., B262:299–316, 1985.

[49]P. Brax and J. Martin. Quintessence and supergravity. Phys. Lett., B468:40–45, 1999.

[50]A. Brignole, G. Degrassi, P. Slavich, and F. Zwirner. On the O(αt2) two-loop corrections to the neutral higgs boson masses in the MSSM. Nucl. Phys., B631: 195–218, 2002.

[51]A. Brignole, L. Ib´anez, and C. Munoz. Toward a theory of soft terms for the supersymmetric Standard Model. Nucl. Phys., B422:125–171, 1994. Erratumibid. B436 (1995) 747–748.

[52]A. Brignole. Radiative corrections to the supersymmetric neutral Higgs boson masses. Phys. Lett., B281:284–294, 1992.

[53]J.D. Brown and J.C. Teitelboim. Dynamical neutralization of the cosmological constant. Phys. Lett., B195:177–182, 1987.

[54]J.D. Brown and J.C. Teitelboim. Neutralization of the cosmological constant by membrane creation. Nucl. Phys., B297:787–836, 1988.

[55]F. Buccella, J.P. Derendinger, S. Ferrara, and C.A. Savoy. Patterns of symmetry breaking in supersymmetric gauge theories. Phys. Lett., 115B:375–379, 1982.

Bibliography 493

[56]W. Buchmuller and D. Wyler. CP violation and R invariance in supersymmetric models of strong and electroweak interactions. Phys. Lett., B121:321, 1983.

[57]W. Buchmuller. Neutrinos, grand unification and leptogenesis. In 2001 European school of high-energy physics (Beatenberg, Switzerland), 2001.

[58]A.J. Buras, P. Gambino, M. Gorbahn, S. Jager, and L. Silvestrini. Universal unitarity triangle and physics beyond the standard model. Phys. Lett., B500:161– 167, 2001.

[59]A.J. Buras, M.E. Lautenbacher, and G. Ostermaier. Waiting for the top quark mass,... Phys. Rev., D50:3433–3446, 1994.

[60]A.J. Buras, M. Misiak, M. Munz, and S. Pokorski. Theoretical uncertainties and phenomenological aspects of B → Xsγ decay. Nucl. Phys., B424:374–398, 1994.

[61]N. Cabibbo, L. Maiani, G. Parisi, and R. Petronzio. Bounds on the fermions and Higgs boson masses in grand unified theories. Nucl. Phys., B158:295–305, 1979.

[62]N. Cabibbo and L. Maiani. The lifetime of charmed particles. Phys. Lett., B79:109–111, 1978.

[63]R.R. Caldwell, R. Dave, and P.J. Steinhardt. Phys. Rev. Lett., 75:2077, 1995.

[64]C.G. Callan, S. Coleman, and R. Jackiw. A new improved energy-momentum tensor. Ann. Phys.(N.Y.), 59:42, 1970.

[65]C.G. Callan, D. Friedan, E.J. Martinec, and M. Perry. Strings in background fields. Nucl. Phys., B262:593, 1985.

[66]P. Candelas, G. Horowitz, A. Strominger, and E. Witten. Vacuum configurations for superstrings. Nucl. Phys., B258:46, 1985.

[67]M. Carena, M. Quiros, A. Riotto, I. Vilja, and C.E.M. Wagner. Nucl. Phys., B503:404, 1997.

[68]S.M. Carroll. Quintessence and the rest of the world. Phys. Rev. Lett., 81:3067– 3070, 1998.

[69]J.A. Casas, J.R. Espinosa, and H.E. Haber. The Higgs mass in the MSSM infrared fixed point scenario. Nucl. Phys., B526:3–20, 1998.

[70]J. A. Casas, A. Lleyda, C. Mu˜noz, and G.G. Ross. Hierarchical supersymmetry breaking and dynamical determination of compactification parameters by nonperturbative e ects. Nucl. Phys., B347:243–269, 1990.

[71]J. A. Casas, A. Lleyda, and C. Mu˜noz. Strong constraints on the parameter space of the MSSM from charge and color breaking. Nucl. Phys., B471:3–58, 1996.

[72]N.P. Chang, S. Ouvry, and X. Wu. N=1 supergravity with nonminimal coupling: a class of models. Phys. Rev. Lett., 51:327–330, 1983.

[73]M. Chanowitz and M.K. Gaillard. The Tev physics of strongly interacting W ’s and Z’s. Nucl. Phys., B261:379–431, 1985.

[74]K. Chetyrkin, M. Misiak, and M. Munz. Weak radiative B-meson decay beyond leading logarithms. Phys. Lett., B400:206–219, 1997.

[75]P. Ciafaloni and A. Strumia. Naturalness upper bounds on gauge mediated soft terms. Nucl. Phys., B494:41–53, 1997.

[76]CKMfitter group (J. Charles et al.). Eur. Phys. J., 41:1–131, 2005. updated results available at http://ckmfitter.in2p3.fr.

494Bibliography

[77]M. Claudson, L.J. Hall, and I. Hinchli e. Low-energy supergravity: false vacua and vacuous predictions. Nucl. Phys., B228:501–528, 1983.

[78]M. Claudson and M. Halpern. Supersymmetric ground state wave functions. Nucl. Phys., B250:689–715, 1985.

[79]A. Cohen, D. Kaplan, and A. Nelson. The more minimal supersymmetric standard model. Phys.Lett., B388:588–598, 1996.

[80]S. Coleman and J. Mandula. All possible symmetries of the S-matrix. Phys. Rev., 159:1251–1256, 1967.

[81]S. Coleman, S. Parke, A. Neveu, and C.M. Sommerfield. Can one dent a dyon? Phys. Rev., 15:544–545, 1977.

[82]S. Coleman, J. Wess, and B. Zumino. Structure of phenomeological lagrangians. Phys. Rev., 177:2239–2250, 1969.

[83]S. Coleman. The invariance of the vacuum is the invariance of the world. Journ. Math. Phys., 7:787, 1966.

[84]J. C. Collins, (1984). Renormalization, Cambridge University Press.

[85]D.M. Cooper, D.R.T. Jones, and P. van Nieuwenhuizen. Nucl. Phys., B167:479, 1980.

[86]E.J. Copeland, A.R. Liddle, D. Lyth, E.D. Stewart, and D. Wands. False vacuum inflation with Einstein gravity. Phys. Rev., D49:6410–6433, 1994.

[87]E.J. Copeland, A.R. Liddle, and D. Wands. Exponential potentials and cosmological scaling solutions. Phys. Rev., D57:4686–4690, 1998.

[88]Supernova cosmology project. Astrophys. J., 517:565, 1999.

[89]C.D. Coughlan, G. German, G.G. Ross, and G. Segr´. The one loop e ective potential and supersymmetry breaking in superstring models. Phys. Lett., 198B:467, 1987.

[90]G.D. Coughlan, W. Fischler, E.W. Kolb, S. Raby, and G.G. Ross. Cosmological problems for the Polonyi potential. Phys.Lett., 131B:59–64, 1983.

[91]E. Cremmer, S. Ferrara, L. Girardello, and A. van Proeyen. Yang-Mills theories with local supersymmetry: Lagrangian, transformation laws and super-Higgs e ect. Nucl. Phys., B212:413–442, 1983.

[92]E. Cremmer, S. Ferrara, C. Kounnas, and D.V. Nanopoulos. Naturally vanishing cosmological constant in N=1 supergravity. Phys. Lett., 133B:61–66, 1983.

[93]G. D’Ambrosio, G.F. Giudice, G. Isidori, and A. Strumia. Minimal flavor violation: an e ective field theory approach. Nucl. Phys., B645:155, 2002.

[94]T. Damour and F.J. Dyson. The Oklo bound on the time variation of the fine structure constant revisited. Nucl. Phys., B480:37–54, 1996.

[95]T. Damour and K. Nordtvedt. General relativity as a cosmological attractor of tensor-scalar theories. Phys. Rev. Lett., 70:2217–2219, 1993.

[96]T. Damour and A.M. Polyakov. The string dilaton and a least coupling principle. Nucl. Phys., B423:532–558, 1994.

[97]S.C. Davis, A.-C. Davis, and W.B. Perkins. Cosmic string zero modes and multiple phase transitions. Phys. Lett., B 408:81–90, 1997.

Bibliography 495

[98]S.C. Davis, A.-C. Davis, and M. Trodden. N=1 supersymmetric cosmic strings. Phys. Lett., B 405:257–264, 1997.

[99]S. Dawson. R parity breaking in supersymmetric theories. Nucl. Phys., B261:297, 1985.

[100]G. Degrassi, P. Gambino, and G.F. Giudice. B → Xsγ in supersymmetry: large contributions beyond the leading order. JHEP, 0012:009, 2000.

[101]J.P. Derendinger. Lecture notes on globally supersymmetric theories in four and two dimensions. Unpublished, preprint ETH-YH/90-21, 1990.

[102]J.P. Derendinger and C.A. Savoy. Quantum e ects and SU 2) × U (1) breaking in supergravity gauge theories. Nucl. Phys., B237:307–328, 1984.

[103]J. P. Derendinger, L. E. Ib´a˜nez, and H. P. Nilles. On the low-energy D = 4, N = 1 supergravity theory extracted from the D = 10, N = 1 superstring. Phys. Lett., 155B:65, 1985.

[104]W. de Sitter. Proc. Kon. Ned. Akad. Wer., 19:217, 1917.

[105]W. de Sitter. Proc. Kon. Ned. Akad. Wer., 20:229, 1917.

[106]M. Dimopoulos, S. Thomas, and J.D. Wells. Sparticle spectroscopy and electroweak symmetry breaking with gauge-mediated supersymmetry breaking. Nucl. Phys., B488:39–91, 1997.

[107]S. Dimopoulos and H. Georgi. Softly broken supersymmetry and SU(5). Nucl. Phys., B193:150, 1981.

[108]S. Dimopoulos, S. Raby, and F. Wilczek. Supersymmmetry and the scale od unification. Phys.Rev., D24:1681–1683, 1981.

[109]S. Dimopoulos and S. Raby. Supercolor. Nucl. Phys., B192:353, 1981.

[110]S. Dimopoulos and S. Thomas. Dynamical relaxation of the supersymmetric CP violating phases. Nucl. Phys., B465:23–33, 1996.

[111]M. Dine, W. Fischler, and M. Srednicki. Supersymmetric technicolor. Nucl. Phys., B189:575–593, 1981.

[112]M. Dine, A.E. Nelson, Y. Nir, and Y. Shirman. New tools for low energy dynamical supersymmetry breaking. Phys. Rev., D53:2658–2669, 1996.

[113]M. Dine, A.E. Nelson, and Y. Shirman. Low energy dynamical supersymmetry breaking simplified. Phys. Rev., D51:1362–1370, 1995.

[114]M. Dine, Y. Nir, and Y. Shirman. Variations on minimal gauge mediated supersymmetry breaking. Phys. Rev., D55:1501, 1997.

[115]M. Dine, R. Rohm, N. Seiberg, and H.P. Nilles. Gluino condensation in superstring models. Phys. Lett., 156B:55, 1985.

[116]M. Dine, N. Seiberg, and E. Witten. Fayet-Iliopoulos terms in string theory. Nucl. Phys., B289:589–598, 1987.

[117]M. Dine and N. Seiberg. Nonrenormalization theorems in superstring theory.

Phys. Rev. Lett., 57:2625, 1986.

[118]P.A.M. Dirac. Quantised singularities in the electromagnetic field. Proc. Roy. Soc., A33:60–72, 1931.

[119]P.A.M. Dirac. The cosmological constants. Nature (London), 139:323, 1937.

496Bibliography

[120]P.A.M. Dirac. New basis for cosmology. Proc. Roy. Soc. London, A165:199–208, 1938.

[121]L.J. Dixon, V.S. Kaplunovsky, and J. Louis. Moduli dependence of string loop corrections to gauge coupling constants. Nucl. Phys., B355:649–688, 1991.

[122]S. Dodelson, W.H. Kinney, and E.W. Kolb. Cosmic microwave background measurements can discreminaate among inflation models. Phys. Rev., D56:3207–3215, 1997.

[123]M. Drees and M. M. Nojiri. Neutralino-nucleon scattering reexamined. Phys. Rev., D48:3483–3501, 1993.

[124]M. Drees and M. M. Nojiri. Neutralino relic density in minimal N=1 supergravity. Phys. Rev., D47:376–408, 1993.

[125]E. Dudas, C. Grojean, S. Pokorski, and C.A. Savoy. Abelian flavor symmetries in supersymmetric models. Nucl. Phys., B481:85–108, 1996.

[126]E. Dudas. Theory and phenomenology of type I strings and M-theory. Class. Quantum Grav., 17:R41–R116, 2000.

[127]A. Einstein. Sitzungsber. Preuss. Akad. Wiss., phus.-math. Klasse VI:142, 1917.

[128]J. Ellis, K. Enqvist, D.V. Nanopoulos, and F. Zwirner. Aspects of the superunification od strong, electroweak and gravitational interactions. Nucl. Phys., B276:14, 1986.

[129]J. Ellis, J.F. Gunion, H.E. Haber, L. Roszkowski, and F. Zwirner. Higgs bosons in a nonminimal supersymmetric model. Phys. Rev., D39:844, 1989.

[130]J. Ellis, C. Kounnas, and D. Nanopoulos. No-scale supersymmetric GUTs. Nucl. Phys., B247:373–395, 1984.

[131]J. Ellis, C. Kounnas, and D. Nanopoulos. Phenomenological SU(1,1) supergravity. Nucl. Phys., B241:406–428, 1984.

[132]J. Ellis, A.B. Lahanas, D. Nanopoulos, and K. Tamvakis. No-scale supersymmetric standard model. Phys. Lett., 134B:429–435, 1984.

[133]J. Ellis, D.V. Nanopoulos, and M. Quiros. On the axion, dilaton, Polonyi, gravitino and shadow matter problems in supergravity and superstring models. Phys. Lett., B 174:176–182, 1986.

[134]J. Ellis, G. Ridolfi, and F. Zwirner. Radiative corrections to the masses of supersymmetric Higgs bosons. Phys. Lett., B 257:83–91, 1991.

[135]U. Ellwanger and M. Rausch de Traubenberg and C.A. Savoy. Phenomenology of supersymmetric models with a singlet. Nucl. Phys., B492:21–50, 1997.

[136]B. Aubert et al. [BABAR Collaboration]. Observation of CP violation in the b0 meson system. Phys. Rev. Lett., 87:091801, 2001.

[137]K. Abe et al. [Belle Collaboration]. Observation of a large CP violation in the neutral B meson system. Phys. Rev. Lett., 87:091802, 2001.

[138]Y. Hayato et al. [Super-Kamiokande Collaboration]. Search for proton decay through p → νK¯ + in a large water cherenkov detector. Phys. Rev. Lett., 83:1529, 1999.

[139]M. Bona et al [UTfit collaboration]. The UTfit collaboration report on the status of the unitarity triangle beyond the standard model I. Model-independent analysis and minimal flavor violation. JHEP, 0603:080, 2006.

Bibliography 497

[140]A.G. Riess et al. Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J., 116:1009–1038, 1998.

[141]D.N. Spergel et al. First year WMAP observations: determination of cosmological parameters. Astrophys. J. Supp., 148:175, 2003.

[142]K. Hagiwara et al. Review of particle physics. Phys. Rev. D, 66:010001, 2002.

[143]M. Ciuchini et al. δmk and k in SUSY at the next-to-leading order. JHEP, 9810:008, 1998.

[144]P.G. Harris et al. Phys. Rev. Lett., 82:904, 1999.

[145]P. Fayet and J. Iliopoulos. Spontaneously broken supergauge symmetries and Goldstone spinors. Phys. Lett., 51B:461–464, 1974.

[146]P. Fayet. Supergauge invariant extension of the Higgs mechanism and a model for the electron and its neutrino. Nucl. Phys., B90:104–124, 1975.

[147]P. Fayet. Fermi-Bose hypersymmetry. Nucl. Phys., B113:135–155, 1976.

[148]P. Fayet. Supersymmetry and weak, electromagnetic and strong interactions. Phys. Lett., 64B:159, 1976.

[149]P. Fayet. Spontaneously broken supersymmetric theories of weak, electromagnetic and strong interactions. Phys. Lett., 69B:489–494, 1977.

[150]P. Fayet. In S. Ferrara, J. Ellis, and P. van Nieuwenhuizen, editors, Unification of the fundamental particle interactions, page 587. Plenum, 1980.

[151]P. Fayet. Supersymmetric grand unification in a six-dimensional space-time. Phys. Lett., B159:121, 1985.

[152]P. Fayet. Nucl. Phys., B263:649, 1986.

[153]J.L. Feng, K.T. Matchev, and T. Moroi. Focus points and naturalness in supersymmetry. Phys. Rev., D61:075005, 2000.

[154]J.L. Feng, K.T. Matchev, and T. Moroi. Multi-TeV scalars are natural in minimal supergravity. Phys. Rev. Lett., 84:2322–2325, 2000.

[155]J.L. Feng and T. Moroi. Supernatural supersymmetry: phenomenological implications of anomaly-mediated supersymmetry breaking. Phys. Rev., D61:095004, 2000.

[156]E. Fermi. An attempt of a theory of beta radiation 1. Z. Phys., 88:161–177, 1934.

[157]E. Fermi. Trends to a theory of beta radiation. Nuovo Cimento, 11:1–19, 1934.

[158]S. Ferrara, J. Iliopoulos, and B. Zumino. Supergauge invariance and the Gell- Mann-Low eigenvalue. Nucl. Phys., B77:413, 1974.

[159]S. Ferrara and E. Remiddi. Absence of the anomalous magnetic moment in a supersymmetric abelian gauge theory. Phys. Lett., 53B:347–350, 1974.

[160]P. Ferreira and M. Joyce. Structure formation with a self-tuning scalar field. Phys. Rev. Lett., 79:4740–4743, 1997.

[161]P. Ferreira and M. Joyce. Cosmology with a primordial scaling field. Phys. Rev., D58:023503, 1998.

[162]R.P. Feynman and M. Gell-Mann. Phys. Rev., 109:193, 1958.

[163]D. Finnell and P. Pouliot. Instanton calculations versus exact results in fourdimensional SUSY gauge theories. Nucl. Phys., B453:225–239, 1995.

498Bibliography

[164]K. Freese, J. Frieman, and A. Gould. Signal modulation in cold dark matter detection. Phys. Rev., D37:3388, 1988.

[165]J.-M. Fr`ere, D.R.T. Jones, and S. Raby. Fermion masses and induction of the weak scale by supergravity. Nucl. Phys., B222:11–19, 1983.

[166]J. Frieman, C. Hill, A. Stebbins, and I. Waga. Cosmology with ultra-light NambuGoldstone bosons. Phys. Rev.Lett., 75:2077–2080, 1995.

[167]C.D. Froggatt and H.B. Nielsen. Hierarchy of quark masses, Cabibbo angles and CP violation. Nucl. Phys., B147:277–298, 1979.

[168]C.D. Froggatt and H.B. Nielsen. Statistical analysis of quark and lepton masses. Nucl. Phys., B164:114–140, 1979.

[169]M. Fukugita and T. Yanagida. Baryogenesis without grand unification. Phys. Lett., B174:45, 1986.

[170]F. Gabbiani, E. Gabrielli, A. Masiero, and L. Silvestrini. A complete analysis of FCNC and CP constraints in general SUSY extensions of the Standard Model. Nucl. Phys., B477:321–352, 1996.

[171]M.K. Gaillard and B.W. Lee. Rare decay modes of the K mesons in gauge theories. Phys. Rev., D10:897, 1974.

[172]M.K. Gaillard, B. Nelson, and Y.-Y. Wu. Gaugino masses in modular invariant supergravity. Phys. Lett., B459:549–556, 1999.

[173]G. Gamberini, G. Ridolfi, and F. Zwirner. On radiative gauge symmetry breaking in the minimal supersymmetric model. Nucl. Phys., B331:331–349, 1990.

[175]R. Gatto, R. Sartori, and M. Tonin. Weak self masses, Cabibbo angles and broken SU(2)×SU(2). Phys. Lett., B28:128–130, 1968.

[176]M. Gell-Mann, R.J. Oakes, and B. Renner. Behavior of current divergences under SU(3)×SU(3). Phys. Rev., 175:2195–2199, 1968.

[177]M. Gell-Mann, P. Ramond, and R. Slansky. Talk at the Sanibel symposium, 1979. preprint CALT-68-709 (unpublished).

[178]H. Georgi. An almost realistic gauge hierarchy. Phys. Lett., B108:283, 1982.

[179]H. Georgi and S.L. Glashow. Gauge theories without anomalies. Phys. Rev., D6:429–431, 1972.

[180]H. Georgi and S.L. Glashow. Unified weak and electromagnetic interactions without neutral currents. Phys. Rev. Lett., 28:1494–1497, 1972.

[181]H. Georgi and S.L. Glashow. Unity of all elementary particle forces. Phys. Rev. Lett., 32:438–441, 1974.

[182]H. Georgi and C. Jarlskog. Soft breaking of supersymmetry. Phys. Lett., 86B:297, 1979.

[183]H. Georgi, H.R. Quinn, and S. Weinberg. Hierarchy of interactions in unified gauge theories. Phys. Rev. Lett., 33:451–454, 1974.

[184]T. Gherghetta, C.F. Kolda, and S.P. Martin. Flat directions in the scalar potential of the supersymmetric standard model. Nucl. Phys., B468:37–58, 1996.