Analyticity as a Robust Constraint on the LHC Cross Section

It is well known that high energy data alone do not discriminate between asymptotic $\ln s$ and $\ln^2s$ behavior of $pp$ and $\bar pp$ cross sections. By exploiting high quality low energy data, analyticity resolves this ambiguity in favor of cross sections that grow asymptotically as $\ln^2s$. We here show that two methods for incorporating the low energy data into the high energy fits give numerically identical results and yield essentially identical tightly constrained values for the LHC cross section. The agreement can be understood as a new analyticity constraint derived as an extension of a Finite Energy Sum Rule.Comment: 8 pages, Latex2e, 2 postscript figures; major changes made; accepted for publication in Phys Rev

Investigations of the pi N total cross sections at high energies using new FESR: log nu or (log nu)^2

We propose to use rich informations on pi p total cross sections below N= 10 GeV in addition to high-energy data in order to discriminate whether these cross sections increase like log nu or (log nu)^2 at high energies, since it is difficult to discriminate between asymptotic log nu and (log nu)^2 fits from high-energy data alone. A finite-energy sum rule (FESR) which is derived in the spirit of the P' sum rule as well as the n=1 moment FESR have been required to constrain the high-energy parameters. We then searched for the best fit of pi p total cross sections above 70 GeV in terms of high-energy parameters constrained by these two FESR. We can show from this analysis that the (log nu)^2 behaviours is preferred to the log nu behaviours.Comment: to be published in Phys. Rev. D 5 pages, 2 eps figure

The structure of N(1535) in the aspect of chiral symmetry

The structure of N(1535) is discussed in dynamical and symmetry aspects based on chiral symmetry. We find that the N(1535) in chiral unitary model has implicitly some components other than meson-baryon one. We also discuss the N(1535) in the chiral doublet picture.Comment: 4 pages, no figure, talk given at Workshop on Chiral Symmetry in Hadron and Nuclear Physics: Chiral07, Osaka, Japan, 13-16 Nov 200

New limits on "odderon" amplitudes from analyticity constraints

In studies of high energy $pp$ and $\bar pp$ scattering, the odd (under crossing) forward scattering amplitude accounts for the difference between the $pp$ and $\bar pp$ cross sections. Typically, it is taken as $f_-=-\frac{p}{4\pi}Ds^{\alpha-1}e^{i\pi(1-\alpha)/2}$ ($\alpha\sim 0.5$), which has $\Delta\sigma, \Delta\rho\to0$ as $s\to\infty$, where $\rho$ is the ratio of the real to the imaginary portion of the forward scattering amplitude. However, the odd-signatured amplitude can have in principle a strikingly different behavior, ranging from having $\Delta\sigma\to$non-zero constant to having $\Delta\sigma \to \ln s/s_0$ as $s\to\infty$, the maximal behavior allowed by analyticity and the Froissart bound. We reanalyze high energy $pp$ and $\bar pp$ scattering data, using new analyticity constraints, in order to put new and precise limits on the magnitude of ``odderon'' amplitudes.Comment: 13 pages LaTex, 6 figure

Regge-cascade hadronization

We argue that the evolution of coloured partons into colour-singlet hadrons has approximate factorization into an extended parton-shower phase and a colour-singlet resonance--pole phase. The amplitude for the conversion of colour connected partons into hadrons necessarily resembles Regge-pole amplitudes since qq-bar resonance amplitudes and Regge-pole amplitudes are related by duality. A `Regge-cascade' factorization property of the N-point Veneziano amplitude provides further justification of this protocol. This latter factorization property, in turn, allows the construction of general multi-hadron amplitudes in amplitude-squared factorized form from (1->2) link amplitudes. We suggest an algorithm with cascade-decay configuration, ordered in the transverse momentum, suitable for Monte-Carlo simulation. We make a simple implementation of this procedure in Herwig++, obtaining some improvement to the description of the event-shape distributions at LEP.Comment: 10 pages, 9 figure

Flavour structure of low-energy hadron pair photoproduction

We consider the process $\gamma\gamma\to H_1\bar H_2$ where $H_1$ and $H_2$ are either mesons or baryons. The experimental findings for such quantities as the $p\bar p$ and $K_SK_S$ differential cross sections, in the energy range currently probed, are found often to be in disparity with the scaling behaviour expected from hard constituent scattering. We discuss the long-distance pole--resonance contribution in understanding the origin of these phenomena, as well as the amplitude relations governing the short-distance contribution which we model as a scaling contribution. When considering the latter, we argue that the difference found for the $K_SK_S$ and the $K^+K^-$ integrated cross sections can be attributed to the s-channel isovector component. This corresponds to the $\rho\omega\to a$ subprocess in the VMD (vector-meson-dominance) language. The ratio of the two cross sections is enhanced by the suppression of the $\phi$ component, and is hence constrained. We give similar constraints to a number of other hadron pair production channels. After writing down the scaling and pole--resonance contributions accordingly, the direct summation of the two contributions is found to reproduce some salient features of the $p\bar p$ and $K^+K^-$ data.Comment: 12 pages, 9 figures, revised version to be published in EPJ

Nonperturbative hyperfine contribution to the b1b_1 and h1h_1 meson masses

Due to the nonperturbative contribution to the hyperfine splitting the mass of the $n^1P_1$ state is strongly correlated with the center of gravity $M_{\rm cog}(n^3P_J)$ of the $n^3P_J$ multiplet: $M(n^1P_1)$ is less than $M_{\rm cog}(n^3P_J)$ by about 40 MeV (20 MeV) for the 1P (2P) state. For $b_1(1235)$ the agreement with experiment is reached only if $a_0(980)$ belongs to the $1^3P_J$ multiplet. The predicted mass of $b_1(2^1P_1)$ is $\approx 1620$ MeV. For the isoscalar meson a correlation between the mass of $h_1$(1170) $(h_1(1380))$ and $M_{cog}(1^3P_J)$ composed from light (strange) quarks also takes place.Comment: 22 pages RevTe

The gluonic condensate from the hyperfine splitting Mcog(χcJ)−M(hc)M_{\rm cog}(\chi_{cJ})-M(h_c) in charmonium

The precision measurement of the hyperfine splitting $\Delta_{\rm HF} (1P, c\bar c)=M_{\rm cog} (\chi_{cJ}) - M(h_c) = -0.5 \pm 0.4$ MeV in the Fermilab--E835 experiment allows to determine the gluonic condensate $G_2$ with high accuracy if the gluonic correlation length $T_g$ is fixed. In our calculations the negative value of $\Delta_{\rm HF} = -0.3 \pm 0.4$ MeV is obtained only if the relatively small $T_g = 0.16$ fm and $G_2 = 0.065 (3)$ GeV${}^4$ are taken. These values correspond to the ``physical'' string tension $(\sigma \approx 0.18$ GeV$^2$). For $T_g \ge 0.2$ fm the hyperfine splitting is positive and grows for increasing $T_g$. In particular for $T_g = 0.2$ fm and $G_2 = 0.041 (2)$ GeV${}^4$ the splitting $\Delta_{\rm HF} = 1.4 (2)$ MeV is obtained, which is in accord with the recent CLEO result.Comment: 9 pages revtex 4, no figure

Effects to Scalar Meson Decays of Strong Mixing between Low and High Mass Scalar Mesons

We analyze the mass spectroscopy of low and high mass scalar mesons and get the result that the coupling strengths of the mixing between low and high mass scalar mesons are very strong and the strengths of mixing for $I=1, 1/2$ scalar mesons and those of I=0 scalar mesons are almost same. Next, we analyze the decay widths and decay ratios of these mesons and get the results that the coupling constants $A'$ for $I=1, 1/2$ which represents the coupling of high mass scalar meson $N'$ -> two pseudoscalar mesons $PP$ are almost same as the coupling $A'$ for the I=0. On the other hand, the coupling constant $A$ for $I=1, I=1/2$ which represents the low mass scalar meson $N$ -> $PP$ are far from the coupling constant $A$ for I=0. We consider a resolution for this discrepancy. Coupling constant $A''$ for glueball $G$ -> $PP$ is smaller than the coupling $A'$. $\theta_P$ is $40^\circ \sim 50^\circ$.Comment: 15 pages, 6 figure