Yukawa sector in non-supersymmetric renormalizable SO(10)

Alejandra Melfo; Borut Bajc; Francesco Vissani; Goran Senjanovic

REVIEW

Yukawa sector in non-supersymmetric renormalizable SO(10)

Borut Bajc, Alejandra Melfo, Goran Senjanovic, Francesco Vissani

High Energy Physics - Phenomenology · Submitted 11 Oct 2005 · 48 references

Pith's verdict: A clean 126+120 non-SUSY SO(10) construction: the neutrino-mass/θ_A correlation survives scrutiny, but the Vcb–θ_A relation misses by a factor of ~7 inside its own two-generation truncation.

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arXiv IDhep-ph/0510139 (version 2)

Pith IDHWYDMHUA, Pith's permanent record of this paper and its review

CitationAlejandra Melfo, Borut Bajc, Francesco Vissani, Goran Senjanovic. "Yukawa sector in non-supersymmetric renormalizable SO(10)." arXiv:hep-ph/0510139 (2005). https://pith.science/paper/HWYDMHUA

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Two things worth knowing. First, this is a careful, honest construction of the minimal non-supersymmetric SO(10) Yukawa sector with 126+120 (126+10 is the warm-up), and the two-generation algebra from Eq. (16) to Eq. (24) is transparent and checkable. Second, of the two headline correlations, one holds up and one does not. That split is the whole story of the paper, and the abstract does not make it clear enough (abstract:s2, abstract:s3). What holds: Eq. (22), the link between neutrino mass degeneracy and how close θ_A is to maximal. It follows from M_N ∝ M1, which the authors claim for both type I and type II seesaw. I checked the type I case — the cross term vanishes because Y120 is antisymmetric, and the residual M2 M1^{-1} M2 piece is suppressed by ε² ~ 10^-4, so M_N ∝ M1 is fine. That correlation is a genuine parameter-free statement and is the paper's real contribution. What doesn't: Eq. (24). With ε_f fixed by Eq. (20), |Vcb| ≤ |cos2θ_A| |εD − εU| ≈ 0.31 × 0.02 ≈ 0.006, against 0.041 observed. That is a factor of ~7, and it is a bound, not an estimate — no choice of phases helps. The authors see it ('even this would not be sufficient...') but blame first-generation effects and loops. That escape does not work: Vcb is a 2–3 mixing, so first-generation effects enter at O(θ13²) ~ 10^-5, and their own loop estimate is 10–20%. The relation fails inside the truncation, not because of it. Eq. (23) has the same flavor: mτ/mb = 3 against ~2 is a 50% gap, and 10–20% corrections do not close it. One place I would push back on the reader: the ε_f are not circular. They are fixed by observed mass ratios, so Eq. (24) is a genuine prediction of Vcb from ms/mb, mc/mt and θ_A. The problem is that the prediction is wrong, not that it is tautological. The PQ/axion discussion and the symmetry-breaking survey are sensible but secondary; the latter leans on Ref. [10] and is appropriately hedged. Bottom line: a competent specialist paper with one solid structural result and one quantitative claim that misses badly. Worth a referee report — the Vcb tension is exactly what should be pressed — but the abstract oversells the Vcb link given what the algebra actually delivers.

Referee report

Major objections (2)

[§II.B.1, Eq. (24) and abstract:s3] The relation |V_cb| = |Re xi - i cos2theta_A Im xi| with xi = cos2theta_A (epsilon_D - epsilon_U) is bounded by |V_cb| <= |cos2theta_A| |epsilon_D - epsilon_U|. Using Eq. (20) and the measured mass ratios, |epsilon_D - epsilon_U| is approximately 0.017, and with |cos2theta_A| <= 0.31 at 99% CL this gives |V_cb| < 0.005, roughly a factor of eight below the observed 0.041. The authors acknowledge the shortfall ('even this would not be sufficient if this prediction is taken at its face value') but attribute the rescue to first-generation effects and loops. For a 2-3 mixing, first-generation effects enter only through the small 1-3 and 1-2 mixings, and the paper's own loop estimate is 10-20%; neither can bridge a factor of eight. The abstract's claim [abstract:s3] should be softened to a qualitative statement, or the rescue should be quantified.
[§II.B.1, Eq. (23)] The relation m_tau/m_b = 3 + 3 sin2theta_A Re[epsilon_E - epsilon_D] gives m_tau/m_b approximately 3 with corrections of at most about 10% from the epsilon terms, while the standard-model extrapolation gives m_tau approximately 2 m_b. The authors acknowledge this ('At first glance, this appears to kill the model') and list possible rescues (large Dirac Yukawa, three-flavor effects) estimated at 10-20%. The gap is about 35%, so the rescues are not quantitatively adequate as stated. Moreover, the same epsilon_D enters Eq. (24), so the phase choices that reduce m_tau/m_b are correlated with the V_cb prediction; the two tensions cannot be relieved independently. The paper should quantify the combined effect or state clearly that the model is not quantitatively viable without additional ingredients.

Minor objections (8)

[§II.A.2, Eq. (9)] The derivation of c_0 approximately m_t/m_b should be shown; the approximation is not obvious from the displayed expression, and the sensitivity to the input masses should be indicated.
[§II.B, Eq. (13)] The step M_2 M_1^{-1} M_2 proportional to M_1 should be explained; it relies on the specific form of M_1 in Eq. (15) and is not transparent as written.
[§II.B, after Eq. (12)] The claim that real 120_H is ruled out because the definitions (12) constrain all three c_i to the same order of magnitude should be made quantitative, or softened to a plausibility argument.
[§III, Eq. (26)] The bound M_R >= 10^13 GeV depends on the assumed heaviest neutrino mass; the value used should be stated explicitly.
[Abstract] The caveat that the results are based on the two-generation truncation [abstract:s4] comes after the claims [abstract:s2, abstract:s3]; consider reordering so that the scope is clear before the results are stated.
[§II.B.1, Eq. (20)] The phases of the epsilon_f parameters are undetermined; the paper should clarify that Eqs. (23) and (24) are consistency relations among observables rather than parameter-free predictions.
[§II.A.4] Typo: 'an give M_PQ approximately M_W' should read 'and give M_PQ approximately M_W'.
[§II.B, Eq. (13) and surrounding text] The superscripts and subscripts in the displayed seesaw expression are garbled; the intended expression should be checked and typeset cleanly.

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The paper

The paper claims

In a non-supersymmetric SO(10) grand unified theory built from Higgs fields in the 126 and 120 representations, two-generation analytic relations tie the neutrino mass splitting, and the small quark mixing $V_{cb}$, to how far the measured

The reading

The paper asks whether ordinary, non-supersymmetric SO(10) grand unification can host a realistic and predictive account of fermion masses, given that the renormalizable see-saw mechanism forces a $126_H$ and that a second Higgs representation is needed to generate any mixing at all. The authors construct the two minimal Yukawa sectors, $126_H$ with $10_H$ and $126_H$ with $120_H$, and show that the first cannot work with a real $10_H$: the ratio that a real bidoublet forces comes out of order $m_t/m_b$, far from one. Complexifying the Higgs then invites a Peccei-Quinn symmetry, which supplies an axion dark matter candidate and solves the strong CP problem as a by-product. The centre of the paper is the $126_H+120_H$ case, where a two-by-two treatment of the second and third generations produces closed-form relations among the atmospheric mixing angle, the neutrino mass splitting, the bottom-to-tau mass ratio, and $V_{cb}$. The claim a sympathetic reader should take away is that in this model large leptonic mixing and small quark mixing are not independent accidents but two readings of the same angle.

What carries the argument

The load-bearing device is a two-by-two parametrisation of the mass matrices in the basis where the $126_H$ Dirac matrix is $M_1 propto diag(sin^2 theta, cos^2 theta)$, with the antisymmetric $120_H$ contribution entering as a single off-diagonal structure. Expanding the diagonalising matrices $L_f$ and $R_f$ to first order in the small parameters $epsilon_f$ turns each fermion sector into two equations, one fixing the third-generation mass scale and one fixing the ratio of second to third generation masses times $sin 2theta$. The mechanism that makes the model predictive is that the type I see-saw mass matrix $M_N^I propto 9c_1^2 M_1 - c_4^2 M_2 M_1^{-1} M_2$ and the type II contribution $M_N^{II} propto M_1$ both reduce to the same diagonal structure, so the angle already fixed by the charged fermions is the leptonic mixing angle, and the neutrino masses are read off directly from the same $sin^2 theta$ and $cos^2 theta$ entries.

Extended reading notes

Core claim

Working in the basis where the $126_H$ contribution $M_1$ is diagonal and proportional to $diag(0,1)$ after a rotation by $theta$, the authors write the charged-fermion mass matrix as $M_f = mu_f$ times a two-by-two matrix whose off-diagonal entries are $i(sin theta cos theta + epsilon_f)$, with $epsilon_f$ scaling as the second-generation mass over the third. Diagonalising to leading order in $epsilon_f$ gives $|mu_f| = m_{f3}$ and $sin 2theta |epsilon_f| = m_{f2}/m_{f3}$. Because both the type I and type II see-saw contributions come out proportional to $M_1$, the same angle $theta$ controls the neutrino sector, and it is identified with the atmospheric mixing angle $theta_A$ up to corrections of order $m_mu/m_tau$. Three relations follow: the fractional neutrino mass splitting equals $cos 2theta_A/(1 - sin^2 2theta_A/2)$ up to $O(epsilon)$, so neutrino degeneracy is measured by how close $theta_A$ is to maximal; $m_tau/m_b = 3 + 3 sin 2theta_A Re[epsilon_E - epsilon_D]$; and $|V_{cb}| = |Re xi - i cos 2theta_A Im xi|$ with $xi = cos 2theta_A (epsilon_D - epsilon_U)$. The last two pull in opposite directions from the first: fitting the small $V_{cb}$ wants $cos 2theta_A$ as large as possible, that is, $theta_A$ as far from $45^circ$ as the data allow.

Load-bearing premise

The relations carry quantitative weight only if dropping the first generation and the loop corrections is genuinely a small perturbation, an assumption the authors state and then explicitly say leaves the $V_{cb}$ prediction and the model itself unjudged.

Editorial extensions

If this is right

If the relation holds after running and after including the first generation, the atmospheric mixing angle stops being a free parameter and becomes a measurement of how degenerate the two heavier neutrinos are.
A value of $theta_A$ measurably away from $45^circ$ is what allows $V_{cb}$ to come out small, so the observed pattern of one large leptonic and one small quark mixing angle is explained rather than assumed.
The model's prediction $m_tau/m_b \approx 3$ at the unification scale sits against the Standard Model extrapolation of about 2, so the charged-lepton and down-quark sectors must receive corrections of order ten to twenty percent from phases, the large Dirac Yukawa coupling, or the full three-flavour fit.
Complexifying either $10_H$ or $120_H$ brings in a Peccei-Quinn symmetry whose breaking scale is tied to the right-handed neutrino mass scale, giving axion dark matter in a theory that otherwise has no stable neutral candidate.
The symmetry-breaking analysis restricts viable patterns to those with an intermediate Pati-Salam scale and $M_R$ above roughly $10^{13}$ GeV, which is what the see-saw needs to keep the heaviest neutrino heavy enough.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The relation between $theta_A$ and the neutrino mass splitting is stated for the two heavier states only; if it survived a three-generation fit, a near-maximal $theta_A$ would be in tension with the atmospheric mass splitting being the larger one, which is a sharper handle than the paper's own numerical remark that $m_2 > 30$ meV.
Because $V_{cb}$ and the neutrino degeneracy both depend on $cos 2theta_A$, a future precision measurement of $theta_A$ would over-determine the framework: the same number would have to reproduce both the quark mixing and the neutrino mass ratio, so the two tests are not independent checks but one check made twice.
The Peccei-Quinn symmetry is introduced to fix a fermion-mass problem, not a cosmological one, and its scale is pinned near the right-handed neutrino scale; this makes the axion mass a derived quantity in this class of models rather than a free parameter, which is a prediction that could be confronted with axion searches.
The paper's own escape hatch, that neglected first-generation effects and loops prevent a verdict on the $V_{cb}$ relation, is the natural place for a follow-up: a full three-generation numerical fit including two-loop Yukawa running would either confirm the correlation or retire it.

Original abstract

We discuss the ordinary, non-supersymmetric SO(10) as a theory of fermion masses and mixings. We construct two minimal versions of the Yukawa sector based on $\bar{126}_H $ and either $10_H$ or $120_H$. The latter case is of particular interest since it connects the absolute neutrino mass scale with the size of the atmospheric mixing angle $\theta_A$. It also relates the smallness of $V_{cb}$ with the largeness of $\theta_A$. These results are based on the analytic study of the second and third generations. Furthermore, we discuss the structure of the light Higgs and the role of the Peccei-Quinn symmetry for dark matter and the predictivity of the theory.

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The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,873 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.57 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.08 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We discuss the ordinary, non-supersymmetric SO(10) as a theory of fermion masses and mixings. We construct two minimal versions of the Yukawa sector based on $\bar{126}_H $ and either $10_H$ or $120_H$. The latter case is of particular interest since it connects the absolute neutrino mass scale with the size of the atmospheric mixing angle $\theta_A$. It also relates the smallness of $V_{cb}$ with the largeness of $\theta_A$. These results are based on the analytic study of the second and third generations. Furthermore, we discuss the structure of the light Higgs and the role of the Peccei-Quinn symmetry for dark matter and the predictivity of the theory.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We discuss the ordinary, non-supersymmetric SO(10) as a theory of fermion masses and mixings.	background 0.54	0.63	0.05	asserted 0.91
s1	We construct two minimal versions of the Yukawa sector based on $\bar{126}_H $ and either $10_H$ or $120_H$.	contribution 0.98	0.95	0.07	asserted 1.00
s2	The latter case is of particular interest since it connects the absolute neutrino mass scale with the size of the atmospheric mixing angle $\theta_A$.	interpretation 0.48	0.77	0.28	asserted 0.97
s3	It also relates the smallness of $V_{cb}$ with the largeness of $\theta_A$.	result 0.86	0.84	0.18	asserted 1.00
s4	These results are based on the analytic study of the second and third generations.	method 0.84	0.86	0.06	asserted 1.00
s5	Furthermore, we discuss the structure of the light Higgs and the role of the Peccei-Quinn symmetry for dark matter and the predictivity of the theory.	contribution 1.00	0.83	0.08	asserted 0.82

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v2

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full text
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relations to other papers

levels run

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (48)

[10]

N. G. Deshpande, E. Keith and P. B. Pal, Phys. Rev. D 47, 2892 (1993) [arXiv:hep-ph/9211232]

View on Pith Pith review arXiv 1993
[1]

H. Georgi, In Coral Gables 1979 Proceeding, Theory and experiments in high energy physics, New York 1975, 329 and H. Fritzsch and P. Minkowski, Annals Phys. 93 (1975) 193

View on Pith 1975
[2]

J. C. Pati and A. Salam, Phys. Rev. D 10 (1974) 275

View on Pith 1974
[3]

R. N. Mohapatra and J. C. Pati, Phys. Rev. D 11 (1975) 2558; G. Senjanovi´ c and R. N. Mohapatra, Phys. Rev. D 12 (1975) 1502; G. Senjanovi´ c, Nucl. Phys. B153 (1979) 334

View on Pith 1975
[4]

P. Minkowski, Phys. Lett. B 67 (1977) 421; T. Yanagida, proceedings of the Workshop on Uniﬁed Theories and Baryon Number in the Universe , Tsukuba, 1979, eds. A. Sawada, A. Sugamoto; S. Glashow, in Cargese 1979, Proceedings, Quarks and Leptons (1979); M. Gell-Mann, P. Ramond, R. Slansky, proceedings of the Supergrav- ity Stony Brook Workshop , New York, 1...

View on Pith 1977
[5]

G. Dvali and A. Vilenkin, Phys. Rev. D 70 (2004) 063501 [arXiv:hep-th/0304043]; G. Dvali, [arXiv:hep-th/0410286]

View on Pith Pith review arXiv 2004
[6]

P. Langacker and M. x. Luo, Phys. Rev. D 44 (1991) 817

View on Pith 1991
[7]

S. Dimopoulos, S. Raby, F. Wilczek, Phys. Rev. D 24 (1981) 1681. L.E. Ib´ a˜ nez, G.G. Ross, Phys. Lett. B 105 (1981) 439. M.B. Einhorn, D.R. Jones, Nucl. Phys. B 196 (1982) 475. W. Marciano, G. Senjanovi´ c, Phys.Rev.D 25 (1982) 3092

View on Pith 1981
[8]

C. S. Aulakh, B. Bajc, A. Melfo, G. Senjanovi´ c and F. Vissani, Phys. Lett. B 588, 196 (2004) [arXiv:hep-ph/0306242]

View on Pith Pith review arXiv 2004
[9]

G. Senjanovi´ c, arXiv:hep-ph/0501244

View on Pith Pith review arXiv
[11]

F. Acampora, G. Amelino-Camelia, F. Buccella, O. Pi- santi, L. Rosa and T. Tuzi, Nuovo Cim. A 108 (1995) 375 [arXiv:hep-ph/9405332]

View on Pith Pith review arXiv 1995
[12]

R. D. Peccei and H. R. Quinn, Phys. Rev. Lett. 38 (1977) 1440

View on Pith 1977
[13]

B. Bajc, A. Melfo, G. Senjanovi´ c and F. Vissani, Phys. Rev. D 70 (2004) 035007 [arXiv:hep-ph/0402122]

View on Pith Pith review arXiv 2004
[14]

C. S. Aulakh and A. Girdhar, Int. J. Mod. Phys. A 20 (2005) 865 [arXiv:hep-ph/0204097]

View on Pith Pith review arXiv 2005
[15]

T. Fukuyama, A. Ilakovac, T. Kikuchi, S. Meljanac and N. Okada, J. Math. Phys. 46, 033505 (2005) [arXiv:hep-ph/0405300]

View on Pith Pith review arXiv 2005
[16]

K. Matsuda, Y. Koide and T. Fukuyama, Phys. Rev. D 64 (2001) 053015 [arXiv:hep-ph/0010026]

View on Pith Pith review arXiv 2001
[17]

K. Matsuda, Y. Koide, T. Fukuyama and H. Nishiura, Phys. Rev. D 65 (2002) 033008 [Erratum-ibid. D 65 (2002) 079904] [arXiv:hep-ph/0108202]; T. Fukuyama and N. Okada, JHEP 0211 (2002) 011 [arXiv:hep-ph/0205066]

View on Pith Pith review arXiv 2002
[18]

H. S. Goh, R. N. Mohapatra and S. P. Ng, Phys. Lett. B 570 (2003) 215 [arXiv:hep-ph/0303055]; H. S. Goh, R. N. Mohapatra and S. P. Ng, Phys. Rev. D 68 (2003) 115008 [arXiv:hep-ph/0308197]; B. Dutta, Y. Mimura and R. N. Mohapatra, Phys. Rev. D 69 (2004) 115014 [arXiv:hep-ph/0402113]

View on Pith Pith review arXiv 2003
[19]

K. S. Babu and C. Macesanu, arXiv:hep-ph/0505200

View on Pith Pith review arXiv
[20]

S. Bertolini and M. Malinsky, arXiv:hep-ph/0504241

View on Pith Pith review arXiv
[21]

B. Bajc, G. Senjanovi´ c, F. Vissani, Phys. Rev. Lett. 90 (2003) 051802 [hep-ph/0210207], and hep-ph/0110310

View on Pith Pith review arXiv 2003
[22]

B. Bajc, G. Senjanovi´ c and F. Vissani, Phys. Rev. D 70 (2004) 093002 [arXiv:hep-ph/0402140]

View on Pith Pith review arXiv 2004
[23]

R. N. Mohapatra, Phys. Rev. D 34 , 3457 (1986). A. Font, L. E. Ib´ a˜ nez and F. Quevedo,Phys. Lett. B228, 79 (1989). S. P. Martin, Phys. Rev. D46, 2769 (1992)

View on Pith 1986
[24]

C.S. Aulakh, K. Benakli, G. Senjanovi´ c, Phys. Rev. Lett. 79 (1997) 2188. C. S. Aulakh, A. Melfo and G. Senjanovi´ c, Phys. Rev. D 57, 4174 (1998); [arXiv:hep-ph/9707256]. C. S. Aulakh, A. Melfo, A. Raˇ sin and G. Senjanovi´ c, Phys. Rev. D 58, 115007 (1998) [arXiv:hep-ph/9712551]. C. S. Aulakh, A. Melfo, A. Raˇ sin and G. Senjanovi´ c, Phys. Lett. B 459 (1999)

View on Pith Pith review arXiv 1997
[25]

B. Bajc and G. Senjanovi´ c, arXiv:hep-ph/0507169

View on Pith Pith review arXiv
[26]

G. Lazarides, Q. Shaﬁ and C. Wetterich, Nucl. Phys. B 181 (1981) 287

View on Pith 1981
[27]

R. N. Mohapatra and G. Senjanovi´ c, Phys. Rev. D 23 (1981) 165

View on Pith 1981
[28]

K. S. Babu and R. N. Mohapatra, Phys. Rev. Lett. 70 (1993) 2845 [arXiv:hep-ph/9209215]. L. Lavoura, Phys. Rev. D 48 (1993) 5440 [arXiv:hep-ph/9306297]

View on Pith Pith review arXiv 1993
[29]

H. Arason, D. J. Castano, E. J. Piard and P. Ramond, Phys. Rev. D 47 (1993) 232 [arXiv:hep-ph/9204225]

View on Pith Pith review arXiv 1993
[30]

S. Weinberg, Phys. Rev. Lett. 40 (1978) 223; F. Wilczek, Phys. Rev. Lett. 40 (1978) 279

View on Pith 1978
[31]

R. N. Mohapatra and G. Senjanovi´ c, Z. Phys. C 17 (1983) 53

View on Pith 1983
[32]

J. E. Kim, Phys. Rept. 150 (1987) 1

View on Pith 1987
[33]

R. Holman, G. Lazarides and Q. Shaﬁ, Phys. Rev. D 27 (1983) 995

View on Pith 1983
[34]

M. B. Wise, H. Georgi and S. L. Glashow, Phys. Rev. Lett. 47 (1981) 402

View on Pith 1981
[35]

J. R. Ellis and M. K. Gaillard, Nucl. Phys. B 150 (1979) 141

View on Pith 1979
[36]

M. A. B. Beg and H. S. B. Tsao, Phys. Rev. Lett. 41 (1978) 278

View on Pith 1978
[37]

R. N. Mohapatra and G. Senjanovi´ c, Phys. Lett. B 79, 283 (1978). 8

View on Pith 1978
[38]

H. Georgi, Hadronic J. 1 (1978) 155

View on Pith 1978
[39]

E. Witten, Phys. Lett. B 91 (1980) 81

View on Pith 1980
[40]

N. Arkani-Hamed and S. Dimopoulos, arXiv:hep-th/0405159; G. F. Giudice and A. Romanino, Nucl. Phys. B 699 (2004) 65 [arXiv:hep-ph/0406088]. N. Arkani-Hamed, S. Dimopoulos, G. F. Giudice and A. Romanino, arXiv:hep-ph/0409232

View on Pith Pith review arXiv 2004
[41]

B. Bajc and G. Senjanovi´ c, Phys. Lett. B 610 (2005) 80 [arXiv:hep-ph/0411193]

View on Pith Pith review arXiv 2005
[42]

P. Nath and R. M. Syed, Phys. Lett. B 506 (2001) 68 [Erratum-ibid. B 508 (2001) 216] [arXiv:hep-ph/0103165]

View on Pith Pith review arXiv 2001
[43]

For a recent analysis and references, see A. Stru- mia and F. Vissani, Nucl. Phys. B 726 (2005) 294 [arXiv:hep-ph/0503246]

View on Pith Pith review arXiv 2005
[44]

F. Vissani and A. Y. Smirnov, Phys. Lett. B 341 (1994) 173 [arXiv:hep-ph/9405399]

View on Pith Pith review arXiv 1994
[45]

V. V. Dixit and M. Sher, Phys. Rev. D 40 (1989) 3765; C. S. Aulakh and A. Girdhar, Nucl. Phys. B 711 (2005) 275 [arXiv:hep-ph/0405074]

View on Pith Pith review arXiv 1989
[46]

G. R. Dvali, A. Melfo and G. Senjanovi´ c, Phys. Rev. Lett. 75, 4559 (1995) [arXiv:hep-ph/9507230]

View on Pith Pith review arXiv 1995
[47]

G. R. Dvali, H. Liu and T. Vachaspati, Phys. Rev. Lett. 80, 2281 (1998) [arXiv:hep-ph/9710301]

View on Pith Pith review arXiv 1998
[557]

[arXiv:hep-ph/9902409]

View on Pith Pith review arXiv

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Seesaw Scale in the Minimal Renormalizable SO(10) Grand Unification
hep-ph 2012-02 conditional novelty 6.0 of 10

The 45_H + 126_H SO(10) Higgs model contains stable, tachyon-free unification regions with B-L breaking as high as 10^14 GeV, provided one Standard Model multiplet is accidentally light in the desert.

Show 8 more citing papers

Five dimensional $SU(5) \times U(1)_{\rm PQ}$ grand unification
hep-ph 2024-12 conditional novelty 5.0 of 10

The authors propose a 5D SU(5) x U(1)_PQ orbifold model in which SU(5) breaking and a high-quality QCD axion from the fifth component of the U(1) field arise from the same boundary conditions, with intermediate-scale ...
Yukawa Sector of Minimal SO(10) Unification
hep-ph 2016-12 conditional novelty 5.0 of 10

A Yukawa sector built from a real 10, a real 120, and a complex 126 Higgs in SO(10), with no symmetry beyond the gauge group, reproduces the full fermion mass and mixing spectrum.
Weakly-Interacting Massive Particles in Non-supersymmetric SO(10) Grand Unified Models
hep-ph 2015-09 conditional novelty 5.0 of 10

A systematic sweep of weakly interacting dark matter candidates in non-supersymmetric SO(10) unification leaves only a handful of models that also unify the gauge couplings and respect the proton lifetime bound.
Fits to SO(10) Grand Unified Models
hep-ph 2013-06 conditional novelty 5.0 of 10

Fitting SO(10) Yukawa relations at the weak scale with full one-loop running, the 10+126 and 10+120+126 Higgs models survive for normal ordering, the 120+126 model does not, and the low Higgs mass pushes the fitted to...
A non Supersymmetric SO(10) Grand Unified Model for All the Physics below $M_{GUT}$
hep-ph 2013-05 conditional novelty 5.0 of 10

A single non-supersymmetric SO(10) model with a Pati-Salam intermediate scale near 10^11 GeV can simultaneously fit coupling unification, fermion masses, leptogenesis, and axion dark matter, at the cost of severe fine tuning.
Fermion Masses in SO(10) Models
hep-ph 2011-02 conditional novelty 5.0 of 10

Across five SO(10) variants, type-I seesaw dominance reproduces the full fermion spectrum while type-II dominance fails in minimal models because the GUT-scale bottom-to-tau mass ratio is not unity.
Addressing the ${\mathbf R_{D^{(*)}}}$ anomalies with an ${\mathbf S_1}$ leptoquark from $\mathbf{SO(10)}$ grand unification
hep-ph 2019-02 conditional novelty 4.0 of 10

A three-coupling S1 leptoquark texture embedded in SO(10) survives all current flavour, electroweak, and LHC constraints while fitting the R_D(*) anomalies.
Light color octet scalars in the minimal SO(10) grand unification
hep-ph 2013-02 conditional novelty 4.0 of 10

Two-loop gauge unification in minimal SO(10) with a light color-octet scalar implies the octet must be lighter than about 2000 TeV today, or about 20 TeV if proton decay stays unseen.

How the literature uses it

55 arXiv papers cite this in 116 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 83 sentences without a confident label

Cites it as support 5 papers

Interestingly, we notice high scale SCPV is impossible in minimal renormalizable SO(10), whose scalar sector only contains a CP-even $45_H$, an $126_H$ and a complex $10_H$ [ref] .

Spontaneous CP Violation and Flavor Changing Neutral Currents in Minimal SO(10) · Introduction · 1.00
It is argued [ref] that a $126_H$ and a real $10_H$ cannot fit even two generation case.

Fermion Masses in SO(10) Models · Non-supersymmetric 0 models · 0.97
This means that the two $SU(2)_L$ doublets in the $10_H$ necessarily take the same vacuum expectation value (vev), which would imply certain mass relations that contradict data [ref] .

Fits to Non-Supersymmetric SO(10) Models with Type I and II Seesaw Mechanisms Using Renormalization Group Evolution · SO(10) Lagrangian · 0.97

Cites it as background 22 papers

The fit of the renormalizable Yukawa couplings to fermion masses and mixings at the electroweak scale has been extensively studied in several papers [ref] .

A Predictive $SO(10)$ Model · Numerical Analysis · 0.96
The Yukawa sector of renormalizable non-supersymmetric $SO(10)$ GUTs has been extensively investigated for its viability in reproducing the low-energy data of fermion masses and mixing parameters [ref] .

Leptogenesis and fermion mass fit in a renormalizable $SO(10)$ model · Introduction · 0.97
In particular, there are scenarios that combine GUT gauge symmetries with the global $U(1)_PQ$ symmetry in four dimensions [ref] .

Five dimensional $SU(5) \times U(1)_{\rm PQ}$ grand unification · Introduction · 0.85

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [10]

N. G. Deshpande, E. Keith and P. B. Pal, Phys. Rev. D 47, 2892 (1993) [arXiv:hep-ph/9211232]

View on Pith Pith review arXiv 1993

[2] [1]

H. Georgi, In Coral Gables 1979 Proceeding, Theory and experiments in high energy physics, New York 1975, 329 and H. Fritzsch and P. Minkowski, Annals Phys. 93 (1975) 193

View on Pith 1975

[3] [2]

J. C. Pati and A. Salam, Phys. Rev. D 10 (1974) 275

View on Pith 1974

[4] [3]

R. N. Mohapatra and J. C. Pati, Phys. Rev. D 11 (1975) 2558; G. Senjanovi´ c and R. N. Mohapatra, Phys. Rev. D 12 (1975) 1502; G. Senjanovi´ c, Nucl. Phys. B153 (1979) 334

View on Pith 1975

[5] [4]

P. Minkowski, Phys. Lett. B 67 (1977) 421; T. Yanagida, proceedings of the Workshop on Uniﬁed Theories and Baryon Number in the Universe , Tsukuba, 1979, eds. A. Sawada, A. Sugamoto; S. Glashow, in Cargese 1979, Proceedings, Quarks and Leptons (1979); M. Gell-Mann, P. Ramond, R. Slansky, proceedings of the Supergrav- ity Stony Brook Workshop , New York, 1...

View on Pith 1977

[6] [5]

G. Dvali and A. Vilenkin, Phys. Rev. D 70 (2004) 063501 [arXiv:hep-th/0304043]; G. Dvali, [arXiv:hep-th/0410286]

View on Pith Pith review arXiv 2004

[7] [6]

P. Langacker and M. x. Luo, Phys. Rev. D 44 (1991) 817

View on Pith 1991

[8] [7]

S. Dimopoulos, S. Raby, F. Wilczek, Phys. Rev. D 24 (1981) 1681. L.E. Ib´ a˜ nez, G.G. Ross, Phys. Lett. B 105 (1981) 439. M.B. Einhorn, D.R. Jones, Nucl. Phys. B 196 (1982) 475. W. Marciano, G. Senjanovi´ c, Phys.Rev.D 25 (1982) 3092

View on Pith 1981

[9] [8]

C. S. Aulakh, B. Bajc, A. Melfo, G. Senjanovi´ c and F. Vissani, Phys. Lett. B 588, 196 (2004) [arXiv:hep-ph/0306242]

View on Pith Pith review arXiv 2004

[10] [9]

G. Senjanovi´ c, arXiv:hep-ph/0501244

View on Pith Pith review arXiv

[11] [11]

F. Acampora, G. Amelino-Camelia, F. Buccella, O. Pi- santi, L. Rosa and T. Tuzi, Nuovo Cim. A 108 (1995) 375 [arXiv:hep-ph/9405332]

View on Pith Pith review arXiv 1995

[12] [12]

R. D. Peccei and H. R. Quinn, Phys. Rev. Lett. 38 (1977) 1440

View on Pith 1977

[13] [13]

B. Bajc, A. Melfo, G. Senjanovi´ c and F. Vissani, Phys. Rev. D 70 (2004) 035007 [arXiv:hep-ph/0402122]

View on Pith Pith review arXiv 2004

[14] [14]

C. S. Aulakh and A. Girdhar, Int. J. Mod. Phys. A 20 (2005) 865 [arXiv:hep-ph/0204097]

View on Pith Pith review arXiv 2005

[15] [15]

T. Fukuyama, A. Ilakovac, T. Kikuchi, S. Meljanac and N. Okada, J. Math. Phys. 46, 033505 (2005) [arXiv:hep-ph/0405300]

View on Pith Pith review arXiv 2005

[16] [16]

K. Matsuda, Y. Koide and T. Fukuyama, Phys. Rev. D 64 (2001) 053015 [arXiv:hep-ph/0010026]

View on Pith Pith review arXiv 2001

[17] [17]

K. Matsuda, Y. Koide, T. Fukuyama and H. Nishiura, Phys. Rev. D 65 (2002) 033008 [Erratum-ibid. D 65 (2002) 079904] [arXiv:hep-ph/0108202]; T. Fukuyama and N. Okada, JHEP 0211 (2002) 011 [arXiv:hep-ph/0205066]

View on Pith Pith review arXiv 2002

[18] [18]

H. S. Goh, R. N. Mohapatra and S. P. Ng, Phys. Lett. B 570 (2003) 215 [arXiv:hep-ph/0303055]; H. S. Goh, R. N. Mohapatra and S. P. Ng, Phys. Rev. D 68 (2003) 115008 [arXiv:hep-ph/0308197]; B. Dutta, Y. Mimura and R. N. Mohapatra, Phys. Rev. D 69 (2004) 115014 [arXiv:hep-ph/0402113]

View on Pith Pith review arXiv 2003

[19] [19]

K. S. Babu and C. Macesanu, arXiv:hep-ph/0505200

View on Pith Pith review arXiv

[20] [20]

S. Bertolini and M. Malinsky, arXiv:hep-ph/0504241

View on Pith Pith review arXiv

[21] [21]

B. Bajc, G. Senjanovi´ c, F. Vissani, Phys. Rev. Lett. 90 (2003) 051802 [hep-ph/0210207], and hep-ph/0110310

View on Pith Pith review arXiv 2003

[22] [22]

B. Bajc, G. Senjanovi´ c and F. Vissani, Phys. Rev. D 70 (2004) 093002 [arXiv:hep-ph/0402140]

View on Pith Pith review arXiv 2004

[23] [23]

R. N. Mohapatra, Phys. Rev. D 34 , 3457 (1986). A. Font, L. E. Ib´ a˜ nez and F. Quevedo,Phys. Lett. B228, 79 (1989). S. P. Martin, Phys. Rev. D46, 2769 (1992)

View on Pith 1986

[24] [24]

C.S. Aulakh, K. Benakli, G. Senjanovi´ c, Phys. Rev. Lett. 79 (1997) 2188. C. S. Aulakh, A. Melfo and G. Senjanovi´ c, Phys. Rev. D 57, 4174 (1998); [arXiv:hep-ph/9707256]. C. S. Aulakh, A. Melfo, A. Raˇ sin and G. Senjanovi´ c, Phys. Rev. D 58, 115007 (1998) [arXiv:hep-ph/9712551]. C. S. Aulakh, A. Melfo, A. Raˇ sin and G. Senjanovi´ c, Phys. Lett. B 459 (1999)

View on Pith Pith review arXiv 1997

[25] [25]

B. Bajc and G. Senjanovi´ c, arXiv:hep-ph/0507169

View on Pith Pith review arXiv

[26] [26]

G. Lazarides, Q. Shaﬁ and C. Wetterich, Nucl. Phys. B 181 (1981) 287

View on Pith 1981

[27] [27]

R. N. Mohapatra and G. Senjanovi´ c, Phys. Rev. D 23 (1981) 165

View on Pith 1981

[28] [28]

K. S. Babu and R. N. Mohapatra, Phys. Rev. Lett. 70 (1993) 2845 [arXiv:hep-ph/9209215]. L. Lavoura, Phys. Rev. D 48 (1993) 5440 [arXiv:hep-ph/9306297]

View on Pith Pith review arXiv 1993

[29] [29]

H. Arason, D. J. Castano, E. J. Piard and P. Ramond, Phys. Rev. D 47 (1993) 232 [arXiv:hep-ph/9204225]

View on Pith Pith review arXiv 1993

[30] [30]

S. Weinberg, Phys. Rev. Lett. 40 (1978) 223; F. Wilczek, Phys. Rev. Lett. 40 (1978) 279

View on Pith 1978

[31] [31]

R. N. Mohapatra and G. Senjanovi´ c, Z. Phys. C 17 (1983) 53

View on Pith 1983

[32] [32]

J. E. Kim, Phys. Rept. 150 (1987) 1

View on Pith 1987

[33] [33]

R. Holman, G. Lazarides and Q. Shaﬁ, Phys. Rev. D 27 (1983) 995

View on Pith 1983

[34] [34]

M. B. Wise, H. Georgi and S. L. Glashow, Phys. Rev. Lett. 47 (1981) 402

View on Pith 1981

[35] [35]

J. R. Ellis and M. K. Gaillard, Nucl. Phys. B 150 (1979) 141

View on Pith 1979

[36] [36]

M. A. B. Beg and H. S. B. Tsao, Phys. Rev. Lett. 41 (1978) 278

View on Pith 1978

[37] [37]

R. N. Mohapatra and G. Senjanovi´ c, Phys. Lett. B 79, 283 (1978). 8

View on Pith 1978

[38] [38]

H. Georgi, Hadronic J. 1 (1978) 155

View on Pith 1978

[39] [39]

E. Witten, Phys. Lett. B 91 (1980) 81

View on Pith 1980

[40] [40]

N. Arkani-Hamed and S. Dimopoulos, arXiv:hep-th/0405159; G. F. Giudice and A. Romanino, Nucl. Phys. B 699 (2004) 65 [arXiv:hep-ph/0406088]. N. Arkani-Hamed, S. Dimopoulos, G. F. Giudice and A. Romanino, arXiv:hep-ph/0409232

View on Pith Pith review arXiv 2004

[41] [41]

B. Bajc and G. Senjanovi´ c, Phys. Lett. B 610 (2005) 80 [arXiv:hep-ph/0411193]

View on Pith Pith review arXiv 2005

[42] [42]

P. Nath and R. M. Syed, Phys. Lett. B 506 (2001) 68 [Erratum-ibid. B 508 (2001) 216] [arXiv:hep-ph/0103165]

View on Pith Pith review arXiv 2001

[43] [43]

For a recent analysis and references, see A. Stru- mia and F. Vissani, Nucl. Phys. B 726 (2005) 294 [arXiv:hep-ph/0503246]

View on Pith Pith review arXiv 2005

[44] [44]

F. Vissani and A. Y. Smirnov, Phys. Lett. B 341 (1994) 173 [arXiv:hep-ph/9405399]

View on Pith Pith review arXiv 1994

[45] [45]

V. V. Dixit and M. Sher, Phys. Rev. D 40 (1989) 3765; C. S. Aulakh and A. Girdhar, Nucl. Phys. B 711 (2005) 275 [arXiv:hep-ph/0405074]

View on Pith Pith review arXiv 1989

[46] [46]

G. R. Dvali, A. Melfo and G. Senjanovi´ c, Phys. Rev. Lett. 75, 4559 (1995) [arXiv:hep-ph/9507230]

View on Pith Pith review arXiv 1995

[47] [47]

G. R. Dvali, H. Liu and T. Vachaspati, Phys. Rev. Lett. 80, 2281 (1998) [arXiv:hep-ph/9710301]

View on Pith Pith review arXiv 1998

[48] [557]

[arXiv:hep-ph/9902409]

View on Pith Pith review arXiv