Central exclusive production of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>η</mml:mi></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>η</mml:mi><mml:mo>

We present a study of the central exclusive production (CEP) of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>η</a:mi></a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:msup><c:mrow><c:mi>η</c:mi></c:mrow><c:mrow><c:mo>′</c:mo></c:mrow></c:msup><c:mo stretchy="false">(</c:mo><c:mn>958</c:mn><c:mo stretchy="false">)</c:mo></c:mrow></c:math> mesons in diffractive proton-proton collisions at high energies. The amplitudes, including pomeron and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>f</g:mi><g:mrow><g:mn>2</g:mn><g:mi mathvariant="double-struck">R</g:mi></g:mrow></g:msub></g:math> reggeon exchanges, are calculated within the tensor-pomeron model. Absorption effects are also taken into account at the amplitude level. We fit some undetermined model parameters (coupling constants and cutoff parameters in form factors) to the WA102 experimental data and then make predictions for the LHC energy <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mrow><j:msqrt><j:mrow><j:mi>s</j:mi></j:mrow></j:msqrt><j:mo>=</j:mo><j:mn>13</j:mn><j:mtext> </j:mtext><j:mtext> </j:mtext><j:mi>TeV</j:mi></j:mrow></j:math>. Both total cross sections and several differential distributions are presented. For <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi>p</l:mi><l:mi>p</l:mi><l:mo stretchy="false">→</l:mo><l:mi>p</l:mi><l:mi>p</l:mi><l:mi>η</l:mi></l:math>, we find an upper limit for the total cross section of <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mrow><o:mn>2.5</o:mn><o:mtext> </o:mtext><o:mtext> </o:mtext><o:mi mathvariant="normal">μ</o:mi><o:mi mathvariant="normal">b</o:mi></o:mrow></o:math> for pseudorapidity of the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>η</s:mi></s:math> meson <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mrow><u:mo stretchy="false">|</u:mo><u:msub><u:mrow><u:mi>η</u:mi></u:mrow><u:mrow><u:mi>M</u:mi></u:mrow></u:msub><u:mo stretchy="false">|</u:mo><u:mo>&lt;</u:mo><u:mn>1</u:mn></u:mrow></u:math> and <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mrow><y:mn>5.6</y:mn><y:mtext> </y:mtext><y:mtext> </y:mtext><y:mi mathvariant="normal">μ</y:mi><y:mi mathvariant="normal">b</y:mi></y:mrow></y:math> for <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mrow><cb:mn>2</cb:mn><cb:mo>&lt;</cb:mo><cb:msub><cb:mrow><cb:mi>η</cb:mi></cb:mrow><cb:mrow><cb:mi>M</cb:mi></cb:mrow></cb:msub><cb:mo>&lt;</cb:mo><cb:mn>5</cb:mn></cb:mrow></cb:math>. For <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mi>p</eb:mi><eb:mi>p</eb:mi><eb:mo stretchy="false">→</eb:mo><eb:mi>p</eb:mi><eb:mi>p</eb:mi><eb:msup><eb:mi>η</eb:mi><eb:mo>′</eb:mo></eb:msup></eb:math>, we predict the cross section to be in the range of <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"><hb:mrow><hb:mn>0.3</hb:mn><hb:mi>–</hb:mi><hb:mn>0.7</hb:mn><hb:mtext> </hb:mtext><hb:mtext> </hb:mtext><hb:mi mathvariant="normal">μ</hb:mi><hb:mi mathvariant="normal">b</hb:mi></hb:mrow></hb:math> for pseudorapidity of the <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"><lb:msup><lb:mi>η</lb:mi><lb:mo>′</lb:mo></lb:msup></lb:math> meson <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"><nb:mo stretchy="false">|</nb:mo><nb:msub><nb:mi>η</nb:mi><nb:mi>M</nb:mi></nb:msub><nb:mo stretchy="false">|</nb:mo><nb:mo>&lt;</nb:mo><nb:mn>1</nb:mn></nb:math> and <rb:math xmlns:rb="http://www.w3.org/1998/Math/MathML" display="inline"><rb:mrow><rb:mn>0.9</rb:mn><rb:mi>–</rb:mi><rb:mn>2.1</rb:mn><rb:mtext> </rb:mtext><rb:mtext> </rb:mtext><rb:mi mathvariant="normal">μ</rb:mi><rb:mi mathvariant="normal">b</rb:mi></rb:mrow></rb:math> for <vb:math xmlns:vb="http://www.w3.org/1998/Math/MathML" display="inline"><vb:mn>2</vb:mn><vb:mo>&lt;</vb:mo><vb:msub><vb:mi>η</vb:mi><vb:mi>M</vb:mi></vb:msub><vb:mo>&lt;</vb:mo><vb:mn>5</vb:mn></vb:math>. This opens the possibility to study diffractive production of pseudoscalar mesons in experiments at the LHC. We discuss if there are arguments from SU(3)-flavor symmetry which would forbid pomeron-pomeron fusion giving an <xb:math xmlns:xb="http://www.w3.org/1998/Math/MathML" display="inline"><xb:mi>η</xb:mi></xb:math> meson. In our opinion such arguments do not exist. We also consider CEP of the pseudoscalars <zb:math xmlns:zb="http://www.w3.org/1998/Math/MathML" display="inline"><zb:mi>η</zb:mi></zb:math> and <bc:math xmlns:bc="http://www.w3.org/1998/Math/MathML" display="inline"><bc:msup><bc:mi>η</bc:mi><bc:mo>′</bc:mo></bc:msup><bc:mo stretchy="false">(</bc:mo><bc:mn>958</bc:mn><bc:mo stretchy="false">)</bc:mo></bc:math> and the pseudovector meson <fc:math xmlns:fc="http://www.w3.org/1998/Math/MathML" display="inline"><fc:msub><fc:mi>f</fc:mi><fc:mn>1</fc:mn></fc:msub><fc:mo stretchy="false">(</fc:mo><fc:mn>1285</fc:mn><fc:mo stretchy="false">)</fc:mo></fc:math> in diffractive proton-proton collisions in a theory with a scalar pomeron. We show that none of these particles can be produced in this way in the scalar-pomeron theory. Thus, experimental observation of any of these particles in the above CEP processes at the LHC would give striking evidence against a scalar character of the pomeron.