Gravity Waves and Proton Decay in a Flipped SU(5) Hybrid Inflation Model

PHYSICAL REVIEW D 97, 123522 (2018) Gravity waves and proton decay in a flipped SU(5) hybrid inflation model † ‡ Mansoor Ur Rehman,1,* Qaisar Shafi,2, and Umer Zubair2, 1Department of Physics, Quaid-i-Azam University, Islamabad 45320, Pakistan 2Bartol Research Institute, Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA (Received 10 April 2018; published 14 June 2018) We revisit supersymmetric hybrid inflation in the context of the flipped SUð5Þ model. With minimal superpotential and minimal Kähler potential, and soft supersymmetry (SUSY) masses of order (1–100) TeV, compatibility with the Planck data yields a symmetry breaking scale M of flipped SUð5Þ close to ð2–4Þ × 1015 GeV. This disagrees with the lower limit M ≳ 7 × 1015 GeV set from proton decay searches by the Super-Kamiokande collaboration. We show how M close to the unification scale 2 × 1016 GeV can be reconciled with SUSY hybrid inflation by employing a nonminimal Kähler potential. Proton decays into eþπ0 with an estimated lifetime of order 1036 years. The tensor to scalar ratio r in this case can approach observable values ∼10−4–10−3. DOI: 10.1103/PhysRevD.97.123522 I. INTRODUCTION flipped SUð5Þ gauge group see [9] where each of two hybrid fields is shown to realize inflation. For no-scale The supersymmetric (SUSY) hybrid inflation model 5 – SUSY flipped SUð Þ models of inflation see [10,11]. [1 5] has attracted a fair amount of attention due to its 5 ≡ 5 1 The flipped SUð Þ SUð Þ × Uð ÞX model [12,13] simplicity and elegance in realizing the grand unified exhibits many remarkable features and constitutes an attrac- theory (GUT) models of inflation [5]. In models with tive choice as a grand unified gauge group. In the flipped minimal Kähler potential, the soft linear and mass squared SUð5Þ model, the doublet-triplet splitting problem is terms play an important role in attaining the scalar spectral elegantly solved due to the missing partner mechanism index compatible with the current experimental observa- [13]. The proton decay occurs via dimension-6 operators tions [6,7]. The next important task is to explore the and is naturally long lived with M around the GUT scale. possibility of realizing the gauge symmetry breaking scale Moreover, it lacks the monopole problem that appears in the M close to a typical GUT scale ∼2 × 1016 GeV. This can, spontaneous breaking of other GUT gauge groups [i.e., 5 4 2 2 10 in turn, adequately suppress the proton decay rate from SUð Þ, SUð ÞC × SUð ÞL × SUð ÞR or SOð Þ]. This dimension-6 operators usually present in GUT models. property also makes the flipped SUð5Þ model an appropriate Achieving M ∼ 2 × 1016 GeV was one of the main pre- choice for the standard version of SUSY hybrid inflation dictions of the original SUSY hybrid inflation model where where gauge symmetry is broken after the end of inflation. 5 only radiative correction was included in otherwise a flat Finally, flipped SUð Þ is also regarded as a natural GUT potential [1]. We, therefore, investigate the possibility of model due to its connection with F-theory [14]. realizing large enough M in the SUSY hybrid inflation It is important to note that the phrase gravity waves in the title refers to potentially observable primordial gravitational model with minimal Kähler potential, including various waves. The prediction of primordial gravitational waves is important corrections [1,3,5–7]. Specifically, we update the a generic feature of the inflation paradigm and originates status of the SUSY flipped SUð5Þ hybrid inflation model from the quantum nature of gravity. These gravity waves [7,8] with minimal Kähler potential and soft SUSY masses ∼1–100 are expected to be observed indirectly through the detection TeV. For other hybrid models of inflation in of B-mode polarization data in the cosmic microwave background anisotropies. Their detection determines the *[email protected] value of the tensor to scalar ratio r, which is usually † [email protected] predicted in a wide range by the various inflation models. ‡ [email protected] The main goal of future experiments [15,16] is therefore the measurement of r within an uncertainty of δr ¼ 0.001. This Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. then defines the observable range of r. Therefore, we also Further distribution of this work must maintain attribution to explore the possibility of realizing this large r range in our the author(s) and the published article’s title, journal citation, model along with the gauge symmetry breaking scale M and DOI. Funded by SCOAP3. around 2 × 1016 GeV. 2470-0010=2018=97(12)=123522(9) 123522-1 Published by the American Physical Society REHMAN, SHAFI, and ZUBAIR PHYS. REV. D 97, 123522 (2018) The outline of the paper is as follows. In Sec. II we where the scalar component of the gauge singlet superfield briefly introduce the SUSY hybrid model of flipped SUð5Þ S acts as the inflaton. The first line in Eq. (4) is relevant for that was first proposed in [8]. We update the status of this inflation and is also responsible for the gauge symmetry model with minimal Kähler potential in Sec. III and check breaking of FSUð5Þ into the MSSM as the 10-plet Higgs its compatibility with the proton lifetime constraint. The pair attains nonzero vacuum expectation value in the c ¯ c minimal model with ∼1–100 TeV scale soft SUSY masses NH; NH direction, is shown to predict fast proton decay. However, with the 10 10¯ c ¯ c 2 help of leading order nonminimal terms in the Kähler h H Hi¼hNHNHi¼M : ð5Þ potential we overcome this problem and the predictions of inflationary parameters are found to be in accordance with The second line in Eq. (4) contains the terms that are the latest Planck data. This is discussed in detail in Sec. IV. involved in the solution of the doublet-triplet splitting → þπ0 The dominant proton decay mode is p e with a problem. The Uð1Þ symmetry plays a key role here. 36 R lifetime estimated to be of order 10 years. Finally, we This symmetry not only eliminates the S2 and S3 terms to provide a brief summary of our findings in Sec. V. realize successful inflation; it also forbids the bilinear term ¯ 5h5h to avoid GUT scale masses of the MSSM Higgs II. SUSY FSU(5) HYBRID INFLATION doublets Hu and Hd. The MSSM μ problem is assumed to be solved by the Giudice-Masiero mechanism [17]. Finally, The minimal Higgs sector of flipped SUð5Þ ≡ the terms in the second line of Eq. (4) mix the color triplets FSUð5Þ ≡ SUð5Þ × Uð1Þ consists of a pair of Higgs X (Dc ; D¯ c ) and (D , D¯ ) to attain GUT scale masses. This superfields (10 ; 10¯ ), and a second pair of 5-plet Higgs H H h h H H then solves the doublet-triplet problem and eliminates superfields (5 , 5¯ ), which are decomposed under the h h dimension-5 proton decay mediated by colored Higgsino standard model (SM) gauge group as exchange. 10 10 1 3 2 1 6 c 3¯ 1 1 3 The terms in the third line of Eq. (4) generate the Dirac H ¼ð ; Þ¼QHð ; ; = ÞþDHð ; ; = Þ ν mass terms for all fermions, where yðdÞ, yðu; Þ, and yðeÞ Nc 1; 1; 0 ; ij ij ij þ Hð Þ denote the corresponding Yukawa couplings. For a dis- 10¯ 10¯ −1 ¯ 3¯ 2 −1 6 ¯ c 3 1 −1 3 H ¼ð ; Þ¼QHð ; ; = ÞþDHð ; ; = Þ cussion of light neutrino masses in this model see [8]. Another possibility to realize light neutrino masses by þ N¯ c ð1; 1; 0Þ; H assuming R breaking at nonrenormalizable level is dis- 5h ¼ð5; −2Þ¼Dhð3; 1; −1=3ÞþHdð1; 2; −1=2Þ; cussed in [18]. As all matter superfields are neutral under ¯ ¯ U 1 symmetry, an additional Z2 symmetry (or matter 5 ¼ð5; 2Þ¼D¯ ð3¯; 1; 1=3ÞþH ð1; 2; 1=2Þ: ð1Þ ð ÞR h h u parity) is assumed [8]. This symmetry not only realizes the The minimal supersymmetric standard model (MSSM) possibility of lightest supersymmetric particle (LSP) as a matter content and the right-handed neutrino reside in cold dark matter candidate but also avoids some unwanted the following representations: terms in the superpotential. In the D-flat direction, the relevant part of the global 10F 10 1 3 2 1 6 c 3¯ 1 1 3 SUSY potential may be written as i ¼ð ; Þi ¼ Qið ; ; = ÞþDi ð ; ; = Þ c 1 1 0 þ Ni ð ; ; Þ; 2 2 2 2 2 2 2 V ¼ κ ðj10Hj − M Þ þ 2κ jSj j10Hj : ð6Þ 5¯f 5¯ −3 c 3¯ 1 −2 3 1 2 −1 2 i ¼ð ; Þi ¼ Ui ð ; ; = ÞþLið ; ; = Þ; Along the inflationary valley (j10 j¼j10¯ j¼0), 1¯e ¼ð1; 5Þ ¼ Ecð1; 1; þ1Þ; ð2Þ H H i i i SUSY is temporarily broken by the vacuum energy κ2 4 where Nc is the right-handed neutrino superfield. density V0 ¼ M , and is restored later at the global 10 10¯ 0 Assuming the following R-charge assignment of the super- minimum (jh Hij ¼ jh Hij ¼ M, jhSij ¼ ). In the infla- fields, tionary trajectory, the effective contributions of one-loop radiative correction and soft SUSY breaking terms can be ¯ ¯ ¯ written as ðS;10H;10H;5h;5h;10i;5i;1iÞ¼ð1;0;0;1;1;0;0;0Þ; ð3Þ 4 the superpotential of the model is given by [8] ðκMÞ N ΔV − ≃ F x ; one loop 8π2 ð Þ ð7Þ ¯ 2 W ¼ κS½10H10H − M ¯ ¯ ¯ Δ ≃ κ 3 2 2 2 þ λ110H10H5h þ λ210H10H5h VSoft am3=2 M x þ MSM x ; ð8Þ ðdÞ10F10F5 ðu;νÞ10F5¯f5¯ ðeÞ1e5¯f5 þ yij i j h þ yij i j h þ yij i j h; ð4Þ with 123522-2 GRAVITY WAVES AND PROTON DECAY IN A FLIPPED … PHYS.

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