<p>We analyze possible new physics (NP) effects on <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(b\rightarrow s\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>b</mi> <mo stretchy="false">→</mo> <mi>s</mi> </mrow> </math></EquationSource> </InlineEquation> transition processes, <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(R({K^{(*)}})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <mo stretchy="false">(</mo> <mmultiscripts> <mi>K</mi> <mrow /> <mrow> <mo stretchy="false">(</mo> <mrow /> <mo>∗</mo> <mo stretchy="false">)</mo> </mrow> </mmultiscripts> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq12"> <EquationSource Format="TEX">\({B_s\rightarrow \mu ^+\mu ^-}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>B</mi> <mi>s</mi> </msub> <mo stretchy="false">→</mo> <msup> <mi>μ</mi> <mo>+</mo> </msup> <msup> <mi>μ</mi> <mo>-</mo> </msup> </mrow> </math></EquationSource> </InlineEquation>, and <InlineEquation ID="IEq13"> <EquationSource Format="TEX">\({B^+\rightarrow K^+\nu {{\bar{\nu }}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>B</mi> <mo>+</mo> </msup> <mo stretchy="false">→</mo> <msup> <mi>K</mi> <mo>+</mo> </msup> <mi>ν</mi> <mover accent="true"> <mrow> <mi>ν</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> </mrow> </math></EquationSource> </InlineEquation> decays. Though recent data for <InlineEquation ID="IEq14"> <EquationSource Format="TEX">\(R({K^{(*)}})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <mo stretchy="false">(</mo> <mmultiscripts> <mi>K</mi> <mrow /> <mrow> <mo stretchy="false">(</mo> <mrow /> <mo>∗</mo> <mo stretchy="false">)</mo> </mrow> </mmultiscripts> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq15"> <EquationSource Format="TEX">\(\textrm{Br}({B_s\rightarrow \mu ^+\mu ^-})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>Br</mtext> <mo stretchy="false">(</mo> <mrow> <msub> <mi>B</mi> <mi>s</mi> </msub> <mo stretchy="false">→</mo> <msup> <mi>μ</mi> <mo>+</mo> </msup> <msup> <mi>μ</mi> <mo>-</mo> </msup> </mrow> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> are compatible with the standard model (SM), there are still rooms for NP beyond the SM. Especially <InlineEquation ID="IEq16"> <EquationSource Format="TEX">\(\textrm{Br}({B^+\rightarrow K^+\nu {{\bar{\nu }}}})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>Br</mtext> <mo stretchy="false">(</mo> <mrow> <msup> <mi>B</mi> <mo>+</mo> </msup> <mo stretchy="false">→</mo> <msup> <mi>K</mi> <mo>+</mo> </msup> <mi>ν</mi> <mover accent="true"> <mrow> <mi>ν</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> </mrow> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> is measured to exceed the theoretical predictions. We parameterize the NP effects in a generic way with explicit NP scale <InlineEquation ID="IEq17"> <EquationSource Format="TEX">\(M_\textrm{NP}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>M</mi> <mtext>NP</mtext> </msub> </math></EquationSource> </InlineEquation> and some possible powers of it. For reasonable ranges of NP fermionic couplings, we find a window of <InlineEquation ID="IEq18"> <EquationSource Format="TEX">\(3.17~\textrm{TeV}\le M_\textrm{NP}\le 14.9~\textrm{TeV}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>3.17</mn> <mspace width="3.33333pt" /> <mtext>TeV</mtext> <mo>≤</mo> <msub> <mi>M</mi> <mtext>NP</mtext> </msub> <mo>≤</mo> <mn>14.9</mn> <mspace width="3.33333pt" /> <mtext>TeV</mtext> </mrow> </math></EquationSource> </InlineEquation> for new particles. When including <InlineEquation ID="IEq19"> <EquationSource Format="TEX">\(\textrm{Br}(B^+\rightarrow K^+\mu ^+\mu ^-)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>Br</mtext> <mo stretchy="false">(</mo> <msup> <mi>B</mi> <mo>+</mo> </msup> <mo stretchy="false">→</mo> <msup> <mi>K</mi> <mo>+</mo> </msup> <msup> <mi>μ</mi> <mo>+</mo> </msup> <msup> <mi>μ</mi> <mo>-</mo> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> and the angular observable <InlineEquation ID="IEq20"> <EquationSource Format="TEX">\({P_5'(B^+\rightarrow K^{*+}\mu ^+\mu ^-)}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>P</mi> <mn>5</mn> <mo>′</mo> </msubsup> <mrow> <mo stretchy="false">(</mo> <msup> <mi>B</mi> <mo>+</mo> </msup> <mo stretchy="false">→</mo> <mmultiscripts> <mi>K</mi> <mrow /> <mrow> <mrow /> <mo>∗</mo> <mo>+</mo> </mrow> </mmultiscripts> <msup> <mi>μ</mi> <mo>+</mo> </msup> <msup> <mi>μ</mi> <mo>-</mo> </msup> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, we have a wider range of the window. Implications of our analysis about specific NP models are discussed.</p>

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New physics effects in \(R({K^{(*)}})\), \({B_s\rightarrow \mu ^+\mu ^-}\), and \({B^+\rightarrow K^+\nu {{\bar{\nu }}}}\)

  • Jong-Phil Lee

摘要

We analyze possible new physics (NP) effects on \(b\rightarrow s\) b s transition processes, \(R({K^{(*)}})\) R ( K ( ) ) , \({B_s\rightarrow \mu ^+\mu ^-}\) B s μ + μ - , and \({B^+\rightarrow K^+\nu {{\bar{\nu }}}}\) B + K + ν ν ¯ decays. Though recent data for \(R({K^{(*)}})\) R ( K ( ) ) and \(\textrm{Br}({B_s\rightarrow \mu ^+\mu ^-})\) Br ( B s μ + μ - ) are compatible with the standard model (SM), there are still rooms for NP beyond the SM. Especially \(\textrm{Br}({B^+\rightarrow K^+\nu {{\bar{\nu }}}})\) Br ( B + K + ν ν ¯ ) is measured to exceed the theoretical predictions. We parameterize the NP effects in a generic way with explicit NP scale \(M_\textrm{NP}\) M NP and some possible powers of it. For reasonable ranges of NP fermionic couplings, we find a window of \(3.17~\textrm{TeV}\le M_\textrm{NP}\le 14.9~\textrm{TeV}\) 3.17 TeV M NP 14.9 TeV for new particles. When including \(\textrm{Br}(B^+\rightarrow K^+\mu ^+\mu ^-)\) Br ( B + K + μ + μ - ) and the angular observable \({P_5'(B^+\rightarrow K^{*+}\mu ^+\mu ^-)}\) P 5 ( B + K + μ + μ - ) , we have a wider range of the window. Implications of our analysis about specific NP models are discussed.