Abstract
We investigate the impact of extra vector-like GUT multiplets on the predicted value of the strong coupling. We find in particular that Yukawa couplings between such extra multiplets and the MSSM Higgs doublets can resolve the familiar two-loop discrepancy between the SUSY GUT prediction and the measured value of α 3. Our analysis highlights the advantages of the holomorphic scheme, where the perturbative running of gauge couplings is saturated at one loop and further corrections are conveniently described in terms of wavefunction renormalization factors. If the gauge couplings as well as the extra Yukawas are of \( \mathcal{O}(1) \) at the unification scale, the relevant two-loop correction can be obtained analytically. However, the effect persists also in the weakly-coupled domain, where possible non-perturbative corrections at the GUT scale are under better control.
Similar content being viewed by others
References
S. Dimopoulos, S. Raby and F. Wilczek, Supersymmetry and the Scale of Unification, Phys. Rev. D 24 (1981) 1681 [SPIRES].
W. Buchmüller, K. Hamaguchi, O. Lebedev and M. Ratz, Supersymmetric standard model from the heterotic string, Phys. Rev. Lett. 96 (2006) 121602 [hep-ph/0511035] [SPIRES].
W. Buchmüller, K. Hamaguchi, O. Lebedev and M. Ratz, Supersymmetric standard model from the heterotic string. II, Nucl. Phys. B 785 (2007) 149 [hep-th/0606187] [SPIRES].
O. Lebedev et al., A mini-landscape of exact MSSM spectra in heterotic orbifolds, Phys. Lett. B 645 (2007) 88 [hep-th/0611095] [SPIRES].
V. Braun, Y.-H. He, B.A. Ovrut and T. Pantev, The exact MSSM spectrum from string theory, JHEP 05 (2006) 043 [hep-th/0512177] [SPIRES].
C. Beasley, J.J. Heckman and C. Vafa, GUTs and Exceptional Branes in F-theory-I, JHEP 01 (2009) 058 [arXiv:0802.3391] [SPIRES].
C. Beasley, J.J. Heckman and C. Vafa, GUTs and Exceptional Branes in F-theory-II: Experimental Predictions, JHEP 01 (2009) 059 [arXiv:0806.0102] [SPIRES].
R. Donagi and M. Wijnholt, Model Building with F-theory, arXiv:0802.2969 [SPIRES].
C. Adam et al., Measuring Unification, arXiv:1007.2190 [SPIRES].
S. Raby, M. Ratz and K. Schmidt-Hoberg, Precision gauge unification in the MSSM, Phys. Lett. B 687 (2010) 342 [arXiv:0911.4249] [SPIRES].
G. Amelino-Camelia, D. Ghilencea and G.G. Ross, The effect of Yukawa couplings on unification predictions and the non-perturbative limit, Nucl. Phys. B 528 (1998) 35 [hep-ph/9804437] [SPIRES].
T. Moroi and Y. Okada, Radiative corrections to Higgs masses in the supersymmetric model with an extra family and antifamily, Mod. Phys. Lett. A 7 (1992) 187 [SPIRES].
T. Moroi and Y. Okada, Upper bound of the lightest neutral Higgs mass in extended supersymmetric Standard Models, Phys. Lett. B 295 (1992) 73 [SPIRES].
K. Tobe and J.D. Wells, Higgs boson mass limits in perturbative unification theories, Phys. Rev. D 66 (2002) 013010 [hep-ph/0204196] [SPIRES].
K.S. Babu, I. Gogoladze and C. Kolda, Perturbative unification and Higgs boson mass bounds, hep-ph/0410085 [SPIRES].
K.S. Babu, I. Gogoladze, M.U. Rehman and Q. Shafi, Higgs Boson Mass, Sparticle Spectrum and Little Hierarchy Problem in Extended MSSM, Phys. Rev. D 78 (2008) 055017 [arXiv:0807.3055] [SPIRES].
S.P. Martin, Extra vector-like matter and the lightest Higgs scalar boson mass in low-energy supersymmetry, Phys. Rev. D 81 (2010) 035004 [arXiv:0910.2732] [SPIRES].
P.W. Graham, A. Ismail, S. Rajendran and P. Saraswat, A Little Solution to the Little Hierarchy Problem: A Vector-like Generation, Phys. Rev. D 81 (2010) 055016 [arXiv:0910.3020] [SPIRES].
S.P. Martin, Raising the Higgs mass with Yukawa couplings for isotriplets in vector-like extensions of minimal supersymmetry, arXiv:1006.4186 [SPIRES].
J. Jiang, T. Li and D.V. Nanopoulos, Testable Flipped SU(5) × U(1) X Models, Nucl. Phys. B 772 (2007) 49 [arXiv:0610054].
R. Barbieri, L.J. Hall, A.Y. Papaioannou, D. Pappadopulo and V.S. Rychkov, An alternative NMSSM phenomenology with manifest perturbative unification, JHEP 03 (2008) 005 [arXiv:0712.2903] [SPIRES].
T. Moroi and Y. Okada, Upper bound of the lightest neutral Higgs mass in extended supersymmetric Standard Models, Phys. Lett. B 295 (1992) 73 [SPIRES].
K. Tobe and J.D. Wells, Higgs boson mass limits in perturbative unification theories, Phys. Rev. D 66 (2002) 013010 [hep-ph/0204196] [SPIRES].
D. Ghilencea, M. Lanzagorta and G.G. Ross, Unification predictions, Nucl. Phys. B 511 (1998) 3 [hep-ph/9707401] [SPIRES].
D. Ghilencea, M. Lanzagorta and G.G. Ross, Strong unification, Phys. Lett. B 415 (1997) 253 [hep-ph/9707462] [SPIRES].
J.L. Jones, Gauge Coupling Unification in MSSM + 5 Flavors, Phys. Rev. D 79 (2009) 075009 [arXiv:0812.2106] [SPIRES].
J. Kopp, M. Lindner, V. Niro and T.E.J. Underwood, On the Consistency of Perturbativity and Gauge Coupling Unification, Phys. Rev. D 81 (2010) 025008 [arXiv:0909.2653] [SPIRES].
R. Sato, T.T. Yanagida and K. Yonekura, Relaxing a constraint on the number of messengers in a low-scale gauge mediation, Phys. Rev. D 81 (2010) 045003 [arXiv:0910.3790] [SPIRES].
S. Abel and V.V. Khoze, Direct Mediation, Duality and Unification, JHEP 11 (2008) 024 [arXiv:0809.5262] [SPIRES].
V.A. Novikov, M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, Exact Gell-Mann-Low Function of Supersymmetric Yang-Mills Theories from Instanton Calculus, Nucl. Phys. B 229 (1983) 381 [SPIRES].
M.A. Shifman and A.I. Vainshtein, Solution of the Anomaly Puzzle in SUSY Gauge Theories and the Wilson Operator Expansion, Nucl. Phys. B 277 (1986) 456 [SPIRES].
M.A. Shifman and A.I. Vainshtein, On holomorphic dependence and infrared effects in supersymmetric gauge theories, Nucl. Phys. B 359 (1991) 571 [SPIRES].
M.A. Shifman, Little Miracles of Supersymmetric Evolution of Gauge Couplings, Int. J. Mod. Phys. A 11 (1996) 5761 [hep-ph/9606281] [SPIRES].
N. Arkani-Hamed and H. Murayama, Holomorphy, rescaling anomalies and exact β-functions in supersymmetric gauge theories, JHEP 06 (2000) 030 [hep-th/9707133] [SPIRES].
N. Arkani-Hamed and H. Murayama, Renormalization group invariance of exact results in supersymmetric gauge theories, Phys. Rev. D 57 (1998) 6638 [hep-th/9705189] [SPIRES].
I. Jack, D.R.T. Jones and C.G. North, Scheme dependence and the NSVZ β-function, Nucl. Phys. B 486 (1997) 479 [hep-ph/9609325] [SPIRES].
I. Jack, D.R.T. Jones and A. Pickering, The connection between the DRED and NSVZ renormalisation schemes, Phys. Lett. B 435 (1998) 61 [hep-ph/9805482] [SPIRES].
L. Calibbi, L. Ferretti, A. Romanino and R. Ziegler, Gauge coupling unification, the GUT scale and magic fields, Phys. Lett. B 672 (2009) 152 [arXiv:0812.0342] [SPIRES].
M.S. Chanowitz, Bounding CKM Mixing with a Fourth Family, Phys. Rev. D 79 (2009) 113008 [arXiv:0904.3570] [SPIRES].
M. Bobrowski, A. Lenz, J. Riedl and J. Rohrwild, How much space is left for a new family of fermions?, Phys. Rev. D 79 (2009) 113006 [arXiv:0902.4883] [SPIRES].
B. Pendleton and G.G. Ross, Mass and Mixing Angle Predictions from Infrared Fixed Points, Phys. Lett. B 98 (1981) 291 [SPIRES].
A. Aranda, J.L. Diaz-Cruz and A.D. Rojas, Anomalies, β-functions and Supersymmetric Unification with Multi-Dimensional Higgs Representations, Phys. Rev. D 80 (2009) 085027 [arXiv:0907.4552] [SPIRES].
P. Langacker and N. Polonsky, The Strong coupling, unification and recent data, Phys. Rev. D 52 (1995) 3081 [hep-ph/9503214] [SPIRES].
P. Langacker and N. Polonsky, Uncertainties in coupling constant unification, Phys. Rev. D 47 (1993) 4028 [hep-ph/9210235] [SPIRES].
M.S. Carena, S. Pokorski and C.E.M. Wagner, On the unification of couplings in the minimal supersymmetric Standard Model, Nucl. Phys. B 406 (1993) 59 [hep-ph/9303202] [SPIRES].
J. Bagger, K.T. Matchev and D. Pierce, Precision corrections to supersymmetric unification, Phys. Lett. B 348 (1995) 443 [hep-ph/9501277] [SPIRES].
L. Roszkowski and M.A. Shifman, Reconciling supersymmetric grand unification with α s (m Z ) ≅ 0.11, Phys. Rev. D 53 (1996) 404 [hep-ph/9503358] [SPIRES].
S. Raby, Grand Unified Theories, published in Particle Data Group collaboration, C. Amsler et al., Review of particle physics, Phys. Lett. B 667 (2008) 1 [SPIRES].
D. Ring, S. Urano and R.L. Arnowitt, Planck scale physics and the testability of SU(5) supergravity GUT, Phys. Rev. D 52 (1995) 6623 [hep-ph/9501247] [SPIRES].
P. Nath and P. Fileviez Perez, Proton stability in grand unified theories, in strings and in branes, Phys. Rept. 441 (2007) 191 [hep-ph/0601023] [SPIRES].
B. Dutta, Y. Mimura and R.N. Mohapatra, Proton Decay and Flavor Violating Thresholds in SO(10) Models, Phys. Rev. Lett. 100 (2008) 181801 [arXiv:0712.1206] [SPIRES].
G.G. Ross, Wilson line breaking and gauge coupling unification, hep-ph/0411057 [SPIRES].
G. Parisi, On the Value of Fundamental Constants, Phys. Rev. D 11 (1975) 909 [SPIRES].
M. Blaszczyk et al., A Z2xZ2 standard model, Phys. Lett. B 683 (2010) 340 [arXiv:0911.4905] [SPIRES].
M. Blaszczyk, S.G. Nibbelink, F. Ruehle, M. Trapletti and P.K.S. Vaudrevange, Heterotic MSSM on a Resolved Orbifold, arXiv:1007.0203 [SPIRES].
H.P. Nilles, The role of classical symmetries in the low-energy limit of superstring theories, Phys. Lett. B 180 (1986) 240 [SPIRES].
L.J. Dixon, V. Kaplunovsky and J. Louis, On Effective Field Theories Describing (2,2) Vacua of the Heterotic String, Nucl. Phys. B 329 (1990) 27 [SPIRES].
I. Antoniadis, K.S. Narain and T.R. Taylor, Higher genus string corrections to gauge couplings, Phys. Lett. B 267 (1991) 37 [SPIRES].
R. Donagi and M. Wijnholt, Breaking GUT Groups in F-theory, arXiv:0808.2223 [SPIRES].
R. Blumenhagen, Gauge Coupling Unification in F-theory Grand Unified Theories, Phys. Rev. Lett. 102 (2009) 071601 [arXiv:0812.0248] [SPIRES].
J.J. Heckman and C. Vafa, An Exceptional Sector for F-theory GUTs, arXiv:1006.5459 [SPIRES].
E. Dudas and E. Palti, On hypercharge flux and exotics in F-theory GUTs, JHEP 09 (2010) 013 [arXiv:1007.1297] [SPIRES].
J. Jiang, T. Li, D.V. Nanopoulos and D. Xie, Flipped SU(5) × U(1) X Models from F-theory, Nucl. Phys. B 830 (2010) 195 [arXiv:0905.3394] [SPIRES].
T. Li, D.V. Nanopoulos and J.W. Walker, Elements of F-ast Proton Decay, arXiv:1003.2570 [SPIRES].
I. Gogoladze, B. He and Q. Shafi, New Fermions at the LHC and Mass of the Higgs Boson, Phys. Lett. B 690 (2010) 495 [arXiv:1004.4217] [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1007.3990
Rights and permissions
About this article
Cite this article
Donkin, I., Hebecker, A. Precision gauge unification from extra Yukawa couplings. J. High Energ. Phys. 2010, 44 (2010). https://doi.org/10.1007/JHEP09(2010)044
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2010)044