Muon and electron $$(g-2)$$ anomalies with non-holomorphic interactions in MSSM
Md Isha Ali, Manimala Chakraborti, Utpal Chattopadhyay, Samadrita Mukherjee
Abstract
Abstract The recent Fermilab muon $$g-2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> result and the same for electron due to fine-structure constant measurement through $${}^{133}\textrm{Cs}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mn>133</mml:mn> </mml:msup> <mml:mtext>Cs</mml:mtext> </mml:mrow> </mml:math> matter-wave interferometry are probed in relation to MSSM with non-holomorphic (NH) trilinear soft SUSY breaking terms, referred to as NHSSM. Supersymmetric contributions to charged lepton $$(g-2)_l$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>g</mml:mi> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mi>l</mml:mi> </mml:msub> </mml:math> can be enhanced via the new trilinear terms involving a wrong Higgs coupling with left and right-handed scalars. Bino-slepton loop is used to enhance the SUSY contribution to $$g-2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> where wino mass stays at 1.5 TeV and the left and right slepton mass parameters for the first two generations are considered to be the same. Unlike many MSSM-based analyses completed before, the model does not require a light electroweakino, or light sleptons, or unequal left and right slepton masses, or a very large higgsino mass parameter. In absence of popular UV complete models, we treat the NH terms at par with MSSM soft terms, in a model independent framework of Minimal Effective Supersymmetry. The first part of the analysis involves the study of $$(g-2)_\mu $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>g</mml:mi> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mi>μ</mml:mi> </mml:msub> </mml:math> constraint along with the limits from Higgs mass, B-physics, collider data, direct detection of dark matter (DM), while focusing on a higgsino DM which is underabundant in nature. We then impose the constraint from electron $$g-2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> where a large Yukawa threshold correction (an outcome of NHSSM) and opposite signs of trilinear NH coefficients associated with $$\mu $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>μ</mml:mi> </mml:math> and e fields are used to satisfy the dual limits of $$\Delta {a_\mu }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:msub> <mml:mi>a</mml:mi> <mml:mi>μ</mml:mi> </mml:msub> </mml:mrow> </mml:math> and $$\Delta {a_e}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:msub> <mml:mi>a</mml:mi> <mml:mi>e</mml:mi> </mml:msub> </mml:mrow> </mml:math> (where the latter comes with negative sign). Varying Yukawa threshold corrections further provide the necessary flavor-dependent enhancement of $$\Delta {a_e}/m_e^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:msub> <mml:mi>a</mml:mi> <mml:mi>e</mml:mi> </mml:msub> <mml:mo>/</mml:mo> <mml:msubsup> <mml:mi>m</mml:mi> <mml:mi>e</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:mrow> </mml:math> compared to that of $$\Delta {a_\mu }/m_\mu ^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:msub> <mml:mi>a</mml:mi> <mml:mi>μ</mml:mi> </mml:msub> <mml:mo>/</mml:mo> <mml:msubsup> <mml:mi>m</mml:mi> <mml:mi>μ</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:mrow> </mml:math> . A larger Yukawa threshold correction through $$A^\prime _e$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>A</mml:mi> <mml:mi>e</mml:mi> <mml:mo>′</mml:mo> </mml:msubsup> </mml:math> for $$y_e$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>y</mml:mi> <mml:mi>e</mml:mi> </mml:msub> </mml:math> also takes away the direct proportionality of $$a_e$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>a</mml:mi> <mml:mi>e</mml:mi> </mml:msub> </mml:math> with respect to $$\tan \beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>tan</mml:mo> <mml:mi>β</mml:mi> </mml:mrow> </mml:math> . With a finite intercept, $$a_e$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>a</mml:mi> <mml:mi>e</mml:mi> </mml:msub> </mml:math> becomes only an increasing function of $$\tan \beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>tan</mml:mo> <mml:mi>β</mml:mi> </mml:mrow> </mml:math> . We identified the available parameter space in the two cases while also satisfying the ATLAS data from slepton pair production searches in the plane of slepton mass parameter and the mass of the lightest neutralino.